Effect of The Aspect Ratio on The Natural Convection in a Rectangular Porous Medium.(Dept.M)

Abstract

The effect of the aspect ratio on natural convection in a two dimensional rectangular cavity filled with fluid eaturated porous media is examined numerically. The vertical walls of the cavity are adiabatic and the horizontal walls are isothermal with lower hotter one and upper colder one. The test is done for aspect ratios 1 to 8 and wide range of Darcy-Rayleigh number Ra up to 800. Results are presented. In terms of the streamlines and isotherms, maximum velocity and stream function, the local and global Nusselt number as well as the number of flow cells. By the increase of the aspect ratio a two dimensional cellular pattern appears with vigorous motion as the Darcy-Rayleigh number increases. The number of flow cells increases with the aspect ratio. The non-dimensional average flow velocity is independent on the aspect ratio and increases linearly with the increase of Ra. The extremun value of non-dimensional stream function decreases with the increase of aspect ratio. The turning points in the local Nu at the isothermal walls occurs at the boundaries of the cells. Its number equals to the cells number and increases as the aspect ratio increases. The global Nu at the isothermal walls is independent on the aspect ratio and increases with Ra due to the relation Nu = 1.59344 in Ra – 5.186 .