Darcy dissipation
= Darcy dissipation
{c}
{title2=$\mathcal D=\mu|\mathbf u|^2/\Pi$}
A <Darcy velocity> $\mathbf u$ driven by pressure in a stationary porous skeleton dissipates mechanical power $\mu|\mathbf u|^2/\Pi$ per bulk volume. It follows by dotting <Darcy law> with the discharge: $-\mathbf u\cdot\nabla p=\mu|\mathbf u|^2/\Pi$. Its contribution to a <heat equation> can be neglected only when it is small relative to the relevant thermal-energy transfer.