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Unformatted text preview: • dA c = differential surface area = P dx An energy balance across the differential element is given as: x dq conv A c dA s dx Fluid T ∞ , h q cond,x q cond,x+dx Heat gain by Conduction = Heat loss by Convection CASE TIP CONDITION (x = L) TEMPERATURE DISTRIBUTION θ / θ b FIN HEAT TRANSFER RATE q fin A Convection heat transfer: h L kd dx x L θ θ ( ) / = = cosh ( ) ( / ) sinh ( ) cosh ( / ) sinh m L x h mk m L x mL h mk mL++ M mL h mk mL mL h mk mL sinh ( / ) cosh cosh ( / ) sinh + + B Adiabatic: d dx x L θ / = = cosh ( ) cosh m L x mLM tanh mL C Prescribed temperature: θ (L) = θ L ( 29 θ θ L b mx m L x mL / sinh sinh ( ) sinh +M mL mL L b (cosh / ) sinh θ θ D Infinite fin (L → ∞ ): θ (L) = 0 Exp(mx) M Fin Effectiveness, ε f , is defined as the ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin....
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 Spring '08
 STERN
 Thermodynamics, Heat, Heat Transfer, heat sink, cosh mL

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