= Heat balance with volumetric heat generation
{title2=$c_{\rm vol}T_t=\nabla\cdot(k\nabla T)+H$}
Integrating <energy> conservation over a fixed material volume gives storage equal to incoming conductive <heat flux> plus internally generated <heat>. Here $c_{\rm vol}$ is <volumetric heat capacity>, with units $\mathrm{J\,m^{-3}\,K^{-1}}$. For a mass-specific <heat capacity>, the <density> factor must be included. Constant isotropic conductivity reduces the divergence to $k\nabla^2T$; variable conductivity must remain inside the divergence.
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