Chapter 11, Problem 11.74P

The power needed to overcome wind and friction dragassociated with an automobile traveling at a constantvelocity of $\text{25 m/s}$ is $\text{9 kW}$ .
(a) Determine the required heat transfer area of theradiator if the vehicle is equipped with an internalcombustion engine operating at an efficiency of $\text{21\%}$ . (Assume $\text{79\%}$ of the energy generated bythe engine is in the form of waste heat removedby the radiator.) The inlet and outlet mean temperatures of the water with respect to the radiator are ${\text{T}}_{m,i}\text{=400 K}$ and ${\text{T}}_{m,o}\text{=330 K}$ , respectively. Cooling air is available at $\text{3 Kg/s}$ and $\text{300 K}$ . The radiator may be analyzed as a cross-flow heat exchangerwith both fluids unmixed with an overall heattransfer coefficient of ${\text{400 W/m}}^2\cdot \text{K}$ .
(b) Determine the required water mass flow rate andheat transfer area of the radiator if the vehicle isequipped with a fuel cell operating at $\text{50\%}$ efficiency. The fuel cell operating temperature islimited to approximately $\text{85\%}$ , so the inlet andoutlet mean temperatures of the water with respectto the radiator are ${\text{T}}_{m,i}\text{=355 K}$ and ${\text{T}}_{m,o}\text{=330 K}$ , respectively. The air inlet temperature is as in part(a). Assume the flow rate of air is proportional tothe surface area of the radiator. Hint: Iteration isrequired.(c) Determine the required heat transfer area of the radiator and the outlet mean temperature of the water for the fuel cell—equipped vehicle if the mass flowrate of the water is the same as in part (a).