Patent Application
20060088746
The present invention relates generally to passive dual-phase cooling arrangements and approaches for fuel cell components and assemblies within a fuel cell stack.
A typical fuel cell system includes a power section in which one or more fuel cells generate electrical power. A fuel cell is an energy conversion device that converts hydrogen and oxygen into water, producing electricity and heat in the process. Each fuel cell unit may include a proton exchange member at the center with gas diffusion layers on either side of the proton exchange member. Anode and cathode catalyst layers are respectively positioned at the inside of the gas diffusion layers. This type of fuel cell is often referred to as a PEM fuel cell.
The reaction in a single fuel cell typically produces less than one volt. A plurality of the fuel cells may be stacked and electrically connected in series to achieve a desired voltage. Electrical current is collected from the fuel cell stack and used to drive a load. Fuel cells may be used to supply power for a variety of applications, ranging from automobiles to laptop computers.
The efficacy of fuel cell power systems in many applications depends largely in part on the cooling apparatus that provides thermal management for the fuel cells. In stationary power and traction PEM fuel cell applications, for example, volumetric power densities are driven upward by the need to reduce the stack size. The higher heat densities are usually removed by pumping a dielectric heat transfer liquid through passages within cold plates or bipolar plates that lie between adjacent membrane electrode assemblies (MEAs). As the coolant passes through the stack, it absorbs the heat of reaction and its temperature increases. The coolant is then pumped to some primary heat exchanger where the heat is dissipated to another fluid stream, be it air, water, etc. Because the fluid has not changed phase, this technique is termed “single phase” cooling.
This single phase technique has several distinct disadvantages, including, for example, the need for pumps, plumbing, large quantities of heat transfer fluid, and active controls to regulate stack temperature during startup, or to accommodate changes in heat output and environmental conditions, resulting in added weight and cost. Power consumed by the pump must be provided by the stack and dissipated by its thermal system, thereby reducing available power and increasing the size of the primary heat exchanger.
The present invention relates generally to passive dual-phase cooling arrangements and approaches for fuel cell components and assemblies within a fuel cell stack. More particularly, the present invention is directed to such passive dual-phase cooling apparatuses that incorporate surface coatings and/or features that effectively extend the critical heat flux of flow field plate coolant channels and/or improves temperature uniformity over the entire channel length while minimizing channel depth so as to reduce cooling plate thicknesses and reducing coolant requirements and weight. “Critical heat flux” means the heat flux beyond which boiling cannot be sustained because liquid no longer wets the surface. To “extend the critical heat flux” means increasing the value of heat flux beyond which boiling cannot be sustained because liquid no longer wets the surface. The present invention is further directed to such passive dual-phase cooling apparatuses that provide thermal management for fuel cell assemblies, stacks, and power systems that incorporate fuel cells.
In accordance with various embodiments, a fuel cell stack assembly of the present invention includes at least one membrane electrode assembly (MEA) and a cooling apparatus. The cooling apparatus includes a heat transfer fluid and at least one fluid flow-field plate configured to facilitate essentially passive, two-phase cooling for the MEA as the MEA is subject to changes in heat flux to the heat transfer fluid from about 0 W/cm2 to about 1.5 W/cm2.
The flow field plate includes a number of fluid flow channels that have a channel depth, a channel spacing, a channel length, and a channel width, the width of the channels being less than about 5 mm. The channel width, channel spacing, channel length, and channel depth are dimensioned in accordance with principles of the present invention to promote nucleated boiling of the heat transfer fluid below a critical heat flux and to prevent dryout as the heat transfer fluid passes along the length of the channels. In one implementation, the cooling apparatus maintains a maximum temperature gradient of less than about 0.2° C./cm in a direction of heat transfer fluid flow as the MEA is subject to changes in heat flux to the heat transfer fluid from about 0 W/cm2 to about 1.5 W/cm2.
The channel width, channel spacing, channel length, and channel depth are preferably dimensioned to promote incipience of the heat transfer fluid at an entry region of the channels and to prevent the heat flux from exceeding the critical heat flux as the heat transfer fluid passes an exit region of the channels. In one configuration, the length of the channels is greater than about 10 cm. In another configuration, the channels have a channel length in a direction of heat transfer fluid flow of about 60 mm to about 230 mm. In a further configuration, the channel spacing is about 1 mm to about 2 mm, and the channel width is about 1 mm to about 3 mm. In yet another configuration, the channel depth may be less than about 1 mm. A ratio of channel length to channel depth may range between about 150 and about 1100.
