<math> \left[ -k \frac{\partial T}{\partial n} + h T(\mathbf{r}) \right]_\Omega = f(\mathbf{r}) </math>
where Ω is the boundary surface and f(<b>r</b>) is a can be an arbitrary functionin general.
== The Analogy between Thermal and Electrostatic Equations ==
<math> \nabla^2 T(\mathbf{r}) = - \frac{w(\mathbf{r})}{k} \quad \leftrightarrow \quad \nabla^2 \Phi(\mathbf{r}) = -\frac{\rho(\mathbf{r})}{\epsilon} </math>
One can see a one-to-one correspondence between the electrostatic and thermal quantities: Temperature T (<b>r</b>) is analogous to the electric scalar potential Φ(<b>r</b>), the volume heat source density w (<b>r</b>) is analogous to the volume charge density ρ(<b>r</b>), and the thermal conductivity k is analogous to the permittivity ε.
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