Abstract
In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.