In a typical implementation, an MEA comprises a surface configured to contact a surface of a flow field plate, and the heat transfer fluid of the cooling apparatus has a boiling point at the operating pressure of less than about 3° C. below a maximum temperature of the MEA surface. The heat transfer fluid may comprises a fluorochemical, a dielectric halocarbon, water or a hydrocarbon.
In some configurations, the fluid flow channels of the flow field plate have inner channel surfaces that incorporate nanostructured features. In other configurations, the fluid flow channels have inner channel surfaces that incorporate microporous features. In certain configurations, the fluid flow channels of the flow field plate have inner channel surfaces that incorporate a coating comprising a substantially planar organic molecule comprising delocalized pi-electrons.
According to another embodiment, a fuel cell stack assembly of the present invention includes at least one MEA and a cooling apparatus comprising at least one flow field plate configured to facilitate essentially passive, two-phase cooling for the MEA. In this embodiment, the flow field plate incorporates fluid flow channels having a channel length defined relative to the direction of coolant flow and a channel depth of less than about 1 mm. The cooling apparatus maintains a maximum temperature gradient of less than about 0.2° C./cm in a direction of coolant flow as the MEA is subject to changes in heat flux to the coolant from about 0 W/cm2 to about 1.5 W/cm2.
In accordance with a further embodiment, a fuel cell stack assembly of the present invention includes at least one MEA and a cooling apparatus comprising at least one flow field plate configured to facilitate essentially passive, two-phase cooling for the MEA. In this embodiment, the flow field plate incorporates fluid flow channels having inner channel surfaces. Each of the inner channel surfaces comprises nanostructured features. The cooling apparatus maintains a maximum temperature gradient of less than about 0.2° C./cm in a direction of coolant flow as the MEA is subject to changes in heat flux to the coolant from about 0 W/cm2 to about 1.5 W/cm2.
The nanostructured features may comprise uniformly oriented nanostructures. The nanostructured features may comprise nanostructures having a predefined geometric shape, such as rods, cones, cylinders, pyramids, tubes, flakes or other shapes. The inner channel surfaces may comprise in excess of about 1 million nanostructures/cm2, such as in excess of about 1 billion nanostructures/cm2, for example. The nanostructured features may have lengths ranging from about 0.1 micron to about 3 micron, but may be a long as about 6 micron.
According to another embodiment, a fuel cell stack assembly includes at least one MEA and a cooling apparatus comprising at least one fluid flow field plate configured to facilitate essentially passive, two-phase cooling for the MEA. In this embodiment, the flow field plate comprises fluid flow channels having inner channel surfaces. Each of the inner channel surfaces comprising microporous features. The cooling apparatus maintains a maximum temperature gradient of less than about 0.2° C./cm in a direction of coolant flow as the MEA is subject to changes in heat flux to the coolant from about 0 W/cm2 to about 1.5 W/cm2. “Microporous features” means micropores surrounded by an assembly of microparticles. The microparticles preferably comprise micron scale sized particles, such as metal, silica, ceramic or diamond. Particles forming micropores may be organic (e.g., latex spheres), or other kind of heteropolymer or heterocyclic material.
In accordance with yet another embodiment, a fuel cell stack assembly of the present invention includes at least one MEA and a cooling apparatus comprising at least one flow field plate configured to facilitate essentially passive, two-phase cooling for the MEA. In this embodiment, the flow field plate incorporates fluid flow channels having inner channel surfaces. Each of the inner channel surfaces incorporates a coating that includes a substantially planar organic molecule comprising delocalized pi-electrons. The cooling apparatus maintains a maximum temperature gradient of less than about 0.2° C./cm in a direction of coolant flow as the MEA is subject to changes in heat flux to the coolant from about 0 W/cm2 to about 1.5 W/cm2. The organic molecule may comprise chains or rings over which a density of the pi-electrons is extensively delocalized. For example, the coating may comprise van der Waals solids.
