Fractal heat transfer device

Information

  • Patent Grant
  • 11598593
  • Patent Number
    11,598,593
  • Date Filed
    Monday, January 6, 2020
    5 years ago
  • Date Issued
    Tuesday, March 7, 2023
    a year ago
Abstract
A heat sink comprising a heat exchange device having a plurality of heat exchange elements each having a surface boundary with respect to a heat transfer fluid, having a fractal variation therebetween, wherein the heat transfer fluid is induced to flow with respect to the plurality of fractally varying heat exchange elements such that flow-induced vortices are generated at non-corresponding locations of the plurality of fractally varying heat exchange elements, resulting in a reduced resonance as compared to a corresponding heat exchange device having a plurality of heat exchange elements that produce flow-induced vortices at corresponding locations on the plurality of heat exchange elements.
Description
FIELD OF THE INVENTION

This invention relates to the field of heat sinks or items that transfer heat between a concentrated source or sink and a fluid.


BACKGROUND OF THE INVENTION

A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. A heat sink is typically physically designed to increase the surface area in contact with the cooling fluid surrounding it, such as the air. Approach air velocity, choice of material, fin (or other protrusion) design and surface treatment are some of the design factors which influence the thermal resistance, i.e. thermal performance, of a heat sink.


A heat sink transfers thermal energy from a higher temperature to a lower temperature fluid medium. The fluid medium is frequently air, but can also be water or in the case of heat exchangers, refrigerants and oil. Fourier's law of heat conduction, simplified to a one-dimensional form in the x-direction, shows that when there is a temperature gradient in a body, heat will be transferred from the higher temperature region to the lower temperature region. The rate at which heat is transferred by conduction, qk, is proportional to the product of the temperature gradient and the cross-sectional area through which heat is transferred:










q
k

==

kA






dT

dx











(
1
)







where qk is the rate of conduction, k is a constant which depends on the materials that are involved, A is the surface area through which the heat must pass, and dT/dx is the rate of change of temperature with respect to distance (for simplicity, the equation is written in one dimension). Thus, according to Fourier's law (which is not the only consideration by any means), heat sinks benefit from having a large surface area exposed to the medium into which the heat is to be transferred.


Consider a heat sink in a duct, where air flows through the duct, and the heat sink base is higher in temperature than the air. Assuming conservation of energy, for steady-state conditions, and applying Newton's law of cooling, gives the following set of equations.










Q
.

=


m
.








c

p
,

i





n





(


T

air
,
out


-

T

air
,

i





n




)







(
2
)








Q
.

=



T
hs

-

T

air
,
av




R
hs








where




(
3
)







T

air
,
av


=



T

air
,
out


+

T

air
,

i





n




2





(
4
)







and {dot over (Q)} is the first derivative of the thermal energy over time—







Q
.

=


dQ
dt

.





Using the mean air temperature is an assumption that is valid for relatively short heat sinks. When compact heat exchangers are calculated, the logarithmic mean air temperature is used. {dot over (m)} is the air mass flow rate in kg/s.


The above equations show that when the air flow through the heat sink decreases, this results in an increase in the average air temperature. This in turn increases the heat sink base temperature. And additionally, the thermal resistance of the heat sink will also increase. The net result is a higher heat sink base temperature. The inlet air temperature relates strongly with the heat sink base temperature. Therefore, if there is no air or fluid flow around the heat sink, the energy dissipated to the air cannot be transferred to the ambient air. Therefore, the heat sink functions poorly.


Other examples of situations in which a heat sink has impaired efficiency: Pin fins have a lot of surface area, but the pins are so close together that air has a hard time flowing through them; Aligning a heat sink so that the fins are not in the direction of flow; Aligning the fins horizontally for a natural convection heat sink. Whilst a heat sink is stationary and there are no centrifugal forces and artificial gravity, air that is warmer than the ambient temperature always flows upward, given essentially-still-air surroundings; this is convective cooling.


The most common heat sink material is aluminum. Chemically pure aluminum is not used in the manufacture of heat sinks, but rather aluminum alloys. Aluminum alloy 1050A has one of the higher thermal conductivity values at 229 W/m·K. However, it is not recommended for machining, since it is a relatively soft material. Aluminum alloys 6061 and 6063 are the more commonly used aluminum alloys, with thermal conductivity values of 166 and 201 W/m·K, respectively. The aforementioned values are dependent on the temper of the alloy.


Copper is also used since it has around twice the conductivity of aluminum, but is three times as heavy as aluminum. Copper is also around four to six times more expensive than aluminum, but this is market dependent. Aluminum has the added advantage that it is able to be extruded, while copper cannot. Copper heat sinks are machined and skived. Another method of manufacture is to solder the fins into the heat sink base.


Another heat sink material that can be used is diamond. With a value of 2000 W/mK it exceeds that of copper by a factor of five. In contrast to metals, where heat is conducted by delocalized electrons, lattice vibrations are responsible for diamond's very high thermal conductivity. For thermal management applications, the outstanding thermal conductivity and diffusivity of diamond is an essential. CVD diamond may be used as a sub-mount for high-power integrated circuits and laser diodes.


Composite materials can be used. Examples are a copper-tungsten pseudoalloy, AlSiC (silicon carbide in aluminum matrix), Dymalloy (diamond in copper-silver alloy matrix), and E-Material (beryllium oxide in beryllium matrix). Such materials are often used as substrates for chips, as their thermal expansion coefficient can be matched to ceramics and semiconductors.


Fin efficiency is one of the parameters which makes a higher thermal conductivity material important. A fin of a heat sink may be considered to be a flat plate with heat flowing in one end and being dissipated into the surrounding fluid as it travels to the other. As heat flows through the fin, the combination of the thermal resistance of the heat sink impeding the flow and the heat lost due to convection, the temperature of the fin and, therefore, the heat transfer to the fluid, will decrease from the base to the end of the fin. This factor is called the fin efficiency and is defined as the actual heat transferred by the fin, divided by the heat transfer were the fin to be isothermal (hypothetically the fin having infinite thermal conductivity). Equations 5 and 6 are applicable for straight fins.










η
f

=


tanh


(

m






L
c


)



m






L
c







(
5
)







m






L
c


=




2


h
f



kt
f




L
f







(
6
)







Where:

    • hf is the convection coefficient of the fin
      • Air: 10 to 100 W/(m2·K)
      • Water: 500 to 10,000 W/(m2·K)
    • k is the thermal conductivity of the fin material
      • Aluminum: 120 to 240 W/(m2·K)
    • Lf is the fin height (m)
    • tf is the fin thickness (m)


Another parameter that concerns the thermal conductivity of the heat sink material is spreading resistance. Spreading resistance occurs when thermal energy is transferred from a small area to a larger area in a substance with finite thermal conductivity. In a heat sink, this means that heat does not distribute uniformly through the heat sink base. The spreading resistance phenomenon is shown by how the heat travels from the heat source location and causes a large temperature gradient between the heat source and the edges of the heat sink. This means that some fins are at a lower temperature than if the heat source were uniform across the base of the heat sink. This non-uniformity increases the heat sink's effective thermal resistance.


A pin fin heat sink is a heat sink that has pins that extend from its base. The pins can be, for example, cylindrical, elliptical or square. A second type of heat sink fin arrangement is the straight fin. These run the entire length of the heat sink. A variation on the straight fin heat sink is a cross cut heat sink. A straight fin heat sink is cut at regular intervals but at a coarser pitch than a pin fin type.


In general, the more surface area a heat sink has, the better it works. However, this is not always true. The concept of a pin fin heat sink is to try to pack as much surface area into a given volume as possible. As well, it works well in any orientation. Kordyban has compared the performance of a pin fin and a straight fin heat sink of similar dimensions. Although the pin fin has 194 cm2 surface area while the straight fin has 58 cm2, the temperature difference between the heat sink base and the ambient air for the pin fin is 50° C. For the straight fin it was 44° C. or 6° C. better than the pin fin. Pin fin heat sink performance is significantly better than straight fins when used in their intended application where the fluid flows axially along the pins rather than only tangentially across the pins.


Another configuration is the flared fin heat sink; its fins are not parallel to each other, but rather diverge with increasing distance from the base. Flaring the fins decreases flow resistance and makes more air go through the heat sink fin channel; otherwise, more air would bypass the fins. Slanting them keeps the overall dimensions the same, but offers longer fins. Forghan, et al. have published data on tests conducted on pin fin, straight fin and flared fin heat sinks. They found that for low approach air velocity, typically around 1 m/s, the thermal performance is at least 20% better than straight fin heat sinks. Lasance and Eggink also found that for the bypass configurations that they tested, the flared heat sink performed better than the other heat sinks tested.


The heat transfer from the heat sink is mediated by two effects: conduction via the coolant, and thermal radiation. The surface of the heat sink influences its emissivity; shiny metal absorbs and radiates only a small amount of heat, while matte black radiates highly. In coolant-mediated heat transfer, the contribution of radiation is generally small. A layer of coating on the heat sink can then be counterproductive, as its thermal resistance can impair heat flow from the fins to the coolant. Finned heat sinks with convective or forced flow will not benefit significantly from being colored. In situations with significant contribution of radiative cooling, e.g. in case of a flat non-finned panel acting as a heat sink with low airflow, the heat sink surface finish can play an important role. Matte-black surfaces will radiate much more efficiently than shiny bare metal. The importance of radiative vs. coolant-mediated heat transfer increases in situations with low ambient air pressure (e.g. high-altitude operations) or in vacuum (e.g. satellites in space).

  • Fourier, J. B., 1822, Theorie analytique de la chaleur, Paris; Freeman, A., 1955, translation, Dover Publications, Inc, NY.
  • Kordyban, T., 1998, Hot air rises and heat sinks—Everything you know about cooling electronics is wrong, ASME Press, NY.
  • Anon, Unknown, “Heat sink selection”, Mechanical engineering department, San Jose State University, Jan. 27, 2010. www⋅engr⋅sjsu⋅edu/dejong/ME%20146%20files/Heat%20Sink⋅pptwww⋅engr⋅sjsu⋅edu/ndejong/ME%20146%20files/Heat%20Sink.ppt
  • Sergent, J. and Krum, A., 1998, Thermal management handbook for electronic assemblies, First Edition, McGraw-Hill.
  • Incropera, F. P. and DeWitt, D. P., 1985, Introduction to heat transfer, John Wiley and sons, NY.
  • Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME May 2001.
  • Lasance, C. J. M and Eggink, H. J., 2001, A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, 21st IEEE SEMI-THERM Symposium.
  • ludens.cl/Electron/Thermal.html
  • Lienard, J. H., IV & V, 2004, A Heat Transfer Textbook, Third edition, MIT
  • Saint-Gobain, 2004, “Thermal management solutions for electronic equipment” 22 Jul. 2008 www⋅fff⋅saint-gobain⋅com/Media/Documents/S0000000000000001036/ThermaCool %20Brochure⋅pdf
  • Jeggels, Y. U., Dobson, R. T., Jeggels, D. H., Comparison of the cooling performance between heat pipe and aluminium conductors for electronic equipment enclosures, Proceedings of the 14th International Heat Pipe Conference, Florianópolis, Brazil, 2007.
  • Prstic, S., Iyengar, M., and Bar-Cohen, A., Bypass effect in high performance heat sinks, Proceedings of the International Thermal Science Seminar Bled, Slovenia, Jun. 11-14,2000.
  • Mills, A. F., 1999, Heat transfer, Second edition, Prentice Hall.
  • Potter, C. M. and Wiggert, D. C., 2002, Mechanics of fluid, Third Edition, Brooks/Cole.
  • White, F. M., 1999, Fluid mechanics, Fourth edition, McGraw-Hill International.
  • Azar, A, et al., 2009, “Heat sink testing methods and common oversights”, Qpedia Thermal E-Magazine, January 2009 Issue. www⋅gats⋅com/cpanel/UploadedPdf/January20092⋅pdf


Several structurally complex heatsink designs are discussed in Hernon, US App. 2009/0321045, incorporated herein by reference.


Several structurally complex heat sink designs are discussed in Hernon, US App. 2009/0321045, incorporated herein by reference.


Heat sinks operate by removing heat from an object to be cooled into the surrounding air, gas or liquid through convection and radiation. Convection occurs when heat is either carried passively from one point to another by fluid motion (forced convection) or when heat itself causes fluid motion (free convection). When forced convection and free convection occur together, the process is termed mixed convection. Radiation occurs when energy, for example in the form of heat, travels through a medium or through space and is ultimately absorbed by another body. Thermal radiation is the process by which the surface of an object radiates its thermal energy in the form of electromagnetic waves. Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the heat and light (IR and visible EM waves) emitted by a glowing incandescent light bulb. Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation.


A heat sink tends to decrease the maximum temperature of the exposed surface, because the power is transferred to a larger volume. This leads to a possibility of diminishing return on larger heat sinks, since the radiative and convective dissipation tends to be related to the temperature differential between the heat sink surface and the external medium. Therefore, if the heat sink is oversized, the efficiency of heat shedding is poor. If the heat sink is undersized, the object may be insufficiently cooled, the surface of the heat sink dangerously hot, and the heat shedding not much greater than the object itself absent the heat sink.


The relationship between friction and convention in heatsinks is discussed by Frigus Primore in “A Method for Comparing Heat Sinks Based on Reynolds Analogy,” available at www⋅frigprim⋅com/downloads/Reynolds_analogy_heatsinks⋅PDF, last accessed Apr. 28, 2010.


This article notes that for, plates, parallel plates, and cylinders to be cooled, it is necessary for the velocity of the surrounding fluid to be low in order to minimize mechanical power losses. However, larger surface flow velocities will increase the heat transfer efficiency, especially where the flow near the surface is turbulent, and substantially disrupts a stagnant surface boundary layer. Primore also discusses heatsink fin shapes and notes that no fin shape offers any heat dissipation or weight advantage compared with planar fins, and that straight fins minimize pressure losses while maximizing heat flow. Therefore, the art generally teaches that generally flat and planar surfaces are appropriate for most heatsinks.


Frigus Primore, “Natural Convection and Inclined Parallel Plates,” www⋅frigprim⋅com/articels2/parallel_pl_Inc⋅html, last accessed Apr. 29, 2010, discusses the use of natural convection (i.e., convection due to the thermal expansion of a gas surrounding a solid heatsink in normal operating conditions) to cool electronics. One of the design goals of various heatsinks is to increase the rate of natural convection. Primore suggests using parallel plates to attain this result. Once again, Primore notes that parallel plate heatsinks are the most efficient and attempts to define the optimal spacing S and angle λ (relative to the direction of the fluid flow) of the heatsink plates of length L according to the below equations:


Optimum Plate Spacing











S
opt

=




k
s



(

L
dT

)


0.25

·


cos


(
γ
)



-
0.25











γ
opt

=

atan


(


1

H


3

W


)










γ
opt

=


π
4

-

0.508



(

H
W

)


-
1.237












H
W

<

3









H
W

>

3






(
1
)







Total heat Dissipation











Q
.

=


k
v

·

k
γ

·

A
c

·

H
0.5

·

dT
1.5










k
γ

=


1
+


1
9




(

H
W

)

2












k
γ

=


0.307
·


(

H
W

)


-
0.5



+

0.696
·


(

H
W

)


-
0.5












H
W

<

3









H
W

>

3






(
2
)







Applied Equation

{dot over (Q)}=ηv·kv·kγ·Ac·H0.5·dTref1.5  (3)

    • dT=Temperature difference (K)
    • Ac=W·D
    • ηv=Volumetric efficiency [--]
    • {dot over (Q)}=Heat dissipation [W]



FIG. 1A shows the length L, spacing S, and angle λ, of the plates of a heatsink. FIG. 1B shows the spatial relationships of Ac, the area of a face, W, the width, D, the depth, H, the height, of a plate of a heatsink.


In another article titled “Natural Convection and Chimneys,” available at www⋅frigprim⋅com/articels2/parallel_plchim⋅html, last accessed Apr. 29, 2010, Frigus Primore discusses the use of parallel plates in chimney heatsinks. One purpose of this type of design is to combine more efficient natural convection with a chimney. Primore notes that the design suffers if there is laminar flow (which creates a re-circulation region in the fluid outlet, thereby completely eliminating the benefit of the chimney) but benefits if there is turbulent flow which allows heat to travel from the parallel plates into the chimney and surrounding fluid.


