Thermal effusivity

In thermodynamics, a material's thermal effusivity, also known as thermal responsivity, is a measure of its ability to exchange energy with its surroundings. It is an intensive quantity defined as the square root of the product of the material's thermal conductivity (${\displaystyle \lambda }$) and its volumetric heat capacity (${\displaystyle \rho c_{p}}$) or as the ratio of thermal conductivity to the square root of thermal diffusivity (${\displaystyle \alpha }$).

${\displaystyle r={\frac {\lambda }{\sqrt {\alpha }}}={\sqrt {\lambda \rho c_{p}}}.}$

Some authors use the symbol ${\displaystyle e}$ to denote the thermal responsivity, although its usage along with an exponential becomes difficult. The SI units for thermal effusivity are ${\displaystyle {\rm {W}}{\sqrt {\rm {s}}}/({\rm {m^{2}K}})}$ or, equivalently, ${\displaystyle {\rm {J}}/({\rm {m^{2}K}}{\sqrt {\rm {s}}})}$. Thermal effusivity can also be a measure of a solid or rigid material's thermal inertia.

Thermal effusivity is a parameter that emerges upon applying solutions of the heat equation to heat flow through a thin surface-like region. It becomes particularly useful when the region is selected adjacent to a material's actual surface. Knowing the effusivity and equilibrium temperature of each of two material bodies then enables an estimate of their interface temperature ${\displaystyle T_{m}}$ when placed into thermal contact. If ${\displaystyle T_{1}}$ and ${\displaystyle T_{2}}$ are the temperature of the two bodies, then upon contact, the temperature of the contact interface (assumed to be a smooth surface) becomes

${\displaystyle T_{m}={\frac {r_{1}T_{1}+r_{2}T_{2}}{r_{1}+r_{2}}}}$

Specialty sensors have also been developed based on this relationship to measure effusivity.

Thermal effusivity and thermal diffusivity are related quantities; respectively a product versus a ratio of a material's intensive heat transport and storage properties. The diffusivity appears explicitly in the heat equation, which is an energy conservation equation, and measures the speed at which thermal equilibrium can be reached by a body. By contrast a body's effusivity (also sometimes called inertia, accumulation, responsiveness etc.) is its ability to resist a temperature change when subjected to a time-periodic, or similarly perturbative, forcing function.