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.

References

References
1.
Chen
,
T. S.
, and
Yuh
,
C. F.
,
1979
, “
Combined Heat and Mass Transfer in Natural Convection on Inclined Surfaces
,”
Numer. Heat Transfer
,
2
, pp.
233
250
.10.1080/10407787908913409
2.
Burgman
,
T. L.
, and
Ramadhyani
,
S.
,
1986
, “
Combined Buoyancy and Thermocapillary Driven Convection in Open Square Cavities
,”
Numer. Heat Transfer
,
9
, pp.
441
451
.10.1080/10407788608913487
3.
Bergman
,
T. L.
,
1986
, “
Numerical Simulation of Double-Diffusive Marangoni Convection
,”
Phys. Fluids
,
29
(
7
), pp.
2103
2108
.10.1063/1.865597
4.
Bayazitoglu
,
Y.
, and
Lam
,
T. T.
,
1987
, “
Marangoni Convection in Radiating Fluids
,”
ASME J. Heat Transfer
,
109
, pp.
717
721
.10.1115/1.3248148
5.
Lee
,
H. M.
, and
Lee
,
K. J.
,
1989
, “
Computational Analysis of Convective Diffusion With Chemical Reaction in a Cavity
,”
Korean J. Chem. Eng.
,
6
(
4
), pp.
330
337
.10.1007/BF02705222
6.
Carpenter
,
B. M.
, and
Homsy
,
G. M.
,
1989
, “
Combined Buoyant Thermocapillary Flow in a Cavity
,”
J. Fluid Mech.
,
207
, pp.
121
132
.10.1017/S0022112089002521
7.
Keller
,
J. R.
, and
Bergman
,
T. L.
,
1989
, “
Prediction of Conjugate Heat Transfer in a Solid-Liquid System: Inclusion of Buoyancy and Surface Tension Forces in the Liquid Phase
,”
ASME J. Heat Transfer
,
111
, pp.
690
698
.10.1115/1.3250738
8.
Keller
,
J. R.
, and
Bergman
,
T. L.
,
1990
, “
Thermosolutal Inducement of No-Slip Free Surfaces in Combined Marangoni-Buoyancy Driven Cavity Flows
,”
ASME J. Heat Transfer
,
112
, pp.
363
369
.10.1115/1.2910386
9.
Costa
,
V. A. F.
,
1997
, “
Double Diffusive Natural Convection in a Square Enclosure With Heat and Mass Diffusive Walls
,”
Int. J. Heat Mass Transfer
,
40
(
17
), pp.
4061
4071
.10.1016/S0017-9310(97)00061-6
10.
Nishimura
,
T.
,
Wakamatsu
,
M.
, and
Morega
,
A. M.
,
1998
, “
Oscillatory Double-Diffusive Convection in a Rectangular Enclosure With Combined Horizontal Temperature and Concentration Gradients
,”
Int. J. Heat Mass Transfer
,
41
(
11
), pp.
1601
1611
.10.1016/S0017-9310(97)00271-8
11.
Jue
,
T. C.
,
1998
, “
Numerical Analysis of Thermosolutal Marangoni and Natural Convection Flows
,”
Numer. Heat Transfer, Part A
,
34
, pp.
633
652
.10.1080/10407789808914007
12.
Mahidjiba
,
A.
,
Mamou
,
M.
, and
Vasseur
,
P.
,
2000
, “
Onset of Double-Diffusive Convection in a Rectangular Porous Cavity Subject to Mixed Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
43
, pp.
1505
1522
.10.1016/S0017-9310(99)00238-0
13.
Kumar
,
B. V. R.
,
Singh
,
P.
, and
Bansod
,
V. J.
,
2002
, “
Effect of Thermal Stratification on Double-Diffusive Natural Convection in a Vertical Porous Enclosure
,”
Numer. Heat Transfer, Part A
,
41
, pp.
421
447
.10.1080/104077802317261254
14.
