Consider a long bar of rectangular cross section (60 mm by 90 mm on a side) and of thermal conductivity 1 W/m · K. The top surface is exposed to a convection process with air at 100ºC and a convection heat transfer coefficient of 100 W/m² · K, while the remaining surfaces are maintained at 50ºC. Using a grid spacing of 30 mm and the Gauss-Seidel iteration method, determine the temperatures at nodes 1, 2, and 3 shown in Fig. P5–64. Use an initial estimate of 0ºC for all the nodal temperatures and a 0.35ºC convergence criterion.

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Fluid T, = 50°C T, = 50°C 1 2 3 نیا T = 100°C h = 100 W/m²-K T₁ = 50°C Ay = 30 mm Ax = 30 mm