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George
07/25/12 6:38pm

Hello Folks,

I am new to Mathematica, but it seems to be the most suitable tool for my issue.

I have to solve a equation which is similar to heat equation on a sphere surface.

The exact expression in a spherical coordinates system is (in LaTeX) :

\frac{\partial{h}}{\partial t} = \frac{1}{n} \left[ \frac{1}{r^2 \sin^2{\phi}} \frac{\partial}{\partial \theta} \left( K \frac{\partial h}{\partial \theta} \right) + \frac{1}{r^2 \sin \phi} \frac{\partial}{\partial \phi} \left( K \sin \phi \frac{\partial h}{\partial \phi}\right) + s(\theta,\phi,t) \right]

K is kind of a diffusion coeff.
s a source term (varying in time and space)
and n a constant (although it might depends on \phi and \theta).
\theta and \phi are defined here in a mathematical way.
r the radius (constant as we deal with a perfect sphere).
(no variation regarding the radius, we only look at the surface of the sphere).

I found that in Mathematica, and in a Cartesian frame, such equation (somewhat not exactly the same but similar) would be:

R = 1
K = 34
myfunc = NDSolve[{D[h[x, y, t], t] ==
R*(D[h[x, y, t], x, x] + D[h[x, y, t], y, y]), h[x, y, 0] == 0,
h[0, y, t] == K*t, h[9, y, t] == K*t, h[x, 0, t] == K*t,
h[x, 9, t] == K*t}, h, {x, 0, 9}, {y, 0, 9}, {t, 0, 6}];

I'm kind of stuck right now, because I do not know how can I switch to the spherical frame. I would appreciate any ideas/suggestions.

Thanks a lot and sorry for bothering you guys with this.

G.












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Subject (listing for 'Heat equation at sphere's surface')
Author Date Posted
Heat equation at sphere's surface George 07/25/12 6:38pm
Re: Heat equation at sphere's surface Michael 07/26/12 07:56am
Re: Re: Heat equation at sphere's surface George 07/26/12 9:14pm
Re: Heat equation at sphere's surface George 07/28/12 7:13pm
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