Investigation of natural convection heat transfer of viscoplastic nanofluids-Casson model in a square enclosure

In this study, natural convection of a viscous nanofluid-casson model with a yield stress in a square enclosure with differentially heated side walls has been studied. The system of coupled nonlinear differential equations for flow, heat transfer and mass transfer were solved by using the finite element method. The effects of yield number (0≤Y≤Y_max), Rayleigh number (〖10〗^3≤Ra≤〖10〗^6 ), Lewis number (2.5≤Le≤7.5) and Buoyancy ratio number (0.1≤N_r≤1), on the flow, heat and mass transfer have been investigated and the yielded and unyielded regions are specified. The results show that the mass distribution in the enclosure is strongly influenced by the Lewis number, but this parameter does not have a significant effect on the flow and temperature fields. The combined effect of Lewis number and yield stress on fluid flow is negligible and as a result, this parameter has no significant effect on unyielded regions. On the other hand, increasing the buoyancy parameter suppressed the convective flow and heat transfer rate in the cavity. It was observed that increasing the buoyancy parameter enhances the effect of viscous force and as a result, the unyielded regions expand in the enclosure and the critical yield stress decreases.