Two transitions of thermosolutal natural convection in the presence of an external magnetic field

Two transitions of thermosolutal natural convection in the presence of an external magnetic field

Badia Ghernaout Djamel Ghernaout  Said Bouabdallah  Aissa Atia 

Laboratory of Mechanics (LME), Department of Mechanical Engineering, University of Laghouat, PO Box 37G, Laghouat 03000, Algeria

Department of Chemical Engineering, College of Engineering, University of Ha’il, PO Box 2440, Ha’il 81441, Saudi Arabia

Corresponding Author Email: 
fibonsaid@gmail.com
Page: 
120-125
|
DOI: 
http://doi.org/10.18280/mmep.040302
Received: 
|
Accepted: 
|
Published: 
30 September 2017
| Citation

OPEN ACCESS

Abstract: 

This paper presents a numerical study of two transitions (onset/oscillatory) of thermosolutal natural convection (TSNC) under the effect of an external magnetic field (MF) in binary mixture. For this, a square enclosure filled with a binary mixture has been considered and exposed to opposing solute and thermal gradients. An external and uniform MF is applied separately in two directions, i.e., vertical and horizontal. The results are given for varying buoyancy ratio (N = 0.75, 1.0 and 1.25), Prandtl number (Pr = 0.71) and Schmidt number (Sc = 3.5). The obtained results show a good agreement with the experimental data available in the literature. We show a strong effect of the buoyancy ratio on the flow field, the thermal and solute structure. The onset of TSNC and oscillatory TSNC flow are determined, and then the oscillatory flow occurs for a periodic time evolution where the phenomena change around in each period time.

Keywords: 

Thermosolutal Natural Convection (TSNC), Magnetic Field (MF), Oscillatory Flows, Onset Flow,

Buoyancy Ratio

1. Introduction
2. Problem Statement and Modeling
3. Numerical Solution Technique
4. Results and Discussion
5. Conclusion
  References

[1] Lee J., Hyen M.T., Kim K.W. (1988). Natural convection in confined fluids with combined horizontal temperature and concentration gradients, Int J Heat Mass Transf, Vol. 31, No. 10, pp. 1969–1977. DOI: 10.1016/0017-9310(88)90106-8

[2] Kamotani Y., Wang J.S., Ostrach S., Jiang H.D. (1985). Experimental study of natural convection in shallow enclosures with temperature and concentration gradients, Int J Heat Mass Transf, Vol. 28, No. 1, pp. 165-173, DOI: 10.1016/0017-9310(85)90018-3

[3] Han H., Kuehn H.T. (1991a). Double diffusive natural convection in a vertical rectangular enclosure – II numerical study, Int J Heat Mass Transf, Vol. 34, No.2, pp. 461-471. DOI: 10.1016/0017-9310(91)90265-G

[4] Han H., Kuehn H.T. (1991b). Double diffusive natural convection in a vertical rectangular enclosure- I experimental study, Int J Heat Mass Transf, Vol. 34, No. 2, pp. 449-459. DOI: 10.1016/0017-9310(91)90264-F

[5] Chen Z.W., Li Y.S., Zhan J.M. (2012). Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity, Int J Heat Mass Transf, Vol. 55, pp. 3633–3640. DOI:10.1016/j.ijheatmasstransfer.2012.02.056

[6] Zhou H., Zebib A. (1994). Oscillatory doublediffusive convection in crystal growth, J Cryst Growth, Vol. 135, pp. 587-593. DOI: 10.1016/0022-0248(94)90151-1

[7] Sezai I., Mohamad A.A. (2000). Double diffusive convection in a cubic enclosure with opposing temperature and concentration gradients, Phys Fluids, Vol. 12, No. 9, pp. 2210-2223. DOI:10.1063/1.1286422

[8] Maatki C., Kolsi L., FOztop H., Chamkha A., Borjini M.N., Aissia H.B., Al-Salem K. (2013). Effects of magnetic field on 3D double diffusive convection in a cubic cavity filled with a binary mixture, Int Commun Heat Mass, Vol. 49, pp. 86-95. DOI: 10.1016/j.icheatmasstransfer.2013.08.019

[9] Ghachem K., Kolsi L., Mâalki C., Hussein A.K., Borjini M.N. (2012). Numerical simulation of threedimensional double diffusive free convection flow and irreversibility studies in a solar distiller, Int Commun Heat Mass, Vol. 39, pp. 869–876. DOI: 10.1016/j.icheatmasstransfer.2012.04.010

[10] Bouabdallah S., Bessaih R. (2012). Effect of magnetic field on 3D flow and heat transfer during solidification from a melt, Int J Numer Method H, Vol. 37, pp. 154-166. DOI: 10.1016/j.ijheatfluidflow.2012.07.002

[11] Ghernaout B., Bouabdallah S., Benchatti A., Bessaih R. (2014). Effect of the buoyancy ratio on oscillatory double-diffusive convection in binary mixture, Numer Heat Tr A-Appl, Vol. 66 No. 8, pp. 928-946. DOI:10.1080/10407782.2014.892386

[12] Ghernaout B., Bouabdallah S., Teggar M., Benniche H. (2015). Double diffusive natural convection in binary mixture under the effect of external magnetic field: steady and oscillatory state, Int J Heat & Tech, Vol. 33, No. 4, pp. 11-18. DOI: 10.18280/ijht.330402

[13] Bessaih R., Bouabdallah S. (2008). Numerical study of oscillatory natural convection during solidification of a liquid metal in a rectangular enclosure with and without magnetic field, Numer Heat Tr A-Appl, Vol. 54, pp. 331-348. DOI: 10.1080/10407780802084660

[14] Beghein C., Haghighat F., Allard F. (1992). Numerical study of double diffusive natural convection in a square cavity, Int. J. Heat Mass Transfer, Vol. 35, No. 4, pp. 833-846. DOI: 10.1016/0017-9310(92)90251-M

[15] Tagawa T., Ozoe H. (1998). Enhanced heat transfer rate measured for natural convection in liquid Gallium in a cubical enclosure under a static magnetic field, J Heat Trans, Vol. 120, No. 4, pp. 1027-1032. DOI: 10.1115/1.2825886

[16] Atia A., Ghernaout B., Bouabdallah S., Bessaïh R. (2016). Three-dimensional oscillatory mixed convection in a Czochralski silicon melt under the axial magnetic field, Appl Therm Eng, Vol. 105, pp.704-715. DOI: 10.1016/j.applthermaleng.2016.03.087

[17] Liu J.P., Tao W.Q. (1999). Bifurcation to oscillatory flow of the natural convection around a vertical channel in rectangular enclosure, Int. J. Numer. Method H, Vol. 9, No. 2, pp. 170-185. DOI: 10.1108/09615539910256027