UPPER AND LOWER RAYLEIGH NUMBER BOUNDS FOR 2-DIMENSIONAL NATURAL-CONVECTION OVER A FINITE HORIZONTAL SURFACE SITUATED IN A FLUID-SATURATED POROUS-MEDIUM

A numerical study is presented of natural convection from a heated upw ard facing finite horizontal surface in a fluid-saturated porous mediu m. The Rayleigh number range for which two-dimensional flows occur is numerically determined as 40 less than or equal to Ra less than or equ al to 600. At higher Rayleigh numbers the flow is shown to become thre e-dimensional with multiple plume formation and growth. At lower Rayle igh numbers the transport is dominated by conduction, and there is gre ater uncertainty in the numerical determination of heat transfer rates by convection models. For the two-dimensional flows the correlation f or the Nusselt number is obtained as Nu = 3.092Ra(0.272). The fundamen tal physical mechanisms of convection in a vast porous medium are pres ented and explained with the aid of the numerical results.