Thermal transport due to transverse phonons in nano and micro particulate media

This paper deals with the calculation of the thermal transport cross section and phase function of transverse phonons for scattering by nano and micro particles. Thermal transport cross section is different than the scattering cross section due to the anisotropic nature of scattering. Exact formulation of the phase function is given for the Rayleigh scattering. This paper also proposes an approximate method to calculate the thermal transport cross section for low contrast scatterer. It is also shown that for SH (horizontally shear) phonons the scattering and transport cross sections are proportional to ?8 rather than the well accepted value of ?4 in the Rayleigh regime where ? is the frequency of the SH phonons. The formulations developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems such as nano composites, nano-micro particle laden systems etc.