# Homework Help: Heat Conducting Material

1. Oct 1, 2009

### Void123

1. The problem statement, all variables and given/known data

Find the temperature distribution in the rectangular sheet given the following boundary conditions:

U(0, y) = U(a, y) = U(x, b) = 0; U(x, 0) = f(x)

2. Relevant equations

U(x, y) = (summation) B (fourier coefficient) [sin ((n*pi*x)/a) sinh ((n*pi*y)/a)]

3. The attempt at a solution

Wouldn't it just be a simple modification of the above formula:

U(x, y) = (summation) B [sin ((n*pi*x)/a) sinh ((n*pi*(b - y))/a)

2. Oct 1, 2009

### nickmai123

I can't help you solve it. However, I will bump it by retyping it with LaTeX for you :-)

$$U\left(x,y\right)=\sum B\sin{\left(\frac{n \pi x}{a}\right)}\sinh{\left(\frac{n\pi(b-y)}{a}\right)}$$