How do I calculate the heat flow at a Dirichlet boundary surface, given a set temperature gradient?

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Mark Lepage
Mark Lepage 2017-12-7
So I am dealing with potential and current flows, but the thermal analogy will work here.
Basically I have a set geometry (a cylinder, with three rings at a certain temperature (Dirichlet boundary's), which results in a temperature gradient across my cylinder. I know the gradient of this temperature is my heat flow, however, I want to calculate how much heat is flowing into and out of the rings.
Is there a way for the PDE toolbox to calculate the resulting heat flow at my Dirichlet boundary conditions?
I have attached a picture of what the resulting PDE solution shows given the Dirichlet boundary conditions I have set. There is a top and bottom ring at a temperature set at 1, and a middle ring with a temperature set at 0. Every other boundary except the rings are insulated.
Any help is greatly appreciated.

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