Combined effects of shear and buoyancy for mixed convection in an enclosure

Mixed convection in an enclosure is studied numerically, by adopting a streamfunction–vorticity formulation with a finite difference numerical solution scheme. Two aspects of this study are worthy of note, namely, the forced convection induced by the moving wall as well as the natural convection generated by buoyancy. Flow is generated by the top horizontal or one of the vertical boundary walls any of which can slide along its own plane, while the induced temperature gradient arising from the boundary conditions initiates buoyancy. A parametric investigation of the numerical solutions helps us to make valuable observations of both the heat transfer and flow processes. For the different parameters studied, streamfunction plots not only reflect the influence of the boundary conditions, but also the effect of the different dimensionless variables on the flow profile. Variations of the flow profiles as a function of time as well as a function of Grashof number are reported. While the Nusselt number varies considerably with time, the isotherms do not change appreciably with Grashof number as the solution approaches steady state.