Solved: Let an aluminum rod of length 20 cm be initially at the uniform temperature of

Chapter 10, Problem 9

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Let an aluminum rod of length 20 cm be initially at the uniform temperature of 25C. Suppose that at time t = 0 the end x = 0 is cooled to 0C while the end x = 20 is heated to 60C, and both are thereafter maintained at those temperatures.(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 thesame 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