Natural Convection in an Externally Heated Vertical or Inclined Square Box Containing Internal Energy Sources

Acharya, Swastik; Goldstein, R. J.

doi:10.1115/1.3247514

Cited by 109 publications

(59 citation statements)

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“…Flow and temperature fields Fig. 2 shows typical streamlines and isotherms for Ra E = 10 6 and various values of Ha and S numbers. All these cases correspond to steady-state flow and are used to demonstrate the different flow patterns that could exist depending firstly on the imposed heating and secondly on the magnitude of the magnetic field.…”

Section: Resultsmentioning

confidence: 99%

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MHD natural convection in a laterally and volumetrically heated square cavity

Sarris

Kakarantzas

Grecos

et al. 2005

International Journal of Heat and Mass Transfer

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Section: Resultsmentioning

confidence: 99%

“…A limited number of numerical works [6][7][8] have been reported for the study of simultaneously laterally and volumetrically heated cavities. These studies, corresponding to higher Pr numbers than those of liquid-metals, showed no oscillatory flows even at very high Ra E and Ra I .…”

Section: Introductionmentioning

confidence: 99%

MHD natural convection in a laterally and volumetrically heated square cavity

Sarris

Kakarantzas

Grecos

et al. 2005

International Journal of Heat and Mass Transfer

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“…Such applications include heat removal from nuclear fuel debris, underground disposal of radioactive waste materials, storage of foodstu , and exothermic chemical reactions in packed-bed reactor (see, for instance, Kakac et al [19]). Acharya and Goldstein [20] studied numerically two-dimensional natural convection of air in an externally heated vertical or inclined square box containing uniformly distributed internal energy sources. Their numerical results showed two distinct¯ow pattern systems depending on the ratio of the internal to the external Rayleigh numbers.…”

Section: Nom Enclaturementioning

confidence: 99%

Double-Diffusive Convection in a Porous Enclosure With Cooperating Temperature and Concentration Gradients and Heat Generation or Absorption Effects

Chamkha¹

2002

Numerical Heat Transfer, Part A: Applications

117

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The problem of unsteady, laminar double-diffusive convective ow of a binary gas mixture in a rectangular enclosure lled with a uniform porous medium is considered. A temperature-dependent heat source or sink is assumed to exist within the enclosure boundaries. Transverse cooperating gradients of heat and mass are applied on the two opposing vertical walls of the enclosure while the other two horizontal walls are adiabatic and impermeable to mass transfer. A numerical solution based on the nite-difference methodology is obtained. Representative results illustrating the effects of the inverse Darcy number, the heat generation or absorption coef cient, and the buoyancy ratio on the contour maps of the streamline, temperature, and concentration as well as the pro les of velocity, temperature, and concentration at the midsection of the enclosure are reported. In addition, results for the average Nusselt and Sherwood numbers are presented in tabulated form and discussed for various parametric conditions.

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“…Representative studies dealing with these effects have been reported previously by such authors as Acharya and Goldstein (1985) [27], Vajravelu and Nayfeh (1992) [28] and Chamkha (1997) [29].…”

Section: Greek Symbolsmentioning

confidence: 99%

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

Chamkha

Al-Mudhaf

Al-Yatama

2004

Inter J Fluid Mech Res

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The problem of steady, laminar, double-diffusive natural convection boundary-layer flow of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-Darcian and thermal dispersion effects is investigated. Also, the model problem allows for possible heat generation or absorption and first-order chemical reaction effects. Both the wall temperature and wall concentration are assumed to have linear variations with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations into a non-similar form that can be solved as an initial-value problem. The resulting equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the microrotation material parameter, concentration to thermal buoyancy ratio, chemical reaction parameter, Schmidt number, heat generation or absorption and the surface suction or injection effects on the fluid velocity, microrotation, temperature and solute concentration as well as the local skin-friction coefficient, local wall microrotation coefficient and the local wall heat and mass transfer coefficients is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed. Greek Symbolseffective thermal diffusivity of the porous medium; α d thermal diffusivity of the porous medium due to thermal dispersion;Introduction Double-diffusive convection is referred to buoyancy-induced flow due to the combined effects of both temperature and concentration gradients. Double-diffusive convection from different geometries embedded in porous media has a wide range of engineering and geophysical applications such as geothermal reservoirs, drying of porous solids, thermal insulation, enhanced oil recovery, packed-bed catalytic reactors, cooling of nuclear reactors, and underground energy transport. Most early studies on porous media have used the Darcy law which is a linear empirical relation between the Darcian velocity and the pressure drop across the porous medium and is limited to relatively slow flows. However, for relatively higher velocity flow situations, the Darcy law becomes inadequate for representing the flow behavior correctly since it does not account for the resulting inertia effects of the porous medium. In this situation, the pressure drop has a quadratic relationship with the volumetric flow rate. The high flow situation is established when the Reynolds number based on the pore size is greater than unity. Vafai and Tien (1981) [1] discussed the importance of inertia effects for high velocity flows in porous media. Double-diffusive convection flow of a Newtonian fluid along a vertical surface embedded in a uniform porous medium was considered by Bejan (1984) [2] based on scale ...

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Natural Convection in an Externally Heated Vertical or Inclined Square Box Containing Internal Energy Sources

Cited by 109 publications

References 0 publications

MHD natural convection in a laterally and volumetrically heated square cavity

MHD natural convection in a laterally and volumetrically heated square cavity

Double-Diffusive Convection in a Porous Enclosure With Cooperating Temperature and Concentration Gradients and Heat Generation or Absorption Effects

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

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