Stability of Swirling Flows with Heat Transfer in a Cylindrical Enclosure with CO/Counter-Rotating End Disks Under an Axial Magnetic Field

Mahfoud, Brahim; Bessaïh, Rachid

doi:10.1080/10407782.2012.654461

Cited by 18 publications

(5 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To allocate more confidence in our numerical results, we have established some comparisons with other experimental and numerical investigations available in the literature. Firstly, a comparison is presented between our numerical results and those obtained by the authors (Kakarantzas et al 2009, Karcher et al 2002, Mahfoud and Bessaïh, 2012. They used a cylindrical cavity of aspect ratio Ar = 4.125 (in this study Ar = R / H), filled with a fluid of low Prandtl number Pr = 0.0203 (liquid alloy GaInSn in eutectic composition), the bottom and lateral wall cooled by circulation of the water, and the upper wall heated electrically.…”

Section: Computer Code Validationmentioning

confidence: 93%

Combination between the Inclinations of the Enclosure and the Magnetic Field Orientation on the Oscillatory Natural Convection

Atia¹,

Bouabdallah²,

Ghernaout³

2016

JAFM

View full text Add to dashboard Cite

In this paper, we study the combination between the inclinations of the enclosure and the magnetic field orientation on the oscillatory natural convection. For this, a cylindrical enclosure filled with electrically conducting fluid, has an aspect ratio equal to 2, and subjected to a vertical temperature gradient and different uniform magnetic field orientations were considered. The finite volume method is used to discretize the equations of continuity, momentum and energy. Our computer program based on the SIMPLER Algorithm has a good agreement with available experimental and numerical results. The time-dependent flow and temperature field are presented in oscillatory state, for different cases: inclination of the cylinder, under the effect of magnetic field in different orientations (δ = 0°, 30°, 45° and 90°) and the combination between them. The results are presented at various inclinations of the cylinder (φ = 0°, 30° and 45°), and the Hartmann numbers Ha ≤ 50. The stability diagrams of the dependence between the complicated situations with the value of the critical Grashof number Grcr and corresponding frequency Frcr, are established according to the numerical results of this investigation. The combination between the studied state has a significant effect on the stabilization of the convective flow, and shows that the best stabilization of oscillatory natural convection is obtained at the inclination of the cylinder φ = 30°, and the applied of radial magnetic field (δ = 0°).

show abstract

Section: Computer Code Validationmentioning

confidence: 93%

Combination between the Inclinations of the Enclosure and the Magnetic Field Orientation on the Oscillatory Natural Convection

Atia¹,

Bouabdallah²,

Ghernaout³

2016

JAFM

View full text Add to dashboard Cite

show abstract

“…(1)-(6), with the associated boundary conditions, are solved using the finitevolume method [10,12]. The components of velocity (u, v, and w) are stored at the staggered locations and the scalar quantities (P, Θ, and Φ) are stored in the center of these volumes.…”

Section: Methodsmentioning

confidence: 99%

“…In the present paper, we extend our previous study [12] and consider the effects of an axial magnetic field on the stability of convective co-rotation flow in a vertical cylinder with a vertical temperature gradient. A parametric study of stability of flow for increasing values of magnetic field strength (Hartmann number, Ha) is performed for fixed values of both Prandtl number (Pr ¼ 0.015) and a aspect ratio (γ ¼ H/R ¼ 2) of the cylinder, equal to 2.…”

Section: Introductionmentioning

confidence: 96%

Magnetohydrodynamic co-rotating flow in a vertical cylindrical container

Mahfoud

Bendjaghlouli

Bessaïh

2016

Numerical Heat Transfer, Part A: Applications

Self Cite

View full text Add to dashboard Cite

The effect of an external axial magnetic field on the liquid metal flow produced by co-rotation of the top and bottom disks in a vertical cylindrical container with a vertical temperature gradient is numerically analyzed. The governing Navier-Stokes, energy, and potential equations along with appropriate boundary conditions are solved using the finite-volume method. Comparisons with the previous results were performed and found to be in excellent agreement. It was observed that the Reynolds number is increased, and the axisymmetric basic state loses stability for circular patterns of axisymmetric vortices and spiral waves. In the mixed convection case the axisymmetric mode disappears, giving an asymmetric mode m ¼ 1. It was also found that the primary thresholds, Re cr corresponding to modes m ¼ 1 and 2, increase with an increase in Hartmann number (Ha). We can therefore conclude that when the magnitude of the magnetic field exceeds a certain value, the instability becomes a steady bifurcation. Finally, stability diagrams were established according to the numerical results of this investigation. These diagrams show the evolution of primary thresholds as a function of Hartmann number for various values of Richardson number. ARTICLE HISTORY

show abstract

“…In this case, the Hartmann layer replaces the Ekman layer and the Ekman boundary layer forms in the vicinity of the rotating disc [14]. The challenges of the stability of mixed flow in an enclosed container are discussed in reference [15], which verified that the uniform magnetic field may be employed to control and stabilize fluid motion. Magnetohydrodynamic effects on the counter-rotating flow and co-rotating flow, associated with heat transfer were studied by Mahfoud and Bessaih [16] and Mahfoud et al [17].…”

Section: Introductionmentioning

confidence: 99%

“…There are several studies in the literature examining vortex breakdown and fluid layers [3][4][5]. Some study is interested in the effect of thermal gradient which is the origin of the increase or decrease of stratification [6][7][8] and a decrease in the number of Nusselt [9,10].…”

Section: Introductionmentioning

confidence: 99%

Buoyancy force and magnetic field effects on laminar vortex breakdown and fluid layers

MAHFOUD

Moussaoui

2023

Journal of Thermal Engineering

View full text Add to dashboard Cite

In this study, the Generalized Integral Transformation Technique (GITT) is used to describe the effect of buoyancy force and magnetic field on the vortex breakdown process generated by the rotation of an electrically conductive fluid. A magnetic field is positioned vertically to stabilize the swirling flow caused by the rotation of the bottom disc of a cylindrical recipient. Three fluids were compared in this study where the range of Richardson number is 0 ≤Ri ≤2.0. When the temperature difference is greater than Ri = 0.1, many layers become visible. These stratified flu id layers act as thermal insulators. In the case of stratification, the increased magnetic field reduces the total number of layers formed in the fluid. The influence of gradient temperature on the distribution of the layers generated is discussed. The limitations between the multilayer structure and the monolayer structure for three fluids are calculated as a function of the flow parameters.

show abstract

Stability of Swirling Flows with Heat Transfer in a Cylindrical Enclosure with CO/Counter-Rotating End Disks Under an Axial Magnetic Field

Cited by 18 publications

References 32 publications

Combination between the Inclinations of the Enclosure and the Magnetic Field Orientation on the Oscillatory Natural Convection

Combination between the Inclinations of the Enclosure and the Magnetic Field Orientation on the Oscillatory Natural Convection

Magnetohydrodynamic co-rotating flow in a vertical cylindrical container

Buoyancy force and magnetic field effects on laminar vortex breakdown and fluid layers

Contact Info

Product

Resources

About