Fuel cell flow field design for thermal management

Abstract

Fuel cell assemblies comprising at least one thermally compensated coolant channel are provided. The thermally compensated coolant channel has a cross-sectional area that decreases in the coolant flow direction along at least a portion of the channel length. In some embodiments, such thermally compensated coolant channels can be used to provide substantially uniform heat flux, and substantially isothermal conditions, in fuel cells operating with substantially uniform current density.

Claims

1. A fuel cell assembly comprising: (a) a first fuel cell comprising: (i) a first anode; (ii) a first cathode; (iii) a first proton exchange membrane electrolyte interposed between said first anode and said first cathode; (iv) a first anode flow field plate adjacent to said first anode, said first anode flow field plate comprising a first anode flow channel for directing a fuel to said first anode; and (v) a first cathode flow field plate adjacent to said first cathode, said first cathode flow field plate comprising a first cathode flow channel for directing an oxidant to said first cathode, wherein a cross-sectional area of said first cathode flow channel decreases in a flow direction of said oxidant along at least a portion of the length of said first cathode flow channel; (b) a second fuel cell comprising: (i) a second anode; (ii) a second cathode; (iii) a second proton exchange membrane electrolyte interposed between said second anode and said second cathode; (iv) a second anode flow field plate adjacent to said second anode, said second anode flow field plate comprising a second anode flow channel for directing said fuel to said second anode; and (v) a second cathode flow field plate adjacent to said second cathode, said second cathode flow field plate comprising a second cathode flow channel for directing said oxidant to said second cathode; and (c) a thermally compensated coolant channel interposed between said first cathode flow field plate and said second anode flow field plate, for directing a coolant in a heat transfer relationship with at least one of said first cathode flow field plate and said second anode flow field plate, said thermally compensated coolant channel having an inlet, an outlet, and a cross-sectional area that decreases monotonically in a flow direction of said coolant from said inlet to said outlet of said thermally compensated coolant channel, such that the width of said thermally compensated coolant channel near said inlet is greater than the width of said thermally compensated coolant channel near said outlet; wherein said first cathode flow field plate comprises a plurality of first cathode flow channels on a first side of said first cathode flow field plate and a corresponding inverse pattern defining a first plurality of grooves on a second side of said first cathode flow field plate, and said second anode flow field plate comprises a plurality of second anode flow channels on a first side of said second anode flow field plate and a corresponding inverse pattern defining a second plurality of grooves on a second side of said second anode flow field plate, and wherein a plurality of thermally compensated coolant channels are formed between said first fuel cell and said second fuel cells by the cooperating surfaces of said second side of said first cathode flow field plate and said second side of said second anode flow field plate.

2. The fuel cell assembly of claim 1 wherein said cross-sectional area of said thermally compensated coolant channel decreases continuously in said flow direction of said coolant along said thermally compensated coolant channel from said inlet to said outlet.

3. The fuel cell assembly of claim 1 wherein said thermally compensated coolant channel has a substantially rectangular cross-section, and a width of said thermally compensated coolant channel decreases in a non-linear fashion in said flow direction of said coolant along at least a portion of the length of said thermally compensated coolant channel.

4. The fuel cell assembly of claim 1 wherein a cross-sectional area of said second cathode flow channel decreases in a flow direction of said oxidant along at least a portion of the length of said second cathode flow channel.

5. The fuel cell assembly of claim 4 wherein said first cathode flow channel and said second cathode flow channel each have a substantially rectangular cross-section, and a width of said first cathode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said first cathode flow channel, and a width of said second cathode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said second cathode flow channel.

6. The fuel cell assembly of claim 4 wherein a cross-sectional area of said first anode flow channel decreases in a flow direction of said fuel along at least a portion of the length of said first anode flow channel, and the cross-sectional area of said second anode flow channel decreases in a flow direction of said fuel along at least a portion of the length of said second anode flow channel.

7. The fuel cell assembly, of claim 6 wherein said first anode flow channel and said second anode flow channel each have a substantially rectangular cross-section, and a width of said first anode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said first anode flow channel, and a width of said second anode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said second anode flow channel.

8. The fuel cell assembly of claim 1 wherein said first cathode flow field plate and said second anode flow field plate are nested, so that said plurality of first cathode channels, said plurality of second anode flow channels, and said plurality of thermally compensated coolant channels are at least partially in the same plane.

