A common procedure for cooling a high-performancecomputer

Chapter 8, Problem 8.55

(choose chapter or problem)

A common procedure for cooling a high-performancecomputer chip involves joining the chip to a heat sinkwithin which circular microchannels are machined.During operation, the chip produces a uniform heatflux at its interface with the heat sink, while a liquidcoolant (water) is routed through the channels. Con-sider a square chip and heat sink, each Lon a side,with microchannels of diameter Dand pitch S?C1D,where the constant C1is greater than unity. Water is supplied at an inlet temperature Tm,iand a total massflow rate (for the entire heat sink).(a) Assuming that is dispersed in the heat sink suchthat a uniform heat flux is maintained at the sur-face of each channel, obtain expressions for thelongitudinal distributions of the mean fluid, Tm(x),and surface, Ts(x), temperatures in each channel.Assume laminar, fully developed flow throughouteach channel, and express your results in terms ofm., qc, C1, D, and/or L, as well as appropriate ther-mophysical properties.(b) For L?12 mm, D?1 mm, C1?2, qc?20 W/cm2,m.?0.010 kg/s, and Tm,i?290 K, compute and plotthe temperature distributions Tm(x) and Ts(x).(c) A common objective in designing such heat sinksis to maximize while maintaining the heat sink atan acceptable temperature. Subject to prescribedvalues of L?12 mm and Tm,i?290 K and theconstraint that Ts,max?50C, explore the effect onof variations in heat sink design and operatingconditions