problem4-31 - PROBLEM 4.31 KNOWN: Dimensions of chip array....

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PROBLEM 4.31 KNOWN: Dimensions of chip array. Conductivity of substrate. Convection conditions. Contact esistance. Expression for resistance of spreader plate. Maximum chip temperature. r F IND: Maximum chip heat rate. SCHEMATIC: ASSUMPTIONS: (1) Steady-state, (2) Constant thermal conductivity, (3) Negligible radiation, (4) All heat transfer is by convection from the chip and the substrate surface (negligible heat transfer from ottom or sides of substrate). b ANALYSIS: From the thermal circuit, () hh hs p h,cnv t,c sp,cnv tsp TT qq q RR R R ∞∞ −− =+ = + ++ ( ) 1 1 1 2 22 h,cnv s,h h R h A hL 100W / m K 0.005m 400K / W ⎡⎤ == = = ⎢⎥ ⎣⎦ ( ) 357 rrrr sub h 1 1.410A 0.344A 0.043A 0.034A 1 0.353 0.005 0 0 R 0.408K / W 4k L 4 80 W / m K 0.005m −+ + + + + + = 42 h R 0.5 10 m K / W R 2.000K / W L 0.005m ′′ ×⋅ = ( ) 1 1 2 sp,cnv sub s,h R h A A
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