9. A fuel cell assembly comprising: (a) a first fuel cell comprising: (i) a first anode; (ii) a first cathode; (iii) a first proton exchange membrane electrolyte interposed between said first anode and said first cathode; (iv) a first anode flow field plate adjacent to said first anode, said first anode flow field plate comprising a first anode flow channel for directing a fuel to said first anode; and (v) a first cathode flow field plate adjacent to said first cathode, said first cathode flow field plate comprising a first cathode flow channel for directing an oxidant to said first cathode, wherein a cross-sectional area of said first cathode flow channel decreases in a flow direction of said oxidant along at least a portion of the length of said first cathode flow channel; (b) a second fuel cell comprising: (i) a second anode; (ii) a second cathode; (iii) a second proton exchange membrane electrolyte interposed between said second anode and said second cathode; (iv) a second anode flow field plate adjacent to said second anode, said second anode flow field plate comprising a second anode flow channel for directing said fuel to said second anode; and (v) a second cathode flow field plate adjacent to said second cathode, said second cathode flow field plate comprising a second cathode flow channel for directing said oxidant to said second cathode; and (c) a thermally compensated coolant channel interposed between said first cathode flow field plate and said second anode flow field plate, for directing a coolant in a heat transfer relationship with at least one of said first cathode flow field plate and said second anode flow field plate, said thermally compensated coolant channel having an inlet, an outlet, and a cross-sectional area that decreases monotonically in a flow direction of said coolant from said inlet to said outlet of said thermally compensated coolant channel, such that the width of said thermally compensated coolant channel near said inlet is greater than the width of said thermally compensated coolant channel near said outlet; wherein: said first cathode flow field plate comprises a plurality of first cathode flow channels on a first side of said first cathode flow field plate and a corresponding inverse pattern defining a first plurality of grooves on a second side of said first cathode flow field plate, and said second anode flow field plate has a first side and a second side, and a plurality of second anode flow channels on said first side of said second anode flow field plate, wherein a plurality of thermally compensated coolant channels are formed between said first fuel cell and said second fuel cells by the cooperating surfaces of said second side of said first cathode flow field plate and a second side of said second anode flow field plate; or said first cathode flow field plate comprises a first side and said second side, and a plurality of first cathode flow channels on said first side of said first cathode flow field plate, and said second anode flow field plate comprises a plurality of said second anode flow channels on a first side of said second anode flow field plate and a corresponding inverse pattern defining a second plurality of grooves on a second side of said second anode flow field plate, wherein a plurality of thermally compensated coolant channels are formed between said first fuel cell and said second fuel cells by the cooperating surfaces of said second side of said first cathode flow field plate and said second side of said second anode flow field plate.

10. The fuel cell assembly of claim 9 wherein said cross-sectional area of said thermally compensated coolant channel decreases continuously in said flow direction of said coolant along said thermally compensated coolant channel from said inlet to said outlet.

11. The fuel cell assembly of claim 9 wherein said thermally compensated coolant channel have a substantially rectangular cross-section, and a width of said thermally compensated coolant channel decreases in a non-linear fashion in said flow direction of said coolant along at least a portion of the length of said thermally compensated coolant channel.

12. The fuel cell assembly of claim 9 wherein a cross-sectional area of said second cathode flow channel decreases in a flow direction of said oxidant along at least a portion of the length of said second cathode flow channel.

13. The fuel cell assembly of claim 12 wherein said first cathode flow channel and said second cathode flow channel each have a substantially rectangular cross-section, and a width of said first cathode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said first cathode flow channel, and a width of said second cathode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said second cathode flow channel.

14. The fuel cell assembly of claim 12 wherein a cross-sectional area of said first anode flow channel decreases in a flow direction of said fuel along at least a portion of the length of said first anode flow channel, and the cross-sectional area of said second anode flow channel decreases in a flow direction of said fuel along at least a portion of the length of said second anode flow channel.

15. The fuel cell assembly of claim 14 wherein said first anode flow channel and said second anode flow channel each have a substantially rectangular cross-section, and a width of said first anode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said first anode flow channel, and a width of said second anode flow channel decreases in accordance with an exponential function along said at least a portion of the length of said second anode flow channel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic of an embodiment of a fuel cell coolant flow field plate comprising a plurality of thermally compensated channels.

(2) FIG. 2 is a schematic of another embodiment of a fuel cell coolant flow field plate comprising a plurality of thermally compensated channels.

(3) FIG. 3 is a schematic of a thermally compensated channel.

(4) FIGS. 4 and 5 are flowcharts illustrating a method for configuring a thermally compensated channel.

(5) FIG. 6 is a graph illustrating channel width and working fluid velocity along a thermally compensated rectangular channel configured according to the method of FIGS. 4 and 5.

(6) FIG. 7 is a graph illustrating the heat flux and temperature of the working fluid along a thermally compensated rectangular channel configured according to the method of FIGS. 4 and 5.

(7) FIG. 8 is a graph illustrating the temperature of the working fluid along the length of a channel for conventional and thermally compensated channels.

