# Mathematical expression

The mathematical definition of the static thermal permeability $k'_0$ given by Lafarge, Lemarinier, Allard and Tarnow is:

\[ k'_0 = \lim_{\omega \rightarrow 0} k'(\omega) \]where the dynamic thermal permeability $k'(\omega)$ is defined as:

\[ \phi\tau = \frac{k'(\omega)}{\kappa}\frac{\partial p}{\partial t} \]In this last expression, $\phi$ is the open porosity of the material. $\tau$ is the temperature excess inside the porous medium subjected to a variation of pressure with respect to time $\partial p/\partial t$. $\kappa$ is the thermal conductivity of air.