problem4-28 - PROBLEM 4.28 KNOWN Dimensions and surface...

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PROBLEM 4.28 KNOWN: Dimensions and surface temperatures of a square channel. Number of chips mounted on outer surface and chip thermal contact resistance. F IND: Heat dissipation per chip and chip temperature. SCHEMATIC: ASSUMPTIONS: (1) Steady state, (2) Approximately uniform channel inner and outer surface temperatures, (3) Two-dimensional conduction through channel wall (negligible end-wall effects), (4) Constant thermal conductivity. ANALYSIS: The total heat rate is determined by the two-dimensional conduction resistance of the channel wall, q = (T 2 – T 1 )/R t,cond(2D) , with the resistance determined by using Equation 4.21 with Case 1 of Table 4.1. For W/w = 1.6 > 1.4 1 ( ) ( ) t,cond(2D) 0.930 ln W / w 0.050 0.387 R 0.00160 K / W 2 L k 2 0.160m 240 W / m K π π = = = T he heat rate per chip is then ( ) ( ) ( ) 2 1 c t,cond 2D 50 20 C T T q 156.3 W N R 120 0.0016 K / W ° = = = < a nd, with q
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