A volumetrically heated plate that is 10 cm wide, 10 cm tall, and 5 mm in thickness is sandwiched between two insulating layers, each 5 mm thick. The plate is to be cooled by air flow through parallel...

A volumetrically heated plate that is 10 cm wide, 10 cm tall, and 5 mm in thickness is sandwiched between two insulating layers, each 5 mm thick. The plate is to be cooled by air flow through parallel microchannels. The air flow is caused by a fan that causes the pressure at the inlet to the microchannels to be 100 Pa larger than the pressure at the exhaust end of the channels. The channels exhaust into atmospheric air. The inlet air is at 298 K temperature. Based on design considerations, the porosity of the plate is not to exceed 25%. The plate is made of a high-thermal-conductivity material and can be assumed to remain isothermal at 363 K. Assuming uniform-size, parallel cylindrical micorchannels with hydraulic diameters in the 50-μm to 1-mm range, calculate the maximum thermal load that can be disposed by the cooling air. Based on these calculations, determine the optimum coolant channel diameter. For simplicity, you may use heat transfer coefficients representing thermally developed flow.