A useful case study to develop lattice Boltzmann method performance: Gravity effects on slip velocity and temperature profiles of an air flow inside a microchannel under a constant heat flux boundary condition

Abstract

Mixed convection heat transfer of air in a 2-D microchannel is investigated numerically by using lattice Boltzmann method. The effects of buoyancy forces on slip velocity and temperature profiles are presented while the microchannel side walls are under a constant heat flux boundary condition. Three states are considered as no gravity, Gr = 100 and Gr = 500. At each state, the value of Knudsen number is chosen as Kn = 0.005, Kn = 0.01 and Kn = 0.02 respectively; while Reynolds number and Prandtl number are kept fixed at Re = 1 and Pr = 0.7. Density-momentum and internal energy distribution functions are used in order to simulate the hydrodynamic and thermal domains in LBM approach. Develop the ability of LBM to simulate the constant heat flux boundary condition along the microchannel walls in the presence of slip velocity and buoyancy forces is proved for the first time at present work. The new and interesting results are achieved such as generating a rotational cell through the fluid flow due to buoyancy forces which leads to see the negative slip velocity at these areas.