Thermodynamics HW Solutions 480

Thermodynamics HW - Chapter 5 Numerical Methods in Heat Conduction 5-87 Heat conduction through a long L-shaped solid bar with specified boundary

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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 1 Heat transfer through the body is given to be transient and two-dimensional. 2 Thermal conductivity is constant. 3 Heat generation is uniform. Properties The conductivity and diffusivity are given to be k = 15 W/m °C and . α 32 10 6 . m 2 140 3 1 2 4 5 6 7 8 q L h , T Insulated / s Analysis The nodal spacing is given to be Δ x = Δ x = l =0.015 m. The explicit finite difference equations are determined on the basis of the energy balance for the transient case expressed as && QG V C TT t i m i m i All sides element i element += + ρ 1 Δ The quantities hT do 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.

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