Numerical study of natural melt convection in cylindrical cavity with hot walls and cold bottom sink

Ahmanache, Abdennacer; Zeraibi, Noureddine

doi:10.2298/tsci110327166a

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…In all cases, Prandtl number is fixed to 0.011 characterizing a silicon melt. According to Ahmanache and Zeraibi , the aspect ratio has no significant effect on fluid flow and heat transfer in such cavity then we limit our study to a single case of aspect ratio A = 1.…”

Section: Resultsmentioning

confidence: 99%

“…Ahmanache and Zeraibi have studied the effects of aspect ratio, exchanger length at various Rayleigh numbers (Ra = 10 3 ‐10 6 ) for material with Pr = 20 in a cylindrical HEM crucible. They observed that Rayleigh number and heat exchanger length influence fluid flow and heat transfer, whereas the cavity aspect ratio (A = 0.5, 1, 1.5 and 2) has no significant effects in such cavity.…”

Section: Introductionmentioning

confidence: 99%

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Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Haddad

Mokhtari

Boutarfaïa

2016

Crystal Research and Technology

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Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle-bottom of the crucible. The finitevolume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 1012 not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10 10 . Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt-crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Haddad

Mokhtari

Boutarfaïa

2016

Crystal Research and Technology

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“…The dimensionless equations of vorticity transport, Poisson, and energy for the gas in the natural convection regime and the heat conduction equations for the enclosures and radiant energy source are [12,13,27]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Studies of convective energy transfer regimes play an important role in science and engineering. Solutions of various natural convection problems in closed and semi-open cavities in non-conjugate [8][9][10][11][12][13][14] and conjugate [15][16][17][18] formulation are published. However, a special interest for practical applications represents investigation of jointly proceeding processes of conduction, convection, and radiation.…”

Section: Introductionmentioning

confidence: 99%

Modelling of the conjugate natural convection in a closed system with the radiant heating source radiant energy distribution by Lambert’s cosine law

Кузнецов

Nee

2018

THERM SCI

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Various types of emitters are often used as energy sources in real engineering systems and technological processes. Investigations of heat transfer basic laws in such systems are of interest. We conducted mathematical modelling of conjugate heat transfer in a closed rectangular cavity under conditions of radiant energy source operating. The 2-D problem of conjugate natural convection in vorticity stream function-temperature dimensionless variables has been numerically solved by means of the finite difference method. Radiant energy distribution along the gas-wall interfaces was set by Lamberts? cosine law. We obtained fields of temperature and stream functions in a wide range of governing parameters (Rayleigh number 104 ? Ra ? 106, the length of radiant heating source 0.15 ? D ? 0.6). Then we analyzed how heat retaining properties of finite thickness heat conducting walls made of different materials affect the heat transfer intensity. Differential characteristics distribution showed significant non-uniformity and non-stationarity of the conjugate heat transfer process under study.

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“…More recently, Raisi [Raisi (2016)] examined the natural convection in a square cavity filled with a non-Newtonian power-law fluid and used the numerical finite difference method based on the control volume formulation and SIMPLE algorithm. Certain studies have also been devoted to natural convection in other geometric configurations: Tzeng et al [Tzeng, Liou and Jou (2005)] considered a triangular enclosure, Basak et al [Basak, Roy, Singh et al (2009)] treated a trapezoid enclosure, while Ahmanache et al [Ahmanache and Zeraibi (2013); Alam, Rahman, Parvin et al 2016] examined a prismatic enclosure. In this first category, relating to natural convection all studies cited above show that if the sidewalls of the cavity are adiabatic, instabilities, loss of symmetry and bifurcation phenomena have been found to depend mainly on Rayleigh numbers, aspect ratio and vertex angles of the enclosure.…”

Section: Introductionmentioning

confidence: 99%

Effect of Richardson Number on Unsteady Mixed Convection in a Square Cavity Partially Heated From Below

Kachi

Bensouici²,

Ferroudj³

et al. 2019

Fluid Dynamics &Amp; Materials Processing

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The objective of the present study is to analyze the laminar mixed convection in a square cavity with moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall while all the other horizontal sides of the cavity are considered adiabatic. The numerical method is based on a finite difference technique where the spatial partial derivatives appearing in the governing equations are discretized using a high order scheme, and time advance is dealt with by a fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative importance of the natural and forced convection, is chosen as the bifurcation parameter. The effect of this non-dimensional number on the behavior of the fluid flow and the heat transfer is analyzed. Although the geometry and boundary conditions concerning the velocity and the temperature are symmetrical with respect to the vertical axis passing through the center of the cavity, the results show the existence of symmetric and asymmetric flow structures, varying according to the considered value of the Richardson number.

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Numerical study of natural melt convection in cylindrical cavity with hot walls and cold bottom sink

Cited by 4 publications

References 27 publications

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Modelling of the conjugate natural convection in a closed system with the radiant heating source radiant energy distribution by Lambert’s cosine law

Effect of Richardson Number on Unsteady Mixed Convection in a Square Cavity Partially Heated From Below

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