Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-03T05:44:11.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetohydrodynamic Natural Convection in a Rotating Enclosure

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 January 2016

H. Saleh  and
I. Hashim
H. Saleh*
Affiliation:
Solar Energy Research Institute, University Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
I. Hashim
Affiliation:
Pusat Pemodelan & Analisis Data, School of Mathematical Sciences, University Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia Research Institute, Center for Modeling & Computer Simulation (RI/CM&CS), King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia
*
*Corresponding author. Email: [email protected] (H. Saleh), [email protected] (I. Hashim)
Get access

Abstract

Magnetohydrodynamic natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this article. The governing equations are in velocity, pressure and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the Hartmann number, 0≤Ha≤70, the inclination angle of the magnetic field, 0°≤θ 90°, the Taylor number, 8.9 x 104≤Ta≤1.1 x 106 and the centrifugal force is smaller than the Coriolis force and the both forces were kept below the buoyancy force. It is found that a sufficiently large Lorentz force neutralizes the effect of buoyancy, inertial and Coriolis forces. Horizontal or vertical direction of the magnetic field was most effective in reducing the global heat transfer.

Keywords

Finite difference methodnatural convectionMHDrotating enclosure

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 279 - 292
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Al-Najem, N. M., Khanafer, K. M. and El-Refaee, M. M., Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field, Int. J. Numer. Meth. Heat Fluid Flow, 8 (1998), pp. 651–672.Google Scholar
[2]Alchaar, S., Vasseur, P. and Bilgen, E., Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field, J. Heat Transfer, 117 (1995), pp. 668–673.Google Scholar
[3]Baig, M. F. and Masood, A., Natural convection in a two-dimensional differentially heated square enclosure undergoing rotation, Numer. Heat Transfer Part A, 40 (2001), pp. 181–202.Google Scholar
[4]Baig, M. F. and Zunaid, M., Numerical simulation of liquid metals in differentially heated enclosure undergoing orthogonal rotation, Int. J. Heat Mass Transfer, 49 (2006), pp. 3500–3513.Google Scholar
[5]Buhler, K. and Oertel, H., Thermal cellular convection in rotating rectangular boxes, J. Fluid Mech., 114 (1982), pp. 261–282.Google Scholar
[6]Garandet, J. P., Albussoiere, T. and Moreau, R., Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field, Int. J. Heat Mass Transfer, 35 (1992), pp. 741–748.CrossRefGoogle Scholar
[7]Hamady, F.J., Lloyd, J. R., Yang, K. T. and Yang, H. Q., A study of natural convection in a rotating enclosure, J. Heat Transfer, 116 (1994), pp. 136–143.Google Scholar
[8]Harlow, F. and Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface, Phys. Fluids, 8 (1965), pp. 2182–2189.Google Scholar
[9]Hoffmann, K. A. and Chiang, S. T., Computational Fluid Dynamics Volume I, Engineering Education System, Kansas, 2000.Google Scholar
[10]Jin, L. F., Tou, S. K. W. and Tso, C. P., Effects of rotation on natural convection cooling from three rows of heat sources in a rectangular cavity, Int. J. Heat Mass Transfer, 48 (2005), pp. 3982–3994.Google Scholar
[11]Ker, Y. T. and Lin, T. F., A combined numerical and experimental study of air convection in a differentially heated rotating cubic cavity, Int. J. Heat Mass Transfer, 39 (1996), pp. 3193–3210.Google Scholar
[12]Ker, Y. T. and Lin, T. F., Time-averaged and reverse transition in oscillatory air convection in a differentially heated rotating cubic cavity, Int. J. Heat Mass Transfer, 40 (1997), pp. 3335–3349.Google Scholar
[13]Lee, T. L. and Lin, T. F., Transient three-dimensional convection of air in a differentially heated rotating cubic cavity, Int. J. Heat Mass Transfer, 39 (1996), pp. 1243–1255.CrossRefGoogle Scholar
[14]Mandal, J. C. and Sonawane, C. R., Simulation of flow inside differentially heated rotating cavity, Int. J. Numer. Meth. Heat Fluid Flow, 23 (2013), pp. 23–54.Google Scholar
[15]Mössner, R. and Gerbeth, G., Buoyant melt flows under the infuence of steady and rotating magnetic felds, J. Crystal Growth, 197 (1999), pp. 341–354.CrossRefGoogle Scholar
[16]Pirmohammadi, M. and Ghassemi, M., Effect of magnetic field on convection heat transfer inside a tilted square enclosure, Int. Commun. Heat Mass Transfer, 36 (2009), pp. 776–780.Google Scholar
[17]Pirmohammadi, M., Ghassemi, M. and Sheikhzadeh, G. A., Effect of a magnetic field on buoyancy-driven convection in differentially heated square cavity, IEEE Transactions Magnetics, 45 (2009), pp. 407–411.Google Scholar
[18]Rudraiah, N., Barron, R.M., Venkatachalappa, M. and Subbaraya, C. K., Effect of a magnetic field on free convection in a rectangular enclosure, Int.J. Eng. Sci., 33 (1995), pp. 1075–1084.CrossRefGoogle Scholar
[19]Tso, C. P., Jin, L. F. and Tou, S. K. W., Numerical segregation of the effects of body forces in a rotating, differentially heated enclosure, Numer. Heat Transfer Part A, 51 (2007), pp. 85–107.Google Scholar