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Research Papers: Heat and Mass Transfer

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

[+] Author and Article Information
M. Saleem

Department of Electrical
and Computer Engineering,
CASE University,
19 Atta Turk Avenue,
G 5/1 Islamabad, Pakistan
e-mail: saleem.cfd@gmail.com

M. A. Hossain

Professor
Bangladesh Academy of Sciences,
Dhaka, Bangladesh
e-mail: anwar@univdhaka.edu

Suvash C. Saha

Postdoctoral Research
School of Chemistry, Physics
and Mechanical Engineering,
Queensland University of Technology,
GPO Box 2434,
Brisbane QLD 4001, Australia
e-mail: s_c_saha@yahoo.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 24, 2013; final manuscript received December 18, 2013; published online March 7, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(6), 062001 (Mar 07, 2014) (9 pages) Paper No: HT-13-1273; doi: 10.1115/1.4026372 History: Received May 24, 2013; Revised December 18, 2013

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

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Figures

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Fig. 1

Flow configuration in coordinate system

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Fig. 2

Numerical values of |ψ|max against time at Gr = 107, Pr = 0.054, W = w = 0.5, Sc = γ = 10, Ha = 20, ξ = 0.0 deg, and Ma = 1000, for different grids

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Fig. 7

Average (a) Nusselt number, (b) Sherwood number at Gr = 106, Pr = 0.054, Ma = 5000, Ha = 50, ξ = 0.0 deg, Sc = 5, W = w = 0.5 for different values of γ

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Fig. 3

Steady state streamlines at Gr = 5 × 105, Pr = 0.054, Ma = 2000, Ha = 20, ξ = 0.0 deg, Sc = γ = 5, w = 0.5 for (a) W = 0 (b) W = 0.5 (c) W = 1

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Fig. 4

Steady state isohalines at Gr = 5 × 105, Pr = 0.054, Ma = 2000, Ha = 20, ξ = 0 deg, Sc = γ = 5, w = 0.5 for (a) W = 0 (b) W = 0.5 (c) W = 1

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Fig. 5

Steady state streamlines at Gr = 2 × 105, Pr = 0.054, Ma = 2500, Ha = 20, ξ = 0.0 deg, Sc = γ = 5, W = 0.5 for (a) w = 0 (b) w = 0.5 (c) w = 1

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Fig. 6

Steady state isohalines at Gr = 2 × 105, Pr = 0.054, Ma = 2500, Ha = 20, ξ = 0.0 deg, Sc = γ = 5, W = 0.5 for (a) w = 0 (b) w = 0.5 (c) w = 1

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Fig. 8

(a) Average Nusselt number, (b) Average Sherwood number at Gr = 106, Pr = 0.054, Ma = 2500, ξ = 0.0 deg, Sc = 10, γ = 100, W = w = 0.5 for different values of Hartmann number

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Fig. 9

Steady state pattern of streamlines at Gr = 5 × 105, Pr = 0.054, Ma = 4000, Ha = 50, Sc = γ = 10, W = w = 0.5 for (a) ξ = 0 deg (b) ξ = 45 deg (c) ξ = 90 deg

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Fig. 10

Steady state pressure contors at Gr = 5 × 105, Pr = 0.054, Ma = 4000, Ha = 50, Sc = γ = 10, W = w = 0.5 for (a) ξ = 0 deg (b) ξ = 45 deg (c) ξ = 90 deg

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Fig. 11

(a) Average Nusselt number, (b) Sherwood number at Gr = 5 × 105, Pr = 0.054, Ma = 4000, Ha = 50, Sc = γ = 10, W = w = 0.5 for different orientations of magnetic field

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