A common procedure for cooling a high-performance computer

Chapter , Problem 8.55

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A common procedure for cooling a high-performance computer chip involves joining the chip to a heat sink within which circular microchannels are machined. During operation, the chip produces a uniform heat flux at its interface with the heat sink, while a liquid coolant (water) is routed through the channels. Consider a square chip and heat sink, each L on a side, with microchannels of diameter D and pitch S C1D, where the constant C1 is greater than unity. Water is supplied at an inlet temperature Tm,i and a total mass flow rate (for the entire heat sink). (a) Assuming that is dispersed in the heat sink such that a uniform heat flux is maintained at the surface of each channel, obtain expressions for the longitudinal distributions of the mean fluid, Tm(x), and surface, Ts(x), temperatures in each channel. Assume laminar, fully developed flow throughout each channel, and express your results in terms of m . , q c, C1, D, and/or L, as well as appropriate thermophysical properties. (b) For L 12 mm, D 1 mm, C1 2, q c 20 W/cm2 , m . 0.010 kg/s, and Tm,i 290 K, compute and plot the temperature distributions Tm(x) and Ts(x). (c) A common objective in designing such heat sinks is to maximize while maintaining the heat sink at an acceptable temperature. Subject to prescribed values of L 12 mm and Tm,i 290 K and the constraint that Ts,max 50 C, explore the effect on of variations in heat sink design and operating conditions. 8.56