In “Sub-Grid Turbulence Modeling for Unsteady Flow with Acoustic Resonance,” available at www⋅metacomptech⋅com/cfd++/00-0473⋅pdf, last accessed Apr. 29, 2010, incorporated herein by reference, Paul Batten et al discuss that when a fluid is flowing around an obstacle, localized geometric features, such as concave regions or cavities, create pockets of separated flow which can generate self-sustaining oscillations and acoustic resonance. The concave regions or cavities serve to substantially reduce narrow band acoustic resonance as compared to flat surfaces. This is beneficial to a heatsink in a turbulent flow environment because it allows for the reduction of oscillations and acoustic resonance, and therefore for an increase in the energy available for heat transfer.


In S. Liu, “Heat Transfer and Pressure Drop in Fractal Microchannel Heat Sink for Cooling of Electronic Chips,” 44 Heat Mass Transfer 221 (2007), Liu et al discuss a heat sink with a “fractal-like branching flow network.” Liu's heat sink includes channels through which fluids would flow in order to exchange heat with the heat sink.


Y. J. Lee, “Enhanced Microchannel Heat Sinks Using Oblique Fins,” IPACK 2009-89059, similarly discusses a heat sink comprising a “fractal-shaped microchannel based on the fractal pattern of mammalian circulatory and respiratory system.” Lee's idea, similar to that of Liu, is that there would be channels inside the heat sink through which a fluid could flow to exchange heat with the heat sink. The stated improvement in Lee's heat sink is (1) the disruption of the thermal boundary layer development; and (2) the generation of secondary flows.


Pence, D. V., 2002, “Reduced Pumping Power and Wall Temperature in Microchannel Heat Sinks with Fractal-like Branching Channel Networks”, Microscale Thermophys. Eng. 5, pp. 293-311, similarly, mentions heat sinks that have fractal-like channels allowing fluid to enter into the heat sink. The described advantage of Pence's structure is increased exposure of the heat sink to the fluid and lower pressure drops of the fluid while in the heat sink.


In general, a properly designed heat sink system will take advantage of thermally induced convection or forced air (e.g., a fan). In general, a turbulent flow near the surface of the heat sink disturbs a stagnant surface layer, and improves performance. In many cases, the heat sink operates in a non-ideal environment subject to dust or oil; therefore, the heat sink design must accommodate the typical operating conditions, in addition to the as-manufactured state.


Prior art heat sink designs have traditionally concentrated on geometry that is Euclidian, involving structures such as the pin fins, straight fins, and flares discussed above.


N J Ryan, D A Stone, “Application of the FD-TD method to modelling the electromagnetic radiation from heatsinks”, IEEE International Conference on Electromagnetic Compatibility, 1997. 10th (1-3 Sep. 1997), pp: 119-124, discloses a fractal antenna which also serves as a heat sink in a radio frequency transmitter.


Lance Covert, Jenshan Lin, Dan Janning, Thomas Dalrymple, “5.8 GHz orientation-specific extruded-fin heatsink antennas for 3D RF system integration”, 23 Apr. 2008 DOI: 10.1002/mop.23478, Microwave and Optical Technology Letters Volume 50, Issue 7, pages 1826-1831, July 2008 also provide a heat sink which can be used as an antenna.


Per Wikipedia en.wikipedia.org/wiki/Fractal (last accessed Apr. 14, 2010), A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” [Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9.] a property called self-similarity. Roots of mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff in studying functions that were analytic but not differentiable; however, the term fractal was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. (Briggs, John (1992). Fractals: The Patterns of Chaos. London: Thames and Hudson, 1992. p. 148.)


A fractal often has the following features: (Falconer, Kenneth (2003). Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, Ltd. Xxv)


It has a fine structure at arbitrarily small scales.


It is too irregular to be easily described in traditional Euclidean geometric language.


It is self-similar (at least approximately or stochastically).


It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). [The Hilbert curve map is not a homeomorphism, so it does not preserve topological dimension. The topological dimension and Hausdorff dimension of the image of the Hilbert map in R2 are both 2. Note, however, that the topological dimension of the graph of the Hilbert map (a set in R) is 1]


It has a simple and recursive definition.


Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that are approximated by fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.


Images of fractals can be created using fractal-generating software. Images produced by such software are normally referred to as being fractals even if they do not have the above characteristics, such as when it is possible to zoom into a region of the fractal that does not exhibit any fractal properties. Also, these may include calculation or display artifacts which are not characteristics of true fractals.


To create a Koch snowflake, one begins with an equilateral triangle and then replaces the middle third of every line segment with a pair of line segments that form an equilateral “bump.” One then performs the same replacement on every line segment of the resulting shape, ad infinitum. With every iteration, the perimeter of this shape increases by one third of the previous length. The Koch snowflake is the result of an infinite number of these iterations, and has an infinite length, while its area remains finite. For this reason, the Koch snowflake and similar constructions were sometimes called “monster curves.”


The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Gottfried Leibniz considered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense).


It was not until 1872 that a function appeared whose graph would today be considered fractal, when Karl Weierstrass gave an example of a function with the non-intuitive property of being everywhere continuous but nowhere differentiable. In 1904, Helge von Koch, dissatisfied with Weierstrass's very abstract and analytic definition, gave a more geometric definition of a similar function, which is now called the Koch curve. (The image at right is three Koch curves put together to form what is commonly called the Koch snowflake.) Waclaw Sierpinski constructed his triangle in 1915 and, one year later, his carpet. Originally these geometric fractals were described as curves rather than the 2D shapes that they are known as in their modern constructions. The idea of self-similar curves was taken further by Paul Pierre Lévy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole described a new fractal curve, the Lévy C curve. Georg Cantor also gave examples of subsets of the real line with unusual properties—these Cantor sets are also now recognized as fractals.


Iterated functions in the complex plane were investigated in the late 19th and early 20th centuries by Henri Poincaré, Felix Klein, Pierre Fatou and Gaston Julia. Without the aid of modern computer graphics, however, they lacked the means to visualize the beauty of many of the objects that they had discovered.


In the 1960s, Benoit Mandelbrot started investigating self-similarity in papers such as How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, which built on earlier work by Lewis Fry Richardson. Finally, in 1975 Mandelbrot coined the word “fractal” to denote an object whose Hausdorff—Besicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computer-constructed visualizations. These images captured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term “fractal”.


A class of examples is given by the Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, and Koch curve. Additional examples of fractals include the Lyapunov fractal and the limit sets of Kleinian groups. Fractals can be deterministic (all the above) or stochastic (that is, non-deterministic). For example, the trajectories of the Brownian motion in the plane have a Hausdorff dimension of 2.


Chaotic dynamical systems are sometimes associated with fractals. Objects in the phase space of a dynamical system can be fractals (see attractor). Objects in the parameter space for a family of systems may be fractal as well. An interesting example is the Mandelbrot set. This set contains whole discs, so it has a Hausdorff dimension equal to its topological dimension of 2—but what is truly surprising is that the boundary of the Mandelbrot set also has a Hausdorff dimension of 2 (while the topological dimension of 1), a result proved by Mitsuhiro Shishikura in 1991. A closely related fractal is the Julia set.


Escape-time fractals— (also known as “orbits” fractals) These are defined by a formula or recurrence relation at each point in a space (such as the complex plane). Examples of this type are the Mandelbrot set, Julia set, the Burning Ship fractal, the Nova fractal and the Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escape-time formulae also give rise to a fractal form when points (or pixel data) are passed through this field repeatedly.


Iterated function systems—These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Highway dragon curve, T-Square, Menger sponge, are some examples of such fractals.


Random fractals—Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Levy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters.


Strange attractors—Generated by iteration of a map or the solution of a system of initial-value differential equations that exhibit chaos.


Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals:


Exact self-similarity—This is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity.


Quasi-self-similarity—This is a loose form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar.


Statistical self-similarity—This is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of “fractal” trivially imply some form of statistical self-similarity. (Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar.


Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.


Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. The connection between fractals and leaves are currently being used to determine how much carbon is contained in trees. (“Hunting the Hidden Dimension.” Nova. PBS. WPMB-Maryland. 28 Oct. 2008.)


In 1999, certain self similar fractal shapes were shown to have a property of “frequency invariance”—the same electromagnetic properties no matter what the frequency—from Maxwell's equations (see fractal antenna). (Hohlfeld R, Cohen N (1999). “Self-similarity and the geometric requirements for frequency independence in Antennae”. Fractals. 7 (1): 79-84).


SUMMARY OF THE INVENTION

Most heat sinks are designed using a linear or exponential relationship of the heat transfer and dissipating elements. A known geometry which has not generally been employed is fractal geometry. Some fractals are random fractals, which are also termed chaotic or Brownian fractals and include random noise components. In deterministic fractal geometry, a self-similar structure results from the repetition of a design or motif (or “generator”) using a recursive algorithm, on a series of different size scales. As a result, certain types of fractal images or structures appear to have self-similarity over a broad range of scales. On the other hand, no two ranges within the design are identical.


A fractal is defined as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.” Mandelbrot, B. B. (1982). That is, there is a recursive algorithm which describes the structure. The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9. This property is termed “self-similarity.” For a more detailed discussion of fractals, see the Wikipedia article thereon at en.wikipedia·org/wiki/Fractal (last accessed Apr. 14, 2010) incorporated herein by reference. Exemplary images of well-known fractal designs can also be viewed on the Wikipedia page. Due to the fact that fractals involve largely self-repeating patterns, each of which serves to increase the surface area in three-dimensional fractals (perimeter in two-dimensional fractals), three dimensional fractals in theory are characterized by infinite surface area (and two-dimensional fractals are characterized by infinite perimeter). In practical implementations, the scale of the smallest features which remain true to the generating algorithm may be 3-25 iterations of the algorithm. Less than three recursions, and the fractal nature is not apparent, while present manufacturing technologies limit the manufacture of objects with a large range of feature scales.


This fractal nature is useful in a heat sink because the rate at which heat is transferred from a surface, either through convection or through radiation, is typically related to, and increasing with, the surface area. Of course, due to limitations in the technology used to build these heat sinks, engineering compromise is expected. However, a feature of an embodiment of the designs proposed herein is that vortices induced by fluid flow over a heat transfer surface will be chaotically distributed over various elements of the surface, thus disrupting the stagnant surface boundary layer and increasing the effective surface area available for heat transfer, while avoiding acoustic resonance which may be apparent from a regular array of structures which produce vortices and turbulence.


Further, a large physical surface area to volume ratio, which is generally useful in heat sink design, can still be obtained using the fractal model. In addition, fractal structures provide a plurality of concave regions or cavities, providing pockets of separated flow which can generate self-sustaining oscillations and acoustic resonance. These pockets serve to reduce the acoustic resonance in turbulent flowing fluid (as compared to flat or Euclidian surfaces), thus allowing for more effective heat transfer between the fractal structure and the surrounding fluid, thereby making the fractal structure ideal for a heat sink.


U.S. Pat. No. 7,256,751, issued to Cohen, incorporated herein by reference, discusses fractal antennas. In the background of this patent, Cohen discusses Kraus' research, noting that Euclidian antennas with low area (and therefore low perimeter) exhibit very low radiation resistance and are thus inefficient. Cohen notes that the advantages of fractal antennas, over traditional antennas with Euclidian geometries, is that they can maintain the small area, while having a larger perimeter, allowing for a higher radiation resistance. Also, Cohen's fractal antenna features non-harmonic resonance frequencies, good bandwidth, high efficiency, and an acceptable standing wave ratio.


In the instant invention, this same wave theory may be applied to fractal heat sinks, especially with respect to the interaction of the heat transfer fluid with the heat sink. Thus, while the heat conduction within a solid heat sink is typically not modeled as a wave (though modern thought applies phonon phenomena to graphene heat transport), the fluid surrounding the heating certainly is subject to wave phenomena, complex impedances, and indeed the chaotic nature of fluid eddies may interact with the chaotic surface configuration of the heat sink.


The efficiency of capturing electric waves in a fractal antenna, achieved by Cohen, in some cases can be translated into an efficiency transferring heat out of an object to be cooled in a fractal heat sink as described herein. See, Boris Yakobson, “Acoustic waves may cool microelectronics”, Nano Letters, ACS (2010). Some physics scholars have suggested that heat can be modeled as a set of phonons. Convection and thermal radiation can therefore be modeled as the movement of phonons. A phonon is a quasiparticle characterized by the quantization of the modes of lattice vibration of solid crystal structures. Any vibration by a single phonon is in the normal mode of classical mechanics, meaning that the lattice oscillates in the same frequency. Any other arbitrary lattice vibration can be considered a superposition of these elementary vibrations. Under the phonon model, heat travels in waves, with a wavelength on the order of 1 μm. In most materials, the phonons are incoherent, and therefore at macroscopic scales, the wave nature of heat transport is not apparent or exploitable.


The thermodynamic properties of a solid are directly related to its phonon structure. The entire set of all possible phonons combine in what is known as the phonon density of states which determines the heat capacity of a crystal. At absolute zero temperature (0 Kelvin or −273 Celsius), a crystal lattice lies in its ground state, and contains no phonons. A lattice at a non-zero temperature has an energy that is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas-like structure of phonons or thermal phonons. However, unlike the atoms which make up an ordinary gas, thermal phonons can be created and destroyed by random energy fluctuations. In the language of statistical mechanics this means that the chemical potential for adding a phonon is zero. For a more detailed description of phonon theory, see the Wikipedia article thereon available at en.wikipedia·org/wiki/Phonon (last accessed Apr. 16, 2010) incorporated herein by reference.


In certain materials, such as graphene, phonon transport phenomena are apparent at macroscopic levels, which make phonon impedance measurable and useful. Thus, if a graphene sheet were formed to resonate at a particular phonon wavelength, the resonant energy would not be emitted. On the other hand, if the graphene sheet were configured using a fractal geometry, the phonon impedance would be well controlled over a broad range of wavelengths, with sharp resonances at none, leading to an efficient energy dissipation device.


Many fractal designs are characterized by concave regions or cavities. See, for example, FIGS. 2 and 3. While sets of concavities may be useful in improving aerodynamics and fluid dynamics to increase turbulence, if they are disposed in a regular array, they will likely produce an acoustic resonance, and may have peaks in a fluid impedance function. On the other hand, the multiscale nature of a fractal geometric design will allow the system to benefit from the concavities, while avoiding a narrowly tuned system.


The present system proposes a fractal-shaped heat sink for the purpose of dissipating heat. The benefits of a fractal heat sink, over a traditional heat sink having a Euclidian geometry may include: (1) the fractal heat sink has a greater surface area, allowing for more exposure of the hot device to the surrounding air or liquid and faster dissipation of heat; and (2) due to the plethora of concave structures or cavities in fractal structures, the fractal heat sink is better able to take advantage of flow mechanics than a traditional heat sink, resulting in heat entering and exiting the heat sink more quickly (3) acoustic properties, especially in forced convection systems.


The invention provides a heat sink to cool an object through convection or radiation. For the smallest heat sink elements, on the order of 10-100 nm, the focus of the heat transfer will be on radiation rather than convection. Electron emission and ionization may also be relevant. Larger heat sink elements, approximately >1 mm in size, will generally rely on convection as the primary form of heat transfer.


In one embodiment, the heat sink comprises a heat exchange device with a plurality of heat exchange elements having a fractal variation therebetween. A heat transfer fluid, such as air, water, or another gas or liquid, is induced to flow through the heat exchange device. The heat transfer fluid has turbulent portions. The fractal variation in the plurality of heat exchange elements substantially reduces the narrow band acoustic resonance as compared to a heat sink having a linear or Euclidian geometric variation between the plurality heat exchange elements. The turbulent flow also disturbs the stagnant surface boundary layer, leading to more efficient heat transfer.


When a heat transfer fluid (air, gas or liquid) is induced to flow over a surface, there may be turbulence in the fluid. The fractal shape of the heat sink serves to reduce the energy lost due to the turbulence, while increasing the surface area of the heat sink subject to turbulence, due to the plethora of concave regions, cavities, and pockets. Therefore, the efficiency of heat transfer may be increased as compared to a heat exchange device having a linear or Euclidian geometric variation between several heat exchange elements.


Preferably, the heat exchange device will include a highly conductive substance whose heat conductivity exceeds 850 W/(m*K). Examples of such superconductors include graphene, diamond, and diamond-like coatings. Alternatively, the heat exchange device may include carbon nanotubes.


Various variations on this heat sink will be apparent to skilled persons in the art. For example, the heat sink could include a heat transfer surface that is connected to the heat exchange device and is designed to accept a solid to be cooled. Alternatively, there could be a connector that is designed to connect with a solid to be cooled in at least one point. In another embodiment, there are at least three connectors serving to keep the solid and the heat sink in a fixed position relative to one another. Various connectors will be apparent to persons skilled in the art. For example, the connector could be a point connector, a bus, a wire, a planar connector or a three-dimensional connector. In another embodiment, the heat sink has an aperture or void in the center thereof designed to accept a solid to be cooled.


