The temperature distribution in a tapered conical cooling fin (Figure) is described by the following differential equation, which has been nondimensionalized

Where u = temperature (0 ≤ u ≤ l).x = axial distance (0 ≤ x ≤ 1), and p is a nondimensional parameter that describes the heat transfer and geometry

where h = a heat transfer coefficient, k = thermal conductivity, L = the length or height of the cone, and m = the slope of the cone wall. The equation has the boundary conditions

u(x = 0) = 0                 u(x = 1) = 1

Solve this equation for the temperature distribution using finite difference methods. Use second-order accurate finite difference analogues for the derivatives Write a computer program to obtain the solution and plot temperature versus axial distance for various values of p = 10, 20, 50, and 100.

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