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.
Issue Section:
Heat and Mass Transfer
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
.10.1080/104077879089134092.
Burgman
, T. L.
, and Ramadhyani
, S.
, 1986
, “Combined Buoyancy and Thermocapillary Driven Convection in Open Square Cavities
,” Numer. Heat Transfer
, 9
, pp. 441
–451
.10.1080/104077886089134873.
Bergman
, T. L.
, 1986
, “Numerical Simulation of Double-Diffusive Marangoni Convection
,” Phys. Fluids
, 29
(7
), pp. 2103
–2108
.10.1063/1.8655974.
Bayazitoglu
, Y.
, and Lam
, T. T.
, 1987
, “Marangoni Convection in Radiating Fluids
,” ASME J. Heat Transfer
, 109
, pp. 717
–721
.10.1115/1.32481485.
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/BF027052226.
Carpenter
, B. M.
, and Homsy
, G. M.
, 1989
, “Combined Buoyant Thermocapillary Flow in a Cavity
,” J. Fluid Mech.
, 207
, pp. 121
–132
.10.1017/S00221120890025217.
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
.10.1115/1.32507388.
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
.10.1115/1.29103869.
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)00061-610.
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)00271-811.
Jue
, T. C.
, 1998
, “Numerical Analysis of Thermosolutal Marangoni and Natural Convection Flows
,” Numer. Heat Transfer, Part A
, 34
, pp. 633
–652
.10.1080/1040778980891400712.
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)00238-013.
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
.10.1080/10407780231726125414.
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.2005.03.01415.
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.i4.2016.
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/s10948-010-0662-717.
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.2010.09.03418.
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-K19.
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
.10.1063/1.138378920.
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.2004.11.00521.
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.2011.10.06922.
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. 062502.10.1115/1.308421123.
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
.10.1108/0961553131130121824.
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
.Copyright © 2014 by ASME
You do not currently have access to this content.
