Natural Convection in an Inclined Square Cavity with Heated and Cooled Adjacent Walls and Filled with a Porous Medium

Steady natural convection flow in an inclined square cavity filled with a porous medium has been investigated. It is assumed that the cavity is heated on one wall and cooled from an adjacent wall, while the other two walls are adiabatic. The governing dimensionless partial differential equations have been solved numerically for the stream function, isotherms, and the local and average Nusselt numbers using a central finite-difference method and Richardson extrapolation. Effects of the various parameters on the flow and heat transfer characteristics have been investigated, namely: Rayleigh numbers 10, 100, and 1000, and the inclined angle of the cavity from 0° to 315° . Special attention is given to the understanding of the effects of the inclination on the heat transfer rates on the heated and cooled walls as well as the flow configurations. It is found that the streamlines, isotherms and the average Nusselt numbers are affected significantly by the inclination of the cavity and the Rayleigh number. Results could be obtained for angles of inclination for Rayleigh numbers up to 100 but for a Rayleigh number of 1000 solutions could not be obtained for all angles of inclination.