Heat Eq 2D stationary, cond+conv

[phiz]

Homework Statement

Hi everybody, I'm trying to solve the heat eq. for a 2D problem which is stationary, and also includes convection. There is no heat source. I am using Matlab.

Homework Equations

domain: x:0:1, y:0:1

u(x,1) = x(1-x)
all other boundaries are 0

The Attempt at a Solution

X(x) = sin(k*pi*x/L)

%-- Fourier coefficients: might be wrong!
u0 = x*(1-x);
a = 2/L*int(u0*sin(kk*pi*x/L),x,0,L)
%--

Y(y) = (exp((y*(vy - (lambda*D^2 + vy^2)^(1/2))))-exp((y*(vy + (4*lambda*D^2 + vy^2)^(1/2)))))

lambda is ofcourse (k*pi/L)^2
(bc's give the exp(..vy+..) term a minus, which is already included in the equation above.

the problem is, that my solution is not stable. At y=0 I find u=0, which is correct, however when y increases towards its limit y=1, i find that the solution increases to infinity.

 

[member 553083]

I'm quite sure that I'm wrong with the Fourier coefficients, but I don't know how to solve it. Does anyone know how to solve this? Thanks in advance!