Chapter 5 Numerical Methods in Heat Conduction 5-112Starting with an energy balance on a volume element, the two-dimensional transient explicitfinite difference equation for a general interior node in rectangular coordinates for T(x, y, t) for the case of constant thermal conductivity k and uniform heat generation is to be obtained. &g0Analysis(See Figure 5-24 in the text). We consider a rectangular region in which heat conduction is significant in the x and y directions, and consider a unit depth of Δz = 1 in the z direction. There is uniform heat generation in the medium, and the thermal conductivity kof the medium is constant. Now we divide the x-y plane of the region into a rectangular meshof nodal points which are spaced Δxand Δyapart in the x and y directions, respectively, and consider a general interior node (m, n) whose coordinates are xm x=Δand . Noting that the volume element centered about the general interior node (m, n)
This is the end of the preview. Sign up
access the rest of the document.
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.