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2. Relevant equations

3. The attempt at a solution

I'm trying to find the steady state solution to the heat equation for a system of spherical shells (looks like http://correlatingcancer.com/wp-content/uploads/2009/01/nanoshell-thumb.jpg" [Broken]) where heat generation Q occurs in the outer shell (so I have two Laplace equations for the inner sphere and the medium outside the system and a Poisson equation for the outer shell). The system is also spherically symmetric, so the equations are just in the radial variable.

I know the solution for the Laplace equation in this case is T(r) = A + B/r and I believe that in the case of the inner region, B must be zero since the solution has to be finite at the origin. This means the solution is a constant. However, if the solution is constant, then the boundary condition on the heat conduction at the inner radius can't hold, since dT/dr = 0. I'm not sure what I'm doing wrong here. Can someone help me out?

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# Steady state heat equation in concentric spherical shells

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