Heat and Mass Transfer from an Inverted Cone in a Porous Medium with Cross-Diffusion Effects

Abstract

The study of double-diffusive convection has received considerable attention during the last several decades since this occurs in a wide range of natural settings. The origins of these studies can be traced to oceanography when hot salty water lies over cold fresh water of a higher density resulting in double-diffusive instabilities known as “salt-fingers,” Stern (35; 36). Typical technological motivations for the study of double-diffusive convection range from such diverse fields as the migration of moisture through air contained in fibrous insulations, grain storage systems, the dispersion of contaminants through water-saturated soil, crystal growth and the underground disposal of nuclear wastes. Double-diffusive convection has also been cited as being of particular relevance in the modeling of solar ponds (Akbarzadeh and Manins (1)) and magma chambers (Fernando and Brandt (12)). Double-diffusive convection problems have been investigated by, among others, Nield (28) Baines and Gill (3), Guo et al. (14), Khanafer and Vafai (17), Sunil et al. (37) and Gaikwad et al. (13). Studies have been carried out on horizontal, inclined and vertical surfaces in a porous medium by, among others, Cheng (9; 10), Nield and Bejan (29) and Ingham and Pop (32). Na and Chiou (24) presented the problem of laminar natural convection in Newtonian fluids over the frustum of a cone while Lai (18) investigated the heat and mass transfer by natural convection from a horizontal line source in saturated porous medium. Natural convection over a vertical wavy cone has been investigated by Pop and Na (33). Nakyam and Hussain (25) studied the combined heat and mass transfer by natural convection in a porous medium by integral methods. Chamkha and Khaled (4) studied the hydromagnetic heat and mass transfer by mixed convection from a vertical plate embedded in a uniform porous medium. Chamkha (5) investigated the coupled heat and mass transfer by natural convection of Newtonian fluids about a truncated cone in the presence of magnetic field and radiation effects and Yih (38) examined the effect of radiation in convective flow over a cone. Cheng (6) used an integral approach to study the heat and mass transfer by natural convection from truncated cones in porous media with variable wall temperature and concentration. Khanafer and Vafai (17) studied the double-diffusive convection in a lid-driven enclosure filled with a fluid-saturated porous medium. Mortimer and Eyring (22) used an elementary transition state approach to obtain a simple model for Soret and Dufour effects in thermodynamically ideal mixtures of substances with molecules of nearly equal size. In their model the flow of heat in the Dufour effect was identified as the transport of the enthalpy change of activation as molecules diffuse. 5