Absorptance

Not to be confused with absorbance or absorption coefficient.

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

Radiometry coefficients

• v
• t
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Quantity		SI units	Notes
Name	Sym.
Hemispherical emissivity	ε	—	Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.
Spectral hemispherical emissivity	εν ελ	—	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	εΩ	—	Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.
Spectral directional emissivity	εΩ,ν εΩ,λ	—	Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance	A	—	Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance	Aν Aλ	—	Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	AΩ	—	Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance	AΩ,ν AΩ,λ	—	Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance".
Hemispherical reflectance	R	—	Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance	Rν Rλ	—	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	RΩ	—	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	RΩ,ν RΩ,λ	—	Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance	T	—	Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance	Tν Tλ	—	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	TΩ	—	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	TΩ,ν TΩ,λ	—	Spectral radiance transmitted by a surface, divided by that received by that surface.
Hemispherical attenuation coefficient	μ	m−1	Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient	μν μλ	m−1	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient	μΩ	m−1	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	μΩ,ν μΩ,λ	m−1	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.