Anthony J. Colozza 

Analex Corporation, Cleveland, Ohio 

Kenneth A. Burke

Glenn Research Center, Cleveland, Ohio

Evaluation of a Passive Heat Exchanger Based 

Cooling System for Fuel Cell Applications

NASA/TM—2011-216962

January 2011
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Anthony J. Colozza 

Analex Corporation, Cleveland, Ohio 

Kenneth A. Burke

Glenn Research Center, Cleveland, Ohio

Evaluation of a Passive Heat Exchanger Based 

Cooling System for Fuel Cell Applications

NASA/TM—2011-216962

January 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-216962 1 

Evaluation of a Passive Heat Exchanger Based 

Cooling System for Fuel Cell Applications

Anthony J. Colozza 

Analex Corporation 

Cleveland, Ohio 44135 

Kenneth A. Burke

National Aeronautics and Space Administration 

Glenn Research Center

Cleveland, Ohio 44135 

Abstract

Fuel cell cooling is conventionally performed with an actively controlled, dedicated coolant loop that 

exchanges heat with a separate external cooling loop. To simplify this system the concept of directly 

cooling a fuel cell utilizing a coolant loop with a regenerative heat exchanger to preheat the coolant 

entering the fuel cell with the coolant exiting the fuel cell was analyzed. The preheating is necessary to 

minimize the temperature difference across the fuel cell stack. This type of coolant system would 

minimize the controls needed on the coolant loop and provide a mostly passive means of cooling the fuel 

cell. The results indicate that an operating temperature of near or greater than 70 °C is achievable with a 

heat exchanger effectiveness of around 90 percent. Of the heat exchanger types evaluated with the same 

type of fluid on the hot and cold side, a counter flow type heat exchanger would be required which has the 

possibility of achieving the required effectiveness. The number of heat transfer units required by the heat 

exchanger would be around 9 or greater. Although the analysis indicates the concept is feasible, the heat 

exchanger design would need to be developed and optimized for a specific fuel cell operation in order to 

achieve the high effectiveness value required. 

Introduction

In previous work (Ref. 1), it has been shown that high thermal conductivity cooling plates can be 

utilized to remove heat generated within a fuel cell. One of the advantages of utilizing this type of cooling 

approach is that a generic cooling loop can be utilized. The fuel cell cooling system does not impose any 

conditions on this generic cooling loop, such as temperature or flow rate. The cooling flow from the 

generic loop is adjusted through the use of a valve so that the internal temperature of the fuel cell is 

maintained at the desired level. A conductive plate system as compared to the more conventional fluid 

cooling system for a fuel cell is shown in Figure 1. The cooling plate system utilizes a manifold to 

exchange heat between the cooling plates and the cooling fluid. Because of the high thermal conductivity 

cooling plates, they effectively spread the heat being transferred to the cooling manifold (heat exchanger) 

and will maintain a uniform temperature gradient across their surface. This temperature uniformity is 

maintained even though the inlet coolant flow temperature to the manifold is much lower than the 

manifold exit coolant flow temperature.

Another alternative method to the conventional cooling loop system utilizes the internal fuel cell 

coolant flow channels, as the conventional system does, but operates with a generic cooling loop similar 

to that used with the conductive cooling plate system. The main issue with utilizing an external cooling 

loop to directly cool the fuel cell is the temperature of the cooling fluid into the stack. As with the cooling 

plate system, the coolant flow into the fuel cell can be controlled with a valve regulating it to maintain the 

proper flow rate to maintain an exit temperature set point. However, considering that the coolant loop 

fluid temperature will be around 25 °C and the desired operating temperature of the fuel cell will be 
NASA/TM—2011-216962 2 

approximately 70 °C, the low inlet temperature from the cooling loop will cause a significant temperature 

gradient within the fuel cell from the area where the coolant enters the fuel cell to where it exits. 

The conventional internal cooling system can be simplified to a mostly passive, single fluid system 

through the use of a heat exchanger between the incoming and exiting fluid flow. This heat exchanger 

would increase the temperature or preheat the inlet coolant flow into the fuel cell to maintain a low 

temperature difference across the fuel cell stack. A flow control valve, similar to that of the cooling plate 

system, would control the heat removal from the fuel cell. This concept is shown in Figure 2. 

Figure 1.—Comparison between a conventional fuel cell cooling system and the cooling 

plate based system (Ref. 1). 

