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IJE TRANSACTIONS A: Basics Vol. 29, No. 4 (April 2016) 563-571
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EFFECT OF MAGNETIC FIELD ON THE ROTATING FLOW IN A SIMILAR CZOCHRALSKI CONFIGURATION
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S. Bouabdallah, A. Atia and A. H. Boughzala
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( Received:
November 02, 2015
– Accepted in Revised Form: April 14, 2016 )
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Abstract
We
present a
numerical study of the rotating flow generated by two
rotating disks in co-/counter-rotating, inside a fixed
cylindrical enclosure
similar to the Czochralski configuration (Cz).
The enclosure having an aspect ratio A =
H/Rc
equal to 2, filled with a low Prandtl number fluid (Pr = 0.011), which
is submitted to a vertical
temperature gradient. The finite volume method has
been used to solve numerically the governing equations of the
studied
phenomenon.We present the steady state flow; and make a comparison between the
flow generated by the
co-/counter-rotating end disks. This study was caried out
for different Richardson numbers; Ri = 0.01, 0.1, 0.5, 1, 2,
3, 5 and
10. The effect of orientation of the magnetic field is
also taken into account for different values of the
Hartmann number (Ha
= 0, 5, 10, 20, 30 and 50). The obtained results show that the
strongest stabilisation of the
velocity field and heat transfer occurs when the flow generated byco-rotating end
disks and the applied of magnetic
field in radial direction provied a more
stabilisation of the convective flow.
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Keywords
Rotating flow, Czochralski, co-/counter-rotating mixed convection, magnetic field
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چکیده
ما در حال
حاضر، مطالعه عددی جریان چرخشی تولید شده را توسط دو دیسک چرخشی در چرخش همسو/
ناهمسو، در داخل محوطه یک استوانه ثابت مشابه پیکربندی Czochralski (Cz) نشان می دهیم. محوطه
دارای نسبت
A = H / RC برابر با 2، پر شده با سیالی با
عدد پرانتل کوچک (01/0 (Pr = می باشد که به گرادیان دما عمودی نسبت داده
می شود. روش حجم محدود برای حل عددی معادلات حاکم پدیده تحت مطالعه استفاده شده
است. ما جریان حالت پایدار را ارائه می دهیم؛ و مقایسه ای بین جریان تولید شده
توسط دیسک های انتهایی با چرخش همسو/ناهمسو نشان می دهیم. این مطالعه
برای عددهای مختلف ریچاردسون Ri برابر با 01/0،
1/0، 5/0، 1، 2، 3، 5 و 10 انجام شد. اثر جهت میدان مغناطیسی نیز برای
مقادیر مختلف عدد هارتمن Ha برابر با 0، 5، 10، 20، 30 و 50 به حساب می
آید. نتایج به دست آمده نشان می دهد که قوی ترین تثبیت میدان
سرعت و انتقال حرارت هنگامی رخ میدهد که جریان، دیسک های انتهایی چرخشbyco تولید می کند و اعمال میدان مغناطیسی در جهت شعاعی، ثبات بیشتری از جریان همرفتی را ایجاد می کند.
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References
1. Tsitverblit,
N. and Kit, E., "Numerical study of axisymmetric vortex breakdown in an
annulus", Acta Mechanica, Vol.
118, No. 1-4, (1996), 79-95.
2. Kharicha,
A., Alemany, A. and Bornas, D., "Influence of the magnetic field and the
conductance ratio on the mass transfer rotating lid driven flow", International
Journal of Heat and Mass Transfer,
Vol. 47, No. 8, (2004), 1997-2014.
3. Granger,
R., "Introduction to vortex dynamics", V. Karman Institute Lecture
Series, Vol. 8, (1986), 158-167.
4. Vogel,
H.U., "Experimentelle ergebnisse über die laminare strömung in einem
zylindrischen gehäuse mit darin rotierender scheibe",
MPIStrömungsforschung, (1968), 342-350.
5. Escudier,
M., "Observations of the flow produced in a cylindrical container by a
rotating endwall", Experiments in fluids, Vol. 2, No. 4, (1984), 189-196.
6. Spohn,
A., Mory, M. and Hopfinger, E., "Experiments on vortex breakdown in a
confined flow generated by a rotating disc", Journal of Fluid Mechanics, Vol. 370, (1998), 73-99.
7. Sotiropoulos,
F., Webster, D.R. and Lackey, T.C., "Experiments on lagrangian transport
in steady vortex-breakdown bubbles in a confined swirling flow", Journal
of Fluid Mechanics, Vol. 466, (2002),
215-248.
8. Lopez,
J., "Axisymmetric vortex breakdown part 1. Confined swirling flow", Journal
of Fluid Mechanics, Vol. 221,
(1990), 533-552.
9. Brown,
G. and Lopez, J., "Axisymmetric vortex breakdown part 2. Physical
mechanisms", Journal of Fluid Mechanics,
Vol. 221, (1990), 553-576.
10. Baradaran Rahimi, A. and Yousefi, E.,
"Transient natural convection flow on an isothermal vertical wall at high
prandtl numbers: Second-order approximation", International Journal of
Engineering, Vol. 14, No. 4,
(2001), 367-376.
11. Sheikhzadeh, G., Babaei, M., Rahmany, V. and
Mehrabian, M., "The effects of an imposed magnetic field on natural
convection in a tilted cavity with partially active vertical walls: Numerical
approach", International Journal of Engineering-Transactions A: Basics, Vol. 23, No. 1, (2009), 65-78.