This heat sink is intended to be used to cool objects, and may be part of a passive or active system. Modern three-dimensional laser and liquid printers can create objects such as the heat sinks described herein with a resolution of features on the order of about 16 μm, making it feasible for those of skilled in the art to use such fabrication technologies to produce objects with a size below 10 cm. Alternatively, larger heat sinks, such as car radiators, can be manufactured in a traditional manner, designed with an architecture of elements having a fractal configuration. For example, a liquid-to-gas heat exchanger (radiator) may be provided in which segments of fluid flow conduit have a fractal relationship over three levels of recursion, i.e., paths with an average of at least two branches. Other fractal design concepts may be applied concurrently, as may be appropriate.


Yet another embodiment of the invention involves a method of cooling a solid by connecting the solid with a heat sink. The heat sink comprises a heat exchange device having a plurality of heat exchange elements having a fractal variation therebetween. A heat transfer fluid having turbulent portions is induced to flow with respect to the plurality of heat exchange elements. The fractal variation in the plurality of heat exchange elements serves to substantially reduce narrow band resonance as compared to a corresponding heat exchange device having a linear or Euclidean geometric variation between a plurality of heat exchange elements.


A preferred embodiment provides a surface of a solid heat sink, e.g., an internal or external surface, having fluid thermodynamical properties adapted to generate an asymmetric pattern of vortices over the surface over a range of fluid flow rates. For example, the range may comprise a range of natural convective fluid flow rates arising from use of the heat sink to cool a heat-emissive object. The range may also comprise a range of flow rates arising from a forced convective flow (e.g., a fan) over the heat sink.


The heat sink may cool an unconstrained or uncontained fluid, generally over an external surface of a heat sink, or a constrained or contained fluid, generally within an internal surface of a heat sink.





BRIEF DESCRIPTION OF THE DRAWINGS


FIG. 1 shows a set of governing equations for a parallel plate heat sink.



FIGS. 1A and 1B show the spatial relationships and dimensional labels for a parallel plate heat sink.



FIG. 3 illustrates a fractal heat sink that is an exemplary embodiment of the invention. In this embodiment, the heat sink is placed either adjacent to or surrounding the object to be cooled.





DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS


FIG. 2 illustrates a heat sink implementing an exemplary embodiment of this invention. Note that the illustration is in two dimensions, but a three-dimensional embodiment is both possible and preferred. There is a heat transfer surface 100 that allows the heat sink to rest comfortably on a surface, such as the solid to be cooled 190, through a connector 214. In the illustrated embodiment, the heat transfer surface 100 is roughly planar, having a closed Euclidian cross-section on the bottom. However, it might also have another shape, for example if the solid to be cooled does not have a planar face. A fractal-shaped heat exchange structure 110 begins at point 111. While only one fractal heat sink is illustrated here, skilled persons in the art will recognize other similar fractal heat sinks that are also intended to be covered by the invention. Note that the heat sink has three branches supported from point 111-branch 160, which supports branch 140, which in turn supports branch 120. Also note that the branch structure initiating from point 111 is nearly identical to that at point 122, 142, and 162 even though only point 111 is a true starting point. Thus, the fractal property of self-similarity is preserved. We call the structure that begins at point 111 the “first motif,” the structure from point 162 the “second motif,” and the structure that begins from point 142 the “third motif”, and from point 122 the “fourth motif.”


Note that, in the embodiment illustrated in FIG. 2, the replication from first to second motif and from second to third motif involves a linear displacement (upward) and a change of scale. In branches not going in the same direction as the prior branch, there is also a rotation. Under the limitations for ideal fractals, the second motif and third motif must be a smaller, exact copy of the first motif. However, due to the limitations imposed by human-made structures and machines, the fractals designed here are generally finite and the second motif will thus be an inexact copy of the first motif, i.e., if there are N levels starting from the first motif, the second motif level will have N−1 levels, if N is very large, the difference is insignificant. In other words, the self-similarity element required in fractals is not preserved perfectly in the preferred designs due to the limitations of available machinery. In addition, the benefits are achieved without requiring fractal relationships over more than a few “orders” of magnitude (iterations of the fractal recursive algorithm). For example, in the embodiment illustrated in FIG. 2, there are no continuing branch divisions and iterations at point 122, even though an ideal fractal would have them. In an ideal fractal, there would be an infinite number of sub-branches from points 111, 122, 142, and 162. However, an imperfect fractal shape, as illustrated in FIG. 2, will serve the purposes of this invention.


Persons of ordinary skill in the art will appreciate the advantages offered by the structure 110 in FIG. 2. The fractal heat sink has a much larger surface area than the heat transfer surface alone because all of the “branches” and “leaves” of the fern-like fractal shape serve to increase the surface area of their circumferential external surface boundary 112 with respect to a heat transfer fluid 113, such as by operation of a fan 102 which induces a flow 103 of surrounding gas. In addition, if a heat transfer fluid is induced to flow above the heat transfer surface 100, the turbulent portions of the heat transfer fluid near the surface will be increased by the textures inherent in the fractal variation in the heat exchange structure 110. Because the fractal pattern is itself non-identically repeating within the fractal design, this flow 103 of gas induced by fan 102 will serve to substantially reduce narrow band acoustic resonance as compared to a corresponding heat exchange device having a repeating design, e.g., a linear or geometric variation between several heat exchange elements, thereby further aiding in the heat transfer process.


In a preferred embodiment, the heat transfer surface 100 and the roughly fractal-shaped heat exchange structure 110 are all made out of an efficient heat conductor, such as copper or aluminum, or more preferably, having a portion whose heat conductivity exceeds 850 W/(m*K), such as graphene with a heat conductivity of between 4840 and 5300 W/(m*K) or diamond with a heat conductivity between 900 and 2320 W/(m*K). This would allow heat to quickly enter the heat sink from the solid and for heat to quickly exit the heat sink through the branches and leaves of the fern-like fractal-shaped heat exchange structure 110. In another embodiment, the heat sink is formed, at least in part, of carbon nanotubes, which display anisotropic heat conduction, with an efficient heat transfer along the long axis of the tube. Carbon nanotubes are submicroscopic hollow tubes made of a chicken-wire-like or lattice of carbon atoms. These tubes have a diameter of just a few nanometers and are highly heat conductive, transferring heat much faster than diamond, and in some cases comparable to graphene. See web.mit·edu/press/2010/thermopower-waves.html (last accessed Apr. 15, 2010) incorporated herein by reference.


Also note that this exemplary embodiment provides a plethora of openings between the branches or fractal subelements to ensure that all of the branches are exposed to the surrounding air, gas or liquid and to allow the heat to escape from the heat sink into the surroundings. In one embodiment of the invention, at least two of these openings are congruent. An embodiment of the invention allows the openings to be filled with the air or liquid from the surrounding medium. Due to the limitation imposed by the solid's flat shape, it is not possible to increase the exposure of the fern-like fractal to the solid. However, the air or liquid outside of the solid are perfect for the fractal's exposure.


Under the phonon model of heat exchange, applicable to carbon nanotubes, graphene materials, and perhaps others, the fractal shape is advantageous to ensure the escape of the phonons into the surrounding fluid medium because the fractal guarantees close to maximal surface exposure to the medium and does not have many parts that are not exposed, as is a problem with many prior art heat sinks. Skilled persons in the art will realize that this could be achieved through many known structures. For example, graphene, which is one-atom-thick carbon and highly heat conductive, would be an advantageous material to use to build the fractal heat sink herein described.


When a turbulently flowing fluid, such as the gas induced to flow 103 by the fan 102, passes around an obstacle, concave regions 180a, 180b, 180c, 280a, 280b, 280c or cavities in the obstacle create pockets of separated flow which generates self-sustaining oscillations and acoustic resonance. The concave regions 180a, 180b, 180c, 280a, 280b, 280c or cavities differ non-incrementally, and have substantially reduced narrow band acoustic resonance as compared to flat regions on the obstacle. This allows for more energy to be available for heat transfer. Skilled persons in the art will note that fractal structure 110 as shown in FIG. 2, as many other fractal structures, has a plurality of concave regions 180a, 180b, 180c, 280a, 280b, 280c to allow for an implementation of this effect.



FIG. 3 illustrates another embodiment of the invention. A solid to be cooled that has an arbitrary shape 290 is located inside (illustrated) or outside (not illustrated) a two-dimensional or three-dimensional roughly fractal shaped 200 heat sink. In one embodiment, the heat sink 200 has an aperture 270 designed to hold the solid. Alternatively, the solid to be cooled might be located outside of the heat sink (not illustrated). Note that, as in FIG. 2, the fractal heat exchange element has multiple motifs, starting with the large triangle motif 210, to progressively smaller triangle motifs 220 and 230. However, note that the fractal does not keep extending infinitely and there are no triangles smaller than the one at motif 230. In other words, the fractal heat sink 200 has multiple recursive fractal iterations of motifs 220 and 230 of motif 210, but the fractal iterations stop at the level of motif 230 for simplicity of design and manufacturability. Also note that the fractal motifs 220 and 230 are of different dimensional sizes from the original fractal motif 210 and protrude from the original fractal motif 210. Here, the first motif is a large triangle, and the latter motifs are smaller triangles, which involve a rotation, linear displacement, and change of scale of the prior motif. In one embodiment, the fractal shape has some apertures in it (not illustrated) to allow the solid to be cooled to connect with other elements. Also, the solid to be cooled is connected to the fractal shape at point connector 240 and through bus wires at 250 and 260. The solid should be connected to the fractal heat sink in at least one point, either through a point connection, a bus wire connection, or some other connection. If it is desired that the solid be fixed inside the heat sink, there may be at least three connection points, as illustrated. However, only one connection point is necessary for heat convection and radiation from the solid to the heat sink. Preferably, the point or bus wire connection is built using a strong heat conductor, such as carbon nanotubes or a diamond-like coating.


Note that, as in FIG. 2, the fractal structure 200 in FIG. 3 has multiple concave regions 280a, 280b, 280c or cavities. When a turbulently flowing fluid passes around this fractal heat sink, the concave regions 280a, 280b, 280c or cavities substantially reduce the narrow band acoustic resonance as compared to a flat or Euclidian structure. This allows for more energy to be available to for heat transfer.


In yet another embodiment of the invention, the heat sink 200 in FIG. 3 could be constructed without the connections at points 240, 250, and 260. In one embodiment, a liquid or gas would fill the aperture 270 with the intent that the liquid or gas surround the solid to be cooled, hold it in place, or suspend it. Preferably, the liquid or gas surrounding the solid would conduct heat from the solid to the heat sink, which would then cause the heat to exit.


Those skilled in the art will recognize many ways to fabricate the heat sinks described herein. For example, modern three-dimensional laser and liquid printers can create objects such as the heat sinks described herein with a resolution of features on the order of 16 μm. Also, it is possible to grow a crystal structure using a recursive growth algorithm or through crystal growth techniques. For example, US Patent Application No. 2006/0037177 by Blum, incorporated herein by reference, describes a method of controlling crystal growth to produce fractals or other structures through the use of spectral energy patterns by adjusting the temperature, pressure, and electromagnetic energy to which the crystal is exposed. This method might be used to fabricate the heat sinks described herein. For larger heat sinks, such as those intended to be used in car radiators, traditional manufacturing methods for large equipment can be adapted to create the fractal structures described herein.


In this disclosure, we have described several embodiments of this broad invention. Persons skilled in the art will definitely have other ideas as to how the teachings of this specification can be used. It is not our intent to limit this broad invention to the embodiments described in the specification. Rather, the invention is limited by the following claims.

Claims
  • 1. A method of cooling a heat transfer surface, comprising: providing a heat sink comprising: a plurality of heat exchange elements arranged in a fractal branching pattern over at least three levels of branching,each heat exchange element having an external surface of a respective branch configured to transfer heat derived from the heat transfer surface to a surrounding flowable heat exchange medium; andflowing the flowable heat exchange medium relative to the external surfaces of the plurality of heat exchange elements, such that the flow of the flowable heat exchange medium successively encounters at least two branch points of different branches,to thereby transfer heat between the heat transfer surface and the heat sink, and between the heat sink and the flowable heat exchange medium,wherein the flowable heat exchange medium has a different temperature than the solid composition; andwherein the flowable heat transfer medium interacts with the fractal branching pattern to induce a broadband acoustic emission.
  • 2. The method according to claim 1, wherein the fractal branching pattern defines a central void space, and the flowable heat transfer medium comprises air, which is induced to flow by a fan.
  • 3. The method according to claim 1, wherein the external surfaces of the plurality of heat exchange elements define a plurality of concave regions.
  • 4. The method according to claim 3, wherein the plurality of concave regions differ by non-uniform increments.
  • 5. The method according to claim 3, wherein the plurality of concave regions interact with the flow of the flowable heat exchange medium without producing narrow band acoustic resonance.
  • 6. The method according to claim 3, wherein the plurality of concave regions interact with the flow of the flowable heat exchange medium to create pockets of separated flow which generate self-sustaining oscillations.
  • 7. The method according to claim 1, wherein the flowable heat transfer medium is induced to flow turbulently with respect to the external surfaces.
  • 8. The method according to claim 1, wherein the plurality of heat exchange elements branch in two dimensions.
  • 9. The method according to claim 1, wherein the plurality of heat exchange elements branch in three dimensions.
  • 10. The method according to claim 1, wherein the flow of the flowable heat exchange medium relative to the external surfaces of the plurality of heat exchange elements, such that the flow of the flowable heat exchange medium successively encounters at least two branch points of different branches, produces an acoustic emission having acoustic power distributed over a wide band.
  • 11. The method according to claim 1, further comprising receiving heat from an electronic device through the heat transfer surface.
  • 12. The method according to claim 1, further comprising inducing the flow of the flowable heat transfer medium with a fan.
  • 13. The method according to claim 1, further comprising actively inducing flow of a liquid heat transfer medium through an internal microchannel within the plurality of heat exchange elements, concurrent with actively inducing flow of the flowable heat exchange medium over the external surfaces of the plurality of heat exchange elements.
  • 14. A heat exchange method, comprising: providing a heat exchanger comprising a branched pattern of heat exchange elements in a multiscale fractal geometric design having at least three levels of branching, defining a plurality of concave regions configured for turbulent interaction with a flowing heat exchange medium; andactively inducing a flow of the heat exchange medium over at least two successive branches of the at least three levels of branching of the heat exchanger, to cause the turbulent interaction with the plurality of concave regions and associated acoustic emissions, the turbulent interaction causing a broadband acoustic emission having an acoustic spread across an acoustic frequency spectrum having a plurality of peaks selectively defined by a configuration of the multiscale fractal geometric design having the at least three levels of branching.
  • 15. A heat sink method, comprising: defining a plurality of concave regions of a heat exchanger comprising a branched pattern of heat exchange elements in a multiscale fractal geometric design, having at least three successive level of branches, the plurality of concave regions being configured to interact with a flowing heat exchange medium to produce turbulent flow; andinducing the turbulent flow of the heat exchange medium with a fan to disturb a surface boundary layer on the heat exchange elements and generate broadband acoustic frequency emission having a spread acoustic spectrum selectively dependent on the plurality of concave regions and the multiscale fractal geometric design.
  • 16. The heat sink method according to claim 15, wherein the turbulent flow of the heat exchange medium generates flow-induced vortices at locations of respective ones of the plurality of heat exchange elements defined by the multiscale fractal geometric design, resulting in a multipeak spread acoustic spectrum.
  • 17. The method according to claim 14, wherein the plurality of concave regions differ in geometric location according to non-uniform increments.
  • 18. The method according to claim 14, wherein the plurality of concave regions interact with the actively induced flow of the heat exchange medium to create pockets of separated flow which generate self-sustaining oscillations.
  • 19. The method according to claim 14, wherein the branched pattern of heat exchange elements branch in three dimensions.
  • 20. The method according to claim 14, wherein the actively induced flow of the heat exchange medium over the heat exchanger causes portions of the heat exchange medium to successively encounter at least two branch points of the branched pattern, in different branches of the branched pattern.
CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a Division of U.S. patent application Ser. No. 14/817,962, filed Aug. 4, 2015, now U.S. Pat. No. 10,527,368, issued Jan. 7, 2020, which is a Continuation of U.S. patent application Ser. No. 13/106,640, filed May 12, 2011, now U.S. Pat. No. 9,228,785, issued Jan. 5, 2016, which is a non-provisional of, and claims benefit of priority under 35 U.S.C. 119(e) from, U.S. Provisional Patent Application No. 61/331,103, filed May 4, 2010, and which claims priority under 35 U.S.C. 371 from PCT Patent Application No. PCT/IB11/01026, filed May 13, 2011, the entirety of which are expressly incorporated herein by reference. This application is related to U.S. patent application Ser. No. 14/984,756, filed Dec. 30, 2015, now U.S. Pat. No. 10,041,745, issued Aug. 7, 2018, which is a Continuation-in-part of U.S. patent application Ser. No. 14/817,962, filed Aug. 4, 2015, and U.S. patent application Ser. No. 15/205,906, filed Jul. 8, 2016, and U.S. patent application Ser. No. 16/056,481, filed Aug. 6, 2018, and PCT Patent Application No. PCT/US16/68641, filed Dec. 27, 2016,