Figure 2.—Heat exchanger cooling system concept diagram.

Fuel Cell 

Stack

.

Fluid from Main System

Cooling Loop

Heat

Exchanger

Pump

Controller

Temperature

Sensors

Conventional Cooling

Loop System

Passive Cooling

Plate Based

System

In Out

Out

In

Accumulator

Controller

Flow Control

Valve

Temperature

Sensors

Fuel Cell

Stack

Fluid from Main System

Cooling Loop

Heat

Exchanger

Temperature

Sensors

Passive Heat Exchanger Based

Cooling System

In

Out

Controller

Flow Control

Valve

In

Out
NASA/TM—2011-216962 3 

Figure 3.—Heat exchanger cooling system temperature and flow layout.

Analysis

The effectiveness of the heat exchanger is the key aspect to the feasibility of this concept. Enough 

heat must be transferred from the warm exit coolant to the cool inlet coolant to bring the temperature 

difference between the inlet and outlet coolant flow within the desired fuel cell operating range while 

maintaining sufficient coolant flow rate through the fuel cell and heat exchanger to remove the excess 

heat generated by the fuel cell during operation. 

To evaluate this concept and assess its feasibility, an energy balance approach was utilized. The waste 

heat of the fuel cell adds energy to the coolant flow thus raising the temperature of the coolant flow. This 

flow then passes through the heat exchanger and transfers some of its heat to the incoming coolant flow, 

thereby increasing the fuel cell inlet coolant temperature. The heat transferred by the heat exchanger will 

depend on the effectiveness of the heat exchanger (ε).The heat exchanger effectiveness is a comparison 

between the actual rate of heat transfer between the hot and cold fluids to the maximum possible heat 

transfer rate for an infinitely sized heat exchanger. The flow rate through the fuel cell, and subsequently 

through the heat exchanger, is determined by the desired temperature difference across the fuel cell (∆Tfc) 

and the heat being generated by the fuel cell (Qfc).

Initially, when the fuel cell is turned on and the coolant flow is started, the fuel cell coolant inlet 

temperature (T1) is near that of the heat exchanger inlet coolant temperature (Tc). As the fuel cell operates, 

the fuel cell imparts waste heat into the exit coolant flow before the heat exchanger transfers it to the inlet 

coolant flow. This raises the inlet temperature of the coolant to the fuel cell. Eventually a steady state 

condition develops between the heat exchanger inlet coolant temperature, the fuel cell inlet coolant 

temperature, and nominal fuel cell stack temperature. This process is illustrated in Figure 3. 

The resultant steady state temperature of the fuel cell inlet coolant will depend on the effectiveness of 

the heat exchanger in transferring heat from the fuel cell coolant outlet back to the fuel cell inlet coolant 

flow. To get to the steady state coolant temperature, the analysis is run through a number of steps “i” until 

a steady state is reached. The heat transfer through the heat exchanger, in each step of the process, is 

given by Equation (1) (Ref. 2) 

hei ε= p ( ) 2i−1 −TTcmQ c  (1) 

The coolant mass flow ( m ), given by Equation (2), is set by the desired fuel cell temperature 

difference, heat being produced by the fuel cell and the specific heat of the coolant at STP(cp). 

p fc

fc

Tc

Q

m

∆  = (2) 

T3

Tc

T2

T1

Heat

Exchanger

Fuel Cell

Qhe

Qfc

Ql
NASA/TM—2011-216962 4 

From Equations (1) and (2) the temperature of the coolant into and out of the fuel cell (T1i and T2i

respectively), can be determined for each incremental step in the analysis. These temperatures are given 

by Equations (3) and (4) respectively.

c

p

he T

cm

Q T i

i +=  1 (3) 

i i T

cm

Q T

p

fc

2 += 1  (4) 

The effectiveness of the heat exchanger limits the amount of heat transferred back to the coolant loop. 

Therefore some heat is lost. This heat loss (Qli) and the subsequent exit temperature (T3i) of the coolant 

from the heat exchanger are calculated by Equations (5) and (6) respectively. 

( ) ε−

ε = 1 i

i

he

l

Q Q (5) 

p

l c cm

Q TT i

i  3 += (6) 

The above equations can be combined to provide an expression for the inlet coolant temperature of the 

fuel cell for each time step ‘i’. This provides an expression for the inlet temperature as a function of the 

heat exchanger effectiveness, inlet cooling temperature and temperature difference across the fuel cell 

given in Equation (7) with the initial condition, at i=0, given in Equation (8). The variables used in this 

equation specify the operating conditions for the fuel cell and heat exchanger. 

