An extremely effective method of cooling high-power density silicon chips involves etching micro-channels, in the back (non-circuit) surface of the chip. The channels are covered with a silicon cap and cooling is maintained by passing water through the channels.

Consider a chip that is 10 mm by 10 mm on a side and in which fifty 10-mm-Iong rectangular micro-channels, each of width W = 50μm and height H = 200μm, have been etched. Consider operating conditions for which water enters each micro-channel at a temperature of 290 K and a flow rate of 10- 4 kg/s, while the chip and cap are at a uniform temperature of 350 K. Assuming fully developed flow in the channel and that all the heat dissipated by the circuits is transferred to the water, determine the water outlet temperature and the chip power dissipation. Water properties may be evaluated at 300 K.

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Circuits Chip. T, Microcharnels Cap, T,