US Referenced Citations (1272)
Number Name Date Kind
2535721 Gaston Dec 1950 A
3308876 Gram, Jr. Mar 1967 A
4463359 Ayata et al. Jul 1984 A
4654092 Melton Mar 1987 A
4660627 Deck Apr 1987 A
4715438 Gabuzda et al. Dec 1987 A
4741292 Novak May 1988 A
4769644 Frazier Sep 1988 A
4790650 Keady Dec 1988 A
4819200 Chua et al. Apr 1989 A
4904073 Lawton et al. Feb 1990 A
4931626 Shikama et al. Jun 1990 A
5092280 Franklin et al. Mar 1992 A
5134685 Rosenbluth Jul 1992 A
5169110 Snaith et al. Dec 1992 A
5224663 Criswell Jul 1993 A
5354017 Levich Oct 1994 A
5371666 Miller Dec 1994 A
5371753 Adsett Dec 1994 A
5396413 Kaneko et al. Mar 1995 A
5430607 Smith Jul 1995 A
5443727 Gagnon Aug 1995 A
5453844 George et al. Sep 1995 A
5461263 Helfrich Oct 1995 A
5465011 Miller et al. Nov 1995 A
5471991 Shinnar Dec 1995 A
5483098 Joiner, Jr. Jan 1996 A
5510598 Kawam et al. Apr 1996 A
5548481 Salisbury et al. Aug 1996 A
5549795 Gregoire et al. Aug 1996 A
5566377 Lee Oct 1996 A
5600073 Hill Feb 1997 A
5616246 Gagnon et al. Apr 1997 A
5649507 Gregoire et al. Jul 1997 A
5655210 Gregoire et al. Aug 1997 A
5714691 Hill Feb 1998 A
5720921 Meserol Feb 1998 A
5774357 Hoffberg et al. Jun 1998 A
5781460 Nguyen et al. Jul 1998 A
5792062 Poon et al. Aug 1998 A
5797736 Menguc et al. Aug 1998 A
5803301 Sato et al. Sep 1998 A
5822721 Johnson et al. Oct 1998 A
5834871 Puskas Nov 1998 A
5839080 Muller et al. Nov 1998 A
5841911 Kopeika et al. Nov 1998 A
5842937 Dalton et al. Dec 1998 A
5843301 Esztergar et al. Dec 1998 A
5845504 LeBleu Dec 1998 A
5846394 Burlatsky et al. Dec 1998 A
5856836 Silverbrook Jan 1999 A
5867386 Hoffberg et al. Feb 1999 A
5870284 Stewart et al. Feb 1999 A
5872443 Williamson Feb 1999 A
5875108 Hoffberg et al. Feb 1999 A
5901246 Hoffberg et al. May 1999 A
5903454 Hoffberg et al. May 1999 A
5920477 Hoffberg et al. Jul 1999 A
5921679 Muzzio et al. Jul 1999 A
5928726 Butler et al. Jul 1999 A
5938333 Kearney Aug 1999 A
5938594 Poon et al. Aug 1999 A
5973770 Carter et al. Oct 1999 A
6002588 Vos et al. Dec 1999 A
6015008 Kogure et al. Jan 2000 A
6048313 Stonger Apr 2000 A
6051075 Kochergin et al. Apr 2000 A
6074605 Meserol et al. Jun 2000 A
6081750 Hoffberg et al. Jun 2000 A
6088634 Muller et al. Jul 2000 A
6090617 Meserol Jul 2000 A
6092009 Glover Jul 2000 A
6122570 Muller et al. Sep 2000 A
6128188 Hanners Oct 2000 A
6138060 Conner et al. Oct 2000 A
6164458 Mandrin et al. Dec 2000 A
6219592 Muller et al. Apr 2001 B1
6248399 Hehmann Jun 2001 B1
6259516 Carter et al. Jul 2001 B1
6276370 Fisch et al. Aug 2001 B1
6277522 Omaru et al. Aug 2001 B1
6292721 Conner et al. Sep 2001 B1
6292830 Taylor et al. Sep 2001 B1
6310746 Hawwa et al. Oct 2001 B1
6313587 MacLennan et al. Nov 2001 B1
6323432 Campbell et al. Nov 2001 B1
6330157 Bezama et al. Dec 2001 B1
6330168 Pedoeem et al. Dec 2001 B1
6333019 Coppens Dec 2001 B1
6333852 Lin Dec 2001 B1
6347263 Johnson et al. Feb 2002 B1
6356444 Pedoeem Mar 2002 B1
6359565 Pedoeem et al. Mar 2002 B1
6382208 Reedy et al. May 2002 B2
6390475 Eckblad et al. May 2002 B1
6398736 Seward Jun 2002 B1
6400996 Hoffberg et al. Jun 2002 B1
6418424 Hoffberg et al. Jul 2002 B1
6422998 Vo-Dinh et al. Jul 2002 B1
6424099 Kirkpatrick et al. Jul 2002 B1
6433749 Thompson Aug 2002 B1
6484132 Hively et al. Nov 2002 B1
6485961 Meserol Nov 2002 B1
6487442 Wood Nov 2002 B1
6502067 Hegger et al. Dec 2002 B1
6512996 Praskovsky et al. Jan 2003 B1
6544187 Seward Apr 2003 B2
6544309 Hoefer et al. Apr 2003 B1
6566646 Iwakawa May 2003 B1
6570078 Ludwig May 2003 B2
6581008 Intriligator et al. Jun 2003 B2
6592822 Chandler Jul 2003 B1
6597906 Van Leeuwen et al. Jul 2003 B1
6606034 Muller et al. Aug 2003 B1
6608716 Armstrong et al. Aug 2003 B1
6610917 Ludwig Aug 2003 B2
6616327 Kearney et al. Sep 2003 B1
6617154 Meserol Sep 2003 B1
6628132 Pfahnl et al. Sep 2003 B2
6640145 Hoffberg et al. Oct 2003 B2
6641471 Pinheiro et al. Nov 2003 B1
6641796 Micco et al. Nov 2003 B2
6679272 Bran et al. Jan 2004 B2
6681589 Brudnicki Jan 2004 B2
6688381 Pence et al. Feb 2004 B2
6689486 Ho et al. Feb 2004 B2
6689947 Ludwig Feb 2004 B2
6691004 Johnson et al. Feb 2004 B2
6707837 Muller Mar 2004 B1
6710723 Muller et al. Mar 2004 B2
6716557 Omaru et al. Apr 2004 B2
6717661 Bernstein et al. Apr 2004 B1
6721572 Smith et al. Apr 2004 B1
6727820 Pedoeem et al. Apr 2004 B2
6736195 Busch et al. May 2004 B2
6742924 Kearney Jun 2004 B2
6751027 Van Den Bossche et al. Jun 2004 B2
6773669 Holaday et al. Aug 2004 B1
6781690 Armstrong et al. Aug 2004 B2
6816786 Intriligator et al. Nov 2004 B2
6849795 Ludwig Feb 2005 B2
6850252 Hoffberg Feb 2005 B1
6852919 Ludwig Feb 2005 B2
6865083 Liu Mar 2005 B2
6876304 Pedoeem et al. Apr 2005 B2
6876320 Puente Baliarda Apr 2005 B2
6895375 Malah et al. May 2005 B2
6898216 Kleinschmidt May 2005 B1
6905595 Gebauer Jun 2005 B2
6906296 Centanni et al. Jun 2005 B2
6909198 Ragwitz et al. Jun 2005 B2
6937473 Cheng et al. Aug 2005 B2
6941973 Hehmann Sep 2005 B2
6942767 Fazzina et al. Sep 2005 B1
6945094 Eggen et al. Sep 2005 B2
6949887 Kirkpatrick et al. Sep 2005 B2
6967315 Centanni et al. Nov 2005 B2
6969327 Aoyama et al. Nov 2005 B2
6971383 Hickey et al. Dec 2005 B2
6972972 Duncan et al. Dec 2005 B2
6980092 Turnbull et al. Dec 2005 B2
6986739 Warren et al. Jan 2006 B2
6988066 Malah Jan 2006 B2
6993377 Flick et al. Jan 2006 B2
6994045 Paszkowski Feb 2006 B2
7001521 Paananen et al. Feb 2006 B2
7006881 Hoffberg et al. Feb 2006 B1
7010991 Lutz et al. Mar 2006 B2
7018418 Amrich et al. Mar 2006 B2
7038123 Ludwig May 2006 B2
7050605 Gerson et al. May 2006 B2
7055262 Goldberg et al. Jun 2006 B2
7080989 Gates Jul 2006 B2
7096121 Intriligator et al. Aug 2006 B2
7103480 Intriligator et al. Sep 2006 B2
7113402 Rutledge et al. Sep 2006 B2
7117108 Rapp et al. Oct 2006 B2
7117131 Binnig Oct 2006 B2
7123359 Armstrong et al. Oct 2006 B2
7128833 Jumppanen et al. Oct 2006 B2
7129091 Ismagilov et al. Oct 2006 B2
7136710 Hoffberg et al. Nov 2006 B1
7177282 Gilbert et al. Feb 2007 B1
7178941 Roberge et al. Feb 2007 B2
7190579 Chao Mar 2007 B2
7195058 Wolford et al. Mar 2007 B2
7204832 Altshuler et al. Apr 2007 B2
7216074 Malah et al. May 2007 B2
7217878 Ludwig May 2007 B2
7226539 Dong et al. Jun 2007 B2
7238085 Montierth et al. Jul 2007 B2
7242988 Hoffberg et al. Jul 2007 B1
7256751 Cohen Aug 2007 B2
7258632 Aoyama et al. Aug 2007 B2
7260299 Di Teodoro et al. Aug 2007 B1
7263130 Mitlin Aug 2007 B1
7265826 Mottin Sep 2007 B2
7267798 Chandler Sep 2007 B2
7271952 Suzuki et al. Sep 2007 B2
7272599 Gilbert et al. Sep 2007 B1
7273456 May et al. Sep 2007 B2
7276026 Skinner Oct 2007 B2
7296014 Gilbert et al. Nov 2007 B1
7303491 Nardacci et al. Dec 2007 B2
7303682 Paananen et al. Dec 2007 B2
7309828 Ludwig Dec 2007 B2
7309829 Ludwig Dec 2007 B1
7327123 Faberman et al. Feb 2008 B2
7327226 Turnbull et al. Feb 2008 B2
7351360 Hougham et al. Apr 2008 B2
7375877 Di Teodoro et al. May 2008 B1
7376553 Quinn May 2008 B2
7379237 Di Teodoro et al. May 2008 B1
7379648 Brooks et al. May 2008 B1
7383607 Johnson Jun 2008 B2
7386211 Di Teodoro et al. Jun 2008 B1
7390408 Kearney et al. Jun 2008 B2
7391561 Di Teodoro et al. Jun 2008 B2
7400804 Di Teodoro et al. Jul 2008 B1
7407586 Jumppanen et al. Aug 2008 B2
7408108 Ludwig Aug 2008 B2
7411791 Chang et al. Aug 2008 B2
7416903 Sklar et al. Aug 2008 B2
7417954 Gilbert et al. Aug 2008 B1
7422910 Fitzgerald et al. Sep 2008 B2
7430352 Di Teodoro et al. Sep 2008 B2
7436585 Di Teodoro et al. Oct 2008 B1
7440175 Di Teodoro et al. Oct 2008 B2
7442360 Tonkovich et al. Oct 2008 B2
7451005 Hoffberg et al. Nov 2008 B2
7485343 Branson et al. Feb 2009 B1
7495671 Chemel et al. Feb 2009 B2
7496000 Vosburgh et al. Feb 2009 B2
7502034 Chemel et al. Mar 2009 B2
7507380 Chang et al. Mar 2009 B2
7507902 Ludwig Mar 2009 B2
7513839 Nardacci et al. Apr 2009 B2
7539533 Tran May 2009 B2
7551519 Slater Jun 2009 B2
7554511 Fager et al. Jun 2009 B2
7558622 Tran Jul 2009 B2
7569354 Okano et al. Aug 2009 B2
7588505 Hebert et al. Sep 2009 B2
7589742 Street et al. Sep 2009 B2
7590589 Hoffberg Sep 2009 B2
7593789 Gougerot et al. Sep 2009 B2
7604956 Drukier Oct 2009 B2
7613604 Malah et al. Nov 2009 B1
7614406 Bran Nov 2009 B2
7630931 Rachev et al. Dec 2009 B1
7638704 Ludwig Dec 2009 B2
7641865 Tonkovich et al. Jan 2010 B2
7643295 Chao et al. Jan 2010 B2
7646029 Mueller et al. Jan 2010 B2
7646607 Gallina et al. Jan 2010 B2
7650319 Hoffberg et al. Jan 2010 B2
7652208 Ludwig Jan 2010 B1
7655341 Strobel et al. Feb 2010 B2
7665225 Goldberg et al. Feb 2010 B2
7689283 Schecter Mar 2010 B1
7696890 Bandholz et al. Apr 2010 B2
7710424 Hutchins et al. May 2010 B1
7724258 Ebert et al. May 2010 B2
7727746 Foody et al. Jun 2010 B2
7728837 Szymanski et al. Jun 2010 B2
7733224 Tran Jun 2010 B2
7740026 Matsui et al. Jun 2010 B2
7744855 Staniforth et al. Jun 2010 B2
7751118 Di Teodoro et al. Jul 2010 B1
7757866 McCutchen Jul 2010 B2
7759571 Ludwig Jul 2010 B2
7767902 Ludwig Aug 2010 B2
7769782 Gilbert et al. Aug 2010 B1
7772966 Turnbull et al. Aug 2010 B2
7778029 Ueno Aug 2010 B2
7782459 Holve Aug 2010 B2
7782527 Brooks et al. Aug 2010 B1
7786370 Ludwig Aug 2010 B2
7796383 Kavanagh Sep 2010 B2
7799557 Oh et al. Sep 2010 B2
7804186 Freda Sep 2010 B2
7805832 Burke et al. Oct 2010 B2
7813822 Hoffberg Oct 2010 B1
7814965 Spokoiny Oct 2010 B1
7830596 Di Teodoro et al. Nov 2010 B1
7835068 Brooks et al. Nov 2010 B1
7848106 Merrow Dec 2010 B2
7850862 Amrich et al. Dec 2010 B2
7852628 Hirohata et al. Dec 2010 B2
7856154 Young Dec 2010 B2
7857756 Warren et al. Dec 2010 B2
7866822 Yokoyama et al. Jan 2011 B2
7871578 Schmidt Jan 2011 B2
7877876 Burke et al. Feb 2011 B2
7891818 Christensen et al. Feb 2011 B2
7901939 Ismagliov et al. Mar 2011 B2
7904187 Hoffberg et al. Mar 2011 B2
7904211 Merrow et al. Mar 2011 B2
7938543 Gerets et al. May 2011 B2
7941019 Brooks et al. May 2011 B1
7955504 Jovanovic et al. Jun 2011 B1
7959880 Tonkovich et al. Jun 2011 B2
7960640 Ludwig Jun 2011 B2
7965643 Gilbert et al. Jun 2011 B1
7966078 Hoffberg et al. Jun 2011 B2
7968789 Stoner et al. Jun 2011 B2
7974714 Hoffberg Jul 2011 B2
7979979 Burke et al. Jul 2011 B2
7987003 Hoffberg et al. Jul 2011 B2
7987677 McCutchen Aug 2011 B2
8003370 Maltezos et al. Aug 2011 B2
8008046 Maltezos et al. Aug 2011 B2
8014150 Campbell et al. Sep 2011 B2
8025801 McCutchen Sep 2011 B2
8030565 Ludwig Oct 2011 B2
8030566 Ludwig Oct 2011 B2
8030567 Ludwig Oct 2011 B2
8030818 Nelson et al. Oct 2011 B2
8031060 Hoffberg et al. Oct 2011 B2
8032477 Hoffberg et al. Oct 2011 B1
8033933 Sullivan et al. Oct 2011 B2
8035024 Ludwig Oct 2011 B2
8037927 Schuette Oct 2011 B2
8040508 Holve Oct 2011 B2
8046313 Hoffberg et al. Oct 2011 B2
8055392 Kitamura et al. Nov 2011 B2
8069038 Malah et al. Nov 2011 B2
8080819 Mueller et al. Dec 2011 B2
8081479 Tanaka Dec 2011 B2
8089173 Freda Jan 2012 B2
8092625 Burke et al. Jan 2012 B2
8093772 Scott et al. Jan 2012 B2
8100205 Gettings et al. Jan 2012 B2
8101160 Staniforth et al. Jan 2012 B2
8102173 Merrow Jan 2012 B2
8103333 Tran Jan 2012 B2
8108036 Tran Jan 2012 B2
8110103 Mormino et al. Feb 2012 B2
8111261 Perlin Feb 2012 B1
8114438 Pipkin et al. Feb 2012 B2
8116024 Erden Feb 2012 B2
8116841 Bly et al. Feb 2012 B2
8117480 Merrow et al. Feb 2012 B2
8137216 Sullivan et al. Mar 2012 B2
8137554 Jovanovic et al. Mar 2012 B2
8137626 Maltezos et al. Mar 2012 B2
8157032 Gettings Apr 2012 B2
8165916 Hoffberg et al. Apr 2012 B2
8167826 Oohashi et al. May 2012 B2
8178990 Freda May 2012 B2
8182473 Altshuler et al. May 2012 B2
8182573 Stark et al. May 2012 B2
8187541 Maltezos et al. May 2012 B2
8203840 Lin et al. Jun 2012 B2
8207821 Roberge et al. Jun 2012 B2
8208698 Bogdan Jun 2012 B2
8210171 Denny et al. Jul 2012 B2
8223062 Bunch et al. Jul 2012 B2
8228671 Ikeda Jul 2012 B2
8232091 Maltezos et al. Jul 2012 B2
8238099 Merrow Aug 2012 B2
8249686 Libbus et al. Aug 2012 B2
8258206 Kanagasabapathy et al. Sep 2012 B2
8262909 Angelescu et al. Sep 2012 B2
