Consider a rod of length 30 for which 2 = 1. Suppose the
Chapter 10, Problem 11(choose chapter or problem)
Consider a rod of length 30 for which 2 = 1. Suppose the initial temperature distributionis given by u(x, 0) = x(60 x)/30 and that the boundary conditions are u(0, t) = 30 andu(30, t) = 0.(a) Find the temperature in the rod as a function of position and time.(b) Plot u versus x for several values of t. Also plot u versus t for several values of x.(c) Plot u versus t for x = 12. Observe that u initially decreases, then increases for awhile, and finally decreases to approach its steady state value. Explain physically why thisbehavior occurs at this point.
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