Let an aluminum rod of length 20 cm be initially at the uniform temperature of 25°C. Suppose that at time t=0, the end x=0 is cooled to 0°C while the end x=20 is heated to 60°C, and both are thereafter maintained at those temperatures. Required:
a. Find the temperature distribution in the rod at any time t.
b. Plot the initial temperature distribution, the final (steady state) temperature distribution, and the temperature distributions at two representative intermediate times on the same set of axes.
c. Plot u versus t for x=5, 10, and 15.
d. Determine how much time must elapse before the temperature at x=5 cm comes(and remains) within 1% of its steady state value.