8268136 McCutchen et al. Sep 2012 B2
8273245 Jovanovic et al. Sep 2012 B2
8273330 York et al. Sep 2012 B2
8273573 Ismagilov et al. Sep 2012 B2
8279597 El-Essawy et al. Oct 2012 B2
8280641 Pellionisz Oct 2012 B1
8285356 Bly et al. Oct 2012 B2
8289710 Spearing et al. Oct 2012 B2
8295046 St. Rock et al. Oct 2012 B2
8295049 West Oct 2012 B2
8296937 Burke et al. Oct 2012 B2
8304193 Ismagilov et al. Nov 2012 B2
8323188 Tran Dec 2012 B2
8329407 Ismagilov et al. Dec 2012 B2
8352400 Hoffberg et al. Jan 2013 B2
8361622 Gottschalk-Gaudig et al. Jan 2013 B2
8363392 Tanaka Jan 2013 B2
8364136 Hoffberg et al. Jan 2013 B2
8369967 Hoffberg et al. Feb 2013 B2
8371291 Haroutunian Feb 2013 B2
8374688 Libbus et al. Feb 2013 B2
8385066 Chang et al. Feb 2013 B2
8388401 Lanahan Mar 2013 B2
8395276 Freda Mar 2013 B2
8395629 Kilpatrick et al. Mar 2013 B1
8396700 Chakrabarty et al. Mar 2013 B2
8397842 Gettings Mar 2013 B2
8400766 Kim Mar 2013 B2
8402490 Hoffberg-Borghesani et al. Mar 2013 B2
8409807 Neely et al. Apr 2013 B2
8412317 Mazar Apr 2013 B2
8414182 Paul et al. Apr 2013 B2
8416297 Finn et al. Apr 2013 B2
8434575 Gettings et al. May 2013 B2
8441154 Karalis et al. May 2013 B2
8449471 Tran May 2013 B2
8451608 Merrow May 2013 B2
8460126 Sullivan et al. Jun 2013 B2
8460189 Libbus et al. Jun 2013 B2
8466583 Karalis et al. Jun 2013 B2
8472763 Liu et al. Jun 2013 B1
8474264 McCutchen Jul 2013 B2
8475616 McCutchen Jul 2013 B2
8482146 Freda Jul 2013 B2
8482915 Merrow Jul 2013 B2
8484000 Gulati Jul 2013 B2
8491683 Brown-Fitzpatrick et al. Jul 2013 B1
8492164 Fitzgerald et al. Jul 2013 B2
8506674 Brown-Fitzpatrick et al. Aug 2013 B1
8506799 Jorden et al. Aug 2013 B2
8516266 Hoffberg et al. Aug 2013 B2
8519250 Ludwig Aug 2013 B2
8525673 Tran Sep 2013 B2
8525687 Tran Sep 2013 B2
8526632 Cutler Sep 2013 B2
8531291 Tran Sep 2013 B2
8539840 Ariessohn et al. Sep 2013 B2
8542484 Tanaka Sep 2013 B2
8544573 Gettings et al. Oct 2013 B2
8547519 Streefkerk et al. Oct 2013 B2
8547692 El-Essawy et al. Oct 2013 B2
8559197 Cullinane et al. Oct 2013 B2
8568330 Mollicone et al. Oct 2013 B2
8577184 Young Nov 2013 B2
8578494 Engler et al. Nov 2013 B1
8583263 Hoffberg et al. Nov 2013 B2
8591430 Amurthur et al. Nov 2013 B2
8595001 Malah et al. Nov 2013 B2
8596821 Brandes et al. Dec 2013 B2
8598730 Freda Dec 2013 B2
8600830 Hoffberg Dec 2013 B2
8602599 Zimmer et al. Dec 2013 B2
8608838 Wong et al. Dec 2013 B2
8621867 Galbraith Jan 2014 B2
8623212 Irvin, Sr. et al. Jan 2014 B2
8633437 Dantus et al. Jan 2014 B2
8634056 Streefkerk et al. Jan 2014 B2
8636910 Irvin, Sr. et al. Jan 2014 B2
8641194 Primeau et al. Feb 2014 B2
8651704 Gordin et al. Feb 2014 B1
8653828 Hancock et al. Feb 2014 B2
8655482 Merrow Feb 2014 B2
8666196 Young Mar 2014 B2
8680754 Premysler Mar 2014 B2
8680991 Tran Mar 2014 B2
8684900 Tran Apr 2014 B2
8684925 Manicka et al. Apr 2014 B2
8695431 Pearce Apr 2014 B2
8697433 Oh et al. Apr 2014 B2
8701276 Burke et al. Apr 2014 B2
8707729 Schmidt et al. Apr 2014 B2
8718752 Libbus et al. May 2014 B2
8725676 Engler et al. May 2014 B1
8725677 Engler et al. May 2014 B1
8750971 Tran Jun 2014 B2
8759721 Alexander Jun 2014 B1
8764243 Zimmer et al. Jul 2014 B2
8764651 Tran Jul 2014 B2
8771499 McCutchen et al. Jul 2014 B2
8784540 Rubit et al. Jul 2014 B2
8790257 Libbus et al. Jul 2014 B2
8790259 Katra et al. Jul 2014 B2
8792978 Wells et al. Jul 2014 B2
8794927 Vassilicos Aug 2014 B2
8808113 Aoyama et al. Aug 2014 B2
8813880 Gettings et al. Aug 2014 B2
8822148 Ismagliov et al. Sep 2014 B2
8829799 Recker et al. Sep 2014 B2
8839527 Ben-Shmuel et al. Sep 2014 B2
8847548 Kesler et al. Sep 2014 B2
8854728 Brooks et al. Oct 2014 B1
8858029 Brandes et al. Oct 2014 B2
8859876 Ludwig Oct 2014 B2
8861075 Dantus et al. Oct 2014 B2
8873168 Boone Oct 2014 B2
8874477 Hoffberg Oct 2014 B2
8875086 Verghese et al. Oct 2014 B2
8877072 Sahai et al. Nov 2014 B2
8882552 Lambert Nov 2014 B2
8883423 Neely Nov 2014 B2
8889083 Ismagilov et al. Nov 2014 B2
8892495 Hoffberg et al. Nov 2014 B2
8897868 Mazar et al. Nov 2014 B2
8901778 Kesler et al. Dec 2014 B2
8901779 Kesler et al. Dec 2014 B2
8907531 Hall et al. Dec 2014 B2
8912687 Kesler et al. Dec 2014 B2
8917962 Nichol et al. Dec 2014 B1
8922066 Kesler et al. Dec 2014 B2
8922153 Nashiki et al. Dec 2014 B2
8928276 Kesler et al. Jan 2015 B2
8933594 Kurs et al. Jan 2015 B2
8937399 Freda Jan 2015 B2
8937408 Ganem et al. Jan 2015 B2
8937482 Lemczyk Jan 2015 B1
8939081 Smith et al. Jan 2015 B1
8940361 Smith et al. Jan 2015 B2
8946938 Kesler et al. Feb 2015 B2
8947186 Kurs et al. Feb 2015 B2
8947430 Green et al. Feb 2015 B1
8948253 Reckwerdt et al. Feb 2015 B2
8957549 Kesler et al. Feb 2015 B2
8961667 McCutchen et al. Feb 2015 B2
8965498 Katra et al. Feb 2015 B2
8968585 Malik et al. Mar 2015 B2
8977588 Engler et al. Mar 2015 B1
8994276 Recker et al. Mar 2015 B2
9003846 Isei et al. Apr 2015 B2
9011646 McCutchen et al. Apr 2015 B2
9023216 Kochergin et al. May 2015 B2
9028405 Tran May 2015 B2
9035499 Kesler et al. May 2015 B2
9042967 Dacosta et al. May 2015 B2
9045651 Chen et al. Jun 2015 B2
9046227 David et al. Jun 2015 B2
9046493 Neely et al. Jun 2015 B2
9050888 Gettings et al. Jun 2015 B2
9061267 Gottschall et al. Jun 2015 B2
9062263 Sevastyanov Jun 2015 B2
9062854 Livesay et al. Jun 2015 B2
9065423 Ganem et al. Jun 2015 B2
9067821 Bleecher et al. Jun 2015 B2
9085019 Zhang et al. Jul 2015 B2
9086213 Harbers et al. Jul 2015 B2
9089016 Recker et al. Jul 2015 B2
9090890 Malik et al. Jul 2015 B2
9090891 Madero et al. Jul 2015 B2
9091865 Hofmann et al. Jul 2015 B2
9098889 Zhao et al. Aug 2015 B2
9103540 Wyrick et al. Aug 2015 B2
9106203 Kesler et al. Aug 2015 B2
9107586 Tran Aug 2015 B2
9121801 Clark et al. Sep 2015 B2
9123467 Wu et al. Sep 2015 B2
9125566 Libbus et al. Sep 2015 B2
9125574 Zia et al. Sep 2015 B2
9134079 Tonkovich et al. Sep 2015 B2
9134622 Streefkerk et al. Sep 2015 B2
9134623 Streefkerk et al. Sep 2015 B2
9137548 Li et al. Sep 2015 B2
9138699 Kulkarni et al. Sep 2015 B2
9155849 Haroutunian Oct 2015 B2
9162260 Dumontier et al. Oct 2015 B2
9165717 Yializis et al. Oct 2015 B1
9167633 Ben-Shmuel et al. Oct 2015 B2
9169014 Elson et al. Oct 2015 B2
9173615 Katra et al. Nov 2015 B2
9186089 Mazar et al. Nov 2015 B2
9197904 Li et al. Nov 2015 B2
9204796 Tran Dec 2015 B2
9207341 Pearce Dec 2015 B2
9207408 Di Teodoro et al. Dec 2015 B1
9228785 Poltorak Jan 2016 B2
9233862 Bose et al. Jan 2016 B2
9239951 Hoffberg et al. Jan 2016 B2
9248501 Johannes et al. Feb 2016 B1
9254496 Dhiman et al. Feb 2016 B2
9256001 Pearce Feb 2016 B2
9261251 Ladewig et al. Feb 2016 B1
9262723 Luvalle Feb 2016 B2
9269489 Wu et al. Feb 2016 B2
9278362 Wells et al. Mar 2016 B2
9278374 Wohl, Jr. et al. Mar 2016 B2
9279073 Bleecher et al. Mar 2016 B2
9284520 Malik et al. Mar 2016 B2
9292916 Rowe Mar 2016 B2
9309162 Azimi et al. Apr 2016 B2
9311670 Hoffberg Apr 2016 B2
9312701 Mor et al. Apr 2016 B1
9314181 Brockway et al. Apr 2016 B2
9318257 Lou et al. Apr 2016 B2
9320131 Williams Apr 2016 B2
9320443 Libbus et al. Apr 2016 B2
9326697 Linker May 2016 B2
9329107 Ismagilov et al. May 2016 B2
9339459 York et al. May 2016 B2
9339616 Denny et al. May 2016 B2
9340802 Trevethick May 2016 B2
9346063 Barbee et al. May 2016 B2
9351353 Recker et al. May 2016 B2
9351928 Staniforth et al. May 2016 B2
9355774 Mathieu et al. May 2016 B2
9360457 Neely et al. Jun 2016 B2
9371173 Smith et al. Jun 2016 B2
9381528 Dhiman et al. Jul 2016 B2
9384885 Karalis et al. Jul 2016 B2
9387892 Gettings et al. Jul 2016 B2
9389204 Cloutier et al. Jul 2016 B2
9392669 Recker et al. Jul 2016 B2
9399999 Horng et al. Jul 2016 B2
9432298 Smith Aug 2016 B1
9435524 Athalye Sep 2016 B2
9803623 Burkle Oct 2017 B2
9901002 Jenkins Feb 2018 B2
9961812 Suorsa May 2018 B2
10041745 Poltorak Aug 2018 B2
10061514 Ignomirello Aug 2018 B2
10084239 Shaver et al. Sep 2018 B2
10120607 Ignomirello Nov 2018 B2
10285312 Suorsa May 2019 B2
10346047 Ignomirello Jul 2019 B2
10352303 Burkle Jul 2019 B2
10512140 Alexander Dec 2019 B2
10527368 Poltorak Jan 2020 B2
10570884 Burkle Feb 2020 B2
10572186 Sicola et al. Feb 2020 B2
10606482 Ignomirello Mar 2020 B2
10725452 Elber et al. Jul 2020 B2
10773214 Nosrati Sep 2020 B2
10779384 Alexander Sep 2020 B2
10789137 Ignomirello et al. Sep 2020 B2
10811331 Xia et al. Oct 2020 B2
10830545 Poltorak Nov 2020 B2
10852069 Poltorak Dec 2020 B2
20010001064 Holaday May 2001 A1
20010031238 Omaru et al. Oct 2001 A1
20010032814 Kearney et al. Oct 2001 A1
20010052343 Reedy et al. Dec 2001 A1
20010053741 Micco et al. Dec 2001 A1
20010056316 Johnson et al. Dec 2001 A1
20020005108 Ludwig Jan 2002 A1
20020010710 Binnig Jan 2002 A1
20020015150 Armstrong et al. Feb 2002 A1
20020032510 Turnbull et al. Mar 2002 A1
20020033992 Den Bossche et al. Mar 2002 A1
20020056358 Ludwig May 2002 A1
20020058469 Pinheiro et al. May 2002 A1
20020062648 Ghoshal May 2002 A1
20020079845 Kirkpatrick et al. Jun 2002 A1
20020080563 Pence et al. Jun 2002 A1
20020083780 Lutz et al. Jul 2002 A1
20020107638 Intriligator et al. Aug 2002 A1
20020113719 Muller et al. Aug 2002 A1
20020128554 Seward Sep 2002 A1
20020151992 Hoffberg et al. Oct 2002 A1
20020167282 Kirkpatrick et al. Nov 2002 A1
20020196706 Kearney Dec 2002 A1
20030030430 Pfahnl et al. Feb 2003 A1
20030032950 Altshuler et al. Feb 2003 A1
20030041801 Hehmann Mar 2003 A1
20030050219 Micco et al. Mar 2003 A1
20030065401 Amrich et al. Apr 2003 A1
20030093278 Malah May 2003 A1
20030093279 Malah et al. May 2003 A1
20030094141 Davis May 2003 A1
20030100824 Warren et al. May 2003 A1
20030137442 Baliarda Jul 2003 A1
20030150232 Brudnicki Aug 2003 A1
20030155110 Joshi et al. Aug 2003 A1
20030156738 Gerson et al. Aug 2003 A1
20030160457 Ragwitz et al. Aug 2003 A1
20030162835 Staniforth et al. Aug 2003 A1
20030165436 Staniforth et al. Sep 2003 A1
20030171667 Seward Sep 2003 A1
20030175566 Fisher et al. Sep 2003 A1
20030182246 Johnson et al. Sep 2003 A1
20030183368 Paradis et al. Oct 2003 A1
20030184450 Muller et al. Oct 2003 A1
20030207338 Sklar et al. Nov 2003 A1
20030220740 Intriligator et al. Nov 2003 A1
20030232020 York et al. Dec 2003 A1
20030235919 Chandler Dec 2003 A1
20040006566 Taylor et al. Jan 2004 A1
20040024937 Duncan et al. Feb 2004 A1
20040065187 Ludwig Apr 2004 A1
20040069125 Ludwig Apr 2004 A1
20040069126 Ludwig Apr 2004 A1
20040069127 Ludwig Apr 2004 A1
20040069128 Ludwig Apr 2004 A1
20040069129 Ludwig Apr 2004 A1
20040069131 Ludwig Apr 2004 A1
20040074379 Ludwig Apr 2004 A1
20040078219 Kaylor et al. Apr 2004 A1
20040094021 Ludwig May 2004 A1
20040099127 Ludwig May 2004 A1
20040099128 Ludwig May 2004 A1
20040099129 Ludwig May 2004 A1
20040099131 Ludwig May 2004 A1
20040104934 Fager et al. Jun 2004 A1
20040118268 Ludwig Jun 2004 A1
20040123864 Hickey et al. Jul 2004 A1
20040129641 Paananen et al. Jul 2004 A1
20040131688 Dov et al. Jul 2004 A1
20040140252 Gebauer Jul 2004 A1
20040150666 Fager et al. Aug 2004 A1
20040150818 Armstrong et al. Aug 2004 A1
20040163528 Ludwig Aug 2004 A1
20040166414 Omaru et al. Aug 2004 A1
20040169771 Washington et al. Sep 2004 A1
20040171939 May et al. Sep 2004 A1
20040182855 Centanni Sep 2004 A1
20040187861 Harrison et al. Sep 2004 A1
20040213084 Kearney Oct 2004 A1
20040217011 Strobel et al. Nov 2004 A1
20040238163 Harman Dec 2004 A1
20040243328 Rapp et al. Dec 2004 A1
20040253365 Warren et al. Dec 2004 A1
20040260209 Ella et al. Dec 2004 A1
20050000879 Kearney et al. Jan 2005 A1
20050003737 Montierth et al. Jan 2005 A1
20050008179 Quinn Jan 2005 A1
20050011829 Dong et al. Jan 2005 A1
20050019311 Holaday et al. Jan 2005 A1
20050061221 Paszkowski Mar 2005 A1
20050066538 Goldberg et al. Mar 2005 A1
20050077227 Kirker et al. Apr 2005 A1
20050087122 Ismagliov et al. Apr 2005 A1
20050087767 Fitzgerald et al. Apr 2005 A1
20050095168 Centanni et al. May 2005 A1
20050101841 Kaylor et al. May 2005 A9
20050106310 Green et al. May 2005 A1
20050116336 Chopra et al. Jun 2005 A1
20050120870 Ludwig Jun 2005 A1
