Ch5-Transient Conduction

Ch5-Transient Conduction - Chapter 5 Transient Conduction...

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Unformatted text preview: Chapter 5 Transient Conduction Solution to the Heat Equation for a Plane Wall with Symmetrical Convection Conditions • If the lumped capacitance approximation can not be made, consideration must be given to spatial, as well as temporal, variations in temperature during the transient process. • For a plane wall with symmetrical convection conditions and constant properties, the heat equation and initial/boundary conditions are: 2 2 1 α ∂ ∂ = ∂ ∂ T T x t (5.26) ( 29 ,0 = i T x T (5.27) = ∂ = ∂ x T x (5.28) ( 29 , ∞ = ∂ - =- ∂ x L T k h T L t T x (5.29) • Existence of seven independent variables: ( 29 , , , , , , α ∞ = i T T x t T T k h (5.30) How may the functional dependence be simplified? Dimensionless temperature difference: * i i T T T T θ θ θ ∞ ∞- ≡ =- * x x L ≡ Dimensionless coordinate: Dimensionless time: * 2 t t Fo L α ≡ ≡ The Fourier Number The Biot Number: solid hL Bi k ≡ ( 29 * * , , θ = f x Fo Bi • Exact Solution:...
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This note was uploaded on 02/01/2012 for the course MECH ENG 225 taught by Professor Koylu during the Spring '11 term at Missouri S&T.

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Ch5-Transient Conduction - Chapter 5 Transient Conduction...

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