Chapter 5 Numerical Methods in Heat Conduction 5-108 A plane wall with variable heat generation and constant thermal conductivity is subjected to combined convection and radiation at the right (node 3) and specified temperature at the left boundary (node 0). The finite difference formulation of the right boundary node (node 3) and the finite difference formulation for the rate of heat transfer at the left boundary (node 0) are to be determined. Assumptions 1 Heat transfer through the wall is given to be steady and one-dimensional. 2 The thermal conductivity is given to be constant. Analysis Using the energy balance approach and taking the direction of all heat transfers to be towards the node under consideration, the finite difference formulations become Right boundary node (all temperatures are in K): 0) 2 / ( ) ( ) ( 3 3 2 3 4 3 4 surr = Δ + Δ − + − + − ∞ x A g x T T kA T T hA T T A εσ Convectio n Δ x T0 • • • • 0 1 2 3 g ( x ) T surr Radiation ε Heat transfer at left surface:
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.