A novel scheme for dissipating heat from the chips ofa

Chapter 8, Problem 8.113

(choose chapter or problem)

A novel scheme for dissipating heat from the chips ofa multichip array involves machining coolant channelsin the ceramic substrate to which the chips areattached. The square chips (Lc?5 mm) are alignedabove each of the channels, with longitudinal andtransverse pitches of SL?ST?20 mm. Water flowsthrough the square cross section (W?5 mm) of eachchannel with a mean velocity of um?1 m/s, and itsproperties may be approximated as ??1000 kg/m3,cp?4180 J/kg?K, ??855?10?6kg/s?m, k?0.610W/m?K, and Pr?5.8. Symmetry in the transversedirection dictates the existence of equivalent conditionsfor each substrate section of length Lsand width ST.(a) Consider a substrate whose length in the flowdirection is Ls?200 mm, thereby providing atotal of NL?10 chips attached in-line above eachflow channel. To a good approximation, all theheat dissipated by the chips above a channel maybe assumed to be transferred to the water flowingthrough the channel. If each chip dissipates 5 W,what is the temperature rise of the water passingthrough the channel?(b) The chip-substrate contact resistance is Rt,c?0.5?10?4m2?K/W, and the three-dimensionalconduction resistance for the Ls?STsubstratesection is Rcond?0.120 K/W. If water enters thesubstrate at 25C and is in fully developed flow,estimate the temperature Tcof the chips and thetemperature Tsof the substrate channel surface.