Consider 1-dimensional steady heat conduction in a rod. Total length of the rod is 3 units....

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Consider 1-dimensional steady heat conduction in a rod. Total length of the rod is 3 units. Everywhere in the rod thermal conductivity is k=1 and heat generation is S=2. At left end of the rod (at x=0) T=1 and at the right end of the rod (at x=3), dT/dx =5 are given as the boundary conditions. a) Consider grid points are located at x=0, 1, 2 and 3, derive the discretization equations using both finite difference and control volume approaches. b) Solve the discretization equation sets using both TDMA and Gauss-Seidel methods. (NOTE: Do not use program.) c) Compare the numerically obtained results with the analytical solution and interpret. d The equation: (kdT) + s = 0 dx dx Consider 1-dimensional steady heat conduction in a rod. Total length of the rod is 3 units. Everywhere in the rod thermal conductivity is k=1 and heat generation is S=2. At left end of the rod (at x=0) T=1 and at the right end of the rod (at x=3), dT/dx =5 are given as the boundary conditions. a) Consider grid points are located at x=0, 1, 2 and 3, derive the discretization equations using both finite difference and control volume approaches. b) Solve the discretization equation sets using both TDMA and Gauss-Seidel methods. (NOTE: Do not use program.) c) Compare the numerically obtained results with the analytical solution and interpret. d The equation: (kdT) + s = 0 dx dx