(8) FIG. 9 is a graph that shows that the heat flux is essentially constant along the length of the thermally compensated channel from the inlet to the outlet.

(9) FIG. 10 is a graph of channel width as a function of normalized distance along the channel from inlet to outlet for conventional and thermally compensated channels.

(10) FIG. 11 is a graph of the velocity of working fluid as a function of normalized distance along the channel from inlet to outlet for conventional and thermally compensated channels.

(11) FIG. 12 is a schematic of an apparatus used to verify the method of FIGS. 4 and 5 for configuring a thermally compensated channel.

(12) FIG. 13 is a graph of the test results and the expected temperature profile, based on the thermal model, for conventional serpentine channels.

(13) FIG. 14 is a graph of the test results and the expected temperature profile, based on the thermal model, for thermally compensated channels.

(14) FIGS. 15A-C illustrate an example embodiment of a pair of corrugated, trapezoidal reactant flow field plates that are stacked so that coolant channels having a cross-sectional area that varies along their length are formed between the cooperating corrugated surfaces of the stacked plates.

(15) FIGS. 16A-C illustrate an example embodiment of a pair of corrugated, trapezoidal reactant flow field plates that are nested so that coolant channels having a cross-sectional area that varies along their length are formed between the cooperating corrugated surfaces of the nested plates.

(16) FIGS. 17A-C illustrate another example embodiment of a pair of corrugated, trapezoidal reactant flow field plates that are nested so that coolant channels having a cross-sectional area that varies along their length are formed between the cooperating corrugated surfaces of the nested plates.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT(S)

(17) In embodiments of the technology described herein, the velocity of the working fluid over the heat transfer surface is adjusted to control the variation of heat flux (heat transfer per unit area) over the heat transfer surface. The velocity of the working fluid can be adjusted to reduce or eliminate the variation in heat flux over the heat transfer surface. If the heat flux is substantially uniform and heat is produced substantially uniformly by the heat source, then the resulting temperature of the heat transfer surface will also be substantially uniform.

(18) An advantage of achieving uniform temperature of the heat transfer surface and substantially uniform heat flux is that it can increase the heat transfer capacity of the heat exchanger. As a consequence, a working fluid with a lower thermal mass can be used to remove the same amount of heat, thereby reducing the parasitic power losses associated with pumping coolant at a higher flow rate to accommodate a fluid or design with poorer heat transfer characteristics. Another advantage of certain embodiments of the technology described herein is that a phase change is not required to achieve substantially uniform heat flux, and so a wide variety of working fluids and broad range of operating temperatures can be used.

(19) FIG. 1 is a schematic of an embodiment of fuel cell coolant flow field plate 100 comprising a plurality of thermally compensated channels 110. Coolant flow field plate 100 further comprises inlet 140 and outlet 150. Thermally compensated channels 110 are configured such that the width of channels nearer inlet 140, for example, in region 120, is greater than the width of channels nearer outlet 150, for example, in region 130.

(20) FIG. 2 is a schematic of another embodiment of fuel cell coolant flow field plate 200 comprising a plurality of thermally compensated channels 210. Coolant flow field plate 200 further comprises inlet 240 and outlet 250. Thermally compensated channels 210 are configured such that the width of channels nearer inlet 240, for example, in region 220 is greater than the width of channels nearer outlet 250, for example, in region 230.

(21) In some embodiments, thermally compensated channels (such as 110 of FIG. 1 or 210 of FIG. 2) can have a rectangular cross-section, or they can have a substantially rectangular cross-section, for example with rounded corners and slightly flared side-walls. In other embodiments, thermally compensated channels can have other cross-sectional shapes including, but not limited to, trapezoidal, triangular, semi-circular cross-sections.

(22) FIG. 3 is schematic of thermally compensated channel 300, such as an individual channel on a coolant flow field plate. Thermally compensated channel 300 has a rectangular cross-section, and comprises heat transfer surface 310. Heat flow across heat transfer surface 310 from a fuel cell (not shown in FIG. 3) is illustrated by arrows 320. The flow of a working fluid entering thermally compensated channel 300 at inlet 330 is illustrated by arrow 335. The flow of a working fluid leaving thermally compensated channel 300 at outlet 340 is illustrated by arrow 345.

(23) FIGS. 4 and 5 are flowcharts illustrating method 400 for configuring a thermally compensated channel. Method 400 comprises a numerical approach that estimates heat flux at a plurality of equally spaced positions along the length of the channel from the inlet to the outlet.

(24) FIG. 4 is a flowchart illustrating a first part of method 400. The first part of method 400 comprises steps 410 through 480.

