A cold plateis an active cooling device that is attachedto

Chapter 8, Problem 8.82

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A cold plateis an active cooling device that is attachedto a heat-generating system in order to dissipate theheat while maintaining the system at an acceptable tem-perature. It is typically fabricated from a material ofhigh thermal conductivity, kcp, within which channelsare machined and a coolant is passed. Consider a cop-per cold plate of height Hand width Won a side, withinwhich water passes through square channels of widthw?h. The transverse spacing between channels ?istwice the spacing between the sidewall of an outerchannel and the sidewall of the cold plate.Consider conditions for which equivalentheat-generatingsystems are attached to the top and bottom of the coldplate, maintaining the corresponding surfaces at the sametemperature Ts. The mean velocity and inlet temperatureof the coolant are umand Tm,i, respectively.(a) Assuming fully developed turbulent flow throughouteach channel, obtain a system of equations that maybe used to evaluate the total rate of heat transfer tothe cold plate, q, and the outlet temperature of thewater, Tm,o, in terms of the specified parameters.(b) Consider a cold plate of width W?100 mm andheight H?10 mm, with 10 square channels of widthw?6 mm and a spacing of ??4 mm betweenchannels. Water enters the channels at a tempera-ture of Tm,i?300 K and a velocity of um?2 m/s. If the top and bottom cold plate surfaces are atTs?360 K, what is the outlet water temperature andthe total rate of heat transfer to the cold plate? Thethermal conductivity of the copper is 400 W/m?K,while average properties of the water may be takento be ??984 kg/m3, cp?4184 J/kg?K, ??489?10?6N?s/m2, k?0.65 W/m?K, and Pr?3.15. Isthis a good cold plate design? How could its perfor-mance be improved?