Marangoni natural convection in a cubical cavity filled with a nanofluid Buongiorno's nanofluid model

Natural convection in a differentially heated cubical cavity filled with a water-based nanofluid under the Marangoni effect from the upper free surface is studied numerically. It is supposed that the Brownian diffusion and thermophoresis are the major slip mechanisms for nanoparticles. Dimensionless governing equations formulated using vector potential functions, vorticity vector and temperature have been solved by the finite difference method of the second-order accuracy. It should be noted that the Marangoni effect is owing to the dependences of surface tension on the temperature and nanoparticles concentration. The effects of the Marangoni number, Lewis number, buoyancy ratio parameter, Brownian diffusion parameter and thermophoresis parameter on nanofluid flow, heat and mass transfer have been analyzed. It has been revealed that a growth of Marangoni number results in the heat transfer rate reduction.