The power needed to overcome wind and friction drag associated with an automobile traveling at a constant velocity of 25 m/s is 9 kW.

(a) Determine the required heat transfer area of the radiator if the vehicle is equipped with an internal combustion engine operating at an efficiency of 35%. (Assume 65% of the energy generated by the engine is in the form of waste heat removed by the radiator.) The inlet and outlet mean temperatures of the water with respect to the radiator are T_m,i = 400 K and T_m,0 = 330 K, respectively. Cooling air is available at 3 kg/s and 300 K. The radiator may be analyzed as a cross-flow heat exchanger with both fluids unmixed with an overall heat transfer coefficient of 400 W/m² ∙ K.

(b) Determine the required water mass flow rate and heat transfer area of the radiator if the vehicle is equipped with a fuel cell operating at 50% efficiency. The fuel cell operating temperature is limited to approximately 85°C, so the inlet and outlet mean temperatures of the water with respect to the radiator are T_m,i = 355 K and T_m,0 = 330 K. respectively. The air inlet temperature is as in part (a). Assume the flow rate of air is proportional to the surface area of the radiator.

(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 flow rate of the water is the same as in part (a).