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Unformatted text preview: Chapter 3 Steady Heat Conduction 3-164 A circuit board houses electronic components on one side, dissipating a total of 15 W through the backside of the board to the surrounding medium. The temperatures on the two sides of the circuit board are to be determined for the cases of no fins and 20 aluminum fins of rectangular profile on the backside. Assumptions 1 Steady operating conditions exist. 2 The temperature in the board and along the fins varies in one direction only (normal to the board). 3 All the heat generated in the chips is conducted across the circuit board, and is dissipated from the backside of the board. 4 Heat transfer from the fin tips is negligible. 5 The heat transfer coefficient is constant and uniform over the entire fin surface. 6 The thermal properties of the fins are constant. 7 The heat transfer coefficient accounts for the effect of radiation from the fins. Properties The thermal conductivities are given to be k = 12 W/m C for the circuit board, k = 237 W/m C for the aluminum plate and fins, and k = 1.8 W/m C for the epoxy adhesive. Analysis ( a ) The thermal resistance of the board and the convection resistance on the backside of the board are R L kA R hA R R R board conv total board conv m W / m. C) m m C / W W / m. C) m m C / W C / W = = = = = = = + = + = 0002 12 01 015 0011 1 1 45 01 015 1481 0011 1481 1492 . ( ( . )( . ) . ( ( . )( . ) . . . . Then surface temperatures on the two sides of the circuit board becomes . Q T T R T T QR Q T T R T T QR =- = + = + = =- =- = - = 1 1 1 2 2 1 37 594 total total board board C ( W)( . 15 1 4 92 C / W) C ( W)( . 15 0 0 11 C / W) . 594 C . 592 C ( b ) Noting that the cross-sectional areas of the fins are constant, the efficiency of these rectangular fins is determined to be 1- 2 m 78 . 13 ) m 002 . )( C W/m. 237 ( ) C . W/m 45 ( 2 2 ) ( ) 2 ( = = = 2245 = kt h tw k w h kA hp a c fin- 1- 1 m m m m = = = tanh tanh( . . ) . . . aL aL 1378 002 1378 002 0975 The finned and unfinned surface areas are 2 unfinned 2 finned m 0090 . ) 15 . )( 002 . ( 20 ) 15 . )( 1 . ( m . 0 126 = 2 002 . 02 . ) 15 . ( 2 ) 20 ( 2 2 ) 20 ( =- = + = + = A t L w A Then, ( ) ( ( )( ) Q Q hA T T Q hA T T Q Q Q h T T A A finned fin fin,max fin fin base unfinned unfinned base total unfinned finned base fin fin unfinned ) = =- =- = + =- + Substituting, the base temperature of the finned surfaces is determined to be C . 395 = + = + + = )] m 0090 . ( ) m 126 . )( 975 . )[( C . W/m 45 ( W 15 + C 37 ) ( 2 2 2 unfinned fin fin total base A A h Q T T 3-117 2 cm R aluminum T 1 R board T R epoxy R board T 1 T R conv T 2 Chapter 3 Steady Heat Conduction Then the temperatures on both sides of the board are determined using the thermal resistance network to be R L kA R L kA aluminum epoxy m W / m. C)W / m....
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