Chapter 5 Numerical Methods in Heat Conduction 5-50 A long solid body is subjected to steady two-dimensional heat transfer. The unknown nodal temperatures and the rate of heat loss from the top surface 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. Properties The thermal conductivity is given to be k = 180 W/m ⋅ °C. Analysis ( a ) The nodal spacing is given to be Δ x = Δ x = l =0.1 m, and the general finite difference form of an interior node equation for steady two-dimensional heat conduction for the case of constant heat generation is expressed as 04 2 node node bottom right top left = + − + + + k l g T T T T T There is symmetry about a vertical line passing through the middle of the region, and thus we need to consider only half of the region. Then, 4 3 2 1 and T T T T = = Therefore, there are there are only 2 unknown nodal temperatures, T 1 and T 3 , and thus we need only 2
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