Thermal diffusion

Here thermal diffusion means the spreading of temperature by thermal conduction. In a stationary homogeneous material with constant thermal conductivity $k$, mass density $\rho$ and specific heat capacity $c$, energy balance and Fourier's law give the heat equation ${\partial }_{t}T=\alpha {\nabla }^{2}T$, where $\alpha =k/(\rho c)$ is the thermal diffusivity.

A disturbance spreads over a length of order $\sqrt{\alpha t}$, so equilibration across thickness $L$ takes a time of order $L^2/\alpha$. This is the heat-transport sense of the term; temperature-gradient-driven separation of components in a mixture is a distinct transport effect.