A novel scheme for dissipating heat from the chips of a

Chapter , Problem 8.113

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A novel scheme for dissipating heat from the chips of a multichip array involves machining coolant channels in the ceramic substrate to which the chips are attached. The square chips (Lc 5 mm) are aligned above each of the channels, with longitudinal and transverse pitches of SL ST 20 mm. Water flows through the square cross section (W 5 mm) of each channel with a mean velocity of um 1 m/s, and its properties may be approximated as 1000 kg/m3 , cp 4180 J/kg K, 855 106 kg/sm, k 0.610 W/mK, and Pr 5.8. Symmetry in the transverse direction dictates the existence of equivalent conditions for each substrate section of length Ls and width ST. (a) Consider a substrate whose length in the flow direction is Ls 200 mm, thereby providing a total of NL 10 chips attached in-line above each flow channel. To a good approximation, all the heat dissipated by the chips above a channel may be assumed to be transferred to the water flowing through the channel. If each chip dissipates 5 W, what is the temperature rise of the water passing through the channel? (b) The chip-substrate contact resistance is R t,c 0.5 104 m2 K/W, and the three-dimensional conduction resistance for the Ls ST substrate section is Rcond 0.120 K/W. If water enters the substrate at 25 C and is in fully developed flow, estimate the temperature Tc of the chips and the temperature Ts of the substrate channel surface. 8.114 Conside