Using of Multi-Phase Thermal Model of the Lattice Boltzmann Method for Simulation of Two-Phase Rayleigh–Bénard Convective Heat Transfer

In this study, the neutral scalar thermal model is presented for single-phase and so, a single-phase Rayleigh–B´enard is investigated. The Shan-Chen model is expressed in the isothermal state, and by combining the two models, the mixed Shan-Chen thermal method is presented. Then, using a mixed model, a two-phase Rayleigh–B´enard with the thermal Shan-Chen method is proposed. Two-phase Rayleigh–B´enard convective heat transfer is simulated at the relatively high Rayleigh numbers (105), different Capillary numbers (10− 3 to 10− 4), and also, various ε parameters (parameters related to the temperature difference and thermal expansion). In twophase Rayleigh–B´enard convective heat transfer increasing the Rayleigh number leads to the increment of Rayleigh–B´enard convective heat transfer between the hot and cold wall and the temperature gradient enhancesin the vicinity of the upper wall, lower wall, and interface. It is worth mentioning, that in the two-phase Rayleigh–B´enard problem, the variations of the interface are changed only by changing the thermal expansion coefficient and the temperature difference between the two walls. The results show that the mixed model can
simulate two-phase thermal flows. The stability of this method is the same as the multi-phase isothermal models,
and it can be applied well for different state equations and relatively high Rayleigh numbers.