How to Find Temperature Distribution in a Rectangular Sheet?

[Void123]

Homework Statement

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)

Homework Equations

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

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)

 

[nickmai123]

Homework Statement

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)

Homework Equations

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

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)

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

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