Natural convection in a differentially-heated square enclosure filled with a nanofluid: Significance of the thermophoresis force and slip/drift velocity

Natural convection in a differentially-heated enclosure is studied, with emphasis on the role of thermophoresis force and slip/drift velocity on particle surface with respect to the main flow. In nanofluid literature, thermophoresis force has been either neglected or erroneous expressions have been used to model its effect. Here, a sufficiently accurate expression for thermophoresis coefficient in liquid solutions and mixtures, backed with a theoretical foundation is introduced and used. A two-phase lattice Boltzmann method (LBM) is employed to capture the slip velocity created by Brownian, thermophoresis and gravitational forces. At Ra = 106 and particle volume concentration of 5%, the nanofluid Nu number is 13% higher than that of the pure fluid, where 5% out of 13% of the enhancement is due to the thermophoresis effect.