Absorption and Transmission

The absorptive (semi-transparent) solids absorb heat radiation in accordance with the specified absorption coefficient.

Restriction:

This feature is available for the HVAC module users only.

This option is available for the Discrete Ordinates model only.

In the absence of emitting the radiative transfer equation (RTE) Equation 2 (see “Discrete Ordinates”) can be written along axis x as:

	(1)

The radiation intensity continuously decreases with distance x that the light traverses:

	(2)

where I0 is the initial intensity of radiation and α, the absorption coefficient, is the characteristic of particular material.

At the interface between two transparent or semi-transparent media with different refractive indices the incident radiation changes its direction in accordance with the Snell’s law:

	(3)

where n1 and n2 are the refractive indices of the first and second medium (n is always equal to 1 for all fluids and for a fully transparent solid material, if its radiation properties are not specified in the Engineering Database) and θ1 and θ2 are the incident and refraction angles correspondingly.

Figure 1. Radiation reflection and transmission at the interface of absorptive media.

The radiation reflection at the interface between two transparent or semi-transparent media with different refractive indices follows the Fresnel’s relation for unpolarized light:

	(4)

where ρ is the reflectivity which define the fraction of reflected radiation.

The fraction of radiation transmitted through the interface is defined as:

	(5)

If the light is normal to the interface, then:

	(6)

The phenomena of absorption, reflection, and transmission may be applied to the passage of light through a semi-transparent solid plate. In case of the incident light is normal to the solid surface, the transmitted intensity can be estimated as shown in Figure 2.

Figure 2. Radiation transmission through a transparent medium.

For an incident beam of intensity I0 that impinges on the front surface of a semi-transparent solid plate of thickness l and absorption coefficient α the total reflected intensity IR from the back face can be estimated as:

	(7)

The total transmitted intensity IT at the back face can be estimated as:

	(8)

The total absorbed intensity IA in the solid plate can be estimated as:

	(9)

So the absorption coefficient α can be expressed as:

	(10)

Thus, the fraction of incident light that is transmitted through a semi-transparent material depends on the losses that are incurred by absorption and reflection.

So in accordance with equation Equation 8, the absorption coefficient α can be approximately expressed as:

	(11)