Numerical Studies of Natural Convection in a Square Cavity

Mariani, Viviana Cocco; Belo, Ivan Moura

doi:10.5380/reterm.v5i1.61673

Cited by 9 publications

(5 citation statements)

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“…L AMINAR natural-convection flow in cavities has significant applications in many engineering areas including cooling of electronic equipment, solar energy collection, and crystal growth in liquids and has been investigated by a number of researchers [1]- [3]. It is well known that unavoidable hydrodynamic movements can be damped with the help of a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

2009

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Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of the governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0 733. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer and the average Nusselt number decreases as Hartmann number increases. The results are presented for Rayleigh number from 10 4 up to 10 6 and are in form of streamlines, isotherms, and Nusselt number for various Rayleigh and Hartman numbers.

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Section: Introductionmentioning

confidence: 99%

Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

2009

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“…Mariani and Belo [9] studied numerically the thermal and fluid dynamics behavior of laminar natural air convection in a bi-dimensional square cavity. The square cavity had two walls heated with different temperatures and two isolated walls.…”

Section: Literature Reviewmentioning

confidence: 99%

Numerical Computation of Buoyancy-Driven Flow and Heat Transfer in Various Aspect Ratios Cavities Filled With Water

Hussain¹,

Hussein²,

Al-Kayiem³

et al. 2012

The International Conference on Applied Mechanics and Mechanica

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Two-dimensional steady laminar natural convection in a differentially heated cavity filled with water and has various aspect ratios due to buoyancy force effect is analyzed numerically. The governing mass, momentum and energy equations are considered and a finite volume algorithm is used to capture the numerical solution. The left vertical side wall of the cavity is linearly heated while the right vertical one is maintained at constant cold temperature. The bottom wall is maintained at constant hot temperature while the top wall is considered thermally insulated. The Rayleigh number is varied from 10 3 to 10 6 , while the cavity aspect ratio (W/H) is varied as 0.5, 1.0 and 2.0 respectively. Results are presented in the form of streamline and isotherm contours. The results of the present work explain that the natural convection phenomenon is significantly influenced by changing the cavity aspect ratio, so that when the aspect ratio is high the convection effect is week and vice versa. Also, it is found that non-uniform heating in the left vertical sidewall of the cavity plays a major role to improve the heat transfer rates. For uniform and nonuniform heating of the bottom wall and left vertical sidewall respectively, the local Nusselt number at these walls increases from its minimum value at the left edge of these walls toward maximum value at the right edge. While, the average Nusselt number for both left side and bottom walls increases with increasing of Rayleigh number.

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“…Double diffusive natural convection in porous enclosures is relevant to a wide range of industrial processes or environmental situations such as oceanography, astrophysics, geology, biology, chemical vapor transformation processes, solar power collectors, furnaces, building heating and cooling systems, heat exchangers, underground disposal of radioactive waste materials, storage of foodstuff, exothermic chemical reactions in packed-bed reactor, crystal growth techniques, such as semiconductors crystal growth and alloys solidifications, where temperature and concentration differences are combined [1][2][3][4]. Furthermore, porous medium saturated with an electrically conducting fluid under a magnetic field has been the subject of numerous recent studies owing to the implication of the phenomenon in many engineering applications including cooling of electronic equipment, geothermal reservoir, solar energy collection and crystal growth in liquids, metallurgical applications involving continuous casting and solidification of metal alloys and others [5,6]. The double diffusive natural convection carried out in a two dimensional cavity filled with a binary fluid and subjected to horizontal temperature and concentration gradients with cooperating volume forces has been analyzed by Gobin and Bennacer [7].…”

Section: Introductionmentioning

confidence: 99%

Non-Darcian effect on double-diffusive natural convection inside aninclined square Dupuit-Darcy porous cavity under a magnetic field

2021

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This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, , about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, , Hartmann number, , Lewis number, , the buoyancy ratio, ,inclination angle, Φ and tilting angle of the magnetic field, ,. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer.

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Numerical Studies of Natural Convection in a Square Cavity

Cited by 9 publications

References 0 publications

Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

Numerical Computation of Buoyancy-Driven Flow and Heat Transfer in Various Aspect Ratios Cavities Filled With Water

Non-Darcian effect on double-diffusive natural convection inside aninclined square Dupuit-Darcy porous cavity under a magnetic field

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