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Chapter5

# Chapter5 - Introduction to Transient Conduction Our...

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ChEn 323 – Chapter 5 – Page 1 ¾ 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. ¾ Transient conditions are created by changing driving forces. ¾ When temperature gradients are small, the lumped capacitance method works just fine. Introduction to Transient Conduction

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ChEn 323 – Chapter 5 – Page 2 Summary of Topics ¾ The Lumped Capacitance Method ¾ Validity of the Lumped Capacitance Method ¾ Spatial Effects ¾ Exact Solutions ¾ Approximate Solution ¾ Total Energy Transfer ¾ Radial System with Convection ¾ Approximate Solutions for Radial Systems ¾ Semi-infinite Solid ¾ Multidimensional Effects ¾ Finite Difference Methods
ChEn 323 – Chapter 5 – Page 3 ¾ 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). ¾ Convective controlled ¾ 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 ρ θ θ θ θ ρ θ θ θ ρ θ θ ρ θ θ ρ θ θ exp & ln ) ; 0 1 So; ( So; If i & & 1/ τ t Lumped Capacitance Method

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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 0 2 2 2 , 2 , 1 , 2 , 2 , 1 , 1 . 0
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Chapter5 - Introduction to Transient Conduction Our...

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