Generalized equation of phonon radiative transport

We write the equation of phonon radiative transport (EPRT) and the Boltzmann transport equation by including an in-scattering term under a relaxation time approximation. The in-scattering term contains a phase function that is exactly analogous to the phase function in the equation of radiative transport (ERT), thereby making EPRT exactly same as ERT. This formulation of EPRT is called the generalized EPRT (GEPRT). GEPRT is totally consistent with EPRT and transport theory; however, GEPRT shows that the mean free path due to particle scattering depends on the acoustic thickness of the medium if scattering is anisotropic and asymmetrical for heat flow in the thickness direction of the medium, irrespective of the boundary condition. GEPRT can be solved using the techniques used for solving ERT.