A. BENDJAGHLOULİ, B. MAHFOUD, D.E. AMEZİANİ

MAGNETOHYDRODYNAMIC FLOW IN A TRUNCATED CONICAL ENCLOSURE

The effect of an axial magnetic field on the flow produced by counter-rotation of the top and bottom disks in a truncated conical enclosure filled with a liquid metal is studied. The governing Navier-Stokes, and potential equations are solved by using the finite-volume method. It was observed that the Reynolds number is increased, the axisymmetric basic state loses stability and giving an asymmetric mode m=1. It is also found that the primary thresholds Recr corresponding to the modes m=1 increase with increasing of the Hartmann number (Ha). Finally, stability diagram (Re-Ha) has been established according to the numerical results of this investigation.

Keywords:

Axisymmetric, Asymmetric Counter-Rotation, Conical Enclosure, Magnetohydrodynamic,

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[1] Batchelor, G.K. (1951). Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quart. J. Mech. Appl. Math., 4(1), 29–41.
[2] Zandbergen, P.J., Dijkstra D. (2004). Von Kármán swirling flows. Annu. Rev. Fluid Mech., (19), 465–491.
[3] Bourgoin, M., Odier, P., Pinton, J.F., Ricard, Y. (2004). An iterative study of time independent induction effects in magnetohydrodynamics. Phys. Fluids, 16(7), 2529-2547.
[4] Touihri, R., Ben Hadid, H., Henry, D. (1999). On the onset of convective instabilities in cylindrical cavities heated from below. II. Effect of a magnetic field. Phys. Fluids, 11(8), 2089–2100.
[5] Sheikholeslami, M., Hatami, M., Ganji, DD. (2014). Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. Journal of Molecular liquids, 190, 112-120.
[6] Sheikholeslami, M., Hatami, M., Domairry, G. (2015). Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field. Journal of the Taiwan Institute of Chemical Engineers, 46,43-50.
[7] Esfahani, J.A., Kianifar, A., Rashidi, S., Bovand, M., Shirvan, K. M. (2015). Control of Wake and Vortex Shedding Behind Solid Circular Obstacle by Magnetohydrodynamics”. Journal of Thermal Engineering, 7(1), 593-597.
[8] Hussein, A. K., Hussain, S. H. (2015).Characteristics of Magnetohydrodynamic Mixed Convection in a Parallel Motion Two-Sided Lid-Driven Differentially Heated Parallelogrammic Cavity with Various Skew Angles. Journal of Thermal Engineering, 3(1),221-235.
[9] Esfahani, J.A., Kianifar, A., Rashidi, S., Bovand, M., Shirvan, K. M. (2015). Control of Wake and Vortex Shedding Behind Solid Circular Obstacle by Magnetohydrodynamics. Journal of Thermal Engineering, 7(1),593-597.
[10] Hussein, A. K., Hussain, S. H. (2015) .Characteristics of Magnetohydrodynamic Mixed Convection in a Parallel Motion Two-Sided Lid-Driven Differentially Heated Parallelogrammic Cavity with Various Skew Angles. Journal of Thermal Volume, 3(1), 221-235.
[11] Dash, S., Singh, N. (2017).Study of Axisymmetric Nature in 3-D Swirling Flow in a Cylindrical Annulus with a Top Rotating Lid under the Influence of Axial Temperature Gradient or Axial Magnetic Field. Journal of Thermal Engineering, 6(3),1588-1606.
[12] Geridönmez, B. P. (2018). Numerical Simulation of Natural Convection in a Porous Cavity Filled With Ferrofluid in Presence of Magnetic Source. Journal of Thermal Engineering, 2(4), 1756-1769
[13]Mahfoud, B., Bendjagloli, A., Bessaïh R. (2016).Magneto-hydrodynamic co-rotating flow in a vertical cylindrical container. Numerical Heat Transfer, Part A, 69,1051-106.
[14]Mahfoud, B., Bessaïh, R. (2016).Magnetohydrodynamic counter-rotating flow in a cylindrical cavity. International Journal of Heat and Mass Transfer, 93,175–185.
[15] Mahfoud, B. Bendjaghloli, A. (2018). Natural convection of a nanofluid in a conical container” Journal of Thermal Engineering, 4,1713-1723.
[16] Patankar, S. (1980). Numerical heat transfer and fluid flow. CRC press.
[17] Escudier, M.P., O’Leary J. , Poole, R.J. (2007). Flow produced in a conical container by a rotating endwall,” International Journal of Heat and Fluid Flow, 28,1418–1428.