(25) At step 410, the channel is configured with an initial set of parameters, the initial set of parameters comprising depth D.sub.0 and width W.sub.0 at the inlet, length of the channel L, mass flow of the working fluid {dot over (m)}, temperature of the working fluid at the inlet T.sub.0, and the wall temperature T.sub.w.

(26) At step 420, the incremental distance x between each of the plurality of equally spaced positions is selected. The incremental distance is selected to provide a desired level of accuracy for the resulting width profile of the channel.

(27) At step 430, method 400 estimates the velocity of the working fluid at the inlet, referred to as the initial velocity v.sub.0 of the working fluid, using equation (1), where {dot over (m)} is the mass flow rate, and .sub.0 is the density of the working fluid at the inlet:

(28) $\begin{array}{cc}{v}_0=\frac{\stackrel{.}{m}}{{}_0{W}_0{D}_0}& \left(1\right)\end{array}$

(29) At step 440, method 400 estimates the hydraulic diameter d.sub.h0 of the channel at the inlet, using equation (2):

(30) $\begin{array}{cc}{d}_{h0}=\frac{4W_0{D}_0}{2\left(W_0+D_0\right)}& \left(2\right)\end{array}$

(31) At step 450, method 400 estimates the physical properties of the working fluid at the inlet temperature T.sub.0. The physical properties comprise density , dynamic viscosity , specific heat C.sub.p, and thermal conductivity k.sub.th.

(32) At step 460, method 400 estimates the convective heat transfer coefficient h.sub.0 at the inlet temperature using equations (3) through (6) as follows:

(33) $\begin{array}{cc}{h}_0=\frac{k_{\mathrm{th}0}{\mathrm{Nu}}_0}{d_{h0}}& \left(3\right)\\ {\mathrm{Nu}}_0=1.86{\left(\mathrm{Pr}\mathrm{Re}\frac{d_{h0}}{L}\right)}^{\frac{1}{3}}{\left(\frac{{}_0}{{}_w}\right)}^{0.14}& \left(4\right)\\ {\mathrm{Pr}}_0=\frac{C_{p0}{}_0}{k_{\mathrm{th}0}}& \left(5\right)\\ {\mathrm{Re}}_0=\frac{{}_0{v}_0{d}_{h0}}{{}_0}& \left(6\right)\end{array}$

(34) where Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number.

(35) At step 470, method 400 estimates the local heat flux, q, using equation (7):
q(0)=h.sub.0(T.sub.wT.sub.0)(7)

(36) At step 480, method estimates the heat transfer, Q, across the initial heat transfer area using equation (8):
Q=q(0)W.sub.0x(8)

(37) Method 400 proceeds to step 510 of FIG. 5.

(38) FIG. 5 is a flowchart illustrating a second part of method 400. The second part of method 400 comprises steps 510 through 550.

(39) At step 510, method 400 increments the current position along the channel by adding the incremental distance x to the previous position.

(40) At step 520, if the current position along the channel exceeds channel length L, then method 400 proceeds to step 530. At step 530, width profile W(x) is output to a storage or display device suitable for serving as input to the configuration of a thermally compensated channel in a fuel cell flow plate. Method 400 proceeds to step 540 and ends.

(41) At step 520, if the current position along the channel does not exceed channel length L, then method 400 proceeds to step 550. At step 550, method 400 estimates the temperature T.sub.i of the working fluid at the current position x.sub.i along the channel using equation (9):

(42) $\begin{array}{cc}{T}_i=\frac{Q_{i-1}}{\stackrel{.}{m}{C}_{\mathrm{pi}-1}}+T_{i-1}& \left(9\right)\end{array}$
where Q.sub.i-1 is the heat transfer across the heat transfer area at the previous position x.sub.i-1 along the channel, {dot over (m)} is the mass flow rate, C.sub.pi-1 is the specific heat at position x.sub.i-1 and T.sub.i-1 is the temperature of the working fluid at position x.sub.i-1.

(43) At step 560, method 400 solves for substantially constant heat flux by adjusting channel width W(x). In other words, method 400 finds channel width W(x) for which the absolute difference in heat flux between q(x.sub.i) and q(x.sub.i-1) is below a predetermined threshold. Alternatively, method 400 can be used to tailor a specific heat flux gradient or profile (for example so that the temperature difference across a fuel cell can be controlled). The solver uses equations (10) through (16):

