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

Abstract

A numerical study is presented of natural convection from a heated upward facing finite horizontal surface in a fluid-saturated porous medium. The Rayleigh number range for which two-dimensional flows occur is numerically determined as 40 ≤ Ra ≤ 600. At higher Rayleigh numbers the flow is shown to become three-dimensional with multiple plume formation and growth. At lower Rayleigh numbers the transport is dominated by conduction, and there is greater uncertainty in the numerical determination of heat transfer rates by convection models. For the two-dimensional flows the correlation for the Nusselt number is obtained as Nu = 3.092Ra^0.272. The fundamental physical mechanisms of convection in a vast porous medium are presented and explained with the aid of the numerical results.

Notes

Address correspondence to Professor G. P. Bud Peterson, Texas A & M University, Office of the Dean of Engineering, 301 Weisenbaker Engrg. Research Center, College Station, TX 77843-3126. E-mail: [email protected]