Chapter 5 Numerical Methods in Heat Conduction 5-110 A plane wall with variable heat generation and variable thermal conductivity is subjected to uniform heat flux and convection at the left (node 0) and radiation at the right boundary (node 2). The implicit transient finite difference formulation of the problem using the energy balance approach method is to be determined. q0 Assumptions 1 Heat transfer through the wall is given to be transient, and the thermal conductivity and heat generation to be variables. 2 Heat transfer is one-dimensional since the plate is large relative to its thickness. 3 Radiation from the left surface, and convection from the right surface are negligible. Convectio Δ x 1 ε • • •0 2 q 0 T surr Radiation h , T ∞ g ( x ) k ( T ) Analysis Using the energy balance approach and taking the direction of all heat transfers to be towards the node under consideration, the implicit finite difference formulations become Left boundary node (node 0): t T T C x A
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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.