Steady State 2-D Heat Equation with Mixed Boundary Conditions

[NickD2]

Homework Statement

I am trying to solve the Laplacian Equation with mixed boundary conditions on a rectangular square that is 1m x 1m.

Homework Equations

$$\nabla$$²T=0

.....T=500K
....________
....|@@@@|
T=500K...|@@@@|...T=500K
....|@@@@|
....|______.|
....Convection
....dT
....-- = h(T(x,0)-300K)
....dy
The square is 1m x 1m
h = 10

The Attempt at a Solution

I started by doing separation of variables and ended up with something that I could not solve...

P.S. Please excuse the .'s and @'s as they are just spacers to keep the geometery of the problem in tact.

Thanks!

 

[fzero]

If you show some of your work, we might be able to figure out exactly what's giving you trouble.