Thermodynamics HW Solutions 228

Thermodynamics HW Solutions 228 - Chapter 15 Steady Heat...

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Chapter 15 Steady Heat Conduction 3-110 Circular aluminum fins are to be attached to the tubes of a heating system. The increase in heat transfer from the tubes per unit length as a result of adding fins is to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat transfer coefficient is constant and uniform over the entire fin surfaces. 3 Thermal conductivity is constant. 4 Heat transfer by radiation is negligible. Properties The thermal conductivity of the fins is given to be k = 186 W/m °C. Analysis In case of no fins, heat transfer from the tube per meter of its length is 180 ° C 25 ° C AD L Qh A T T b no fin 2 no fin no fin 22 m m m W / m C m C W == = =− = ° ° = ππ 1 0 05 1 01571 40 01571 180 25 974 (. ) ( ) . & () ( . ) ( . ) ( ) The efficiency of these circular fins is, from the efficiency curve, 97 . 0 08 . 0 m) C)(0.001 W/m 186 ( C W/m 40 2 001 . 0 005 . 0 2 22 . 1 0.025 ) 2 / 001 . 0 ( 03 . 0 ) 2 / ( m 005 . 0 2 / ) 05 . 0 06 . 0 ( 2 / ) ( fin o o 2 1 2 1 2 = η = + = + = + = + = = = kt h t L r t r D D L Heat transfer from a single fin is W 53 . 11 C ) 25 180 )( m 001916 . 0 )( C . W/m 40 ( 97 . 0 ) ( m 001916 .
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