12. Rahmannezhad, J., Ramezani, A. and Kalteh,
M., "Numerical investigation of magnetic field effects on mixed convection
flow in a nanofluid-filled lid-driven cavity", International Journal of Engineering
Trans. A: Basics, Vol. 26,
(2013), 1213-1224.
13. Davidson, P., "Magnetohydrodynamics in
materials processing", Annual Review of Fluid Mechanics, Vol. 31, No. 1, (1999), 273-300.
14. Tian, X.-Y., Zou, F., Li, B.-W. and He,
J.-C., "Numerical analysis of coupled fluid flow, heat transfer and
macroscopic solidification in the thin slab funnel shape mold with a new type
embr", Metallurgical and Materials Transactions B, Vol. 41, No. 1, (2010), 112-120.
15. Cramer, A., Pal, J. and Gerbeth, G.,
"Experimental investigation of a flow driven by a combination of a
rotating and a traveling magnetic field", Physics of Fluids (1994-present), Vol. 19, No. 11, (2007), 109-118.
16. Koal, K., Stiller, J. and Grundmann, R.,
"Linear and nonlinear instability in a cylindrical enclosure caused by a
rotating magnetic field", Physics of Fluids (1994-present), Vol. 19, No. 8, (2007), 88-107.
17. Moreau, R.J., "Magnetohydrodynamics,
Springer Science & Business Media,
Vol. 3, (2013).
18. Davidson, P., Kinnear, D., Lingwood, R.,
Short, D. and He, X., "The role of ekman pumping and the dominance of
swirl in confined flows driven by lorentz forces", European Journal of
Mechanics-B/Fluids, Vol. 18, No.
4, (1999), 693-711.
19. Ben Hadid, H., Henry, D. and Touihri, R.,
"Unsteady 3d buoyancy-driven convection in a circular cylindrical cavity
and its damping by magnetic field", Journal of Crystal Growth, Vol. 180, No. 3-4, (1997), 433-441.
20. Talmage, G., Shyu, S.-H., Walker, J. and Lopez,
J., "Inertial effects in the rotationally driven melt motion during the
czochralski growth of silicon crystals with a strong axial magnetic
field", Zeitschrift Fur Angewandte Mathematik Und Physik ZAMP, Vol. 51, No. 2, (2000), 267-289.
21. Bouabdallah, S. and Bessaih, R.,
"Magnetohydrodynamics stability of natural convection during phase change
of molten gallium in a three-dimensional enclosure", Fluid Dynamics & Materials
Processing, Vol. 6, No. 3,
(2010), 251-276.
22. Mahfoud, B. and Bessaïh, R., "Stability
of swirling flows with heat transfer in a cylindrical enclosure with
co/counter-rotating end disks under an axial magnetic field", Numerical
Heat Transfer, Part A: Applications,
Vol. 61, No. 6, (2012), 463-482.
23. Bessaih, R., Marty, P. and Kadja, M.,
"Hydrodynamics and heat transfer in disk driven rotating flow under axial
magnetic field", International Journal of Transport Phenomena, Vol. 5, No., (2003), 259-278.
24. Davidson, P. and Pothérat, A., "A note
on bödewadt–hartmann layers", European Journal of Mechanics-B/Fluids, Vol. 21, No. 5, (2002), 545-559.
25. Mahfoud, B. and Bessaih, R.,
"Oscillatory swirling flows in a cylindrical enclosure with
co-/counter-rotating end disks submitted to a vertical temperature
gradient", Fluid Dynamics & Materials Processing, Vol. 8, No. 1, (2012), 1-26.
26. Ziapour, B.M. and Rahimi, F., "Numerical
study of natural convection heat transfer in a horizontal wavy absorber solar
collector based on the second law analysis", International Journal of
Engineering, Vol. 29, No. 1,
(2016), 109-117.
27. Patankar, S., "Numerical heat transfer
and fluid flow, CRC press, (1980).
28. Atia, A., Bouabdallah, S., Teggar, M. and
Benchatti, A., "Numerical study of mixed convection in cylindrical
czochralski configuration for crystal growth of silicon",
International Journal of Heat and Technology, Vol. 33, No. 1, (2015), 39-46.
29. Wang, B.-F., Ma, D.-J., Guo, Z.-W. and Sun,
D.-J., "Linear instability analysis of rayleigh–bénard convection in a
cylinder with traveling magnetic field", Journal of Crystal Growth, Vol. 400, (2014), 49-53.
30. Kakarantzas, S., Sarris, I., Grecos, A. and
Vlachos, N., "Magnetohydrodynamic natural convection in a vertical
cylindrical cavity with sinusoidal upper wall temperature", International
Journal of Heat and Mass Transfer,
Vol. 52, No. 1, (2009), 250-259.
31. Karcher, C., Kolesnikov, Y., Andreev, O. and
Thess, A., "Natural convection in a liquid metal heated from above and
influenced by a magnetic field", European Journal of Mechanics-B/Fluids, Vol. 21, No. 1, (2002), 75-90.
32. Omi, Y. and Iwatsu, R., "Numerical study
of swirling flows in a cylindrical container with co-/counter-rotating end
disks under stable temperature difference", International Journal of Heat and
Mass Transfer, Vol. 48, No. 23,
(2005), 4854-4866.
33. Bouabdallah, S. and Bessaїh, R., "Effect
of magnetic field on 3d flow and heat transfer during solidification from a
melt", International Journal of Heat and Fluid Flow, Vol. 37, (2012), 154-166.
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