Absorptance Explained

In the study of heat transfer, absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power.

Mathematical definitions

Hemispherical absorptance

Hemispherical absorptance of a surface, denoted is defined as^[1]

A = (\Phi ^{a} _{e})/(\Phi ^{i} _{e}) , where

• is the radiant flux absorbed by that surface;
• is the radiant flux received by that surface.

Spectral hemispherical absorptance

Spectral hemispherical absorptance in frequency and spectral hemispherical absorptance in wavelength of a surface, denoted and respectively, are defined as

\begin{align} A _{\nu} & = (\Phi ^{a} _{e,\nu})/(\Phi ^{i} _{e,\nu}) , \\ A _{λ} & = (\Phi ^{a} _{e,λ})/(\Phi ^{i} _{e,λ}) , \end{align} where

• is the spectral radiant flux in frequency absorbed by that surface;
• is the spectral radiant flux in frequency received by that surface;
• is the spectral radiant flux in wavelength absorbed by that surface;
• is the spectral radiant flux in wavelength received by that surface.

Directional absorptance

Directional absorptance of a surface, denoted, is defined as

A _{\Omega} = (L ^{a} _{e ,\Omega})/(L ^{i} _{e ,\Omega}) , where

• is the radiance absorbed by that surface;
• is the radiance received by that surface.

Spectral directional absorptance

Spectral directional absorptance in frequency and spectral directional absorptance in wavelength of a surface, denoted and respectively, are defined as

\begin{align} A _{\nu,\Omega} & = (L ^{a} ^{e,\Omega,\nu})/(L ^{i} ^{e,\Omega,\nu}) , \\[ 4 pt] A _{λ,\Omega} & = (L ^{a} ^{e,\Omega,λ})/(L ^{i} ^{e,\Omega,λ}) , \end{align} where

• is the spectral radiance in frequency absorbed by that surface;
• is the spectral radiance received by that surface;
• is the spectral radiance in wavelength absorbed by that surface;
• is the spectral radiance in wavelength received by that surface.

Notes and References

1. Web site: Thermal insulation — Heat transfer by radiation — Physical quantities and definitions. ISO 9288:1989. ISO catalogue. 1989. 2015-03-15.