Thermodynamics HW Solutions 446

Thermodynamics HW Solutions 446 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-53 Heat conduction through a long L-shaped solid bar with specified boundary conditions is considered. The unknown nodal temperatures are to be determined with the finite difference method. √ Assumptions 1 Heat transfer through the body is given to be steady and two-dimensional. 2 Thermal conductivity is constant. 3 Heat generation is uniform. Properties The thermal conductivity is given to be k = 45 W/m ⋅ °C. • • • 120 3 1 2 4 5 6 7 8 • • • • • q L h , T ∞ Insulated Analysis ( a ) The nodal spacing is given to be Δ x = Δ x = l =0.015 m, and the general finite difference form of an interior node for steady two-dimensional heat conduction for the case of constant heat generation is expressed as 4 2 node bottom right top left = + − + + + k l g T T T T T & We observe that all nodes are boundary nodes except node 5 that is an interior node. Therefore, we will have to rely on energy balances to obtain the finite difference equations. Using energy balances, the finite have to rely on energy balances to obtain the finite difference equations....
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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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