- #1
samuelandjw
- 22
- 0
The length of the side of the square is a. The boundary conditions are the following:
(1) the left edge is kept at temperature T=C2
(2) the bottom edge is kept at temperature T=C1
(3) the top and right edges are perfectly insulated, that is [tex]\dfrac{\partial T}{\partial x}=0,\dfrac{\partial T}{\partial y}=0[/tex]
Solve for [tex]T(x,y)[/tex] in steady state.
The situation is described by the Laplace equation. It would be a bit difficult to directly solve for this problem since this is a mixed BC problem. I want to break it down into several (for example, two) problems that are easier to solve. So far I don't have any idea how to break it down, since the mixed BC makes it difficult to break down the problem. Does anybody have any suggestion?
Thanks.
(1) the left edge is kept at temperature T=C2
(2) the bottom edge is kept at temperature T=C1
(3) the top and right edges are perfectly insulated, that is [tex]\dfrac{\partial T}{\partial x}=0,\dfrac{\partial T}{\partial y}=0[/tex]
Solve for [tex]T(x,y)[/tex] in steady state.
The situation is described by the Laplace equation. It would be a bit difficult to directly solve for this problem since this is a mixed BC problem. I want to break it down into several (for example, two) problems that are easier to solve. So far I don't have any idea how to break it down, since the mixed BC makes it difficult to break down the problem. Does anybody have any suggestion?
Thanks.