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Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state...

Question:

Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer th

Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are described by the following ordinary differential equation: T" – TQ2 = -a?T. T(x = 0) = 0 T(x = L) = 2 T is the temperature distribution in a rod, a = hP/kA, h is the heat transfer coefficient, P, A and L are the perimeter, the cross section and the length of the rod, respectively and k is its heat conductivity. Ta is the temperature of the surrounding air and und ©2 are the temperatures at both ends of the rod. Use numerical values given in Figure 1 to compute temperatures in nodes 2, 3 and 4. 2 3 4 77777777 Figure 1: L = 0.01m, , = 0°C,, = 100°C, a = 400m-1,T, = 0°C, Ax = 0.0025m

Answers

Given T ra = a ta with B-C. T(0) - 04 Ta= oc I T(L) = Oz cohere a= hoa Taaoc 0; 2=0.0025 Fe1000 We have dI = 0 Totat Tin Te

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