Purchase Solution

# Heat Equation : Non-Homogeneous PDE

Not what you're looking for?

Please see the attached file for the fully formatted problem.

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...

##### Solution Summary

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.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.