( ) ( ) ε−++∆ε= − 1 1i fc 1i 1 TTTT c (7) 

1i=0 = TT c (8) 

Equation (7) was solved for heat exchanger effectiveness values that ranged from 40 to 90 percent 

and for various coolant temperatures and difference between the fuel cell inlet and outlet coolant 

temperature. These results are shown in Figures 4 through 6. In these figures, inlet temperature is plotted 

as a function of the time step, which in this case is in seconds. After a number of time steps a steady state 

condition will be reached. 

In the following figures, it can be seen that the rate at which the steady state inlet temperature is 

reached is dependent on the effectiveness of the heat exchanger. The higher the effectiveness, the longer it 

takes to reach a steady state condition. Four cases were shown where variations in the coolant temperature 

and temperature difference were examined. Increasing the coolant loop temperature and/or the 

temperature difference across the fuel cell stack increased the fuel cell coolant inlet temperature. This inturn increases the operating temperature of the fuel cell. 

The steady state inlet temperature defines the operating temperature of the fuel cell once this steady 

state is achieved, for a given heat exchanger effectiveness. Figure 8 shows the effect of coolant 

temperature and fuel cell temperature difference on the steady state temperature for each of the cases 

given in Figures 4 through 7. 
NASA/TM—2011-216962 5 

Figure 4.—Fuel cell inlet temperature with a coolant temperature of 20 °C and 5 °C temperature 

difference across the fuel cell for heat exchanger effectiveness values of 0.4 through 0.9. 

Figure 5.—Fuel cell inlet temperature with a coolant temperature of 20 °C and 7 °C temperature 

difference across the fuel cell for heat exchanger effectiveness values of 0.4 through 0.9. 

Coolant Temp 20°C, Delta T 5°C

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80

Time Step (s)

0.4

0.5

0.6

0.7

0.8

0.9

Coolant Temp 20°C, Delta T 7°C

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80

Time Step (s)

0.4

0.5

0.6

0.7

0.8

0.9
NASA/TM—2011-216962 6 

Figure 6.—Fuel cell inlet temperature with a coolant temperature of 20 °C and 7 °C temperature 

difference across the fuel cell for heat exchanger effectiveness values of 0.4 through 0.9.

Figure 7.—Fuel cell inlet temperature with a coolant temperature of 20 °C and 7 °C temperature 

difference across the fuel cell for heat exchanger effectiveness values of 0.4 through 0.9.

Coolant Temp 25 °C, Delta T 5  °C

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Time Step (s)

0.4

0.5

0.6

0.7

0.8

0.9

Coolant Temp 25°C, Delta T 7°C

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Time Step (s)

0.4

0.5

0.6

0.7

0.8

0.9
NASA/TM—2011-216962 7 

Figure 8.—Steady state maximum fuel cell inlet coolant temperature.

From Figure 8, it can be seen that increasing the coolant temperature and/or the temperature 

difference across the fuel cell can provide a considerable increase in the inlet temperature of the coolant 

and therefore minimum operating temperature of the fuel cell. 

For a minimum operating temperature of 65 °C, the required heat exchanger effectiveness will 

decrease from approximately 0.91 to 0.84 by increasing the coolant loop temperature from 20 to 25 °C 

and increasing the temperature difference across the fuel cell from 5 from 7 °C. 

Heat Exchanger Design

For this concept to be viable, the heat exchanger design must meet the effectiveness requirements 

determined in the previous section. At a minimum, the heat exchanger effectiveness will need to be 0.84 

or higher. This number is dependent on the desired temperature difference within the fuel cell, desired 

operating temperature, and available heat exchanger inlet coolant temperature. A smaller temperature 

difference, lower heat exchanger inlet coolant temperature, or higher fuel cell operating temperature will 

each increase the required heat exchanger effectiveness. 

The heat exchanger design is constrained by the proposed design concept. The cold fluid entering 

the heat exchanger is the same as the hot fluid. Therefore their specific heat values or fluid capacity rates 

(Ch {W/K} for the hot fluid and Cc {W/K} for the cold fluid) are the same as given in Equation (9). 

