Write a Matlab code for this problem.

In the final worked example of this chapter we discuss the cooling of a circular fin by means of convective heat transfer along its length. Convection gives rise to a temperature-dependent heat loss or sink term in the governing equation. Shown in Figure 4.9 is a cylindrical fin with uniform cross-sectional area A. The base is at a temperature of 100 degree C (T_B) and the end is insulated. The fin is exposed to an ambient temperature of 20 degree C. One-dimensional heat transfer in this situation is governed by d/dx (kA dT/dx) - hP (T - T_infinity) = 0 where h is the convective heat transfer coefficient, P the perimeter, k the thermal conductivity of the material and T_infinity the ambient temperature. Calculate the temperature distribution along the fin and compare the results with the analytical solution given by T - T_infinity/T_B - T_infinity = cosh[n (L - x)]/cosh (nL) where n^2 = hP/(kA), L is the length of the fin and x the distance along the fin. Data L = 1 m, hP/(kA) = 25 m^-2 (note kA is constant)