Heat equation PDE for spherical case

[FiberOptix]

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

 

[FiberOptix]

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.

 

[alle.fabbri]

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?

 

[mheslep]

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.

Come now, try some googling. Wiki?
http://en.wikipedia.org/wiki/Heat_equation
with several methods. Separation of variables:
http://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat_equation_using_Fourier_series

 

[FiberOptix]

Come now, try some googling. Wiki?
http://en.wikipedia.org/wiki/Heat_equation
with several methods. Separation of variables:
http://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat_equation_using_Fourier_series

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.

 

[mheslep]

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.

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.