Chapter5 - ChEn 323 Chapter 5 Page 1 Our treatment of...

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Unformatted text preview: ChEn 323 Chapter 5 Page 1 Our treatment of steady state conduction has been one of increasing complexity, e.g., 1-D steady state and then 2-D steady state. We now move to transient analysis. Transient conditions are created by changing driving forces. When temperature gradients are small, the lumped capacitance method works just fine. Introduction to Transient Conduction ChEn 323 Chapter 5 Page 2 Summary of Topics The Lumped Capacitance Method Validity of the Lumped Capacitance Method Spatial Effects Exact Solutions Approximate Solution Total Energy Transfer Radial System with Convection Approximate Solutions for Radial Systems Semi-infinite Solid Multidimensional Effects Finite Difference Methods ChEn 323 Chapter 5 Page 3 The basis is that the temperature within the solid is uniform at an instant; e.g., conduction is very fast as compound to other heat transfer mechanism (convection, radiation). Convective controlled Energy Equation based approach E st conv out q E = & ( ) = = = = = = = = = t Vc hA T T T T t hA Vc T T dt d hA Vc dt d hA Vc dt d dt dT T T dt dT Vc T T hA E E s i i i s i t s s s st out exp & ln ) ; 1 So; ( So; If i & & 1/ t Lumped Capacitance Method ChEn 323 Chapter 5 Page 4 Validity of Lumped Parameter Method ( ) ( ) ( ) ( ) Number} {Fourier or, again; exponent the at Looking B if valid , experience on Based B if valid parameter Lumped g; Rearrangin ; Conditions State Steady At i i 2 2 2 2 , 2 , 1 , 2 , 2 , 1 , 1 ....
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This note was uploaded on 03/26/2008 for the course CHEN 323 taught by Professor Johnbaldwin during the Fall '03 term at Texas A&M.

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Chapter5 - ChEn 323 Chapter 5 Page 1 Our treatment of...

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