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Thermodynamics HW Solutions 285

# Thermodynamics HW Solutions 285 - Chapter 3 Steady Heat...

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Chapter 3 Steady Heat Conduction 3-174 A hot plate is to be cooled by attaching aluminum fins of square cross section on one side. The number of fins needed to triple the rate of heat transfer is to be determined. Assumptions 1 Steady operating conditions exist. 2 The temperature along the fins varies in one direction only (normal to the plate). 3 Heat transfer from the fin tips is negligible. 4 The heat transfer coefficient is constant and uniform over the entire fin surface. 5 The thermal properties of the fins are constant. 6 The heat transfer coefficient accounts for the effect of radiation from the fins. Properties The thermal conductivity of the aluminum fins is given to be k = 237 W/m °C. Analysis Noting that the cross-sectional areas of the fins are constant, the efficiency of the square cross- section fins can be determined to be 1 - 2 2 2 m 99 . 12 m) 002 . 0 )( C W/m. 237 ( m) 002 . 0 C)( . W/m 20 ( 4 4 = ° ° = = = ka ha kA hp a c 919 . 0 m 04 . 0 m 99 . 12 ) m 04 . 0 m 99 . 12 tanh( tanh 1 - -1 fin = × × = = η aL aL The finned and unfinned surface areas, and heat transfer rates from these areas are W 0048 . 0 36 C ) 25 85 )( m 000004 . 0 0.03 )( C . W/m 20 ( ) ( W 35328 . 0 C ) 25 85 )( m 0.00032
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