Physics:Absorptance

Short description: Ability of a material to absorb radiant energy

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

[math]\displaystyle{ A = \mathrm{ \frac{\Phi_e^a}{\Phi_e^i} }, }[/math]

where

• [math]\displaystyle{ \mathrm{\Phi_e^a} }[/math] is the radiant flux absorbed by that surface;
• [math]\displaystyle{ \mathrm{\Phi_e^i} }[/math] 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

[math]\displaystyle{ \begin{align} 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{align} }[/math]

where

• [math]\displaystyle{ \mathrm{\Phi_{e,\nu}^a} }[/math] is the spectral radiant flux in frequency absorbed by that surface;
• [math]\displaystyle{ \mathrm{\Phi_{e,\nu}^i} }[/math] is the spectral radiant flux in frequency received by that surface;
• [math]\displaystyle{ \mathrm{\Phi_{e,\lambda}^a} }[/math] is the spectral radiant flux in wavelength absorbed by that surface;
• [math]\displaystyle{ \mathrm{\Phi_{e,\lambda}^i} }[/math] is the spectral radiant flux in wavelength received by that surface.

Directional absorptance

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

[math]\displaystyle{ A_\Omega = \frac{L_\mathrm{\mathrm{e},\Omega}^\mathrm{a}}{L_{\mathrm{e},\Omega}^\mathrm{i}}, }[/math]

where

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

[math]\displaystyle{ \begin{align} 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{align} }[/math]

where

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