=1 c

h

C

C (9) 

Heat Exchanger Effectiveness 

Maxmum Inlet Temperature

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Coolant Temp 20 °C, Delta T 5 °C

Coolant Temp 20 °C, Delta T 7 °C

Coolant Temp 25 °C, Delta T 5 °C

Coolant Temp 25 °C, Delta T 7 °C
NASA/TM—2011-216962 8 

For a fluid capacity rate ratio of 1, the theoretical effectiveness for various types of heat exchangers 

are known as a function of the number of heat transfer units (Ntu), given by Equation (10) (Ref. 3). This 

equation is based on the heat exchanger fluid heat transfer surface area (A {m2

}), the thermal conductance 

from one fluid to the next (U, {W/m2

K}), and the fluid capacity rate (C, {W/K}). 

Ntu = AU

C (10) 

The number of heat transfer units is a non-dimensional quantity that expresses the heat transfer 

capability or size of the heat exchanger (Ref. 3), In general the smaller the number of heat transfer units, 

the lower the effectiveness of the heat exchanger. As the value of Ntu increases, the heat transfer 

effectiveness will asymptotically approach a limit based on the heat exchanger configuration. Theoretical 

data on the heat exchanger effectiveness for various types of heat exchangers, given in Reference 1, was 

used to assess their applicability to the heat exchanger requirements for this concept. A number of types 

of heat exchangers were considered. The simplest designs were a counter flow and parallel flow heat 

exchanger. In these designs the hot and cold fluids flow in separate tubes or channels. In the counter flow 

design they flow in opposite directions where as in the parallel design they flow in the same direction, as 

shown in Figures 9 and 10 respectively. 

Figure 9.—Illustration of a counter flow heat exchanger.

Figure 10.—Illustration of a parallel flow heat exchanger.
NASA/TM—2011-216962 9 

A similar design to the counter flow and parallel flow heat exchangers is a cross flow heat exchanger. 

In a cross flow design, the warm fluid enters the heat exchanger 90° from the cold fluid. There are three 

variations of this design approach. The first is where both the hot and cold fluids are unmixed as they 

travel through the heat exchanger in discrete individual passages. All the heat transfer takes place through 

the passage walls. The second type of cross flow heat exchanger is where one of the fluids is allowed to 

mix within a dedicated chamber adjacent to the passages for the second fluid and is not constrained to 

individual passages. And the third variation is where both fluids are in adjacent separate chambers but 

each fluid is allowed to mix and is not constrained to individual passageways. The cross flow heat 

exchanger is illustrated in Figure 11. 

The next type of configuration combines both the parallel and counter flow heat exchangers. Fluid 

enters and exits from the same side of the heat exchanger and follows a U-shaped path within the heat 

exchanger. Part of the flow is counter flow to the cold fluid and part is parallel. The cold fluid is mixed 

and flows over the inner hot fluid tubes contained by an outer shell. This design is illustrated in Figure 12. 

The illustration shows one counter and parallel pass however this type of heat exchanger can be 

constructed with multiple passes through a serpentine path before exiting.

The last heat exchanger configuration, shown in Figure 13, is a split flow type. This configuration is 

similar to the parallel-counter flow design, show in Figure 12, except that the entrance for the cold fluid is 

at the center of the heat exchanger and there are two exits. Portions operate similarly to both parallel and 

counter flow heat exchangers. As with the parallel-counter flow design, the cooling fluid flows in an outer 

shell and is mixed while the warm fluid passes through a U-shaped tube. 

Figure 11.—Illustration of a cross flow heat exchanger and its variations.
NASA/TM—2011-216962 10

Figure 12.—Illustration of a parallel-counter flow, shell mixed heat exchanger.

Figure 13.—Illustration of a split flow, shell mixed heat exchanger.

The heat exchanger effectiveness will differ considerably over a range of Ntu for the different heat 

exchanger geometries, shown in Figures 9 through 13. The heat exchanger effectiveness is given by 

Equation (11) (Ref. 3) for the ratio of hot to cold fluid capacity rates of 1 as given by Equation (9). 

h in c in

coutc in

tt

tt

q

q

,,

,,

max −

− ==ε (11) 

The heat exchanger effectiveness values, for the different types of heat exchangers are given in 

Reference 3. The calculated values for a fluid capacity ratio of 1, were plotted and are shown in 

Figures 14 through 16. Figure 14 shows the effectiveness for counter and parallel flow heat exchangers. 

