Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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,

  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
    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


    User Avatar
    Gold Member

  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


    User Avatar
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook