# Glossary for Radiative Heat Transfer

Absorption

The process of converting radiation intercepted by matter to internal thermal energy.

Absorptivity

Fraction of the incident radiation absorbed by matter. Modifiers: directional, hemispherical, spectral, total. The spectral directional absorptivity reads

$\alpha_{\lambda, \theta}(\lambda, \theta, \phi) \equiv \frac{I_{\lambda, i, \mathrm{abs}}(\lambda, \theta, \phi)}{I_{\lambda, i}(\lambda, \theta, \phi)}$

For most engineering calculation, a spectral, hemispherical absorptivity $\alpha_{\lambda}(\lambda)$ is defined as

$\alpha_{\lambda}(\lambda) \equiv \frac{G_{\lambda, \mathrm{abs}}(\lambda)}{G_{\lambda}(\lambda)}$

Finally The total, hemispherical absorptivity, $\alpha,$ represents an integrated average over both direction and wavelength. It is defined as the fraction of the total irradiation absorbed by a surface

$\alpha \equiv \frac{G_{\mathrm{abs}}}{G} = \frac{\int_{0}^{\infty} \alpha_{\lambda}(\lambda) G_{\lambda}(\lambda) d \lambda}{\int_{0}^{\infty} G_{\lambda}(\lambda) d \lambda}$
Blackbody

The ideal emitter and absorber. Modifier referring to ideal behavior. Denoted by the subscript $b$

Diffuse

Modifier referring to the directional independence of the intensity associated with emitted, reflected, or incident radiation

Directional

Modifier referring to a particular direction. Denoted by the subscript $\theta$

Directional distribution

Refers to variation with direction.

Emission

The process of radiation production by matter at a non-zero temperature. Modifiers: diffuse, blackbody, spectral.

Emissive power

Rate of radiant energy emitted by a surface in all directions per unit area of the surface, $E\left(\mathrm{W} / \mathrm{m}^{2}\right)$ Modifiers: spectral, total, blackbody.

Emissivity

Ratio of the radiation emitted by a surface to the radiation emitted by a blackbody at the same temperature. Modifiers: directional, hemispherical, spectral, total.

Gray surface

A surface for which the spectral absorptivity and the emissivity are independent of wavelength over the spectral regions of surface irradiation and emission.

Hemispherical

Modifier referring to all directions in the space above a surface.

Intensity

Rate of radiant energy propagation in a particular direction, per unit area normal to the direction, per unit solid angle about the direction, $I\left(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{sr}\right)$ Modifier: spectral.

Rate at which radiation is incident on a surface from all directions per unit area of the surface, $G\left(\mathrm{W} / \mathrm{m}^{2}\right)$ Modifiers: spectral, total, diffuse.

Kirchhoff’s law

Relation between emission and absorption properties for surfaces irradiated by a blackbody at the same temperature.

Planck’s law

Spectral distribution of emission from a blackbody. The blackbody spectral intensity reads

$I_{\lambda, b}(\lambda, T)=\frac{2 h c_{o}^{2}}{\lambda^{5}\left[\exp \left(h c_{o} / \lambda k_{B} T\right)-1\right]}$

where $h=6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$ and $k_{B}=1.381 \times 10^{-23} \mathrm{J} / \mathrm{K}$ are the universal Planck and Boltzmann constants, respectively, $c_{o}=2.998 \times 10^{8} \mathrm{m} / \mathrm{s}$ is the speed of light in vacuum, and $T$ is the absolute temperature of the blackbody (K). since the blackbody is a diffuse emitter, it follows that its spectral emissive power is

$E_{\lambda, b}(\lambda, T)=\pi I_{\lambda, b}(\lambda, T)=\frac{C_{1}}{\lambda^{5}\left[\exp \left(C_{2} / \lambda T\right)-1\right]}$

where the first and second radiation constants are

$C_{1}=2 \pi h c_{o}^{2}=3.742 \times 10^{8} \mathrm{W} \cdot \mu \mathrm{m}^{4} / \mathrm{m}^{2}, \quad C_{2}=\left(h c_{o} / k_{B}\right)=1.439 \times 10^{4} \mu \mathrm{m} \cdot \mathrm{K}$

Rate at which radiation leaves a surface due to emission and reflection in all directions per unit area of the surface, $J\left(\mathrm{W} / \mathrm{m}^{2}\right)$ Modifiers spectral, total.

Reflection

The process of redirection of radiation incident on a surface. Modifiers: diffuse, specular.

Reflectivity

Fraction of the incident radiation reflected by matter. Modifiers: directional, hemispherical, spectral, total. The spectral, directional reflectivity, $\rho_{\lambda, \theta}(\lambda, \theta, \phi),$ of a surface is defined as the fraction of the spectral intensity incident in the direction of $\theta$ and $\phi$ which is reflected by the surface. We have

$\rho_{\lambda, \theta}(\lambda, \theta, \phi) \equiv \frac{I_{\lambda, i, \mathrm{ref}}(\lambda, \theta, \phi)}{I_{\lambda, i}(\lambda, \theta, \phi)}$

The spectral, hemispherical reflectivity $\rho_{\lambda}(\lambda)$ is then defined as the fraction of the spectral irradiation that is reflected by the surface,

$\rho_{\lambda}(\lambda) \equiv \frac{G_{\lambda, \text { ref }}(\lambda)}{G_{\lambda}(\lambda)}$

which is equivalent to

$\rho_{\lambda}(\lambda)=\frac{\int_{0}^{2 \pi} \int_{0}^{\pi / 2} \rho_{\lambda, \theta}(\lambda, \theta, \phi) I_{\lambda, i}(\lambda, \theta, \phi) \cos \theta \sin \theta d \theta d \phi}{\int_{0}^{2 \pi} \int_{0}^{\pi / 2} I_{\lambda, i}(\lambda, \theta, \phi) \cos \theta \sin \theta d \theta d \phi}$

The total, hemispherical reflectivity $\rho$ is then defined as

$\rho \equiv \frac{G_{\mathrm{ref}}}{G}=\frac{\int_{0}^{\infty} \rho_{\lambda}(\lambda) G_{\lambda}(\lambda) d \lambda}{\int_{0}^{\infty} G_{\lambda}(\lambda) d \lambda}$
Semitransparent

Refers to a medium in which radiation absorption is a volumetric process.

Solid angle

Region subtended by an element of area on the surface of a sphere with respect to the center of the sphere, $\omega(\mathrm{sr})$

Spectral

Modifier referring to a single-wavelength (monochromatic) component. Denoted by the subscript $\lambda$

Spectral distribution

Refers to variation with wavelength.

Specular

Refers to a surface for which the angle of reflected radiation is equal to the angle of incident radiation.

Stefan-Boltzmann law

Emissive power of a blackbody. The total emissive power of a blackbody $E_b$ may be expressed

$E_{b}=\sigma T^{4}$

where the Stefan-Boltzmann constant has the numerical value

$\sigma=5.670 \times 10^{-8} \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}^{4}$

Electromagnetic energy emitted by matter at a non-zero temperature and concentrated in the spectral region from approximately 0.1 to $100 \mu \mathrm{m}$

Total

Modifier referring to all wavelengths.

Transmission

The process of thermal radiation passing through matter.

Transmissivity

Fraction of the incident radiation transmitted by matter. Modifiers: hemispherical, spectral, total.

$\tau_{\lambda}=\frac{G_{\lambda, \text { tr }}(\lambda)}{G_{\lambda}(\lambda)}$

and integrated over the wavelength

$\tau=\frac{G_{\mathrm{tr}}}{G}$

The total transmissivity $\tau$ is related to the spectral component $\tau_{\lambda}$ by

$\tau=\frac{\int_{0}^{\infty} G_{\lambda, \mathrm{tr}}(\lambda) d \lambda}{\int_{0}^{\infty} G_{\lambda}(\lambda) d \lambda}=\frac{\int_{0}^{\infty} \tau_{\lambda}(\lambda) G_{\lambda}(\lambda) d \lambda}{\int_{0}^{\infty} G_{\lambda}(\lambda) d \lambda}$
Wien’s displacement law

Locus of the wavelength corresponding to peak emission by a blackbody.