This includes two design variations that have characteristics of counter and parallel flow designs. Of the 

heat exchanger types shown in Figure 14 the counter flow design provides the highest effectiveness 

values. The effectiveness for the counter flow design exceed the minimum desired effectiveness value of 

0.84 at a Ntu of approximately 6 and reach an effectiveness of 0.9 at an Ntu of 9. The other heat exchanger 

types shown in this figure do not exceed an effectiveness of 0.6 over the range of Ntu shown. 

Figure 15 shows the heat exchanger effectiveness for cross-flow heat exchangers. None of the crossflow heat exchangers, shown in Figure 15, achieve an effectiveness above 0.8, with the cross-flow heat 

exchanger having both fluids unmixed achieving the highest effectiveness of approximately 0.78. 
NASA/TM—2011-216962 11

Figure 14.—Heat exchanger effectiveness for counter and parallel type heat exchangers.

Figure 15.—Heat exchanger effectiveness for cross-flow heat exchangers.
NASA/TM—2011-216962 12

Figure 16.—Heat exchanger effectiveness for multiple-pass cross flow heat exchangers.

Effectiveness values for the last type of heat exchanger are shown in Figure 16. This heat exchanger 

is a combination of counter-flow and cross-flow type heat exchangers. In this type of heat exchanger, the 

headers in which the fluid enters and leaves the heat exchanger operate in a cross-flow manner where as 

the inner core operates in a counter-flow manner. In general, the performance of this type of heat 

exchanger is better than a cross-flow design but not as effective as a pure counter-flow one. 

In practice, it is difficult to construct a true counter flow heat exchanger that has multiple fluid passes. 

Therefore this combination of cross-flow headers with a counter-flow core better represents the 

effectiveness of an actual multi-pass counter-flow heat exchanger. From Figure 16, it can be seen that as 

the cross flow Ntu increases the effectiveness of the heat exchanger increases. The heat exchanger will 

reach an effectiveness of 0.84 at a counter-flow Ntu of approximately 3 or greater depending on the crossflow Ntu. The maximum effectiveness is approximately 0.9. 

The number of heat transfer units required to achieve the desired effectiveness will determine the 

overall size of the heat exchanger. This size is based on the total heat exchange area, A, given by 

Equation (10). The fluid capacity rate, C, is given by Equation (12). 

cmC p =  (12) 

For this design water is used as the cooling fluid. The specific heat of water, cp, varies with the 

temperature of the water (Ref. 4) as shown in Figure 17. However, over the coolant temperature ranges of 

20 to 25 °C inlet and 65 °C outlet, the change in specific heat is minimal. Therefore an average specific 

value of cp = 4,181.3 J/kg K was utilized in the heat exchanger sizing. The coolant mass flow ( m {kg/s}) 

is given by Equation (2) and is determined based on the desired temperature difference across the fuel cell 

and its operating power output. Heat Exchanger Effectiveness
NASA/TM—2011-216962 13

Figure 17.—Specific heat of water as a function of temperature.

The overall thermal conductance of the heat from the warm fluid to the cold fluid (U, {W/m2

K}) is 

given by Equation (13). For this analysis, the heat exchanger wall thickness (a) was assumed to be 1 mm 

and constructed from aluminum with a thermal conductivity of 235 W/mK. 

kw

a

h

U

+ = 2

1 (13) 

Since the hot and cold fluids are the same, the heat transfer coefficient, h, is the same for both. The heat 

transfer coefficient is dependent on the Nusselt number based on diameter (Nu) for the flow, given by 

Equation (14) (Ref. 3). The thermal conductivity of water, kf, at 65 °C is 0.656 W/mK. 

d

k

h

Nu f = (14) 

The value of the Nusselt number will depend on the Reynolds number of the fluid. The Reynolds 

number (Re) is given by Equation (15) (Ref. 3) where d is the diameter of the fluid passage and μ is the 

viscosity of water at 65 °C, (μ =4.53×10–4 N s/m2

). A fluid passage diameter of 1 cm was used in the 

subsequent heat exchanger sizing. The same size passage was used for both the hot and cold passages of 

the heat exchanger. 

4160

4170

4180

4190

4200

4210

4220

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Specific Heat (J/kg-K)

Temperature (°C)
NASA/TM—2011-216962 14

μπ = d

4m Re (15) 

For Reynolds number values below 2,300 with a constant heat flux, the Nusselt number is a constant 

value of 4.36. For Reynolds numbers above 2,300 and below 5×106

, it is given by Equation (16) (Ref. 2). 

