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Assume I have a bounded material with heat sources inside. The material is known (i.e. I know heat capacity and all relevant data) and the temperature of the boundary is fixed. I solved the (steady state) heat equation and hence know the temperature distribution.

How do I compute the heat flow through the boundary? I expect something like

$$ \int_\Gamma k\cdot \nabla T $$ where $\Gamma$ is the boundary and $T$ the temperature. Is this correct? If so, what value for $k$ do I have to use?

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Have a look at this question. physics.stackexchange.com/questions/31687/… –  fneron Jul 10 '12 at 15:48

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