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 = Φ e a Φ e i , {\displaystyle A=\mathrm {\frac {\Phi _{e}^{a}}{\Phi _{e}^{i}}} ,}
where
Φ e a {\displaystyle \mathrm {\Phi _{e}^{a}} } is the radiant flux absorbed by that surface; Φ e i {\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 Aν and Aλ respectively, are defined as
A ν = Φ e , ν a Φ e , ν i , A λ = Φ e , λ a Φ e , λ i , {\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
Φ e , ν a {\displaystyle \mathrm {\Phi _{e,\nu }^{a}} } is the spectral radiant flux in frequency absorbed by that surface; Φ e , ν i {\displaystyle \mathrm {\Phi _{e,\nu }^{i}} } is the spectral radiant flux in frequency received by that surface; Φ e , λ a {\displaystyle \mathrm {\Phi _{e,\lambda }^{a}} } is the spectral radiant flux in wavelength absorbed by that surface; Φ e , λ i {\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 AΩ, is defined as
A Ω = L e , Ω a L e , Ω i , {\displaystyle A_{\Omega }={\frac {L_{\mathrm {\mathrm {e} ,\Omega } }^{\mathrm {a} }}{L_{\mathrm {e} ,\Omega }^{\mathrm {i} }}},}
where
L e , Ω a {\displaystyle L\mathrm {_{e,\Omega }^{a}} } is the radiance absorbed by that surface; L e , Ω i {\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 Aν,Ω and Aλ,Ω respectively, are defined as
A ν , Ω = L e , Ω , ν a L e , Ω , ν i , A λ , Ω = L e , Ω , λ a L e , Ω , λ i , {\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
L e , Ω , ν a {\displaystyle L\mathrm {_{e,\Omega ,\nu }^{a}} } is the spectral radiance in frequency absorbed by that surface; L e , Ω , ν i {\displaystyle L\mathrm {_{e,\Omega ,\nu }^{i}} } is the spectral radiance received by that surface; L e , Ω , λ a {\displaystyle L\mathrm {_{e,\Omega ,\lambda }^{a}} } is the spectral radiance in wavelength absorbed by that surface; L e , Ω , λ i {\displaystyle L\mathrm {_{e,\Omega ,\lambda }^{i}} } is the spectral radiance in wavelength received by that surface.
Other radiometric coefficients
References