Mixed convection in a square cavity by a perturbation technique

This paper describes a numerical solution procedure to study unsteady two-dimensional laminar mixed convection in a porous medium. It is assumed in this study that, the convecting fluid and the porous medium are everywhere in local thermodynamic equilibrium. The cavity is square and the flow is driven by a forcing flow across the top boundary. A stable vertical temperature gradient is applied by specifying isothermal horizontal boundaries. The results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. Local and global distributions of Nusselt number are presented for the above configuration. Velocity profiles are presented inside the enclosure for better understanding of the influence of the flow field on the thermal field. Comparisons with previously published work are performed and found to be in good agreement. Knowledge of this behavior is of important for the design of thermal insulation systems and other practical applications.