Chapter 5 Numerical Methods in Heat Conduction 5-19 A plane wall with variable heat generation and constant thermal conductivity is subjected to combined convection, radiation, and heat flux at the left (node 0) and specified temperature at the right boundary (node 5). The finite difference formulation of the left boundary node (node 0) and the finite difference formulation for the rate of heat transfer at the right boundary (node 5) are to be determined. Convection Δ x g ( x ) 1 ε • • • • •0 2 3 4 • 5 T surr Radiation q 0 h, T ∞ T s 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 Left boundary node (all temperatures are in K): 0) 2 / ( ) ( ) (000 10 40 4 surr = Δ + + Δ − + − + − ∞ x A g A q x T T kA T T
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