Consider the microchannel cooling arrangement of .107.

Chapter 8, Problem 8.109

(choose chapter or problem)

Consider the microchannel cooling arrangement of 8.107. However, instead of assuming theentire chip and cap to be at a uniform temperature,adopt a more conservative (and realistic) approach thatprescribes a temperature of Ts?350 K at the base ofthe channels (x?0) and allows for a decrease in tem-perature with increasing xalong the side walls of eachchannel.(a) For the operating conditions prescribed in Problem8.107 and a chip thermal conductivity of kch?140 W/m?K, determine the water outlet tempera-ture and the chip power dissipation. Heat transferfrom the sides of the chip to the surroundings andfrom the side walls of a channel to the cap may beneglected. Note that the spacing between channels,??S?W, is twice the spacing between the sidewall of an outer channel and the outer surface ofthe chip. The channel pitch is S?L/N, whereL?10 mm is the chip width and N?50 is thenumber of channels.(b) The channel geometry prescribed in Problem8.107 and considered in part (a) is not optimized,and larger heat rates may be dissipated by adjust-ing related dimensions. Consider the effect ofreducing the pitch to a value of S?100?m,while retaining a width of W?50 ?m and a flowrate per channel of m?1?10?4kg/s