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 in thickness. The plate is to be cooled by airflow through...

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 in thickness. The plate is to be cooled by airflow through parallel microchannels. The airflow is caused by a fan which causes the pressure at 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-sized parallel cylindrical micorchannels with hydraulic diameters in the 50 μm to 1 mm, 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.