Consider heat conduction through the wall of a pipe with inside wall temperature of 200oc and outside temperature of 80oc. the wall is 0.05 m thick with inside radius r0 of 0.05 m and outer radius rn of 0.1 m. thermal conductivity of the wall is 1w/moc. the differential equation which describes the radial temperature distribution is dt dr + r d 2t dr 2 = 0 solving the above equation with finite difference method on n equally-spaced node points along the radial direction, together with application of temperature boundary conditions at inner and outer wall yields the following system of equations: t1 = 200 ri ∆r 2 − 1 ∆r ti−1 − 2ri ∆r 2 ti + ri ∆r 2 + 1 ∆r ti+1 = 0 i = 2, 3, n − 1 tn = 80 ri is radial position of the nodes and can be written as ri = r0 + ∆r (i − 1) i = 1, 2, n radial spacing between the nodes ∆r can be computed as: ∆r = rn − r0 n − 1 (a) solve the temperature values t using thomas method with number of nodes n = 11. remember that radius ri is not constant. provide the m-files. (b) plot the temperature profiles, i. e. t versus ri . make sure the axis are properly labeled.