Thermodynamics HW Solutions 438

Thermodynamics HW Solutions 438 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-48 A long solid body is subjected to steady two-dimensional heat transfer. The unknown nodal temperatures are to be determined. Assumptions 1 Heat transfer through the body is given to be steady and two-dimensional. 2 There is no heat generation in the body. Properties The thermal conductivity is given to be k = 20 W/m C. Analysis The nodal spacing is given to be x = x = l =0.02 m, and the general finite difference form of an interior node for steady two-dimensional heat conduction for the case of no heat generation is expressed as 4 / ) ( 4 bottom right top left node 2 node node bottom right top left T T T T T k l g T T T T T + + + = = + + + + & ( a ) There is symmetry about the insulated surfaces as well as about the diagonal line. Therefore 2 3 T T = , and are the only 3 unknown nodal temperatures. Thus we need only 3 equations to determine them uniquely. Also, we can replace the symmetry lines by insulation and utilize the mirror-image concept them uniquely....
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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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