This paper concerns the study of the influence of an external magnetic field on the reverse flow occurring in the steady mixed convection of two Newtonian immiscible fluids filling a vertical channel under the Oberbeck–Boussinesq approximation. The two isothermal boundaries are kept either at different or at equal temperatures. The velocity, the temperature, and the induced magnetic field are obtained analytically. The results are presented graphically and discussed for various values of the parameters involved in the problem (in particular, the Hartmann number and the buoyancy coefficient) and are compared with those for a single Newtonian fluid. The occurrence of the reverse flow is explained and carefully studied.
Issue Section:
Fundamental Issues and Canonical Flows
References
1.
Chamkha
, A. J.
, 2002
, “On Laminar Hydromagnetic Mixed Convection Flow in a Vertical Channel With Symmetric and Asymmetric Wall Heating Conditions
,” Int. J. Heat Mass Transfer
, 45
(12
), pp. 2509
–2525
.2.
Borrelli
, A.
, Giantesio
, G.
, and Patria
, M.
, 2015
, “Magnetoconvection of a Micropolar Fluid in a Vertical Channel
,” Int. J. Heat Mass Transfer
, 80
(1), pp. 614
–625
.3.
Borrelli
, A.
, Giantesio
, G.
, and Patria
, M.
, 2016
, “Influence of an Internal Heat Source or Sink on the Magnetoconvection of a Micropolar Fluid in a Vertical Channel
,” Int. J. Pure Appl. Math.
, 108
(2), pp. 425
–450
.4.
Miguel
, U.
, and Sheng
, X.
, 2014
, “The Immersed Interface Method for Simulating Two-Fluid Flows
,” Numer. Math.: Theory Methods Appl.
, 7
(4
), pp. 447
–472
.5.
Rickett
, L. M.
, Penfold
, R.
, Blyth
, M. G.
, Purvis
, R.
, and Cooker
, M. J.
, 2015
, “Incipient Mixing by Marangoni Effects in Slow Viscous Flow of Two Immiscible Fluid Layers
,” IMA J. Appl. Math.
, 80
(5
), pp. 1582
–1618
.6.
Kusaka
, Y.
, 2016
, “Classical Solvability of the Stationary Free Boundary Problem Describing the Interface Formation Between Two Immiscible Fluids
,” Anal. Math. Phys.
, 6
(2
), pp. 109
–140
.7.
Chamkha
, A. J.
, 2000
, “Flow of Two-Immiscible Fluids in Porous and Nonporous Channels
,” ASME J. Fluids Eng.
, 122
(1
), pp. 117
–124
.8.
Kumar
, J. P.
, Umavathi
, J.
, and Biradar
, B. M.
, 2011
, “Mixed Convection of Magneto Hydrodynamic and Viscous Fluid in a Vertical Channel
,” Int. J. Non-Linear Mech.
, 46
(1
), pp. 278
–285
.9.
Malashetty
, M. S.
, Umavathi
, J. C.
, and Kumar
, J. P.
, 2006
, “Magnetoconvection of Two-Immiscible Fluids in Vertical Enclosure
,” Heat Mass Transfer
, 42
(11
), pp. 977
–993
.10.
Kumar
, J. P.
, Umavathi
, J. C.
, Chamkha
, A. J.
, and Ramarao
, Y.
, 2015
, “Mixed Convection of Electrically Conducting and Viscous Fluid in a Vertical Channel Using Robin Boundary Conditions
,” Can. J. Phys.
, 93
(6
), pp. 698
–710
.11.
Wakale
, A. B.
, Venkatasubbaiah
, K.
, and Sahu
, K. C.
, 2015
, “A Parametric Study of Buoyancy-Driven Flow of Two-Immiscible Fluids in a Differentially Heated Inclined Channel
,” Comput. Fluids
, 117
(1), pp. 54
–61
.12.
Barannyk
, L. L.
, Papageorgiou
, D. T.
, Petropoulos
, P. G.
, and Vanden-Broeck
, J.-M.
, 2015
, “Nonlinear Dynamics and Wall Touch-Up in Unstably Stratified Multilayer Flows in Horizontal Channels Under the Action of Electric Fields
,” SIAM J. Appl. Math.
, 75
(1
), pp. 92
–113
.13.
Mohammadi
, A.
, and Smits
, A. J.
, 2016
, “Stability of Two-Immiscible-Fluid Systems: A Review of Canonical Plane Parallel Flows
,” ASME J. Fluids Eng.
, 138
(10
), p. 100803
.14.
Kumar
, J. P.
, Umavathi
, J.
, Chamkha
, A. J.
, and Pop
, I.
, 2010
, “Fully-Developed Free-Convective Flow of Micropolar and Viscous Fluids in a Vertical Channel
,” Appl. Math. Modell.
, 34
(5
), pp. 1175
–1186
.15.
Aung
, W.
, and Worku
, G.
, 1986
, “Developing Flow and Flow Reversal in a Vertical Channel With Asymmetric Wall Temperature
,” ASME J. Heat Transfer
, 108
(2
), pp. 299
–304
.16.
Borrelli
, A.
, Giantesio
, G.
, and Patria
, M. C.
, 2013
, “Numerical Simulations of Three-Dimensional MHD Stagnation-Point Flow of a Micropolar Fluid
,” Comput. Math. Appl.
, 66
(4
), pp. 472
–489
.17.
Bhattacharyya
, S.
, and Gupta
, A.
, 1998
, “MHD Flow and Heat Transfer at a General Three-Dimensional Stagnation Point
,” Int. J. Non-Linear Mech.
, 33
(1
), pp. 125
–134
.18.
Borrelli
, A.
, Giantesio
, G.
, and Patria
, M.
, 2013
, “On the Numerical Solutions of Three-Dimensional MHD Stagnation-Point Flow of a Newtonian Fluid
,” Int. J. Pure Appl. Math.
, 86
(2), pp. 425
–442
.19.
Ferraro
, V. C. A.
, and Plumpton
, C.
, 1961
, An Introduction to Magneto-Fluid Mechanics
, Oxford University Press, Oxford, UK.Copyright © 2017 by ASME
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