Lecture 4 - dA c = differential surface area = P dx An...

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Lecture Notes 4 Dr. Srinath Ekkad
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Thermal Energy Generation Processes within the medium may cause energy to be converted to thermal energy 1. Electrical Resistance Heating Electrical energy Thermal energy = Rate of energy generated (W) = I 2 R e = Volumetric generation rate (W/m 3 ) = I 2 R e /Volume 1. Nuclear Fission Nuclear bonding energy thermal energy Nuclear absorption and deceleration in fuel element 1. Chemical bonding energy thermal energy Exothermic reactions act as heat source Endothermic reactions act as heat sink
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Plane wall with heat generation x 0 L T s T s -L T(x) q . T s -L 0 L q = 0 . T o
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Cylinder with heat generation T(r) q . r r o 0 T s T(r) q=0 . r r o 0 T s T o
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Extended Surfaces - Fins Fins increase the effective heat transfer area and enhance heat transfer Many heat exchangers use fins to enhance heat transfer Heat transfer analysis of fins Assumptions 1-D along the fin (x-direction only) Steady state Constant properties Negligible radiation No heat generation Constant h
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A c = cross-sectional area P = perimeter
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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 / b FIN HEAT TRANSFER RATE q fin A Convection heat transfer: h L kd dx x L ( ) / = -= 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 / = = cosh ( ) cosh m L x mL-M tanh mL C Prescribed temperature: (L) = L ( 29 L b mx m L x mL / sinh sinh ( ) sinh +-M mL mL L b (cosh / ) sinh- D Infinite fin (L ): (L) = 0 Exp(-mx) M Fin Effectiveness, 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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This note was uploaded on 03/30/2008 for the course ME 3304 taught by Professor Stern during the Spring '08 term at Virginia Tech.

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Lecture 4 - dA c = differential surface area = P dx An...

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