Thermodynamics HW Solutions 445

Thermodynamics HW Solutions 445 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-52 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 Δ x = Δ x = l =0.01m, 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 node bottom right top left 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 a vertical line passing through the nodes 1 and 3. Therefore, 2 3 T T = , , and are the only 4 unknown nodal temperatures, and thus we need only 4 equations to determine them uniquely. Also, we can replace the symmetry lines by insulation and utilize equations to determine 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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