The Prandtl number (Pr) is 2.88 for water at 65 °C. 

( )

( 7.1218 ( ) 8 ( ) Pr 1 )

RePr 1000 Nu

2/1 32 + −

− =

f

f (16) 

The friction factor, f, is given by Equation (17) (Ref. 2). 

2 79.0( ln(Re) )64.1 − f = − (17) 

Using the above equations with the specified number of heat transfer units, the heat transfer area, given in 

Equation (10), can be calculated. This area is then used to determine the required size of the heat 

exchanger. The heat exchanger length, L, is given by Equation (18) for a specified number of coolant 

tubes, nt, and the number of passes, np, each tube makes within the heat exchanger. The heat exchanger is 

arranges so that the cold fluid flows through tubes and the hot fluid flows around the tubes in a counter 

flow arrangement. The spacing between the tubes is the same as the tube diameter. 

t pndn

A L

π = (18) 

The thickness of the heat exchanger, t, is given by Equation (19). The thickness is dependent on the 

number of stacked tubes, ns, in the thickness direction. 

( ) ndt s += 12 (19) 

The final heat exchanger dimension, the width, w, is given by Equation (20). 















 = +1

2

s

pt

n

nn

dw (20) 

Specifying the tube diameter, number of tubes, passes per tube and how they are stacked will 

establish the thickness and width of the heat exchanger. The length will vary as a function of the required 

heat exchange surface area. These values and the subsequent heat exchanger length and width are given in 

Table 1. 

TABLE 1.—HEAT EXCHANGER LAYOUT SPECIFICATIONS

Variable Value

Tube diameter....................................................................1 cm

Number of coolant tubes....................................................... 35

Number of passes per tube...................................................... 2 

Stacked number of tubes......................................................... 4 

Heat exchanger thickness...................................................9 cm

Heat exchanger width ......................................................36 cm
NASA/TM—2011-216962 15

Using the values specified in Table 1 for the heat exchanger, the required heat exchanger length was 

plotted as a function of the power being dissipated by the fuel cell for various temperature differences 

across the fuel cell. Graphs were produced for Ntu values of 6 through 10, shown in Figures 18 through 22 

respectively.

Figure 18.—Required heat exchanger length for Ntu of 6. 

Figure 19.—Required heat exchanger length for Ntu of 7. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Heat Exchanger Length (m)

Thermal Power (W)

Ntu = 6 Delta T=3

Delta T=4

Delta T=5

Delta T=6

Delta T=7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Heat Exchanger Length (m)

Thermal Power (W)

Ntu=7 Delta T=3

Delta T=4

Delta T=5

Delta T=6

Delta T=7
NASA/TM—2011-216962 16

Figure 20.—Required heat exchanger length for Ntu of 8. 

Figure 21.—Required heat exchanger length for Ntu of 9. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Heat Exchanger Length (m)

Thermal Power (W)

Ntu=8 Delta T=3

Delta T=4

Delta T=5

Delta T=6

Delta T=7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Heat Exchanger Length (m)

Thermal Power (W)

Ntu=9 Delta T=3

Delta T=4

Delta T=5

Delta T=6

Delta T=7
NASA/TM—2011-216962 17

Figure 22.—Required heat exchanger length for Ntu of 10. 

The required heat exchanger length results, shown in Figures 18 through 22, follow the same general 

pattern with increasing thermal power. For a given thermal power level and fuel cell temperature 

difference (delta T), the required length increases with increasing Ntu, as would be expected. At low 

thermal power levels, near or below 350 W, the required heat exchanger length increases significantly. 

This is due to the low mass flow rates required at these power levels, which in turn causes the flow 

through the heat exchanger to be laminar. To avoid this, a smaller heat exchanger tube diameter could be 

used to increase the Reynolds number of the flow at the lower power levels. This would induce turbulent 

flow thereby significantly increasing the heat transfer within the heat exchanger and reducing the required 

heat exchanger length at the lower thermal power levels. 

At thermal power levels beyond 350 W, the required heat exchanger length increases linearly with 

increasing thermal power. The slope of this increase is low and the slop decreases with increasing 

temperature difference across the fuel cell. The lower the required temperature difference across the fuel 

cell, the greater the heat exchanger length. This is expected since the smaller the temperature difference 

across the fuel cell is achieved by increasing the inlet fluid temperature, which requires a larger heat 

exchanger area. 