The above summary of the present invention is not intended to describe each embodiment or every implementation of the present invention. Advantages and attainments, together with a more complete understanding of the invention, will become apparent and appreciated by referring to the following detailed description and claims taken in conjunction with the accompanying drawings.
a is an illustration of a fuel cell and its constituent layers;
b illustrates a unitized cell assembly having a monopolar configuration in accordance with an embodiment of the present invention;
c illustrates a unitized cell assembly having a monopolar/bipolar configuration in accordance with an embodiment of the present invention;
a is a block diagram of a passive dual-phase cooling apparatus for cooling a power system employing fuel cells;
b shows a coolant channel arrangement provided on a bipolar flow field plate that is well suited for implementing embodiments of the present invention;
c is a partial perspective view of several coolant channels of the flow field plate shown in
While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It is to be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the invention as defined by the appended claims.
In the following description of the illustrated embodiments, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration, various embodiments in which the invention may be practiced. It is to be understood that the embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.
The present invention is directed to passive dual-phase cooling approaches that remove relatively small heat fluxes from relatively large surfaces in fuel cell devices by boiling. The specific illustrative embodiments described below are for purposes of explanation, and not of limitation.
A passive dual-phase cooling methodology of the present invention may be incorporated in fuel cell assemblies and stacks of varying types, configurations, and technologies. A typical fuel cell is depicted in
The fuel cell 10 shown in
The electrolyte membrane 16 permits only the hydrogen ions or protons to pass through the electrolyte membrane 16 to the cathode portion of the fuel cell 10. The electrons cannot pass through the electrolyte membrane 16 and, instead, flow through an external electrical circuit in the form of electric current. This current can power an electric load 17, such as an electric motor, or be directed to an energy storage device, such as a rechargeable battery.
Oxygen flows into the cathode side of the fuel cell 10 via the second fluid transport layer 19. As the oxygen passes over the cathode 18, oxygen, protons, and electrons combine to produce water and heat.
Individual fuel cells, such as that shown in
A number of different fuel cell technologies can be employed to construct UCAs in accordance with the principles of the present invention. For example, a UCA packaging methodology of the present invention can be employed to construct proton exchange membrane (PEM) fuel cell assemblies. PEM fuel cells operate at relatively low temperatures (about 175° F./80° C.), have high power density, can vary their output quickly to meet shifts in power demand, and are well suited for applications where quick startup is required, such as in automobiles for example.
Alternately, the present invention may be used in non-UCA fuel cell stacks, such as a fuel cell stack that includes bipolar plates (BPP's) stacked alternately with MEA's.
The proton exchange membrane used in a PEM fuel cell is typically a thin solid polymer electrolyte sheet that allows hydrogen ions to pass through it. The membrane is typically coated on both sides with highly dispersed metal or metal alloy particles (e.g., platinum or platinum/ruthenium) that are active catalysts. The electrolyte used is typically a solid perfluorinated sulfonic acid polymer. Use of a solid electrolyte is advantageous because it reduces corrosion and electrolyte containment problems.
Hydrogen is fed to the anode side of the fuel cell where the catalyst promotes the hydrogen atoms to release electrons and become hydrogen ions (protons). The electrons travel in the form of an electric current that can be utilized before it returns to the cathode side of the fuel cell where oxygen has been introduced. At the same time, the protons diffuse through the membrane to the cathode, where the hydrogen ions are recombined and reacted with oxygen to produce water.
A membrane electrode assembly (MEA) is the central element of PEM fuel cells, such as hydrogen fuel cells. As discussed above, typical MEAs comprise a polymer electrolyte membrane (PEM) (also known as an ion conductive membrane (ICM)), which functions as a solid electrolyte.
One face of the PEM is in contact with an anode electrode layer and the opposite face is in contact with a cathode electrode layer. Each electrode layer includes electrochemical catalysts, typically including platinum metal. Fluid transport layers (FTLs) facilitate gas transport to and from the anode and cathode electrode materials and conduct electrical current.
In a typical PEM fuel cell, protons are formed at the anode via hydrogen oxidation and transported to the cathode to react with oxygen, allowing electrical current to flow in an external circuit connecting the electrodes. The FTL may also be called a gas diffusion layer (GDL) or a diffuser/current collector (DCC). The anode and cathode electrode layers may be applied to the PEM or to the FTL during manufacture, so long as they are disposed between PEM and FTL in the completed MEA.
