Thermal radiation
Our formulation is based on gray body radiation theory, which means that the monochromatic emissivity of the body is independent of the wavelength of propagation of the radiation. Only diffuse (nondirectional) reflection is considered. Attenuation of the radiation in the cavity medium is not considered. Using these assumptions together with the assumption of isothermal and isoemissive cavity facets, we can write the equations for radiation fluxes per unit area into cavity facets as
where qcj is the flux into facet j; ϵi,ϵj are the emissivities of facets i,j; σ is the Stefan-Boltzmann constant; Fij is the geometrical view factor matrix; θi,θj are the temperatures of facets i,j; θZ is the value of absolute zero on the temperature scale being used; and δij is the Kronecker delta.
In the case of an open cavity ( ∑jFij≠1 ) exposed to an external ambient temperature, θamb , the effect of radiation to the external medium is accounted for by modifying Equation 1 to
where Fi,amb=(1−∑jFij) .
In the special case of blackbody radiation, where no reflection takes place (emissivity equal to one), Equation 2 reduces to