problem4-27 - PROBLEM 4.27 KNOWN Disc-shaped electronic...

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PROBLEM 4.27 KNOWN : Disc-shaped electronic devices dissipating 100 W mounted to aluminum alloy block with prescribed contact resistance. FIND: (a) Temperature device will reach when block is at 27 ° C assuming all the power generated by the device is transferred by conduction to the block and (b) For the operating temperature found in part (a), he permissible operating power with a 30-pin fin heat sink. t SCHEMATIC: ASSUMPTIONS: (1) Two-dimensional, steady-state conduction, (2) Device is at uniform temperature, 1 , (3) Block behaves as semi-infinite medium. T P ROPERTIES: Table A.1 , Aluminum alloy 2024 (300 K): k = 177 W/m K. ANALYSIS: (a) The thermal circuit for the conduction heat flow between the device and the block hown in the above Schematic where R s e is the thermal contact resistance due to the epoxy-filled interface, ( ) 2 e t,c c t,c R R A R D 4 π ′′ ′′ = = ( ) ( ) 2 5 2 e R 5 10 K m W 0.020m 4 0.159K W π = × = The thermal resistance between the device and the block is given in terms of the conduction shape factor, able 4.1, as T ( ) b
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