Thermodynamics HW Solutions 447

Thermodynamics HW Solutions 447 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-54E A long solid bar is subjected to steady two-dimensional heat transfer. The unknown nodal temperatures and the rate of heat loss from the bar through a 1-ft long section are to be determined. Assumptions 1 Heat transfer through the body is given to be steady and two-dimensional. 2 Heat is generated uniformly in the body. 3 The heat transfer coefficient also includes the radiation effects. Properties The thermal conductivity is given to be k = 16 Btu/h.ft °C. Analysis The nodal spacing is given to be Δ x = Δ x = l =0.2 ft, and the general finite difference form of an interior node for steady two-dimensional heat conduction is expressed as TTT T T gl k left top right bottom node node ++ + + = 40 2 & ( a ) There is symmetry about the vertical, horizontal, and diagonal lines passing through the center. Therefore, 9 7 3 1 T T T T = = = and , and are the only 3 unknown nodal temperatures, and thus we need only 3 equations to determine them uniquely. Also, we can replace the symmetry lines by insulation and
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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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