Natural Convection in a Square Inclined Cavity Filled with a Porous Medium with Sinusoidal Temperature Distribution on Both Side Walls

Abstract

The problem of natural convection in an inclined square cavity filled with a fluid-saturated porous medium with sinusoidal temperature distribution on the side walls is presented, and the numerical results are obtained. Dimensionless equations governing the mathematical model together with the boundary conditions are obtained, and the problem is solved by finite differential method of second-order accuracy. The numerical results of streamlines and isotherms are investigated, and the effect of different inclination angles of the cavity, amplitude ratio of the sinusoidal temperature, and phase deviation are discussed. The cavity inclination angle and the periodic thermal boundary conditions are proposed to be control parameters for heat and fluid flow inside the cavity. Interesting results for these new parameters have been obtained, such as, the behaviour of the convective cells is completely changed compared with no inclination of the cavity and the increase in inclination angle determines an increase in the average Nusselt number and fluid flow rate. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature.