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]

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

where

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

{\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

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

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

where

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

{\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

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

Other radiometric coefficients

Radiometry coefficients
v
t
e
Quantity		SI units	Notes
Name	Sym.	SI units	Notes
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	$ε ν$ $ε λ$	—	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	$ε Ω$	—	Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.
Spectral directional emissivity	$ε Ω, ν$ $ε Ω, λ$	—	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	$A ν$ $A λ$	—	Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	$A Ω$	—	Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance	$A Ω, ν$ $A Ω, λ$	—	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	$R ν$ $R λ$	—	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	$R Ω$	—	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	$R Ω, ν$ $R Ω, λ$	—	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	$T ν$ $T λ$	—	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	$T Ω$	—	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	$T Ω,ν$ $T Ω, λ$	—	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	$μ ν$ $μ λ$	m⁻¹	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient	$μ Ω$	m⁻¹	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	$μ Ω, ν$ $μ Ω, λ$	m⁻¹	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

References

^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorptance". doi:10.1351/goldbook.A00035
^ ^a ^b ^c ^d "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

[GoldBook-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorptance". doi:10.1351/goldbook.A00035

[ISO_9288-1989-2] "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

[1]

[2]

Absorptance

Mathematical definitions

Hemispherical absorptance

Spectral hemispherical absorptance

Directional absorptance

Spectral directional absorptance

Other radiometric coefficients

References

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