ABSTRACT
Buoyancy-driven phenomena in enclosures filled with porous media have been actively under investigation for several years. They have received a great deal of attention due to a large number of technical applications such as thermal insulating systems, solar power collectors, geothermal applications, nuclear reactors, matrix heat exchangers, separation processes in chemical industries, dispersion of chemical contaminants through water-saturated soil, solidification of casting, oil extraction, storage of nuclear waste materials, grain storage systems, groundwater hydrology, and crude oil production, etc. These applications of porous media in many practical problems can be found in the well-known books by Pop and Ingham (2001), Bejan et al. (2004),
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Ingham and Pop (2005), Vafai (2005), Vadasz (2008), de Lemos (2012), and Nield and Bejan (2013). Aydin et al. (1999) and Sarris et al. (2002) have indicated that there exist only a limited amount of works published on convective flow in fluid-filled cavities (non-porous medium) with a more complex case of cooling from the top wall, mainly with periodic temperature conditions imposed upon the bottom or side walls. For example, Poulikakos (1985) studied an enclosure with its left side wall differentially heated: one half of the wall is heated and the other half is cooled, and the remaining walls are insulated. He showed that a penetrating thermal layer is formed, the size of which is a function of Rayleigh number and aspect ratio of the enclosure. Bilgen et al. (1995) used a system of discrete temperature sources placed periodically on the bottom wall of a shallow cavity. Lage and Bejan (1993) studied enclosures with one side wall heated using a pulsating heat flux and the other side wall cooled at constant temperature. They showed that at high Rayleigh numbers, the buoyancy-driven flow has the tendency to resonate to the periodic heating that has been supplied from the side. Studies of natural convection in molten glass cells with periodic heating from above and specified temperature on the side walls for Rayleigh numbers up to 107 were made by Wright and Rawson (1973) and Burley et al. (1978). Periodic heating from above has strong implications for the glass industry, where the main objective is to increase the mixing of the glass melt.
