I want to solve the transient heat equation on a ball. The boundary condition is

Question

I want to solve the transient heat equation on a ball. The boundary condition is the same over the hole outer surface. So this should reduce to a one-dimensional problem in radial direction. However I cannot use the one-dim heat equation, since the surface through which the heat flows goes quadratic with the radius.

Is the following approach correct: Take the heat equation, transform it into sperical coordinates and eliminate the derivatives in angular directions. I think the last part is justified, because of the rotational symmetry of the boundary condition. So I end up with this equation:

Explanation / Answer

That sounds about right to me. Although I've never done this for the heat equation specifically, that's much the same approach we use to solve the Schr

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