(44) $\begin{array}{cc}{h}_i=\frac{k_{\mathrm{thi}}{\mathrm{Nu}}_i}{d_{\mathrm{hi}}}& \left(10\right)\\ {\mathrm{Nu}}_i=1.86{\left(\mathrm{Pr}\mathrm{Re}\frac{d_{hi}}{L}\right)}^{\frac{1}{3}}{\left(\frac{{}_i}{{}_w}\right)}^{0.14}& \left(11\right)\\ {\mathrm{Pr}}_i=\frac{C_{pi}{}_i}{k_{\mathrm{th}i}}& \left(12\right)\\ {\mathrm{Re}}_i=\frac{{}_i{v}_i{d}_{hi}}{{}_i}& \left(13\right)\\ d_{hi}=\frac{4W_i{D}_0}{2\left(W_i+D_0\right)}& \left(14\right)\\ v_i=\frac{\stackrel{.}{m}}{{}_i{W}_i{D}_0}& \left(15\right)\\ q\left(x_i\right)=h_i\left(T_w-T_i\right)& \left(16\right)\end{array}$

(45) A suitable numerical solver can be used such as a Generalized Reduced Gradient algorithm for solving non-linear problems.

(46) When the numerical solver has converged to a solution for channel width W(x.sub.i), method 400 proceeds to step 570. At step 570, channel width W(x.sub.i) is stored in a channel width profile record.

(47) At step 580, method 400 estimates the heat transfer across the current heat transfer area W(x.sub.i)x using equation (17):
Q.sub.i=q(x.sub.i)W.sub.ix(17)

(48) Method 400 then returns to step 510.

(49) Method 400 describes the method for configuring a thermally compensated channel for a channel having a rectangular cross-section with a varying width and a substantially constant depth along its length. In other embodiments, a thermally compensated channel can have a rectangular cross-section with a varying or constant width and a varying depth. In some embodiments, a thermally compensated channel can have a cross-section that is not rectangular or substantially rectangular, but has some other cross-sectional channel shape. A thermally compensated channel can be configured by a suitable adjustment of the velocity of the working fluid in the channel through the appropriate alteration in the channel's cross-sectional area.

(50) FIG. 6 is a graph illustrating channel width and working fluid velocity along a thermally compensated channel with rectangular cross-section configured according to method 400 of FIGS. 4 and 5.

(51) The channel width decreases from 2.5 mm at the inlet to approximately 1.1 mm at the outlet. The decreasing channel width is associated with a corresponding increase in velocity of the working fluid along the channel length. The velocity increases from approximately 0.185 m/s at the inlet to 0.418 m/s at the outlet.

(52) FIG. 7 is a graph illustrating the heat flux and temperature of the working fluid along a thermally compensated rectangular channel configured according to method 400 of FIGS. 4 and 5.

(53) The heat flux is held essentially constant. In the example shown, the heat flux is approximately 12.7 W/cm.sup.2. The temperature of the working fluid increases along the channel from 25 C. at the inlet to approximately 41.3 C. at the outlet.

(54) FIG. 8 is a graph illustrating the temperature of the working fluid along the length of a channel for a conventional channel and for a thermally compensated channel. Line 810 shows the variation in temperature of the working fluid along the length of a conventional channel. In this example, the conventional channel has a rectangular cross-section and constant width, depth and cross-sectional area along its length. Line 820 shows the variation in temperature of the working fluid along the length of a thermally compensated channel such as the one illustrated in FIGS. 6 and 7.

(55) FIG. 8 shows that more heat is removed from the fuel cell by a configuration comprising thermally compensated channels since the temperature of the working fluid at the outlet is higher than it is for the conventional channel, even though the inlet temperature at each inlet is the same.

(56) FIG. 9 is a graph illustrating the heat flux along the length of a channel for a conventional channel and a thermally compensated channel. Line 910 shows the heat flux along the length of a conventional channel. In this example, the conventional channel has a rectangular cross-section and constant width, depth and cross-sectional area along its length. Line 920 shows the heat flux along the length of a thermally compensated channel such as the one illustrated in FIGS. 6 and 7.

(57) FIG. 9 shows that the heat flux can be essentially constant along the length of the thermally compensated channel from the inlet to the outlet. Since the thermally compensated channel is configured to keep the heat flux essentially constant along the length of the channel, heat is removed more uniformly and isothermal operation is possible.

(58) FIG. 10 is a graph of the channel width as a function of normalized distance along the channel from inlet to outlet for a conventional channel and a thermally compensated channel. Line 1010 shows the channel width of a conventional channel having essentially constant channel width. Line 1020 shows the channel width of a thermally compensated channel, such as the one illustrated in FIGS. 6 and 7.

(59) FIG. 11 is a graph of the velocity of working fluid as a function of normalized distance along the channel from inlet to outlet for a conventional channel and a thermally compensated channel. Line 1110 shows the velocity of working fluid along the length of a conventional channel having substantially constant channel width, depth and cross-sectional area along its length. Line 1120 shows the velocity of working fluid along the length of a thermally compensated channel such as the one illustrated in FIGS. 6 and 7.

