INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2003; 27:941–960 (DOI: 10.1002/er.927) Small and moderate Prandtl number convection in a porous layer heated from below P. Vadasz n,y Department of Mechanical Engineering, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa SUMMARY The weak turbulence regime associated with porous media non-steady and non-periodic convection, in models allowing temporal irregular (i.e. chaotic) solutions is reviewed, and the conditions for its validity are specified. The rich dynamics linked to the transition from steady convection to chaos is demonstrated and explained analytically as well as computationally. Copyright # 2003 John Wiley & Sons, Ltd. KEY WORDS: weak turbulence; hysteresis; porous media; free convection; chaos 1. INTRODUCTION The wide variety of engineering applications of transport phenomena in porous media provide the solid practical motivation for this investigation. Examples of such applications are listed in Bejan (1995) and Nield and Bejan (1999), such as insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat generating materials such as grain and coal. The latter applications fall into the category of energy self-sufficiency and pollution of the environment. In addition one needs to indicate some geophysical applications, such as groundwater flow (where the heat transfer analogy may apply to the mass transfer equations when considering underground water contamination) and the flow of magma in the earth mantle close to the earth crust. The distinction between modern applications of convection in porous media, that include small values of Prandtl number and consequently moderate values of the Darcy–Prandtl number, and traditional applications which are typically associated with moderate values of Prandtl number (high values of the Darcy–Prandtl number), is of particular interest in the present review. The resulting effect of high values of the Darcy–Prandtl number yields a very small coefficient of the time derivative term in Darcy’s equation hence allowing the neglect of this term. On the other hand, small Prandtl number convection can be associated with liquid metals ðPr ¼ Oð10 3 ÞÞ: The process of solidification of binary alloys can be selected in particular as an appropriate example of small Prandtl number convection in porous media as the mushy layer, which forms on the interface between the solid phase and the liquid metal to be solidified Received 31 January 2002 Accepted 6 January 2003 Copyright # 2003 John Wiley & Sons, Ltd. y E-mail: peter.vadasz@nau.edu n Correspondence to: P. Vadasz, Department of Mechanical Engineering, Northern Arizona University, PO Box 15600, Flagstaff, AZ 86011-5600, USA.