Chapter 5 Numerical Methods in Heat Conduction 5-80Starting with an energy balance on a disk volume element, the one-dimensional transient explicit finite difference equation for a general interior node for Tzin a cylinder whose side surface is insulated for the case of constant thermal conductivity with uniform heat generation is to be obtained. t(,)Analysis We consider transient one-dimensional heat conduction in the axial z direction in an insulated cylindrical rod of constant cross-sectional area A with constant heat generation and constant conductivity kwith a mesh size of 0g&zΔin the z direction. Noting that the volume element of a general interior node m involves heat conduction from two sides and the volume of the element is zAVΔ=element, the transient explicit finite difference formulation for an interior node can be expressed as tTTxCAxAgxTTkAxTTkAimimimimimimΔ−Δ=Δ+Δ−Δ−++−1011+ρ&••m-1 mm+1 InsulationDisk
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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.