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Research Papers: Fundamental Issues and Canonical Flows

Reverse Flow in Magnetoconvection of Two Immiscible Fluids in a Vertical Channel

[+] Author and Article Information
Alessandra Borrelli

Dipartimento di Matematica e Informatica,
Università degli Studi di Ferrara,
via Machiavelli 30,
Ferrara 44121, Italy
e-mail: brs@unife.it

Giulia Giantesio

Dipartimento di Matematica e Fisica,
Università Cattolica del Sacro Cuore,
via Musei 41,
Brescia 25121, Italy
e-mail: giulia.giantesio@unicatt.it

Maria Cristina Patria

Dipartimento di Matematica e Informatica,
Università degli Studi di Ferrara,
via Machiavelli 30,
Ferrara 44121, Italy
e-mail: pat@unife.it

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 16, 2016; final manuscript received May 2, 2017; published online July 10, 2017. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 139(10), 101203 (Jul 10, 2017) (16 pages) Paper No: FE-16-1751; doi: 10.1115/1.4036670 History: Received November 16, 2016; Revised May 02, 2017

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.

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References

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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. [CrossRef]
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Figures

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Fig. 1

Physical configuration and coordinate system

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Fig. 2

Symmetric heating (Tw1=Tw2=T0): effects of H0 and μ on the motion

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Fig. 3

Asymmetric heating—natural convection: influence of M1, k, and γ on the velocities and on the induced magnetic fields

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Fig. 4

Asymmetric heating—mixed convection: influence of σ, k, and λ on the velocities and on the induced magnetic fields

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Fig. 5

Asymmetric heating—mixed convection: channel occupied by mercury and seawater

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Fig. 6

Reverse flow for a single fluid

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Fig. 7

Reverse flow in case II

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Fig. 8

Reverse flow in case IM when λ1 and M vary

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Fig. 9

Reverse flow in case IIM

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Fig. 10

Behavior of the reverse flow for a single fluid or when μ varies for two fluids

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Fig. 11

Behavior of the reverse flow when γ varies for two fluids

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