Snoussia
,
L. B.
,
Chouikh
,
R.
, and
Guizani
,
A.
,
2005
, “
Numerical Study of the Natural Convection Flow Resulting From the Combined Buoyancy Effects of Thermal and Mass Diffusion in a Cavity With Differentially Heated Side Walls
,”
Desalination
,
182
, pp.
143
150
.10.1016/j.desal.2005.03.014
15.
Hossain
,
M. A.
,
Molla
,
M. M.
, and
Gorla
,
R. S. R.
,
2004
, “
Conjugate Effect of Heat and Mass Transfer in Natural Convection Flow from an Isothermal Sphere With Chemical Reaction
,”
Int. J. Fluid Mech. Res.
,
31
(
4
), pp.
319
331
.10.1615/InterJFluidMechRes.v31.i4.20
16.
Shi
,
W.
,
Li
,
G.
,
Liu
,
X.
,
Li
,
Y. R.
,
Peng
,
L.
, and
Imaishi
,
N.
,
2010
, “
Thermocapillary Convection and Buoyant Thermocapillary Convection in the Annular Pools of Silicon Melt and Silicone Oil
,”
J. Supercond. Nov. Magn.
,
23
, pp.
1169
1172
.10.1007/s10948-010-0662-7
17.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2011
, “
The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
54
, pp.
374
378
.10.1016/j.ijheatmasstransfer.2010.09.034
18.
Rudraiah
,
N.
,
Venkatachalappa
,
M.
, and
Subbaraya
,
C. K.
,
1995
, “
Combined Surface Tension and Buoyancy Driven Convection in a Rectangular Open Cavity in the Presence of a Magnetic Field
,”
Int. J. Non linear Mech.
,
30
, pp.
759
770
.10.1016/0020-7462(95)00026-K
19.
Gelfgat
,
A. Y.
, and
Bar-Yoseph
,
P. Z.
,
2001
, “
The Effect of An External Magnetic Field on Oscillatory Instability of Convective Flows in a Rectangular Cavity
,”
Phys. Fluids
,
13
(
8
), pp.
2269
2278
.10.1063/1.1383789
20.
Hossain
,
M. A.
,
Hafiz
,
M. Z.
, and
Rees
,
D. A. S.
,
2005
, “
Buoyancy and Thermocapillary Driven Convection Flow of an Electrically Conducting Fluid in an Enclosure With Heat Generation
,”
Int. J. Therm. Sci.
,
44
, pp.
676
684
.10.1016/j.ijthermalsci.2004.11.005
21.
Zhang
,
Y.
, and
Zheng
,
L.
,
2012
, “
Analysis of MHD Thermosolutal Marangoni Convection With the Heat Generation and a First-Order Chemical Reaction
,”
Chem. Eng. Sci.
,
69
, pp.
449
455
.10.1016/j.ces.2011.10.069
22.
Huang
,
H.
, and
Zhou
,
X.
,
2009
, “
The Impact of Normal Magnetic Fields on Instability of Thermocapillary Convection in a Two-Layer Fluid System
,”
ASME J. Heat Transfer
,
131
, p. 062502.10.1115/1.3084211
23.
Saleem
,
M.
,
Hossain
,
M. A.
, and
Gorla
,
R. S. R.
,
2013
, “
Effect of Magnetic Field on Thermocapillary Convection in a System of Two Immiscible Liquid Layers in a Rectangular Cavity
,”
Int. J. Numer. Methods Heat Fluid Flow
,
23
(
3
), pp.
405
426
.10.1108/09615531311301218
24.
Roache
,
P. J.
,
1998
,
Computational Fluid Dynamics
, revised ed.,
Hermosa
,
Albuquerque, NM
.
25.
Minkowycz
,
W. J.
,
Sparrow
,
E. M.
, and
Murthy
,
J. Y.
,
2006
,
Handbook of Numerical Heat Transfer
, 2nd ed.,
Wiley
,
Hoboken, NJ
.
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