In Figure 4-12, consider a point
P located on a semi-transparent surface that has an emissivity
εu, diffuse reflectivity
ρd,u, specular reflectivity
ρs,u, absorptivity
αu, refractive index
nu, and temperature
Tu on the upside, and an emissivity
εd, diffuse reflectivity
ρd,d, specular reflectivity
ρs,d, absorptivity
αd, refractive index
nd, and temperature
Td on the downside. As the surface is assumed semi-transparent, some radiation is transmitted through the body.
The total incoming radiative flux at P is called
irradiation, and is denoted
Gu on the upside and
Gd on the downside. The total diffuse outgoing radiative flux at
P is called
radiosity and denoted
Ju on the upside and
Jd on the downside. This radiosity is the sum of diffusively reflected radiation, emitted radiation and transmitted radiation coming from the other side of the semi-transparent layer:
The net inward radiative heat fluxes on the upside and downside, qu and
qd, are then given by the difference between the irradiation and the radiosity:
Using Equation 4-77 to
Equation 4-82,
Ju and
Jd can be eliminated and a general expression is obtained for the net inward heat fluxes into the semi-transparent body based on
Gu,
Gd,
Tu and
Td: