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.^[1]

Mathematical definitions

Hemispherical absorptance

Hemispherical absorptance of a surface, denoted A is defined as^[2]

${\displaystyle A=\mathrm {\frac {\Phi _{e}^{a}}{\Phi _{e}^{i}}} ,}$

where

• ${\displaystyle \mathrm {\Phi _{e}^{a}} }$ is the radiant flux absorbed by that surface;
• ${\displaystyle \mathrm {\Phi _{e}^{i}} }$ 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^[2]

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

where

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

Directional absorptance

Directional absorptance of a surface, denoted A_Ω, is defined as^[2]

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

where

• ${\displaystyle L\mathrm {_{e,\Omega }^{a}} }$ is the radiance absorbed by that surface;
• ${\displaystyle L\mathrm {_{e,\Omega }^{i}} }$ 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^[2]

${\displaystyle {\begin{aligned}A_{\nu ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\nu }^{a}} }{L\mathrm {_{e,\Omega ,\nu }^{i}} }},\\[4pt]A_{\lambda ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\lambda }^{a}} }{L\mathrm {_{e,\Omega ,\lambda }^{i}} }},\end{aligned}}}$

where

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

Other radiometric coefficients

References