Consider one-dimensional steady state heat conduction in a rod with constant internal thermal generation (g) and...

   

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Consider one-dimensional steady state heat conduction in a rod with constant internal thermal generation (g) and thermal conductivity (k), as sketched in the figure below: x=0 T=0 2 3 i-1 i i+1 4x L N-2 N-1 N x=L T, = 1 The temperature is fixed at zero at the left end (T1 = 0) and at one at the right end (T, = 1). The ratio of internal thermal generation to thermal conductivity (S=q/k) is fixed at S= 10. The overall length of the rod is L = 1. Approximate the solution to this heat conduction problem using the finite difference method as discussed in class. Uniform grid spacing (4x = constant) can be used. Find: (a) The plots of the center temperature versus iterations for both Jacobi Iteration and Gauss- Seidel Iteration (comparing the convergence of the two solvers) (b) The plots of Delta magnitude for temperature, {8}], versus iterations for both Jacobi Iteration and Gauss-Seidel Iteration solvers (c) The plot of center temperature versus grid spacing (d) The plot of the temperature distribution along the rod Consider one-dimensional steady state heat conduction in a rod with constant internal thermal generation (g) and thermal conductivity (k), as sketched in the figure below: x=0 T=0 2 3 i-1 i i+1 4x L N-2 N-1 N x=L T, = 1 The temperature is fixed at zero at the left end (T1 = 0) and at one at the right end (T, = 1). The ratio of internal thermal generation to thermal conductivity (S=q/k) is fixed at S= 10. The overall length of the rod is L = 1. Approximate the solution to this heat conduction problem using the finite difference method as discussed in class. Uniform grid spacing (4x = constant) can be used. Find: (a) The plots of the center temperature versus iterations for both Jacobi Iteration and Gauss- Seidel Iteration (comparing the convergence of the two solvers) (b) The plots of Delta magnitude for temperature, {8}], versus iterations for both Jacobi Iteration and Gauss-Seidel Iteration solvers (c) The plot of center temperature versus grid spacing (d) The plot of the temperature distribution along the rod

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Given the problem statement you are asked to solve a onedimensional steadystate heat conduction problem in a rod with constant internal heat generatio... View the full answer