***Differential Equation Problem***
Find the steady-state temperature distribution in a spherical shell of inner
radius 1 and outer radius 2 if the inner surface is held at 0 and the outer surface has its upper half at
100 and lower half at 0.

Question

***Differential Equation Problem***
Find the steady-state temperature distribution in a spherical shell of inner
radius 1 and outer radius 2 if the inner surface is held at 0 and the outer surface has its upper half at
100 and lower half at 0.

anonymous · Answer

I know the model requires Legendre Polynomials to account for the spherical geometry.

anonymous · Answer

Ok here is what i have so far...

Laplacian(F) = 0 due to steady state behaviour
the laplacian is in shperical corrdinates so..:

anonymous · Answer

1/r(r^2*dF/dr) = 0 due to spherical symmetry