(60) The method described above is one approach to configuring a thermally compensated channel. Other suitable methods for adjusting the dimensions of the channel, the velocity of the working fluid and/or the local heat transfer area can be used to configure a channel to substantially compensate for the increase in the temperature of the working fluid along the length of the channel or, in other words, to compensate for the decrease in the temperature difference between the working fluid and the heat transfer surface along the length of the channel.

(61) An experiment was conducted in order to validate the method described above for configuring a thermally compensated channel. The experiment compared the behavior of a conventional channel to the behavior of a thermally compensated channel.

(62) FIG. 12 is a schematic of apparatus 1200 used to verify the method of FIGS. 4 and 5 for configuring a thermally compensated channel. Apparatus 1200 comprises simulated reactant flow field plate 1210, coolant flow field plate 1220, clamping plates 1230A and 1230B, inlet and outlet ports 1240A and 1240B for hot fluid, inlet and outlet ports 1250A and 1250B for cold fluid, and one or more thermocouples 1260A through 1260D.

(63) Simulated reactant flow field plate 1210 was maintained at an essentially constant temperature to simulate a fuel cell operating at uniform current density. Coolant flow field plate 1220 comprises an arrangement of channels. In a first embodiment, the channels are conventional channels arranged in a serpentine pattern. In a second embodiment, the channels are thermally compensated channels and configured to produce uniform heat flux across the heat transfer area. Thermocouples 1260A through 1260D were used to measure the temperature of fluid flowing across coolant flow field plate 1220.

(64) Simulated reactant flow field plate 1210 is situated on the hot side of the heat exchanger. Fluid in flow field plate 1210 has a mass flow rate of {dot over (m)}.sub.h, and the temperature of the fluid at inlet and outlet ports 1240A and 1240B is T.sub.hi and T.sub.ho respectively.

(65) Coolant flow field plate 1220 is situated on the cool side of the heat exchanger. Fluid in controlled flow field plate 1220 has a mass flow rate of {dot over (m)}.sub.c, and the temperature of the fluid at inlet and outlet ports 1250A and 1250B is T.sub.ci and T.sub.co respectively.

(66) Simulated reactant flow field plate 1210 and coolant flow field plate 1220 cover an equivalent active area. The working fluid was deionized water. To avoid temperature gradients on the hot side of the heat exchanger, the deionized water was pumped across plate 1210 at significantly higher flow rates on the hot side relative to the cold side.

(67) A first test was conducted using the first embodiment of coolant flow field plate 1220 (serpentine channels). Table 1 lists the parameters for the first test.

(68) TABLE-US-00001 TABLE 1 Parameter Serpentine Channels T.sub.ci [ C.] 23 T.sub.co [ C.] 60 T.sub.hi [ C.] 68 T.sub.ho [ C.] 64 Channel Length [m] 2.1 W.sub.0 [m] 0.0016 D.sub.0 [m] 0.00400 {dot over (m)}.sub.c [kg/s] 0.00067 {dot over (m)}.sub.h [kg/s] 0.033

(69) FIG. 13 is a graph displaying the test results and the expected temperature profile for serpentine channels. FIG. 13 shows there is good agreement between the expected temperature profile 1310 (calculated using a model) and data points 1320A through 1320D measured by thermocouples 1260A through 1260D respectively of FIG. 12. The root mean square error is less than 2 C.

(70) A second test was conducted using the second embodiment of coolant flow field plate 1220 (thermally compensated channels). Table 2 lists the parameters for the second test.

(71) There are a variety of suitable configurations of the channel geometry that can be used to compensate at least partially for the increase in temperature of the working fluid along the length of the channel. For the purposes of the second test, the channel was configured to have a substantially rectangular cross-section, a constant depth, and a channel width configured to follow an exponential function with respect to the position along the channel length, and a y-intercept of 0.0025 and a base of 0.00278.

(72) TABLE-US-00002 TABLE 2 Parameter Thermally Compensated Channels T.sub.ci [ C.] 24 T.sub.co [ C.] 45 T.sub.hi [ C.] 68 T.sub.ho [ C.] 60 Channel Length [m] .1505 W.sub.0 [m] 0.0025 D.sub.0 [m] 0.00300 {dot over (m)}.sub.c [kg/s] 0.0050 {dot over (m)}.sub.h [kg/s] 0.033

(73) FIG. 14 is a graph of the test results and the expected temperature profile for thermally compensated channels. FIG. 14 shows there is good agreement between the expected temperature profile 1410 (calculated using a model) and data points 1420A through 1420D measured by thermocouples 1260A through 1260D respectively of FIG. 12. The root mean square error is less than 2 C.

