2. Consider an aluminum alloy circular rod (k = 180 W/mK) whose length is L = 20 cm and the base diameter is b = 1 cm. The base of the rod is maintained at a temperature of To = 180C. The rod is losing heat by convection to the ambient air at T = 25C with a heat transfer coefficient of h = 25 W/m.K. (1) Determine the temperature distribution along the rod in the x direction using analytical solution; (2) Determine the temperature distribution along the rod in the x direction using the finite difference method. Determine the number of nodes that gives you a solution with an averaged relative error < 1% compared to the analytical solution; (3) Plot both the analytical and numerical solutions at different grid numbers; (4) Plot the relative error distribution at different grid numbers; (5) Evaluate the L2-norm error, E2, for each grid number with the following definition 71/2 , = X num -Tomaly/analy x