# Heat Equation : Non-Homogeneous PDE

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2.

(30 points) A thin, one-dimensional rod of heat-conducting material with length L = pi is internally and uniformly heated at a rate of alpha degrees per unit time. This means that the temperature of the rod, u(x, t), satisfies the inhomogeneous heat equation ....

where K is the thermal diffusivity. Suppose the temperature is initially zero throughout the bar, and the temperatures at the left and right ends are fixed at zero.

Hint: There are (at least) two ways to solve steady state solution to the problem, let u(x, t)= ... problem for v(x, t), then solve for v(x, t) Another way is to solve for u(x, t) directly using approach is acceptable. You can get extra credit and can reconcile the two answers. You can also use eigenfunction expansions...

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A heat equation is investigated. The solution is detailed and well presented. The solution was given a rating of "5" by the student who originally posted the question.

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