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 A is defined as

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

where

• ⁠${\mathrm{\Phi }}_{\mathrm{e}}^{\mathrm{a}}$⁠ is the radiant flux absorbed by that surface;
• ⁠${\mathrm{\Phi }}_{\mathrm{e}}^{\mathrm{i}}$⁠ 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 A_ν and A_λ respectively, are defined as

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

where

• ⁠${\mathrm{\Phi }}_{\mathrm{e},\mathrm{\nu }}^{\mathrm{a}}$⁠ is the spectral radiant flux in frequency absorbed by that surface;
• ⁠${\mathrm{\Phi }}_{\mathrm{e},\mathrm{\nu }}^{\mathrm{i}}$⁠ is the spectral radiant flux in frequency received by that surface;
• ⁠${\mathrm{\Phi }}_{\mathrm{e},\mathrm{\lambda }}^{\mathrm{a}}$⁠ is the spectral radiant flux in wavelength absorbed by that surface;
• ⁠${\mathrm{\Phi }}_{\mathrm{e},\mathrm{\lambda }}^{\mathrm{i}}$⁠ is the spectral radiant flux in wavelength received by that surface.

Directional absorptance

Directional absorptance of a surface, denoted A_Ω, is defined as

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

where

• ⁠$L{}_{\mathrm{e},\mathrm{\Omega }}^{\mathrm{a}}$⁠ is the radiance absorbed by that surface;
• ⁠$L{}_{\mathrm{e},\mathrm{\Omega }}^{\mathrm{i}}$⁠ 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 A_ν,Ω and A_λ,Ω respectively, are defined as

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

where

• ⁠$L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\nu }}^{\mathrm{a}}$⁠ is the spectral radiance in frequency absorbed by that surface;
• ⁠$L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\nu }}^{\mathrm{i}}$⁠ is the spectral radiance received by that surface;
• ⁠$L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\lambda }}^{\mathrm{a}}$⁠ is the spectral radiance in wavelength absorbed by that surface;
• ⁠$L{}_{\mathrm{e},\mathrm{\Omega },\mathrm{\lambda }}^{\mathrm{i}}$⁠ is the spectral radiance in wavelength received by that surface.