Any suitable PEM may be used in the practice of the present invention. Useful PEM thicknesses range between about 200 μm and about 15 μm. The PEM is typically comprised of a polymer electrolyte that is an acid-functional fluoropolymer, such as Nafion® (DuPont Chemicals, Wilmington Del.), Flemion® (Asahi Glass Co. Ltd., Tokyo, Japan), and polymers having a highly fluorinated backbone and recurring pendant groups according to the formula YOSO2—CF2—CF2—CF2—CF2—O-[polymer backbone]where Y is H+ or another monovalent cation, such as an alkali metal cation. The latter polymers are described in WO2004062019. The polymer electrolytes useful in the present invention are typically preferably copolymers of tetrafluoroethylene and one or more fluorinated, acid-functional comonomers.
Typically, the polymer electrolyte bears sulfonate functional groups. The polymer electrolyte typically has an acid equivalent weight of 1200 or less, more typically 1100, and most typically about 1000. Equivalent weights as low as 800 or even 700 might be used.
Any suitable FTL may be used in the practice of the present invention. Typically, the FTL is comprised of sheet material comprising carbon fibers. The FTL is typically a carbon fiber construction selected from woven and non-woven carbon fiber constructions. Carbon fiber constructions which may be useful in the practice of the present invention may include: Toray Carbon Paper, SpectraCarb Carbon Paper, AFN non-woven carbon cloth, Zoltek Carbon Cloth, and the like. The FTL may be coated or impregnated with various materials, including carbon particle coatings, hydrophilizing treatments, and hydrophobizing treatments such as coating with polytetrafluoroethylene (PTFE).
Any suitable catalyst may be used in the practice of the present invention, including platinum blacks or fines, ink containing carbon-supported catalyst particles (as described in US20040107869 and herein incorporated by reference), or nanostructured thin film catalysts (as described in U.S. Pat. No. 6,482,763 and U.S. Pat. No. 5,879,827, both incorporated herein by reference). The catalyst may be applied to the PEM or the FTL by any suitable means, including both hand and machine methods, including hand brushing, notch bar coating, fluid bearing die coating, wire-wound rod coating, fluid bearing coating, slot-fed knife coating, three-roll coating, vacuum coating, screen printing or decal transfer. Coating may be achieved in one application or in multiple applications.
Direct methanol fuel cells (DMFC) are similar to PEM cells in that they both use a polymer membrane as the electrolyte. In a DMFC, however, the anode catalyst itself draws the hydrogen from liquid methanol fuel, eliminating the need for a fuel reformer. DMFCs typically operate at a temperature between 120-190° F./49-88° C. A direct methanol fuel cell can be subject to UCA packaging in accordance with the principles of the present invention.
Referring now to
In one configuration, a PEM layer 22 is fabricated to include an anode catalyst coating 30 on one surface and a cathode catalyst coating 32 on the other surface. This structure is often referred to as a catalyst-coated membrane or CCM. According to another configuration, the first and second FTLs 24, 26 are fabricated to include an anode and cathode catalyst coating 30, 32, respectively. In yet another configuration, an anode catalyst coating 30 can be disposed partially on the first FTL 24 and partially on one surface of the PEM 22, and a cathode catalyst coating 32 can be disposed partially on the second FTL 26 and partially on the other surface of the PEM 22.
The FTLs 24, 26 are typically fabricated from a carbon fiber paper or non-woven material or woven cloth. Depending on the product construction, the FTLs 24, 26 can have carbon particle coatings on one side. The FTLs 24, 26, as discussed above, can be fabricated to include or exclude a catalyst coating.
In the particular embodiment shown in
Flow field plates 40 and 42 are positioned adjacent the first and second edge seal systems 34 and 36, respectively. Each of the flow field plates 40, 42 includes a field of gas flow channels 43 and ports through which hydrogen and oxygen feed fuels pass. The flow field plates 40, 42 also incorporate coolant channels and ports configured to facilitate passive dual-phase cooling in accordance with the present invention. The coolant channels are incorporated on surfaces of the flow field plates 40, 42 opposite the surfaces incorporating the gas flow channels 43.
