Diffusion asymptotics of a kinetic model for gas-particle mixtures with energy exchanges

In this paper, we propose a non-isothermal kinetic model for the interactions between dust particles and gas molecules. We assume that gas-dust collisions follow a diffuse reflection mechanism at the surface of the dust particles. The surface temperature of the particles is treated as a function of time and space, satisfying a transport-like equation. The key novelty of this model is its ability to derive both the conservation of total energy in the system and an explicit expression for entropy. After adimensionalising the equations, we perform a formal diffusive asymptotic analysis leading to a coupled system of partial differential equations. In particular, we examine the limiting case where the mass ratio between gas and dust, as well as the Mach and Knudsen numbers, approach zero.