An electrical current is passed through a horizontal copper rod 2 mm in diameter and 30 cm long, located in an air stream at 0 oC. The ends of the rod are maintained at 20 oC and the convective heat transfer coefficient is estimated to be 30 W/m2K. Neglecting heat loss by radiation, determine the temperature distribution along the electric wire under steady conditions. (1) Draw a schematic diagram of the system. (10 pts) (2) Obtain the governing equation for steady state heat transfer in the electric wire. (10 pts) (3) Obtain the analytical solution for the temperature distribution along the electric wire under steady conditions if the electrical current is i) 0 Amperes, ii) 40 Amperes, and iii) 60 Amperes. (20 pts) (4) Consider a total of three, five, seven and eleven (four cases) equally spaced nodes along the electric wire, obtain the finite difference formulation of each interior node. (20 pts) (5) When the electrical current is 60 Amperes, obtain the numerical solution to the temperatures at the nodes and validate the numerical results with the prediction from the analytical solution. How does the number of nodes affect the numerical results? (30 pts) (6) Obtain the governing equation if heat loss by radiation is considered. Can we use the same numerical method to obtain the temperatures at each node? Why? (10 pts)