Increase lattice Boltzmann method ability to simulate slip flow regimes with dispersed CNTs nanoadditives inside: Develop a model to include buoyancy forces in distribution functions of LBM for slip velocity

In this study, the mixed convection of flow in a microchannel containing nanofluid is simulated by the Lattice Boltzmann Method. The water/functionalized multi-wall carbon nanotubes nanofluid is selected as the working fluid. The cold nanofluid passes through the warm walls of the microchannel to cool them down. The buoyancy forces caused by the mass of the nanofluid change the hydrodynamic properties of the flow. Accordingly, the gravitational term is included as an external force in the Boltzmann equation and Boltzmann's hydrodynamic and thermal equations are rewritten under new conditions. The flow analysis is performed for different values of slip coefficient and Grashof number. The results are expressed in terms of velocity and temperature profiles, contours of streamlines and isotherms beside the slip velocity and temperature jump diagrams. It is observed that the effect of buoyancy force changes the motion properties of the flow in the input region and increases the hydrodynamic input length of flow. These changes are particularly evident at higher values of Grashof numbers and create a rounded circle in the opposite direction of the flow at the microchannel input. The negative slip velocity caused by the vortex resulted in a temperature jump at the input flow region.