A cylindrical aluminum fin with adiabatic tip is attached to a wall with surface temperature of 300°C, and is exposed to ambient air condition of 15°C with convection heat transfer coefficient of 150 W/m² · K. The fin has a uniform cross section with diameter of 1 cm, length of 5 cm, and thermal conductivity of 237 W/m · K. Assume steady one-dimensional heat transfer along the fin and the nodal spacing to be uniformly 10 mm,

(a) Obtain the finite difference equations for use with the Gauss-Seidel iterative method,

(b) Determine the nodal temperatures using the Gauss- Seidel iterative method and compare the results with the analytical solution.