Thermodynamics HW Solutions 501

Thermodynamics HW Solutions 501 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-112 Starting with an energy balance on a volume element, the two-dimensional transient explicit finite 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. & g 0 Analysis (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 Δ z = 1 in the z direction. There is uniform heat generation in the medium, and the thermal conductivity k of the medium is constant. Now we divide the x-y plane of the region into a rectangular mesh of nodal points which are spaced Δ x and Δ y apart in the x and y directions, respectively, and consider a general interior node ( m , n ) whose coordinates are x m x and . Noting that the volume element centered about the general interior node ( m , n )
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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.

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