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.

Hemispherical absorptance
Hemispherical absorptance of a surface, denoted $A$ is defined as
 * $$A = \mathrm{ \frac{\Phi_e^a}{\Phi_e^i} },$$

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

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
 * $$\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}$$ 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.