Lattice Boltzmann simulation of natural convection in cubical enclosures for Bingham plastic fluid

Abstract

The purpose of this work is the study of the hydrodynamic and thermal characteristics of a Bingham plastic fluid contained in a differentially heated cubic cavity, at the center of which a cube-shaped obstacle has been placed. The effect of some parameters in this kind of configuration, such as the Rayleigh number Ra, Bingham number Bn, and the obstacle size e in the cavity, are very important in heat exchange. The study consists in analyzing those parameters at a fixed value of the Prandtl number Pr = 10, while Ra, Bn, and e vary in the ranges 10+3–10+6, 0–20, and 0–0.75, respectively. In order to resolve the dynamic governing equations, we use the multiple relaxation time scheme of the lattice Boltzmann method (LBM/MRT) incorporating the Papanastasiou exponential modification approach. The Finite Difference Method (FDM) is used for the energy equation discretization. The obtained results show that the buoyancy intensity leads to considerable modifications on streamlines and isotherms. Concerning the influence of the viscoplasticity of the Bingham fluid, we note a diminution of central cells and a modification of the Nusselt number evolution due to the increase of the Bingham number. The growth of the obstacle size was found to decrease the heat transfer rate. This diminution is proportional to the growth of the Bingham number.