Summary and Conclusion

The analysis has shown that for high heat exchanger effectiveness values, greater then 0.84, the 

concept of preheating the incoming coolant with the heated exit coolant can achieve and maintain both a 

fuel cell operating temperature of 65 °C and a minimum temperature difference across the fuel cell. The 

achievable fuel cell operating temperature was highly dependent on the heat exchanger inlet coolant fluid 

temperature and allowable temperature difference across the fuel cell. For a heat exchanger effectiveness 

of 0.9, changes in inlet coolant temperature of 5 °C (from 20 to 25 °C) and a change in the allowable 

temperature difference across the fuel cell of 2 °C (from 5 to 7 °C) increased the steady state operating 

temperature of the fuel cell from 65 to 88 °C. 

The steady state operating temperature was achieved fairly quickly for the cases analyzed. As would 

be expected, the lower the effectiveness of the heat exchanger, the lower the steady state temperature and 

the more quickly it would achieve this temperature. The time to achieve steady state ranged from 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Heat Exchanger Length (m)

Thermal Power (W)

Ntu=10 Delta T=3

Delta T=4

Delta T=5

Delta T=6

Delta T=7
NASA/TM—2011-216962 18

approximately 5 sec for a heat exchanger effectiveness of 0.4 to approximately 35 sec for a heat 

exchanger with an effectiveness of 0.9. 

To achieve the high heat exchanger effectiveness values desired, a number of different heat exchanger 

configurations were considered as shown in Figures 9 through 13. Of these configurations, a counter flow 

type arrangement was the only configuration that could achieve the required effectiveness range, as 

shown in Figures 14 and 16. From these figures, it can be seen that the number of heat transfer units for 

the heat exchanger need to be at least 6 and more likely 9 or 10 depending on the operating requirements. 

With a Ntu of 9, and the design point values given in Table 1, the dimensions of the heat exchanger would 

be approximately 0.09- by 0.36- by 0.35-m with a volume of 0.011 m3

. If a cross flow heat exchanger 

could be constructed with the desired effectiveness, the required heat exchanger size is reasonable. 

This analysis suggests that utilizing a regenerative heat exchanger to maintain the operating 

temperature and temperature difference within a fuel cell is feasible and worth further study. However, 

the required high heat exchanger effectiveness indicates that significant heat exchanger design, 

development, and optimization would be required to produce a system that can meet the desired goals 

under real world operational conditions. 

References

1. Colozza, A.J. and Burke, K.A., “Fuel Cell Thermal Management Through Conductive Cooling 

Plates,” NASA/TM—2008-215149, May 2008. 

2. Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons 

Publisher, 1990. 

3. Kays, W.M. and London, A.L., Compact Heat Exchangers, McGraw-Hill Publisher, 1984. 

4. The Engineering Toolbox, Water-Thermal Properties, www.EngineeringToolBox.com, October 2009. 
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4. TITLE AND SUBTITLE

Evaluation of a Passive Heat Exchanger Based Cooling System for Fuel Cell Applications 

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6. AUTHOR(S)

Colozza, Anthony, J.; Burke, Kenneth, A. 

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WBS 038957.04.06.02.02.03 

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John H. Glenn Research Center at Lewis Field 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Fuel cell cooling is conventionally performed with an actively controlled, dedicated coolant loop that exchanges heat with a separate 

external cooling loop. To simplify this system the concept of directly cooling a fuel cell utilizing a coolant loop with a regenerative heat 

exchanger to preheat the coolant entering the fuel cell with the coolant exiting the fuel cell was analyzed. The preheating is necessary to 

minimize the temperature difference across the fuel cell stack. This type of coolant system would minimize the controls needed on the 

coolant loop and provide a mostly passive means of cooling the fuel cell. The results indicate that an operating temperature of near or greater 

than 70 °C is achievable with a heat exchanger effectiveness of around 90 percent. Of the heat exchanger types evaluated with the same type 

of fluid on the hot and cold side, a counter flow type heat exchanger would be required which has the possibility of achieving the required 

effectiveness. The number of heat transfer units required by the heat exchanger would be around 9 or greater. Although the analysis 

indicates the concept is feasible, the heat exchanger design would need to be developed and optimized for a specific fuel cell operation in 

order to achieve the high effectiveness value required. 

15. SUBJECT TERMS

Cooling systems; Fuel cells; Heat exchangers 

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