Applications of lattice Boltzmann method for double-diffusive convection in the cavity: a review

Over the years, the lattice Boltzmann method (LBM) has been evolved as a substitute and efficient numerical tool to mimic the single/multiphase fluid flow and transport problems. LBM has been mainly advantageous in multi-physics and multiphase flow applications. On the other hand, double-diffusive convection has extensive occurrence in domestic and industrial activities. The type of convection in which the combined effect of temperature and concentration gradients (resulting in the density variation) on fluid's hydrodynamic and thermal characteristics is called double-diffusive convection (DDC). The importance of DDC has been recognized in various engineering applications, and it has thoroughly been investigated experimentally, theoretically, and numerically. This paper is proposed to deliver a brief review of double-diffusive convection by computational approach (mainly lattice Boltzmann method and Navier–Stokes equation-based solvers). This review explores the illustration of some of the practical applications of DDC, studies of DDC in various heated cavities. The paper also gives insights into LBM formulation of DDC under various external force conditions. A table compromising various empirical correlations of the average Nusselt numbers and average Sherwood numbers as a function of different governing parameters has been discussed.