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Problem 4.30. 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 air flow

through parallel microchannels. The air flow 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-size 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.

Fig: 1