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Heat equation PDE for spherical case

  1. Jan 23, 2009 #1
    Hello, I believe this is my first post. I would like to solve the heat equation PDE with some special (but not complicated) initial conditions, my scenario is as follows:

    A perfectly spherical mass of water, where the outer surface is at some particular temperature at t=0 (but not held at that temperature).

    It seems simple enough but for some reason I have not been able to find all that much satisfying those conditions. Any help would be sincerely appreciated, even if it's only to point out a resource.

    Thank you,

    FiberOptix
     
  2. jcsd
  3. Jan 28, 2009 #2
    Come now, it's almost been a week! I'm interested in 1D and 2D solutions as well if that makes it easier. I hope to have something soon, and if this really is a big problem for most people I'll write it up in latex and post a link.
     
  4. Jan 29, 2009 #3
    Hi,
    have you tried separation of variables? the solution should look similar to the l=0 free wave solution of spherically symmetric Schroedinger equation with t replaced by -it.
    This help?
     
  5. Jan 30, 2009 #4

    mheslep

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  6. Feb 2, 2009 #5
    Actually if you look at my initial post you may find that there are a few details that make the generalization from these resources a little difficult, hence my plea for help on this forum. I even found a few better resources than those by googling but not until I got Carslaw & Jeager's book from the library here was I really on the right track.
     
  7. Feb 2, 2009 #6

    mheslep

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    Yes, sorry, so you did. IIRC the often missed trick for full sphere problems is forcing the boundary condition u(t,theta=0) == u(t,theta=2pi). Same with the first derivative BC's.
     
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