# Thermal effusivity

In thermodynamics, the thermal effusivity, thermal inertia or thermal responsivity of a material is defined as the square root of the product of the material's thermal conductivity and its volumetric heat capacity.[1][2]

${\displaystyle e={\sqrt {\left(\lambda \rho c_{\text{p}}\right)}}}$
Thermal effusivity sensor typically used in the direct measurement of materials.

Here, ${\displaystyle \lambda }$ is the thermal conductivity, ${\displaystyle \rho }$ is the density and ${\displaystyle c_{\text{p}}}$ is the specific heat capacity. The product of ${\displaystyle \rho }$ and ${\displaystyle c_{\text{p}}}$ is known as the volumetric heat capacity.

A material's thermal effusivity is a measure of its ability to exchange thermal energy with its surroundings.

If two semi-infinite[i] bodies initially at temperatures ${\displaystyle T_{1}}$ and ${\displaystyle T_{2}}$ are brought in perfect thermal contact, the temperature at the contact surface ${\displaystyle T_{m}}$ will be given by their relative effusivities.[3]

${\displaystyle T_{m}=T_{1}+\left(T_{2}-T_{1}\right){\frac {e_{2}}{e_{2}+e_{1}}}={\frac {e_{1}T_{1}+e_{2}T_{2}}{e_{1}+e_{2}}}}$

This expression is valid for all times for semi-infinite bodies in perfect thermal contact. It is also a good first guess for the initial contact temperature for finite bodies.

Direct measurement of thermal effusivity may be performed using specialty sensors, as pictured.

## Thermal Effusivity vs Thermal Effusance [4]

"Thermal effusance", is a newly coined term as a result of some discussions within ASTM where a specific researcher from the UK has determined that he does not accept the common term thermal effusivity and has invented his own term "thermal effusance". He distinguishes the difference as follows: "A materials thermal effusivity is a measure of its ability to exchange thermal energy with its surroundings. Although the quantity of thermal effusivity can be expressed in bulk property terms of e = √k∙ρ∙Cρ when measured, it is not measured in terms of bulk properties." Given the logic of this argument, the same could be said for other heat transfer properties such as thermal conductivity. The distinction is addressed in understanding that in measuring non-solid bulk material the values are typically described as "effective" thermal effusivity and "effective" thermal conductivity.

## Applications

One application of thermal effusivity is the quasi-qualitative measurement of coolness or warmth feel of materials on textiles and fabrics. When a textile or fabric is measured from the surface with short test times by any transient method or instrument, the measured effusivity includes various heat transfer mechanisms, including conductivity, convection and radiation, as well as contact resistance between the sensor and sample.