20050126373 Ludwig Jun 2005 A1
20050126374 Ludwig Jun 2005 A1
20050126766 Lee et al. Jun 2005 A1
20050128751 Roberge et al. Jun 2005 A1
20050131089 Kocon et al. Jun 2005 A1
20050137032 Aoyama et al. Jun 2005 A1
20050159894 Intriligator et al. Jul 2005 A1
20050164281 Oh et al. Jul 2005 A1
20050174473 Morgan et al. Aug 2005 A1
20050187759 Malah et al. Aug 2005 A1
20050213436 Ono et al. Sep 2005 A1
20050220681 Chang et al. Oct 2005 A1
20050245659 Chen Nov 2005 A1
20050248299 Chemel et al. Nov 2005 A1
20050251952 Johnson Nov 2005 A1
20050265915 Tonkovich et al. Dec 2005 A1
20050267685 Intriligator et al. Dec 2005 A1
20050272110 Drukier Dec 2005 A1
20050272159 Ismagilov et al. Dec 2005 A1
20050275626 Mueller et al. Dec 2005 A1
20060002110 Dowling et al. Jan 2006 A1
20060011326 Yuval Jan 2006 A1
20060018013 Suzuki et al. Jan 2006 A1
20060022214 Morgan et al. Feb 2006 A1
20060024435 Holunga et al. Feb 2006 A1
20060025245 Aoyama et al. Feb 2006 A1
20060032364 Ludwig Feb 2006 A1
20060037177 Blum et al. Feb 2006 A1
20060072289 Rutledge et al. Apr 2006 A1
20060087509 Ebert et al. Apr 2006 A1
20060090632 Ludwig May 2006 A1
20060097855 Turnbull et al. May 2006 A1
20060113065 Wolford et al. Jun 2006 A1
20060124550 Paananen et al. Jun 2006 A1
20060129161 Amrich et al. Jun 2006 A1
20060148591 Hebert et al. Jul 2006 A1
20060149343 Altshuler et al. Jul 2006 A1
20060154352 Foody et al. Jul 2006 A1
20060155398 Hoffberg et al. Jul 2006 A1
20060162719 Gougerot et al. Jul 2006 A1
20060165898 Kodas et al. Jul 2006 A1
20060167784 Hoffberg Jul 2006 A1
20060172824 Nardacci et al. Aug 2006 A1
20060179676 Goldberg et al. Aug 2006 A1
20060191534 Hickey et al. Aug 2006 A1
20060200253 Hoffberg et al. Sep 2006 A1
20060200258 Hoffberg et al. Sep 2006 A1
20060200259 Hoffberg et al. Sep 2006 A1
20060200260 Hoffberg et al. Sep 2006 A1
20060237178 Katoh et al. Oct 2006 A1
20060245987 Schmidt Nov 2006 A1
20060250114 Faberman et al. Nov 2006 A1
20060260638 Fani et al. Nov 2006 A1
20060262876 LaDue Nov 2006 A1
20060275185 Tonkovich et al. Dec 2006 A1
20070016476 Hoffberg et al. Jan 2007 A1
20070032733 Burton Feb 2007 A1
20070041083 Di Teodoro et al. Feb 2007 A1
20070041159 Bate Feb 2007 A1
20070053513 Hoffberg Mar 2007 A1
20070055151 Shertukde et al. Mar 2007 A1
20070058346 Yeh Mar 2007 A1
20070059763 Okano et al. Mar 2007 A1
20070061022 Hoffberg-Borghesani et al. Mar 2007 A1
20070061023 Hoffberg et al. Mar 2007 A1
20070061735 Hoffberg et al. Mar 2007 A1
20070070038 Hoffberg et al. Mar 2007 A1
20070087756 Hoffberg Apr 2007 A1
20070091948 Di Teodoro et al. Apr 2007 A1
20070104431 Di Teodoro et al. May 2007 A1
20070109542 Tracy et al. May 2007 A1
20070121198 Suzuki et al. May 2007 A1
20070121199 Suzuki et al. May 2007 A1
20070121200 Suzuki et al. May 2007 A1
20070129711 Altshuler et al. Jun 2007 A1
20070131409 Asahi Jun 2007 A1
20070145915 Roberge et al. Jun 2007 A1
20070169928 Dayan et al. Jul 2007 A1
20070172954 Ismagilov et al. Jul 2007 A1
20070175472 Pipkin et al. Aug 2007 A1
20070189026 Chemel et al. Aug 2007 A1
20070191740 Shertukde et al. Aug 2007 A1
20070206016 Szymanski et al. Sep 2007 A1
20070206023 Street et al. Sep 2007 A1
20070221218 Warden et al. Sep 2007 A1
20070230135 Feger et al. Oct 2007 A1
20070236406 Wen et al. Oct 2007 A1
20070239003 Shertukde et al. Oct 2007 A1
20070242955 Kavehrad Oct 2007 A1
20070258329 Winey Nov 2007 A1
20070267176 Song et al. Nov 2007 A1
20070273504 Tran Nov 2007 A1
20070276270 Tran Nov 2007 A1
20070297285 Cross et al. Dec 2007 A1
20070299292 Cross et al. Dec 2007 A1
20080001735 Tran Jan 2008 A1
20080003649 Maltezos et al. Jan 2008 A1
20080004904 Tran Jan 2008 A1
20080013747 Tran Jan 2008 A1
20080017219 Franklin Jan 2008 A1
20080024733 Gerets et al. Jan 2008 A1
20080024923 Tomimoto et al. Jan 2008 A1
20080036921 Yokoyama et al. Feb 2008 A1
20080037927 Kurihara et al. Feb 2008 A1
20080040749 Hoffberg et al. Feb 2008 A1
20080043029 Nardacci et al. Feb 2008 A1
20080080137 Otsuki et al. Apr 2008 A1
20080103655 Turnbull et al. May 2008 A1
20080108122 Paul et al. May 2008 A1
20080115916 Schuette May 2008 A1
20080121373 Wang et al. May 2008 A1
20080121374 Wang et al. May 2008 A1
20080135211 Yassour Jun 2008 A1
20080139901 Altshuler et al. Jun 2008 A1
20080145633 Kodas et al. Jun 2008 A1
20080149304 Slaughter Jun 2008 A1
20080151694 Slater Jun 2008 A1
20080168987 Denny et al. Jul 2008 A1
20080173059 Gautreau et al. Jul 2008 A1
20080192576 Vosburgh et al. Aug 2008 A1
20080204757 Manning Aug 2008 A1
20080233356 Loher et al. Sep 2008 A1
20080268246 Stark et al. Oct 2008 A1
20080271777 Stoner et al. Nov 2008 A1
20080278558 Kojima Nov 2008 A1
20080281238 Oohashi et al. Nov 2008 A1
20080294019 Tran Nov 2008 A1
20080294152 Altshuler et al. Nov 2008 A1
20080294153 Altshuler et al. Nov 2008 A1
20090002549 Kobayashi Jan 2009 A1
20090004074 Tonkovich et al. Jan 2009 A1
20090016019 Bandholz et al. Jan 2009 A1
20090017941 Sullivan et al. Jan 2009 A1
20090021270 Bandholz et al. Jan 2009 A1
20090021513 Joshi et al. Jan 2009 A1
20090032104 Lee et al. Feb 2009 A1
20090042200 Okano et al. Feb 2009 A1
20090042739 Okano et al. Feb 2009 A1
20090045967 Bandholz et al. Feb 2009 A1
20090046425 Kavanagh Feb 2009 A1
20090050293 Kuo Feb 2009 A1
20090071624 Zhang et al. Mar 2009 A1
20090074627 Fitzgerald et al. Mar 2009 A1
20090079981 Holve Mar 2009 A1
20090086436 Kluge Apr 2009 A1
20090103296 Harbers et al. Apr 2009 A1
20090135042 Umishita et al. May 2009 A1
20090146435 Freda Jun 2009 A1
20090159461 McCutchen et al. Jun 2009 A1
20090161312 Spearing et al. Jun 2009 A1
20090162853 Clark et al. Jun 2009 A1
20090162920 Vanhoutte et al. Jun 2009 A1
20090166273 Mormino et al. Jul 2009 A1
20090173334 Krs et al. Jul 2009 A1
20090181805 Sullivan et al. Jul 2009 A1
20090200176 McCutchen et al. Aug 2009 A1
20090207087 Fang et al. Aug 2009 A1
20090208582 Johnston et al. Aug 2009 A1
20090213382 Tracy et al. Aug 2009 A1
20090217691 Schmidt et al. Sep 2009 A1
20090227876 Tran Sep 2009 A1
20090236333 Ben-Shmuel et al. Sep 2009 A1
20090236334 Ben-Shmuel et al. Sep 2009 A1
20090236335 Ben-Shmuel et al. Sep 2009 A1
20090241545 McCutchen Oct 2009 A1
20090245017 Paul et al. Oct 2009 A1
20090261047 Merrow Oct 2009 A1
20090261228 Merrow Oct 2009 A1
20090262454 Merrow Oct 2009 A1
20090262455 Merrow Oct 2009 A1
20090265043 Merrow et al. Oct 2009 A1
20090272404 Kim Nov 2009 A1
20090274549 Mitchell et al. Nov 2009 A1
20090275014 Maltezos et al. Nov 2009 A1
20090275113 Maltezos et al. Nov 2009 A1
20090318779 Tran Dec 2009 A1
20090321045 Hernon Dec 2009 A1
20090321046 Hernon et al. Dec 2009 A1
20090321047 Chen Dec 2009 A1
20090325215 Okano et al. Dec 2009 A1
20100012586 Angelescu et al. Jan 2010 A1
20100016568 Okano et al. Jan 2010 A1
20100016569 Okano et al. Jan 2010 A1
20100018862 Okano et al. Jan 2010 A1
20100021634 Kodas et al. Jan 2010 A1
20100021725 Gottschalk-Gaudig Jan 2010 A1
20100021933 Okano et al. Jan 2010 A1
20100042408 Malah et al. Feb 2010 A1
20100043213 Burke et al. Feb 2010 A1
20100043214 Burke et al. Feb 2010 A1
20100043215 Burke et al. Feb 2010 A1
20100043224 Burke et al. Feb 2010 A1
20100044018 Furberg et al. Feb 2010 A1
20100047043 Burke et al. Feb 2010 A1
20100047044 Burke et al. Feb 2010 A1
20100047052 Burke et al. Feb 2010 A1
20100047053 Burke et al. Feb 2010 A1
20100047962 Burke et al. Feb 2010 A1
20100063393 Moradi et al. Mar 2010 A1
20100067182 Tanaka et al. Mar 2010 A1
20100067188 Tanaka Mar 2010 A1
20100067195 Tanaka Mar 2010 A1
20100067205 Tanaka Mar 2010 A1
20100067206 Tanaka Mar 2010 A1
20100073477 Finn et al. Mar 2010 A1
20100076642 Hoffberg et al. Mar 2010 A1
20100085713 Balandin et al. Apr 2010 A1
20100089549 Su et al. Apr 2010 A1
20100094152 Semmlow Apr 2010 A1
20100100328 Moore et al. Apr 2010 A1
20100101181 Hamm-Dubischar Apr 2010 A1
20100110826 D'herde May 2010 A1
20100115785 Ben-Shmuel et al. May 2010 A1
20100115947 Galbraith May 2010 A1
20100121318 Hancock et al. May 2010 A1
20100136676 Vanhoutte et al. Jun 2010 A1
20100139306 Krenik Jun 2010 A1
20100150718 Freda Jun 2010 A1
20100151267 Kodas et al. Jun 2010 A1
20100165498 Merrow et al. Jul 2010 A1
20100171145 Morgan et al. Jul 2010 A1
20100182809 Cullinane et al. Jul 2010 A1
20100195868 Lu Aug 2010 A1
20100196811 Gottschalk-Gaudig et al. Aug 2010 A1
20100202071 Preumont et al. Aug 2010 A1
20100208065 Heiner et al. Aug 2010 A1
20100219296 Shelman-Cohen Sep 2010 A1
20100221343 Johnston et al. Sep 2010 A1
20100221819 Foody et al. Sep 2010 A1
20100226202 Vassilicos et al. Sep 2010 A1
20100233026 Ismagliov et al. Sep 2010 A1
20100235285 Hoffberg Sep 2010 A1
20100236236 Mankame et al. Sep 2010 A1
20100252648 Robinson Oct 2010 A1
20100258198 Tonkovich et al. Oct 2010 A1
20100270904 Kim Oct 2010 A1
20100277733 Holve Nov 2010 A1
20100285142 Staniforth et al. Nov 2010 A1
20100287822 Wei et al. Nov 2010 A1
20100302093 Bunch et al. Dec 2010 A1
20100302678 Merrow Dec 2010 A1
20100307665 McCutchen Dec 2010 A1
20100311070 Oh et al. Dec 2010 A1
20100314985 Premysler Dec 2010 A1
20100317420 Hoffberg Dec 2010 A1
20110004513 Hoffberg Jan 2011 A1
20110029922 Hoffberg et al. Feb 2011 A1
20110031236 Ben-Shmuel et al. Feb 2011 A1
20110032632 Erden Feb 2011 A1
20110039078 Brennan Fournet et al. Feb 2011 A1
20110049904 Freda Mar 2011 A1
20110060533 Jorden et al. Mar 2011 A1
20110075903 Turiel Martinez Mar 2011 A1
20110080802 Vassilicos et al. Apr 2011 A1
20110083825 Merrow Apr 2011 A1
20110092817 Cloutier et al. Apr 2011 A1
20110093099 Tran et al. Apr 2011 A1
20110109910 Georgakoudi et al. May 2011 A1
20110115358 Kim May 2011 A1
20110115624 Tran May 2011 A1
20110117025 Dacosta et al. May 2011 A1
20110133655 Recker et al. Jun 2011 A1
20110142734 Ismagliov et al. Jun 2011 A1
20110152729 Oohashi et al. Jun 2011 A1
20110156896 Hoffberg et al. Jun 2011 A1
20110167110 Hoffberg et al. Jul 2011 A1
20110172807 Merrow Jul 2011 A1
20110174462 Arik et al. Jul 2011 A1
20110174468 Lu et al. Jul 2011 A1
20110174622 Ismagilov et al. Jul 2011 A1
20110176966 Ismagilov et al. Jul 2011 A1
20110177494 Ismagilov et al. Jul 2011 A1
20110177586 Ismagilov et al. Jul 2011 A1
20110177609 Ismagilov et al. Jul 2011 A1
20110179950 Wong et al. Jul 2011 A1
20110181422 Tran Jul 2011 A1
20110182068 Harbers et al. Jul 2011 A1
20110202150 Tran et al. Aug 2011 A1
20110226460 Sommer Sep 2011 A1
20110240382 Gettings et al. Oct 2011 A1
20110240383 Gettings et al. Oct 2011 A1
20110253629 Jovanovic et al. Oct 2011 A1
20110265480 McCutchen Nov 2011 A1
20110280019 Zimmer et al. Nov 2011 A1
20110292596 El-Essawy et al. Dec 2011 A1
20110298371 Brandes et al. Dec 2011 A1
20110311769 Chen et al. Dec 2011 A1
20120009668 Hass Jan 2012 A1
20120017232 Hoffberg et al. Jan 2012 A1
20120026506 Primeau et al. Feb 2012 A1
20120026770 West Feb 2012 A1
20120031272 Rubit et al. Feb 2012 A1
20120035767 Runkana et al. Feb 2012 A1
20120036016 Hoffberg et al. Feb 2012 A1
20120040778 Aoyama et al. Feb 2012 A1
20120043037 Polat et al. Feb 2012 A1
20120057974 Freda Mar 2012 A1
20120064243 Akay et al. Mar 2012 A1
20120074051 Gebauer et al. Mar 2012 A1
20120074062 Jovanovic et al. Mar 2012 A1
20120080944 Recker et al. Apr 2012 A1
20120088608 Sullivan et al. Apr 2012 A1
20120092157 Tran Apr 2012 A1
20120095352 Tran Apr 2012 A1
20120097591 Berthold et al. Apr 2012 A1
20120105020 Scott et al. May 2012 A1
20120112531 Kesler et al. May 2012 A1
20120112532 Kesler et al. May 2012 A1
20120112534 Kesler et al. May 2012 A1
20120112535 Karalis et al. May 2012 A1
20120112536 Karalis et al. May 2012 A1
20120112538 Kesler et al. May 2012 A1
20120112691 Kurs et al. May 2012 A1
20120114709 Staniforth et al. May 2012 A1
20120116769 Malah et al. May 2012 A1
20120119569 Karalis et al. May 2012 A1
20120119575 Kurs et al. May 2012 A1
20120119576 Kesler et al. May 2012 A1
20120119698 Karalis et al. May 2012 A1
20120138058 Fu et al. Jun 2012 A1
20120142814 Kanagasabapathy et al. Jun 2012 A1
