where q is the heat transfer rate or heat flux density with units of W/m<sup>2</sup>, T is the temperature expressed in °C or °K, ∇ is the gradient operator and k is the thermal conductivity with units of W/(m.K). It can be shown that the distribution of temperature is governed by the heat diffusion equation subject to the appropriate boundary conditions:
<math> \frac{\partial T}{\partial t} - \alpha \nabla^2 T(\mathbf{r}) = \frac{\partial T}{\partial t} - \alpha \left( \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} + \frac{\partial^2\psi}{\partial z^2} = -f(\mathbf{r}right) = 0 </math>
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<math>\Delta T(\mathbf{r}) = \nabla^2 T(\mathbf{r}) = -\frac{\rho(\mathbf{r})}{\epsilon}</math>
where Φ(<b>r</b>) is the electric scalar potential expressed in Volts [v], ρ(<b>r</b>) is the volume charge density expressed in C/m<sup>3</sup>, and ε = ε<sub>r</sub> ε<sub>0</sub> is the permittivity of the medium having the units of F/m.