Chapter 5 Numerical Methods in Heat Conduction 5-87 Heat conduction through a long L-shaped solid bar with specified boundary conditions is considered. The temperature at the top corner (node #3) of the body after 2, 5, and 30 min is to be determined with the transient explicit finite difference method. Assumptions 1Heat transfer through the body is given to be transient and two-dimensional.2 Thermal conductivity is constant. 3 Heat generation is uniform. PropertiesThe conductivity and diffusivity are given to be k= 15 W/m⋅°C and . α=×−32 106. m2•••1403124 5 6 7 8•••••qLh, T∞Insulated/sAnalysis The nodal spacing is given to be Δx=Δx=l=0.015 m. The explicit finite difference equations are determined on the basis of the energy balance for the transient case expressed as &&QGVCTTtimimiAll sideselementielement∑+=−+ρ1ΔThe quantities hTdo not change with time, and thus we do not need to use the superscript i for them. Also, the energy balance expressions can be simplified using the definitions of thermal diffusivity
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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.