LaPlace Equation in Polar

  • Thread starter EsponV
  • Start date
  • #1
15
0

Homework Statement


Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2
inside the half disk 0<r<R, 0<phi<pi
Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi



Homework Equations


I'm assuming the Laplace equation and the given bc conditions


The Attempt at a Solution


I attempted the solution, which I think up until this point is correct, but I've gotten stuck trying to figure out the constants.

http://img708.imageshack.us/img708/707/p2150074.jpg [Broken]

Thank you all for your help.
 
Last edited by a moderator:

Answers and Replies

  • #2
15
0
I just got a email telling me I had a response, however I don't see it in the thread. Anyhow, the picture that only shows half the page of paper because that's all the work I had done on it. I got stuck at that point and wasn't sure how to go about calculating the unknown constants (if I had done everything correctly to that point).
 

Related Threads on LaPlace Equation in Polar

  • Last Post
Replies
4
Views
3K
Replies
2
Views
21K
  • Last Post
Replies
0
Views
1K
M
  • Last Post
Replies
7
Views
1K
Replies
3
Views
7K
  • Last Post
Replies
0
Views
988
Replies
6
Views
5K
Replies
2
Views
4K
Replies
3
Views
2K
Top