Thermodynamics HW Solutions 276

Thermodynamics HW Solutions 276 - Chapter 3 Steady Heat...

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Chapter 3 Steady Heat Conduction ( b ) Noting that the cross-sectional areas of the fins are constant, the efficiency of these rectangular fins is determined to be 2 cm 1 - 2 m 80 . 10 ) m 002 . 0 )( C W/m. 386 ( ) C . W/m 45 ( 2 2 ) ( ) 2 ( = ° ° = = = kt h tw k w h kA hp a c η fin -1 -1 m m m == × × = tanh tanh( . . ) .. . aL aL 1080 0 02 0 02 0985 The finned and unfinned surface areas are 2 unfinned 2 finned m 0090 . 0 ) 15 . 0 )( 002 . 0 ( 20 ) 15 . 0 )( 1 . 0 ( m 0.126 = 2 002 . 0 02 . 0 ) 15 . 0 ( 2 ) 20 ( 2 2 ) 20 ( = = + = + = A t L w A Then, && () & ( & ( QQ h A T T Qh A T T Q h T T A A finned fin fin,max fin fin base unfinned unfinned base total unfinned finned base fin fin unfinned ) =− =+ = + ηη ) Substituting, the base temperature of the finned surfaces determine to be C 39.5 ° = + ° ° = + + = )] m 0090 . 0 ( ) m 126 . 0 )( 985 . 0 )[( C . W/m 45 ( W 15 + C 37 ) ( 2 2 2 unfinned fin fin total base A A h Q T T & R R R epoxy board copper T T 1 Then the temperatures on both sides of the board are determined using the thermal resistance network to be
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