(74) In some embodiments, a fuel cell flow field plate comprises at least one cooling channel with a cross-sectional area or width that decreases from inlet to outlet. In some embodiments, the cross-sectional area or width of the cooling channel decreases continuously from inlet to outlet.

(75) In some embodiments, a fuel cell flow field plate comprises at least one channel for convective cooling, the channel comprising a first region in which the channel has a substantially constant cross-sectional area or width, and a second region in which the channel has a diminishing cross-sectional area or width. The first region may facilitate the distribution of a working fluid from an inlet port to the fuel cell flow field plate. The second region may facilitate the distribution of the working fluid across the fuel cell flow field plate from the first region to an outlet port.

(76) In some embodiments, a fuel cell flow field plate comprises at least one channel for convective cooling, the channel comprising a first region in which the channel has a substantially constant cross-sectional area or width, a second region following the first region in which the channel has a diminishing cross-sectional area or width, and a third region following the second region in which the channel has a substantially constant cross-sectional area or width.

(77) Embodiments of the apparatus and method described above can be used to configure thermally compensated coolant channels for fuel cells having conventional cathode and anode flow field designs such as cathode and anode flow field designs and operating with non-uniform current density.

(78) Embodiments of the apparatus and method described above can be used to configure thermally compensated coolant channels that are particularly suitable for use in fuel cells operating with substantially uniform current density; for example, having unconventional reactant flow field channels on the anode and/or the cathode.

(79) Fuel cell cathode and anode flow channels having a cross-sectional area that varies along the channel length in various manners are described in Applicant's U.S. Pat. No. 7,838,169, which is herein incorporated by reference in its entirety, and in Applicant's U.S. Patent Application Publication No. US2015/0180052 which is also herein incorporated by reference in its entirety. Under certain operating conditions, fuel cells with reactant channel profiles as described in these documents can be operated with substantially uniform current density, and also at extremely high current densities where thermal management can be challenging. In these situations, it can be particularly desirable to configure the fuel cell coolant channels to be able to provide substantially uniform heat flux across the fuel cell active area when a suitable coolant is directed through them. For example, this approach can be used for fuel cells in motive applications, operating at high current densities in the range of about 1 A/cm.sup.2 to about 2 A/cm.sup.2, or about 1 A/cm.sup.2 to about 3 A/cm.sup.2, and in some cases at operating at current densities exceeding 3 A/cm.sup.2.

(80) Thus, aspects of the apparatus and methods described herein relate to fuel cell assemblies comprising thermally compensated coolant channels in combination with oxidant and/or fuel reactant channels having special profiles (such as described in U.S. Pat. No. 7,838,169 and U.S. Patent Application Publication No. US2015/0180052), and methods for operating such fuel cell assemblies, for example, to provide substantially uniform current density and substantially uniform heat flux between the fuel cell and the coolant across the fuel cell active area. This can allow a substantially uniform plate temperature, or substantially isothermal conditions, to be maintained across the fuel cell active area during operation of the fuel cell. This can in turn aid in maintaining on-going uniformity of current density.

(81) In some embodiments, a fuel cell comprises:

(82) an anode;

(83) a cathode;

(84) a proton exchange membrane electrolyte interposed between the anode and the cathode;

(85) an anode flow field plate adjacent the anode, the anode flow field plate comprising at least one anode flow channel for directing fuel to the anode;

(86) a cathode flow field plate adjacent the cathode, the cathode flow field plate comprising at least one cathode flow channel for directing oxidant to the cathode; and

(87) at least one thermally compensated coolant channel between the cathode flow field plate and the anode flow field plate, for directing a coolant in contact with at least one of the flow field plates.

(88) The thermally compensated coolant channel has a cross-sectional area that decreases in the coolant flow direction along at least a portion of the channel length. In some embodiments, the channel is substantially rectangular in cross-section and the width of the channel decreases non-linearly while the depth remains substantially constant.

(89) In some embodiments, the cross-sectional area of the at least one cathode flow channel decreases in the oxidant flow direction along at least a portion of the channel length and/or the cross-sectional area of the at least one anode flow channel decreases in the fuel flow direction along at least a portion of the channel length. In some embodiments, the cross-sectional area of the at least one cathode flow channel and/or the at least one anode flow channel decreases in accordance with an exponential function. In such embodiments in which the cross-sectional area of the anode or cathode flow channels decreases in the reactant flow direction along at least a portion of the length of the respective channel, the characteristics of these reactant flow channels can vary continuously and smoothly as a function of distance along the channel, or can vary in stepwise, discrete or discontinuous manner, such as described in co-owned U.S. Patent Application Publication No. US2015/0180052, for example.

