MRT-LBM Simulation of Natural Convection in a Rayleigh-Benard Cavity With Linearly Varying Temperatures on the Sides: Application to a Micropolar Fluid

Abstract

A two-dimensional numerical simulation is conducted to study natural convection flow and heat transfer characteristics in a square cavity filled with a micropolar fluid. The lower and upper walls of the cavity are respectively subject to isothermal heating and cooling while the temperatures of both vertical sides decrease linearly in the upwards direction. The Lattice-Boltzmann Method (LBM), with the multi-relaxation time (MRT) scheme for the collision process, is used to solve the problem with the objective to assess the ability and efficiency of this numerical method to describe the micropolar fluid behavior under the effect of the imposed thermal boundary conditions. Computations are carried out for Rayleigh number, , and material parameter (vortex viscosity), , varying respectively in the ranges 10 3  10 6 and 0 2. Combined effects of these parameters on the multiplicity of solutions and critical values of from which transitions occur are investigated for Pr 7. An increase of the material parameter is shown to increase the critical Rayleigh numbers, which confirms the stabilizing effect of the micropolar fluid compared to the Newtonian case ( 0). The study covers both steady and unsteady aspects of the problem under consideration. Initial perturbations play an important role in the cooling process of the hot bottom wall in the present configuration. The bicellular ascending and descending flows are two solutions mirror images of each other but they lead to very different quantities of heat from the bottom wall.

Simulation of Natural Convection by Multirelaxation Time Lattice Boltzmann Method in a Triangular Enclosure

“…Numerous of the previous researches on natural convection have focused on rectangular enclosures with a vertical (Rayleigh-Benard convection) or a horizontal gradient of temperature [9,10], while others have studied rectangular cavities partially heated or cooled [11,12]. Natural convection in triangular enclosures [13][14][15] has been treated also due to its widespread use in many industrial and domestic systems such as building roofs and solar power, etc.…”