Free convection from one thermal and solute source in a confined porous medium

Abstract

This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 N +10, 0 R t 200, 10 −2 Le 200, and 0.125 L 0.875, where N, R t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

“…The main eddy is moved toward the outer wall, and the formation of hydrodynamic boundary layers are visible around the segment, top and outer walls. A similar observation was predicted by Zhao et al (2007) and Liu et al (2008) for discrete heating and salting on the right wall of a rectangular porous cavity. A close observation of the streamlines, isotherms, and isoconcentrations reveals that the location of the segment has a distinct effect on the flow pattern, temperature, and concentrations fields.…”

“…This is due to the fact that many engineering systems may be characterized by double-diffusive convective flow with a discrete heat and solute source on one of the vertical walls, such as zone melting, alloy solidification, hazardous thermo-chemical spreading and liquid fuel storage tank. Using the Darcy model, Zhao et al (2007) conducted a numerical study of double-diffusive convection from a single thermal and solute source in a square enclosure. Their numerical simulations for a wide parameter range reveals that the source location plays a vital role in altering the heat and mass transfer rates in the cavity.…”

“…The existing studies on double-diffusive natural convection subject to partial heating and salting have been restricted to square enclosures (Zhao et al 2007;Liu et al 2008). Although the influence of discrete heating and salting on the thermosolutal convection in a rectangular porous cavity have been addressed, they do not always adequately represent the important practical situations in which the flow domain is a porous layer bounded by two vertical concentric cylinders since curvature effects can be important.…”

Magnetic Field Effect on Natural Convection in a Porous Cavity Heating from below and Salting from Side

“…The review of the literature on double-diffusive natural convection in fluids filled with a porous medium shows that most of studies focus on the thermosolutal effect inside cavities or enclosures where different boundary conditions apply. Studies by Bahloul et al [11], Zhao et al [12], Liu et al [13], Zhao et al [14], and Mamou et al [15], for example, used boundary conditions of heating and salting from side. Other studies by Bourich et al [16] and Mansour et al [17] investigated heating from below and salting from sides.…”

“…Some studies, for example, Zhao et al [18] and Alloui et al [19], looked at double-diffusive natural convection in boundary conditions of heating and salting from below. Many studies used a Darcy model to formulate the momentum equation; see for example, Liu et al [13] Zhao et al [14], Mamou et al [15], Alloui et al [19], Trevisan and Bejan [20], Mamou et al [21], Bourich et al [22], Saeid and Pop [23], Saleh and Hashim [24], and Akbal and Baytaş [25]. For non-Darcy, see for instance, Zhao et al [12], Zhao et al [18], and Goyeau et al [26].…”