Absorptance

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 Template:Mvar is defined as

$A=\frac{{\mathrm{\Phi }}_e^a}{{\mathrm{\Phi }}_e^i},$

where

• Template:Tmath is the radiant flux absorbed by that surface;
• Template:Tmath 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 Template:Math and Template:Math respectively, are defined as

$\begin{array}{cc}{A}_{\nu }& =\frac{{\mathrm{\Phi }}_{e,\nu }^a}{{\mathrm{\Phi }}_{e,\nu }^i},\\ A_{\lambda }& =\frac{{\mathrm{\Phi }}_{e,\lambda }^a}{{\mathrm{\Phi }}_{e,\lambda }^i},\end{array}$

where

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

Directional absorptance

Directional absorptance of a surface, denoted Template:Math, is defined as

$A_{\mathrm{\Omega }}=\frac{L_{\mathrm{e},\mathrm{\Omega }}^{\mathrm{a}}}{L_{\mathrm{e},\mathrm{\Omega }}^{\mathrm{i}}},$

where

• Template:Tmath is the radiance absorbed by that surface;
• Template:Tmath 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 Template:Math and Template:Math respectively, are defined as

$\begin{array}{cc}{A}_{\nu ,\mathrm{\Omega }}& =\frac{L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\nu }}^{\mathrm{a}}}{L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\nu }}^{\mathrm{i}}},\\ A_{\lambda ,\mathrm{\Omega }}& =\frac{L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\lambda }}^{\mathrm{a}}}{L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\lambda }}^{\mathrm{i}}},\end{array}$

where

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