(90) Similarly, in some embodiments of a thermally compensated coolant channel, characteristics of the coolant channel (such as cross-sectional area or width) or the velocity of the working fluid, for example, vary continuously or smoothly as a function of distance along the channel. In other embodiments, characteristics of a thermally compensated coolant channel vary as a function of distance along the channel in a stepwise, discrete or discontinuous manner, for example, to approximately compensate for the increase in the temperature of the working fluid along the length of the channel. For example, performance benefits can be obtained by using thermally compensated coolant channels that incorporate discrete variations, such as for example, a step-wise decrease in cross-sectional area along at least a portion of the channel, or a cross-sectional area that decreases in accordance with a piecewise linear function along at least a portion of the channel length. In some embodiments, thermally compensated coolant channels can contain discrete features that reduce the effective cross-sectional area and obstruct coolant flow, where the density and/or size of those features increases in the coolant flow direction to decrease the cross-sectional area and/or increase the flow velocity on average in the flow direction along the channel. Examples of such features are ribs, tapered ribs or pillars.

(91) The fuel cell reactant flow field plates and coolant flow field plates can be made from a suitable electrically conductive material, including graphite, carbon, composite materials and various metals. Depending on the plate material, the channels can be formed by milling, molding, stamping, embossing or corrugating, for example. The coolant channels can be formed in separate coolant flow field plates, or can be formed in the anode and/or cathode reactant flow field plates on the opposite surface from the reactant channels.

(92) In some embodiments of the fuel cell assemblies, the reactant flow field plates are stamped, embossed or corrugated so that channels are formed on both sides. Such plates can be stacked or nested so that coolant channels are formed between the cooperating surfaces of the anode and cathode flow field plates. If the anode and cathode flow field channels have a cross-sectional area that varies along the channel length, the corresponding channel on the opposite face of each plate will also have a cross-sectional area that varies along the channel length.

(93) For example, FIGS. 15A-C show a pair of corrugated, trapezoidal reactant flow field plates, 151 and 153, that are stacked one on top of the other. FIG. 15A shows a cross-sectional view of anode plate 151 on top of cathode plate 153. FIG. 15B shows an enlarged view of a portion of FIG. 15A, with fuel flow channels 152 on the upper surface of anode plate 151, and oxidant flow channels 154 on the lower surface of cathode plate 153. Coolant channels 155 are formed between the cooperating corrugated surfaces of the pair of stacked plates 151 and 153. FIG. 15C is an isometric view of corrugated, trapezoidal reactant flow field plates 151 and 153 stacked to define coolant channels 155 between their cooperating surfaces. The cross-sectional area of the fuel, oxidant and coolant channels, 152, 154 and 155, respectively, varies along their length.

(94) FIGS. 16A-C show a pair of corrugated, trapezoidal reactant flow field plates, 161 and 163, that are nested together. FIG. 16A shows a cross-sectional view of anode plate 161 on top of cathode plate 163. FIG. 16B shows an enlarged view of a portion of FIG. 16A, with fuel flow channels 162 on the upper surface of anode plate 161, and oxidant flow channels 164 on the lower surface of cathode plate 163. Coolant channels 165 are formed between the cooperating corrugated surfaces of the pair of nested plates 161 and 163. FIG. 16C is an isometric view of corrugated, trapezoidal reactant flow field plates 161 and 163 nested to define coolant channels 165 between their cooperating surfaces. The cross-sectional area of the fuel, oxidant and coolant channels, 162, 164 and 165, respectively, varies along their length.

(95) FIGS. 17A-C show a pair of corrugated, trapezoidal reactant flow field plates, 171 and 173, that are also nested together. FIG. 17A shows a cross-sectional view of anode plate 171 on top of cathode plate 173. FIG. 17B shows an enlarged view of a portion of FIG. 17A, with fuel flow channels 172 on the upper surface of anode plate 171, and oxidant flow channels 174 on the lower surface of cathode plate 173. A pair of coolant channels, 175A and 175B, is formed by the cooperating corrugated surfaces for each channel of the nested plates 171 and 173. FIG. 17C is an isometric view of corrugated, trapezoidal reactant flow field plates 171 and 173 nested to define pairs of coolant channels, 175A and 175B, between their cooperating surfaces. The cross-sectional area of the fuel, oxidant and coolant channels, 172, 174, 175A and 175B, respectively, varies along their length.

(96) While particular elements, embodiments and applications of the present invention have been shown and described, it will be understood, that the invention is not limited thereto since modifications can be made by those skilled in the art without departing from the scope of the present disclosure, particularly in light of the foregoing teachings.