The Differential Approximation or P1 is also a simplification of the Radiation Transport Equation, which assumes that the radiation intensity is isotropic or direction independent at a given location in space. The full form of the radiant energy equation and the derivation of the P1 model for radiation are given in Modest [8]. Only a brief summary will be given here.

The spectral radiative heat flux in the diffusion limit for an emitting, absorbing, and linearly scattering medium, can be computed as:

(8–31)

The equation for the spectral incident radiation that results from substituting the above terms into the radiation transport equation:

(8–32)

where is the linear anisotropy coefficient.