In the configuration depicted in
c illustrates a UCA 50 which incorporates multiple MEAs 25 through employment of one or more bipolar flow field plates 56. In the configuration shown in
The UCA configurations shown in
In accordance with the present invention, an alternative approach to single-phase cooling of fuel cell assemblies, stacks, and power systems involves passive two-phase or thermosyphon cooling. In the context of a power system 120 that incorporates fuel cells 122, and as shown in the generalized depiction of
Implementing a passive two-phase cooling approach for fuel cells according to the present invention provides a number of advantages over conventional cooling approaches. For example, no active controls or pump are required to maintain isothermal operation. Systems can be designed to maintain fuel cell stack temperatures uniform to within relatively tight ranges, such as within 2° C. for example. Coolant channels incorporated in flow field plates may be significantly reduced in thickness/depth. For example, coolant channels as thin as 4-8 mil are readily achievable, which can reduce flow field plate (e.g., bipolar plate) thickness relative to conventional flow field plate configurations. Reductions in flow field plate thickness provides a concomitant reduction in fuel cell stack thickness. Such a system operates at or near atmospheric pressure and is less prone to leakage.
A two-phase cooling system of the present invention provides for an isothermal heat sink or source which operates at a temperature slightly below the MEA temperature. In one implementation, for example, an appropriate heat transfer fluid may have a boiling point at the operating pressure of less than about 3° C. below a maximum temperature of the MEA surface. Such a sink has great potential for controlling the temperature and humidity of input gas streams.
A variety of heat transfer fluids may be used, including water, a hydrocarbon, a fluorochemical, or a dielectric halocarbon. In one configuration, hydrofluoroether fluids, such as 3M NOVEC hydrofluoroether fluids, may be used. These fluids have excellent environmental, health, safety and regulatory properties and do not foul the membrane/catalyst assemblies if they leak into the stack. Such fluids are non-corrosive, thus enabling the use of common materials like aluminum and copper for plumbing and heat exchangers.
In accordance with one embodiment, and with reference to
According to one configuration, the depth, d, of the coolant channels 102 is preferably less than about 1 mm. For example, the coolant channels 102 may have a depth of less than about 0.7 mm. By way of further example, the coolant channels 102 may have a depth of less than about 0.5 mm. In other configurations, the coolant channels 102 may have a depth of less than about 0.3 mm. In yet other configurations, the coolant channels 102 may have a depth of about 0.1 mm.
In some implementations, the coolant channels 102 may have a channel length, L, greater than about 10 cm. In other implementations, the coolant channels 102 may have a channel length, L, that ranges from about 60 mm to about 230 mm. In one particular configuration, for example, the coolant channels 102 may have a channel spacing, s, of about 1 mm to about 2 mm, a channel width, w, of about 1 mm to about 3 mm, and a channel length, L, ranging from about 60 mm to about 230 mm. A ratio of the channel length, L, to channel depth, d, typically ranges between about 150 and about 1100.
The heat transfer characteristics of a flow field plate of the type described above can be further enhanced by inclusion of surface coatings and/or features in the coolant channels that advantageously extend the critical heat flux. A variety of surface coatings and features may be employed to effectively increase the critical heat flux. Examples of such surface coatings and features that can be incorporated in the coolant channels of flow field plates include nanostructured features, microporous features, and coatings comprising a substantially planar organic molecule that comprises delocalized pi-electrons, such as are found in van der Waals solids.
One technique for ensuring reliable incipience even at low heat fluxes is the use of a porous coating on the heated surface (i.e., in the coolant channels). These coatings encourage incipience by creating nucleation sites. In saturated boiling from discrete heat sources, coated coolant channel surfaces can exhibit incipience heat fluxes of about 0.2-0.5 W/cm2, 80% lower than uncoated surfaces with a 90% reduction in incipience superheat and over a 300% increase in nucleate boiling heat transfer coefficients.
For a prescribed active area width, W, length, L, and heat flux Q″, there are certain values of channel width, w, channel spacing, s, and channel depth, d, that allow proper operation as shown in
Increasing the critical heat flux of flow field plate coolant channels can be achieved by appropriate selection of channel dimensions in addition to, or exclusive of, appropriate surface coatings and/or features, such as microporous and nanostructured features, details of which are described in the Example provided below. In general, the nanostructured features can be uniformly oriented nanostructures and/or have a predefined geometric shape. The inner channel surfaces can comprise in excess of about 1 million nanostructures/cm2. For example, the inner channel surfaces can comprise in excess of about 1 billion nanostructures/cm2. The nanostructured features may have lengths ranging from about 0.1 micron to about 3 micron and aspect ratios (length to mean diameter) of greater than about 3. Nanostructured features suitable for use in the present invention may comprise metal-coated whiskers of organic pigment, most preferably C.I. PIGMENT RED 149 (PR-149 perylene red). The crystalline whiskers have substantially uniform but not identical cross-sections, and high length-to-width ratios. The microporous features may comprise assemblies of microparticles, as described previously.
