A horizontal aluminum cylinder of length 120 cm and diameter 5cm is supported at one end (x=0cm) by a wall maintained at 500 K and at the other end (x=120cm) by a wall maintained at 350K. The cylinder is also supported from below by a thin insulating slab that extends into the cylinder at the position x=70cm, thermally isolating adjacent portions of the aluminum from one another (ie no heat can flow through the cylinder across the insulated slab boundary). This entire system intially at thermal equilibrium, is suddenly exposed to a flow of hot gases T(infinity)=800 K; h=80W/m^2K.

A) plot the temperature distribution in all relevant dimensions for each side of the aluminum cylinder as a function of position for 5 different time intervals, ranging between (and explicitely including t=0 and t= infinity

B) Using a finite difference approach, estimate the steady state temp distriubtion within the rod at the new equilibrium state (ie as t goes to infinity)