Consider steady two-dimensional heat transfer in a long solid bar (k = 25 W/m K) of

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Consider steady two-dimensional heat transfer in a long solid bar (k = 25 W/m · K) of square cross section (3 cm × 3 cm) with the prescribed temperatures at the top, right, bottom, and left surfaces to be 100°C, 200°C, 300°C, and 500°C, respectively. Heat is generated in the bar uniformly at a rate of ė = 5 × 106 W/m3. Using a uniform mesh size Δx = Δy = 1 cm determine

(a) The finite difference equations

(b) The nodal temperatures with the Gauss-Seidel iterative method.

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