An apparatus shown generally in block diagram form in
The flat front of this channel plate formed the inside of the fluid channels. An adhesive backed film (3M vinyl film nominally 0.004″ thick) was applied in layers as needed to create the desired channel thickness, t. It is noted that in this disclosure, the channel thickness, t, is referred to herein interchangeably as channel depth, d. The film or film layers were cut in advance such that, when applied to the channel plate, they created interchannel ribs. The interchannel ribs were present only over the heated region. To study the effects of the channel wall surfaces, the channel plate was modified before the ribs were applied with various treatments as described in Table 1 below.
A similar assembly formed the second wall of the channel region. While this assembly has heaters and the same channel surface treatment as the first, ribs were not applied to it nor was it instrumented with thermocouples. Also, it contained a 0.25 inch diameter hole through which liquid entered and pairs of 0.25 inch diameter holes through which vapor exited the assembly. The plate assembly was clamped together with bolts.
The apparatus was designed to allow heated regions 4 inches wide and 76, 152, 229, 305 and 381 mm in length. The various length corresponding to the activation of heater pairs 1-5. Only the first 3 lengths were used in this study. For all lengths, liquid return was provided by a liquid return hole. This hole connected with a brass hose bard. For each length, only the two vapor passages immediately above that heated region were open to similar hose barbs. For example, the apparatus was configured for 2 heaters (heated region 6 inches high). Thus, all vapor holes were plugged except those immediately above the active region. These connected via the hose barbs to the condenser assembly.
The condenser was a conventional water-cooled shell and tube heat exchanger cooled by tap water. The manifold connecting the apparatus to the condenser had a clear section to allow viewing of the liquid height or head acting on the liquid return line. For purposes of the experiment, this was adjusted to keep the liquid head at the top of the channels or active region.
The heaters were connected in parallel as needed to a Kepco Model BOP 20-20M (20V, 20A) bipolar operational power supply/amplifier controlled via analog connection to a National Instruments Labview data acquisition system. The voltage to the heaters and the thermocouple temperature were monitored with this same data acquisition system.
The apparatus was run using Fluorinert FC-87 or perfluoropentane. This fluid boils at 29° C. and has a molecular weight of 288 g/mol. This is similar to HFE-7200 which has a molecular weight of 264 g/mol and, with a boiling point of 76° C., may be considered a preferred fluid for actual PEM fuel cells. FC-87 was used because its 30° C. boiling point minimized heat losses and stresses in the Plexiglas.
The automated data acquisition system was typically programmed to start at 4 VDC and then advance in 0.5 VDC increments every 15 minutes. Previous experiments showed that steady state was reached in this time period. At the end of each time interval, the system rapidly acquired 100 measurements, averaged them, and logged the result. The data include time of measurement, heater voltage, and top (T3), bottom (T1), and center (T2) temperatures.
The results discussed below are generally presented with wall heat flux as the independent variable. It should be noted that there are three heat fluxes one can refer to when discussing such data. The heat flux Q″gen is the heat flux generated on one MEA which is the product of the current density and the cell overpotential. Assuming that there is one bipolar or cooling plate between every two adjacent MEAs, then each cooling plate will receive approximately ½ Q″gen on each of its two surfaces and will dissipate a total heat flux of Q″gen. The heat flux reported in the following results, Q″ is the heat flux applied to each plate surface during the experiment. Thus,
Q″˜Q″gen/2 [1]
A third heat flux useful for comparison to other literature sources is the channel wall heat flux. Assuming that the ribs are roughly adiabatic, then this flux is equal to
Q″lit=(w+s)Q″/w [2]
The difference between thermocouple temperatures T2 and T3 was used as a measure of temperature variation across the plate.
Temperature Variation=T3−T2[3]
Data derived from the experimental arrangement discussed above are presented in
The y-axis label for
As is demonstrated by the data graphically depicted in
The foregoing description of the various embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.
