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LaPlace Equation in Polar

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    I'm assuming the Laplace equation and the given bc conditions

    3. 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: May 4, 2017
  2. jcsd
  3. Feb 16, 2010 #2
    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).
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