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Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the steady-state temperature distribution in the 2D object if it is 1 m x 1 m and has a thermal conductivity of 10 W/m-K. (Use the fine grid from part b.) 300°C Using the same grid, conditions, and geometry in part c, determine the time for the center temperature to reach steady-state if the body is initially at a temperature of 2S C. Note: the thermal diffusivity of the body is 1x104 m2/s. d) Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the steady-state temperature distribution in the 2D object if it is 1 m x 1 m and has a thermal conductivity of 10 W/m-K. (Use the fine grid from part b.) 300°C Using the same grid, conditions, and geometry in part c, determine the time for the center temperature to reach steady-state if the body is initially at a temperature of 2S C. Note: the thermal diffusivity of the body is 1x104 m2/s. d)
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