Kinetic equation for particle transport and heat transfer in nonisothermal turbulent flows

The physical situation of two-phase nonisothermal turbulent fluid flows laden with nonevaporating spherical particles is considered. A closed kinetic equation for the transport of particles and their temperature is derived by solving the involved closure problem using the functional method. The equation is exact when the fluctuations of fluid flow variables along the particle path are distributed as Gaussian. For the case of homogeneous turbulent flows, macroscopic equations describing the time evolution of statistical properties related to particle velocity and temperature are obtained by taking various moments of the closed kinetic equation. These equations are computed for the case of homogeneous shear turbulent flow with constant temperature gradient, and the results are compared with the data of our direct numerical simulation study.