# Radiative transfer through transparent media

The information on radiation fundamentals and properties is used to find the net rate of energy transfer to/from a material by radiation. Because of the complexities possible in a complete treatment of the spectral and directional characteristics of radiation, it is useful to first develop some simple if less accurate methods for approximating the radiative transfer. If radiation provides only 10 percent of the total heat transfer by all modes, then it is perfectly acceptable to determine the radiative transfer to within 20 percent, as any error is only $\pm$ 2 percent of the total heat transfer. If radiation is 90 percent of the total heat transfer (often the case in radiant heaters and coal-fired steam generators,) then a much more accurate approach is indicated.

## Radiative heat transfer between two areas

Consider first a surface of area A, temperature T , and total emissivity ε. The rate of radiative energy emission from this surface per unit area is $E = \varepsilon \sigma {T^4}.$ Let the surroundings in all directions be at temperature T. If the surroundings are far from surface A or are black, then little of the energy emitted from A will be reflected from the surroundings, and the rate of energy incident on A per unit area from the surroundings is denoted by the symbol G, and is given by

$G = \sigma T_\infty ^4$

The net radiative heat flux on surface A is the difference between the emitted and absorbed radiative fluxes, or

$q'' = E - \alpha G = \varepsilon \sigma {T^4} - \alpha \sigma T_\infty ^4$

See Main Article Radiative heat transfer between two areas.

## Configuration factor

In more complex cases than radiative heat transfer between two areas, a surface is exchanging radiative energy with multiple surfaces, each with a different temperature and different properties. It is instructive to first examine the radiative exchange between a single pair of these surfaces.

See Main Article Configuration factor.

## Configuration factor algebra

The reciprocity equations

dFd1 − d2dA1 = dFd2 − d1dA2

dA1Fd1 − 2 = A2dF2 − d1

or

A1F1 − 2 = A2F2 − 1

and the summation relation,

$\sum\limits_{k = 1}^N {{F_{j - k}}} = 1$

and the associative relation

Fj − (k + l) = Fjk + Fjl

from configuration factor are the basis of configuration factor algebra.

See Main Article Configuration factor algebra.

## References

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.