Consider steady two dimensional heat transfer in a long solid bar (k 25 W m K) of square cross section (2 cm 2 cm) with heat generated in the bar uniformly at a rate of e 3 10 6 W m 3 The left and bottom surfaces maintain a constant temperature of 200C The top and right surfaces are subjected to co...

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

Question:

Consider steady two-dimensional heat transfer in a long solid bar (k = 25 W/m · K) of square cross section (2 cm × 2 cm) with heat generated in the bar uniformly at a rate of ė = 3 × 10⁶ W/m³. The left and bottom surfaces maintain a constant temperature of 200°C. The top and right surfaces are subjected to convection with ambient air temperature of 100°C and heat transfer coefficient of 250 W/m² · K. 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.