A silicon chip is cooled by passing water through microchannels etched in the back of the chip, as shown in Fig. P8–106. The channels are covered with a silicon cap. Consider a 10-mm × 10-mm-square chip in which N = 50 rectangular microchannels, each of width W = 50 mm and height H = 200 mm have been etched. Water enters the microchannels at a temperature T_i = 290 K, and a total flow rate of 0.005 kg/s. The chip and cap are maintained at a uniform temperature of 350 K. Assuming that the flow in the channels is fully developed, all the heat generated by the circuits on the top surface of the chip is transferred to the water, and using circular tube correlations, determine:

(a) The water outlet temperature, T_e
(b) The chip power dissipation, Ẇ_e

Evaluate liquid water properties at a bulk mean temperature of 298 K. Is this a good assumption?

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Circuits generating power W H 10 mm W T₁ ***** 10 mm Te Chip, T Cap, Ts