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[SOLVED] Laplace to Heat

dwsmith

Well-known member
Feb 1, 2012
1,673
The steady state temperature $u(x,y)$ in a rectangular plate $0\leq x\leq L$, $0\leq y\leq M$, is sought, under the condition that the edge $x = 0$ is maintained at zero degrees, $x = L$ is kept at $u(L,y) = y$ degrees, and the edges $y = 0$ and $y = M$ are insulated. The appropriate differential equation $\nabla^2u = 0$.

Since the vertical boundary conditions are insulated, wouldn't this be the same as just dealing with $u_t=u_{xx}$ since Fourier coefficients for those boundaries will be 0?
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Saying that the boundaries are insulated does NOT mean that the Fourier coefficients are 0. It means that the derivatives there are 0 and so the coefficients of the sine terms are 0.
 

dwsmith

Well-known member
Feb 1, 2012
1,673
Wasn't thinking figured out this post.
 
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