Consider two parallel plane surfaces of infinite extent that have different uniform temperatures (Figure 1). The space between the surfaces either is a vacuum or contains a material that does not interact with radiative energy; the surface properties are independent of wavelength (*gray surfaces*). A useful *radiative exchange* result is the net transfer from a unit area of surface 1 across the separation space to surface 2. This is derived in standard heat transfer texts by flux or ray tracing methods, Siegel and Howell (1992). The Emissivity (which equals the *absorptivity* for a gray surface) of each surface is assumed independent of the angular direction of emission. Reflected energy, however, can be diffuse, specular (mirror-like), or can have an arbitrary angular distribution, and the same result is obtained. The surface properties can depend on temperature. For these conditions, after accounting for all exchanges between the parallel boundaries, the net energy flux (W/m^{2}) transferred ...

#### References

- Siegel, R. and Howell, J. R. (1992)
*Thermal Radiation Heat Transfer*, 3rd edn., Hemisphere Publishing Corporation, Washington DC. - Siegel, R. and Spuckler, C. M. (1994) Approximate solution methods for spectral radiative transfer in high refractive index layers,
*Int. J. of Heat and Mass Trans.*, 37 (Suppl. 1), 403-413. DOI: 10.1016/0017-9310(94)90040-X - Viskanta, R. and Grosh, R. J. (1962) Effect of surface emissivity on heat transfer by simultaneous conduction and radiation,
*Int. J. of Heat and Mass Trans.*, 5, 729-734. DOI: 10.1016/0017-9310(62)90203-X