20120150651 Hoffberg et al. Jun 2012 A1
20120152626 Gettings et al. Jun 2012 A1
20120152627 Gettings et al. Jun 2012 A1
20120160030 Pearce Jun 2012 A1
20120161580 Pearce Jun 2012 A1
20120163119 Pearce Jun 2012 A1
20120163120 Pearce Jun 2012 A1
20120164184 Pipkin et al. Jun 2012 A1
20120164644 Neely et al. Jun 2012 A1
20120168389 Kochergin et al. Jul 2012 A1
20120169267 Nashiki et al. Jul 2012 A1
20120174650 Ariessohn et al. Jul 2012 A1
20120175173 Gettings et al. Jul 2012 A1
20120184338 Kesler et al. Jul 2012 A1
20120193085 Whittle et al. Aug 2012 A1
20120193221 McCutchen et al. Aug 2012 A1
20120193923 Freda Aug 2012 A1
20120196336 McCutchen et al. Aug 2012 A1
20120228952 Hall et al. Sep 2012 A1
20120228953 Kesler et al. Sep 2012 A1
20120228954 Kesler et al. Sep 2012 A1
20120235501 Kesler et al. Sep 2012 A1
20120235502 Kesler et al. Sep 2012 A1
20120235503 Kesler et al. Sep 2012 A1
20120235504 Kesler et al. Sep 2012 A1
20120235566 Karalis et al. Sep 2012 A1
20120235567 Karalis et al. Sep 2012 A1
20120235633 Kesler et al. Sep 2012 A1
20120235634 Hall et al. Sep 2012 A1
20120239117 Kesler et al. Sep 2012 A1
20120242159 Lou et al. Sep 2012 A1
20120242225 Karalis et al. Sep 2012 A1
20120248886 Kesler et al. Oct 2012 A1
20120248887 Kesler et al. Oct 2012 A1
20120248888 Kesler et al. Oct 2012 A1
20120248981 Karalis et al. Oct 2012 A1
20120255548 Denny et al. Oct 2012 A1
20120256494 Kesler et al. Oct 2012 A1
20120261514 Boone Oct 2012 A1
20120285660 Poltorak Nov 2012 A1
20120292246 Jovanovic et al. Nov 2012 A1
20120293952 Herring et al. Nov 2012 A1
20120298037 Paul et al. Nov 2012 A1
20120301888 Neely et al. Nov 2012 A1
20120318671 McCutchen et al. Dec 2012 A1
20120320524 El-Essawy et al. Dec 2012 A1
20120329171 Ismagliov et al. Dec 2012 A1
20120330109 Tran Dec 2012 A1
20130001090 Rubinson et al. Jan 2013 A1
20130009783 Tran Jan 2013 A1
20130010257 Primeau et al. Jan 2013 A1
20130018236 Altshuler et al. Jan 2013 A1
20130029345 Neely et al. Jan 2013 A1
20130042893 Ariessohn et al. Feb 2013 A1
20130056460 Ben-Shmuel et al. Mar 2013 A1
20130083960 Kostrzewski et al. Apr 2013 A1
20130095494 Neely Apr 2013 A1
20130098127 Isei et al. Apr 2013 A1
20130101995 Rustem et al. Apr 2013 A1
20130107530 Wyrick et al. May 2013 A1
20130147598 Hoffberg et al. Jun 2013 A1
20130150730 Altshuler et al. Jun 2013 A1
20130155687 Zimmer et al. Jun 2013 A1
20130156091 Li et al. Jun 2013 A1
20130156092 Li et al. Jun 2013 A1
20130156095 Li et al. Jun 2013 A1
20130167441 Sevastyanov Jul 2013 A1
20130170176 Athalye Jul 2013 A1
20130170999 Vassilicos Jul 2013 A1
20130172691 Tran Jul 2013 A1
20130182214 Hofmann et al. Jul 2013 A1
20130188397 Wu et al. Jul 2013 A1
20130197105 Pipkin et al. Aug 2013 A1
20130202182 Rowe Aug 2013 A1
20130206165 Busnaina et al. Aug 2013 A1
20130207468 Wu et al. Aug 2013 A1
20130207601 Wu et al. Aug 2013 A1
20130208560 Kulkarni et al. Aug 2013 A1
20130214539 Freda Aug 2013 A1
20130231574 Tran Sep 2013 A1
20130231906 Luvalle Sep 2013 A1
20130244238 Neely et al. Sep 2013 A1
20130252373 Siau et al. Sep 2013 A1
20130252848 Okano et al. Sep 2013 A1
20130260367 Lowery, Jr. et al. Oct 2013 A1
20130266944 Neely et al. Oct 2013 A1
20130273522 Lowery, Jr. et al. Oct 2013 A1
20130273523 Neely et al. Oct 2013 A1
20130274712 Schecter Oct 2013 A1
20130284830 Wells et al. Oct 2013 A1
20130286666 Bakk Oct 2013 A1
20130288873 Barbee et al. Oct 2013 A1
20130299148 Hernon et al. Nov 2013 A1
20130299415 McCutchen Nov 2013 A1
20130306385 Gettings et al. Nov 2013 A1
20130309778 Lowe et al. Nov 2013 A1
20130312638 Parker et al. Nov 2013 A1
20130312787 Suzuki Nov 2013 A1
20130322471 Rossbach Dec 2013 A1
20130334824 Freda Dec 2013 A1
20130335731 Jorden Dec 2013 A1
20130339216 Lambert Dec 2013 A1
20130344794 Shaw et al. Dec 2013 A1
20140005364 Gottschall et al. Jan 2014 A1
20140021288 Elson et al. Jan 2014 A1
20140037958 Gerber Feb 2014 A1
20140043825 Brandes et al. Feb 2014 A1
20140046023 Gottschall et al. Feb 2014 A1
20140057210 Malik et al. Feb 2014 A1
20140057277 Malik et al. Feb 2014 A1
20140057278 Madero et al. Feb 2014 A1
20140057279 Malik et al. Feb 2014 A1
20140076642 Gettings et al. Mar 2014 A1
20140077946 Tran Mar 2014 A1
20140079782 York et al. Mar 2014 A1
20140089241 Hoffberg et al. Mar 2014 A1
20140096763 Barmore Apr 2014 A1
20140098542 Zimmer et al. Apr 2014 A1
20140107638 Hancock et al. Apr 2014 A1
20140111671 Cao et al. Apr 2014 A1
20140120523 Lowery, Jr. et al. May 2014 A1
20140127790 Malik et al. May 2014 A1
20140127796 Malik et al. May 2014 A1
20140134678 Foody et al. May 2014 A1
20140143064 Tran May 2014 A1
20140163425 Tran Jun 2014 A1
20140165607 Alexander Jun 2014 A1
20140166575 Bose et al. Jun 2014 A1
20140170646 Kelley et al. Jun 2014 A1
20140173452 Hoffberg et al. Jun 2014 A1
20140180153 Zia et al. Jun 2014 A1
20140207463 Nakanishi Jul 2014 A1
20140212006 Zhao et al. Jul 2014 A1
20140217331 Hata et al. Aug 2014 A1
20140218588 Ifuku et al. Aug 2014 A1
20140235965 Tran Aug 2014 A1
20140238012 Miller Aug 2014 A1
20140249429 Tran Sep 2014 A1
20140255205 Shelman-Cohen Sep 2014 A1
20140266849 Suorsa Sep 2014 A1
20140266850 Suorsa Sep 2014 A1
20140267123 Ludwig Sep 2014 A1
20140278158 Miller Sep 2014 A1
20140322515 Parker et al. Oct 2014 A1
20140325866 McCutchen et al. Nov 2014 A1
20140326277 Nettesheim et al. Nov 2014 A1
20140332081 Fitzgerald et al. Nov 2014 A1
20140334653 Luna et al. Nov 2014 A1
20140336953 Johnson et al. Nov 2014 A1
20140338895 Paulsen Nov 2014 A1
20140340870 Premysler Nov 2014 A1
20140345152 Ben-Shmuel et al. Nov 2014 A1
20140346055 McCutchen et al. Nov 2014 A1
20140355270 Brandes et al. Dec 2014 A1
20140360607 Fletcher et al. Dec 2014 A1
20140360699 van Schoor et al. Dec 2014 A1
20140361688 Recker et al. Dec 2014 A1
20140362660 Pearce Dec 2014 A1
20140369006 Williams Dec 2014 A1
20140377826 Trevethick Dec 2014 A1
20150008842 Harbers et al. Jan 2015 A1
20150015869 Smith et al. Jan 2015 A1
20150021108 Gettings et al. Jan 2015 A1
20150023023 Livesay et al. Jan 2015 A1
20150037169 Veltman et al. Feb 2015 A1
20150068069 Tran et al. Mar 2015 A1
20150069831 Kesler et al. Mar 2015 A1
20150094914 Abreu Apr 2015 A1
20150099264 Ismagilov et al. Apr 2015 A1
20150105687 Abreu Apr 2015 A1
20150110599 Freda Apr 2015 A1
20150138355 Tillotson May 2015 A1
20150163867 Recker et al. Jun 2015 A1
20150181685 Sekhar et al. Jun 2015 A1
20150183520 Elson Jul 2015 A1
20150203822 Tremolada et al. Jul 2015 A1
20150204559 Hoffberg et al. Jul 2015 A1
20150231635 Okano et al. Aug 2015 A1
20150236546 Kesler et al. Aug 2015 A1
20150250646 Lipford et al. Sep 2015 A1
20150251217 Wohl, Jr. et al. Sep 2015 A1
20150252998 Brandes et al. Sep 2015 A1
20150255994 Kesler et al. Sep 2015 A1
20150282261 Recker et al. Oct 2015 A1
20150287141 Parker, Jr. Oct 2015 A1
20150291760 Storti et al. Oct 2015 A1
20150293140 Barille Oct 2015 A1
20150328601 Vassilicos Nov 2015 A1
20150342093 Poltorak Nov 2015 A1
20150353880 Clark et al. Dec 2015 A1
20150359467 Tran Dec 2015 A1
20150366006 Ben-Shmuel et al. Dec 2015 A1
20150377831 Wheeler et al. Dec 2015 A1
20160001108 Zhou et al. Jan 2016 A1
20160005732 Wood Jan 2016 A1
20160010778 Malik Jan 2016 A1
20160034422 Brandt Feb 2016 A1
20160045114 Dacosta et al. Feb 2016 A1
20160051960 Ismagilov et al. Feb 2016 A1
20160051982 Rawle Feb 2016 A1
20160083025 Gettings et al. Mar 2016 A1
20160087687 Kesler et al. Mar 2016 A1
20160103387 Nishimori et al. Apr 2016 A1
20160129361 Howard May 2016 A1
20160138805 Martin et al. May 2016 A1
20160140834 Tran May 2016 A1
20160145397 Kornfield et al. May 2016 A1
20160154126 Pearce Jun 2016 A1
20160157978 Tutak Jun 2016 A1
20160160795 Miller Jun 2016 A1
20160176452 Gettings et al. Jun 2016 A1
20160230214 Barbee et al. Aug 2016 A1
20160249439 Recker et al. Aug 2016 A1
20160276979 Shaver et al. Sep 2016 A1
20160320149 Poltorak Nov 2016 A1
20170059263 Sun et al. Mar 2017 A1
20170097197 Poltorak Apr 2017 A1
20170175711 Burkle Jun 2017 A1
20170252701 Nosrati Sep 2017 A1
20180017345 Poltorak Jan 2018 A1
20180249563 Alexander Aug 2018 A1
20180275637 Elber et al. Sep 2018 A1
20180298882 Burkle Oct 2018 A1
20180340743 Poltorak Nov 2018 A1
20190021186 Poltorak Jan 2019 A1
20190383269 Burkle Dec 2019 A1
20200084865 Alexander Mar 2020 A1
20200126891 Huitink et al. Apr 2020 A1
20200149832 Poltorak May 2020 A1
20200249119 Imrie Aug 2020 A1
20200271097 Burkle Aug 2020 A1
20200273769 Xia et al. Aug 2020 A1
20200375013 Alexander Nov 2020 A1
20210014986 Xia et al. Jan 2021 A1
Foreign Referenced Citations (2)
Number Date Country
WO9904429 Jan 1999 WO
WO2008086479 Jul 2008 WO
Non-Patent Literature Citations (105)
Entry
Ake Malhammar, A Method for Comparing Heat Sinks Based on Reynolds Analogy, France, Sep. 29-Oct. 2004.
Alharbi, Ali Y., Deborah V. Pence, and Rebecca N. Cullion. “Thermal characteristics of microscale fractal-like branching channels.” Journal of Heat Transfer 126.5 (2004): 744-752.
Ali Y. Alharbi et al, Thermal Characteristics of Microscale Fractal-Like Branching Channels, J. Heat Transfer, vol. 126, Issue 5, Oct. 2004.
Andrews, Earl H. “Scramjet development and testing in the United States.” AIAA paper 1927 (2001): 2001.
Arovas, Daniel, “Lecture Notes on Thermodynamics and Statistical Mechanics (A Work in Progress)”, U.C. San Diego, 2013.
Azar, A, et al., 2009, “Heat sink testing methods and common oversights”, Qpedia Thermal E-Magazine, Jan. 2009.
Balasubramania, K. et al, Pressure Drop Characteristics and Instabilities During Flow Boiling in Parallel and Oblique Finned Microchannels—A Comparative Study, 2012.
Batten, Paul, et al. “Sub-Grid Turbulence Modeling for Unsteady Flow with Acoustic Resonance,” available at www.metacomptech.com/cfd++/00/0473.pdf, last accessed Apr. 29, 2010.
Baurle, R. A., and D. R. Eklund. “Analysis of dual-mode hydrocarbon scramjet operation at Mach 4-6.5.” Journal of Propulsion and Power 18.5 (2002): 990-1002.
Bentley, Peter J., and Jonathan P. Wakefield. “Generic evolutionary design.” Soft Computing in Engineering Design and Manufacturing. Springer London, 1998. 289-298.
Bohr, T., M.H. Jensen, G. Paladin and A. Vulpiani. Dynamical Systems Approach to Turbulence, Cambridge University Press, 1998.
Boming Yu et al, Fractal-Like Tree Networks Reducing the Thermal Conductivity, 2006 The American Physical Society.
Bonetto, F. et al, Fourier Law, Atlanta, GA 20006.
Boris Yakobson, “Acoustic waves may cool microelectronics”, Nano Letters, ACS (2010).
Boudreau, Albert H. “Hypersonic air-breathing propulsion efforts in the air force research laboratory.” AIAA 3255.1 (2005):10.
Calamas, David, “Thermal Transport in Systems With Hierarchical Bifurcating Geometries”, Ph.D. Dissertation The University of Alabama Tuscaloosa, 2013.
Cardy, J., G. Falkovich and K. Gawedzki (2008) Non-equilibrium statistical mechanics and turbulence. Cambridge University Press.
Chapman, Christopher L., Seri Lee, and Bill L. Schmidt. “Thermal performance of an elliptical pin fin heat sink.” Semiconductor Thermal Measurement and Management Symposium, 1994. Semi-Therm X., Proceedings of 1994 IEEE/CPMT 10th. IEEE, 1994.
Chen Yongping et al, Characteristics of Heat and Fluid Flow in Fractal Tree-Like Channel Heat Sink, 2009.
Cockrell Jr, Charles E. “Technology Roadmap for Dual-Mode Scramjet Propulsion to Support Space-Access Vision Vehicle Development.” (2002).
Coolingzone.com—Heat Sinks and Reynolds Analogy, http://www.coolingzone.com/library.php?read=536; downloaded from internet on Dec. 8, 2015.
Covert, Lance Nicholas. Dual-function heatsink antennas for high-density three-dimensional integration of high-power transmitters. Diss. University of Florida, 2008.
Crane, Jackson T. Radial parallel plate flow with mechanical agitation. Diss. Massachusetts Institute of Technology, 2013.
Dannelley, Daniel. Enhancement of extended surface heat transfer using fractal-like geometries. Diss. The University of Alabama Tuscaloosa, 2013.
Davidson, P. A. (2004). Turbulence: An Introduction for Scientists and Engineers. Oxford University Press. ISBN 978-0-19-852949-1; scholarpedia.org.
Dewan, A., et al. “The effect of fin spacing and material on the performance of a heat sink with circular pin fins.” Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 224.1 (2010): 35-46.
Donbar, J., et al. “Post-test analysis of flush-wall fuel injection experiments in a scramjet.” AIAA Paper 3197 (2001): 2001.
Durbin P. A., and B. A. Pettersson Reif. Statistical Theory and Modeling for Turbulent Flows. Johns Wiley & Sons, 2001.
en.wikipedia.org/wild/Chaos_theory.
en.wikipedia.org/wild/Fractal.
en.wikipedia.org/wild/Heat_sink.
en.wikipedia.org/wild/Phonon.
Escher, W., B. Michel, and D. Poulikakos. “Efficiency of optimized bifurcating tree-like and parallel microchannel networks in the cooling of electronics.” International Journal of Heat and Mass Transfer 52.5 (2009): 1421-1430.
Falkovich, G., and K.R. Sreenivasan. Lessons from hydrodynamic turbulence, Physics Today, vol. 59, No. 4, pp. 43-49 (Apr. 2006).
Falkovich, G., Scholarpedia, “Cascade and scaling”; Jin, Y.; Uth, M.-F.; Kuznetsov, A. V.; Herwig, H. (Feb. 2, 2015). “Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study”. Journal of Fluid Mechanics 766: 76-103. Bibcode:2015JFM . . . 766 . . . 76J. doi:10.1017/jfm.2015.9.
Fichera, A., and A. Pagano. “Modelling and control of rectangular natural circulation loops.” International journal of heat and mass transfer 46.13 (2003): 2425-2444.
Fichera, Alberto, et al. “A modeling strategy for rectangular thermal convection loops.” World Congress. vol. 15. No. 1. 2002.
Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., 2001, Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME May.
Fourier, J. B., 1822, Theorie analytique de la chaleur, Paris; Freeman, A., 1955, translation, Dover Publications, Inc, NY.
Frigus Primore in “A Method for Comparing Heat Sinks Based on Reynolds Analogy,” available at www.frigprim.com/downloads/Reynolds_analogy_heatsinks.PDF.
Frigus Primore, “Natural Convection and Chimneys,” www.frigprim.com/articels2/parallel_plchim.html.
Frigus Primore, “Natural Convection and Inclined Parallel Plates,” www.frigprim.com/articels2/parallel_pl_Inc.html.
G. K. Batchelor, The theory of homogeneous turbulence. Cambridge University Press, 1953.
Garibaldi, Dott Ing Pietro. Single-phase natural circulation loops: effects of geometry and heat sink temperature on dynamic behavior and stability. Diss. Ph. D. Thesis, 2008.
Gruber, Mark, et al. “Newly developed direct-connect high-enthalpy supersonic combustion research facility.” Journal of Propulsion and Power 17.6 (2001): 1296-1304.
Henry et al.; “Design Considerations for the Airframe-Integrated Scramjet”; First International Symposium on Air Breathing Engines, Marseille, France, Jun. 19-23, 1972, 56 pages.
Hone, J., Carbon Nanotubes: Thermal Properties, New York, NY 2004.
Hong, F. J., et al. “Conjugate heat transfer in fractal-shaped microchannel network heat sink for integrated microelectronic cooling application.” International Journal of Heat and Mass Transfer 50.25 (2007): 4986-4998.
Incropera, F.P. and DeWitt, D.P., 1985, Introduction to heat transfer, John Wiley and sons, NY.
International Preliminary Report on Patentability and Written Opinion for counterpart application PCT/IB2011/001026 dated Feb. 9, 2016.
International Search Report for counterpart application PCT/IB2011/001026 dated Dec. 6, 2011.
Jackson, K., et al. “Calibration of a newly developed direct-connect high-enthalpy supersonic combustion research facility.” AIAA paper (1998): 98-1510.
Jeggels, Y.U., Dobson, R.T., Jeggels, D.H., Comparison of the cooling performance between heat pipe and aluminium conductors for electronic equipment enclosures, Proceedings of the 14th International Heat Pipe Conference, Florianopolis, Brazil, 2007.
Jie Li et al, Computational Analysis of Nanofluid Flow in Microchannels with Applications to Micro-Heat Sinks and Bio-MEMS, Raleigh, North Carolina 2008.
Kay, Ira W., W. T. Peschke, and R. N. Guile. “Hydrocarbon-fueled scramjet combustor investigation.” Journal of Propulsion and Power 8.2 (1992): 507-512.
Kolmogorov, Andrey Nikolaevich (1941). “Dissipation of Energy in the Locally Isotropic Turbulence”. Proceedings of the USSR Academy of Sciences (in Russian) 32: 16-18., translated into English by Kolmogorov, Andrey Nikolaevich (Jul. 8, 1991). Proceedings of the Royal Society A 434 (1980): 15-17. Bibcode:1991RSPSA.434 . . . 15K. doi:10.1098/rspa.1991.0076.
Kolmogorov, Andrey Nikolaevich (1941). “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers”. Proceedings of the USSR Academy of Sciences (in Russian) 30: 299-303., translated into English by V. Levin. Kolmogorov, Andrey Nikolaevich (Jul. 8, 1991). Proceedings of the Royal Society A 434 (1991): 9-13. Bibcode:1991RSPSA.434 . . . 9K. doi:10.1098/rspa.1991.0075.
Kordyban, T., 1998, Hot air rises and heat sinks—Everything you know about cooling electronics is wrong, ASME Press, NY.
Lance Covert, Jenshan Lin, Dan Janning, Thomas Dalrymple, “5.8 GHz orientation-specific extruded-fin heatsink antennas for 3D RF system integration”, Apr. 23, 2008 DOI: 10.1002/mop.23478, Microwave and Optical Technology Letters vol. 50, Issue 7, pp. 1826-1831, Jul. 2008.
Lasance, C.J.M and Eggink, H.J., 2001, A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, 21st IEEE Semi-Therm Symposium.
Lee, Y.J., “Enhanced Microchannel Heat Sinks Using Oblique Fins,” IPACK 2009-89059 (2009).
Li, Wentao, et al. “Fractal-based thinned planar-array design utilizing iterative FFT technique.” International Journal of Antennas and Propagation 2012 (2012).
Lienard, J.H., IV & V, 2004, A Heat Transfer Textbook, Third edition, MIT.
Liu et al, Heat Transfer and Pressure Drop in Fractal Microchannel Heat Sink for Cooling of Electronic Chips, 44 Heat Mass Transfer 221 (2007).
Liu, S., et al., “Heat Transfer and Pressure Drop in Fractal Microchannel Heat Sink for Cooling of Electronic Chips,” 44 Heat Mass Transfer 221 (2007).
Liu, Y. L., X. B. Luo, and W. Liu. “Cooling behavior in a novel heat sink based on multilayer staggered honeycomb structure.” J. Energy Power Eng 4.22 (2010): e28.
Liu, Yonglu, Xiaobing Luo, and Wei Liu. “MNHMT2009-18211.” (2009).
ludens.cl/Electron/Thermal.html.
Mandelbrot, B.B., The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9. (1982).
McCowan, Iain, et al. “Speech acquisition in meetings with an audio-visual sensor array.” Multimedia and Expo, 2005. ICME 2005. IEEE International Conference on. IEEE, 2005.
McDonough, J. M., (2007). Introductory Lectures on Turbulence—Physics, Mathematics, and Modeling.
Meyer, Josua P., Van Der Vyver, Hilde, “Heat Transfer Characteristics of a Quadratic Koch Island Fractal Heat Exchanger”, Heat Transfer Engineering, 26(9):22-29, 2005, Taylor & Francis Inc., ISSN: 0145-7632 print / 1521-0537 online, DOI: 10.1080/01457630500205638.
Mills, A.F., 1999, Heat transfer, Second edition, Prentice Hall.
MIT Media Relations, “MIT Researchers Discover New Way of Producing Electricity”, Press Release; Mar. 7, 2010; 2 pages.
Naphon, Paisarn, Setha Klangchart, and Somchai Wongwises. “Numerical investigation on the heat transfer and flow in the mini-fin heat sink for CPU.” International Communications in Heat and Mass Transfer 36.8 (2009): 834-840.
Nicole Delong Okamoto, Unknown, “Heat sink selection”, Mechanical engineering department, San Jose State University [Jan. 27, 2010]. www.engr.sjsu.edu/ndejong/ME%20146%20files/Heat%20Sink.ppt.
Palac, Donald T., Charles J. Trefny, and Joseph M. Roche. Performance Evaluation of the NASA GTX RBCC Flowpath. National Aeronautics and Space Administration, Glenn Research Center, 2001.
Paul Battern, “Sub-Grid Turbulence Modeling for Unsteady Flow with Acoustic Resonance,” available at www.metacomptech.com/cfd++/00-0473.pdf.
Peles, Yoav, et al. “Forced convective heat transfer across a pin fin micro heat sink.” International Journal of Heat and Mass Transfer 48.17 (2005): 3615-3627.
Pence, D. V., 2002, “Reduced Pumping Power and Wall Temperature in Microchannel Heat Sinks with Fractal-like Branching Channel Networks”, Microscale Thermophys. Eng. 5, pp. 293-311.
Potter, C.M. and Wigget, D.C., 2002, Mechanics of fluid, Third Edition, Brooks/Cole.
Prstic, S., Iyengar, M., and Bar-Cohen, A., 2000, Bypass effect in high performance heat sinks, Proceedings of the International Thermal Science Seminar Bled, Slovenia, Jun. 11-14.
Roknaldin, Farzam, and Arunima Panigrahy. “Board level thermal analysis via Large Eddy Simulation (LES) tool.” Thermal and Thermomechanical Phenomena in Electronic Systems, 2004. ITHERM'04. The Ninth Intersociety Conference on. IEEE, 2004.
Ryan, NJ, DA Stone, “Application of the FD-TD method to modelling the electromagnetic radiation from heatsinks”, IEEE International Conference on Electromagnetic Compatibility, 1997. 10th (Sep. 1-3, 1997), pp. 119-124.
Saint-Gobain, 2004, “Thermal management solutions for electronic equipment” Jul. 22, 2008 www.fff.saint-gobain.com/Media/Documents/S0000000000000001036/ThermaCool%-20Brochure.pdf.
Search Report PCT/IB11/01026 dated May 13, 2011.
Senn, S. M., et al, Laminar Mixing, Heat Transfer and Pressure Drop, Zurich, Switzerland, 2003.
Sergent, J. and Krum, A., 1998, Thermal management handbook for electronic assemblies, First Edition, McGraw-Hill.
Shaeri, M. R., and M. Yaghoubi. “Numerical analysis of turbulent convection heat transfer from an array of perforated fins.” International Journal of Heat and Fluid Flow 30.2 (2009): 218-228.
Sui, Y., Teo, C. J., Lee, P. S., Chew, Y. T., & Shu, C. (2010). Fluid flow and heat transfer in wavy microchannels. International Journal of Heat and Mass Transfer, 53(13), 2760-2772.
Tavaragiri, Abhay, Jacob Couch, and Peter Athanas. “Exploration of FPGA interconnect for the design of unconventional antennas.” Proceedings of the 19th ACM/SIGDA international symposium on Field programmable gate arrays. ACM, 2011.
Unknown, “Heat sink selection”, Mechanical engineering department, San Jose State University [Jan. 27, 2010]. www.engr.sjsu.edu/ndejong/ME%20146%20files/Heat%20Sink.pptwww.engr.sjsu.e- du/ndejong/ME%20146%20files/Heat%20Sink.ppt.
Van der Vyver, Hilde. Heat transfer characteristics of a fractal heat exchanger. Diss. 2009.
Vijayan et al. “Investigations on the Effect of Heater and Cooler Orientation on the Steady State, Transient and Stability Behaviour of Single-Phase Natural Circulation in a Rectangular Loop”; Government of India, Bhabha Atomic Research Centre, 2001.
Wagh, Kanchan H. “A Review on Fractal Antennas for Wireless Communication.” IJRECE 3.2 (2015): 37-41.
Wang et al., Flow and Thermal Characteristics of Offset Branching Network, Aug. 12, 2009, International Journal of Thermal Science, vol. 49, pp. 272-280.
Wang Xiangqi, New Approaches to Micro-Electronic Component Cooling, Doctoral Dissertation, National University of Singapore, 2007.
web.mit.edu/press/2010/thermopower-waves.html.
White, F.M., 1999, Fluid mechanics, Fourth edition, McGraw-Hill International.
Wikipedia article en.wikipedia.org/wiki/Fractal.
Wikipedia article en.wikipedia.org/wiki/Phonon.
Wikipedia article Heat Sink.org/wiki/Heatsink.
Yamaha, ProjectPhone, informational brochure.
Yong-Jiun Lee et al, Enhanced Microchannel Heat Sinks Using Oblique Fins, IPack 2009-89059, San Francisco, CA, 2009.
Zhou, Feng, and Ivan Catton. “A numerical investigation of turbulent flow and heat transfer in rectangular channels with elliptic scale-roughened walls.” Journal of Heat Transfer 135.8 (2013): 081901.
Related Publications (1)
Number Date Country
20200149832 A1 May 2020 US
Provisional Applications (1)
Number Date Country
61331103 May 2010 US
Continuations (2)
Number Date Country
Parent 14817962 Aug 2015 US
Child 16735592 US
Parent 13106640 May 2011 US
Child 14817962 US