Double-Diffusive Natural Convection with Marangoni and Cooling Effects

Double-diffusive natural convection in an open top square cavity and heated from the side is studied numerically. Constant temperatures and concentration are imposed along the right and left walls while the heat balance at the surface is assumed to obey Newton-s law of cooling. The finite difference method is used to solve the dimensionless governing equations. The numerical results are reported for the effect of Marangoni number, Biot number and Prandtl number on the contours of streamlines, temperature and concentration. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. The parameters involved are as follows; the thermal Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number, 0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number, 5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal dominated, N = 0.8 , and compositional dominated, N = 1.3 .

Authors:

• Norazam Arbin
• Ishak Hashim

Keywords:

• Double-diffusive
• Marangoni effects
• heat and mass transfer.

References:

[1] M. A. Teamah, A. F. Elsafty, E. Z. Massoud, Numerical simulation of
double diffusive natural convective flow in an inclined rectangular
enclosure in the presence of magnetic field and heat source, Int. J.
Thermal Sciences, Vol. 52, p. 161-175, 2012.
[2] T. Nishimura, M. Wakamatsu, A. M. Morega, Oscillatory doublediffusive
convection in a rectangular enclosure with combined horizontal
temperature and concentration gradients, Int. J. Heat Mass Transfer, Vol.
41, p. 1601-1611, 1998.
[3] V. A. F. Costa, Double diffusive natural convection in a square
enclosure with heat and mass diffusive walls, Int. J. Heat Mass Transfer,
Vol. 40, p. 4061-4071, 1997.
[4] A. J. Chamka, H. Al-Naser, Hydromagnetic double-diffusive convection
in a rectangular enclosure with opposing temperature and concentration
gradients, Int. J. Heat Mass Transfer, Vol. 45, p. 2465-2483, 2002.
[5] M. A. Teamah, Numerical simulation of double diffusive natural
convection in rectangular enclosure in the presence of magnetic field and
heat source, Int. J. Thermal Sciences, Vol. 47, p. 237-248, 2008.
[6] M. Bourich, A. Amahmid, M. Hasnaoui, Double diffusive convection in
a porous enclosure submitted to cross gradients of temperature and
concentration, Energy Conversion and Management, Vol. 45, p. 1655-
1670, 2004.
[7] A. C. Baytas, A. F. Baytas, D. B. Ingham, I. Pop, Double diffusive
natural convection in an enclosure filled with a step type porous layer:
Non-Darcy flow, Int. J. Heat Thermal Sciences, Vol. 48, p. 665-673,
2009.
[8] Y. Li, Z. Chen, J. Zhan, Double-diffusive Marangoni convection in a
rectangular cavity: Transition to chaos, Int. J. Heat Mass Transfer, Vol.
53, p. 5223-5231, 2010.
[9] C. F. Chen, C. L. Chan, Stability of buoyancy and surface tension driven
convection in a horizontal double-diffusive fluid layer, Int. J. Heat Mass
Transfer, Vol. 53, p. 1563-1569, 2010.
[10] V. A. F. Costa, Double-diffusive natural convection in parallelogrammic
enclosures, Int. J. Heat Mass Transfer, Vol. 47, p. 2913-2926, 2004.
[11] E. Papanicolaou, V. Belessiotis, Double-diffusive natural convection in
an asymmetric trapezoidal enclosure: unsteady behaviour in the laminar
and the turbulent-flow regime, Int. J. Heat Mass Transfer, Vol. 48, p.
191-209, 2005.
[12] S. Sivasankaran, M. Bhuwaneswari, Y. J. Kim, C. J. Ho, K. L. Pan,
Numerical study on magneto-convection of cold water in an open cavity
with variable fluid properties, Int. J. Heat and Fluid Flow, Vol. 32, p.
932-942, 2011.
[13] H. Saleh, N. Arbin, R. Roslan, I. Hashim, Visualization and analysis of
surface tension and cooling effects on differentially heated cavity using
heatline concept, Int. J. Heat Mass Transfer, Vol. 55, p. 6000-6009,
2012.
[14] M. A. Teamah, W. M. El-Maghlany, Numerical simulation of doublediffusive
mixed convection flow in rectangular enclosure with insulated
moving lid, Int. J. Thermal Sciences, Vol. 49, p. 1625-1638, 2010.
[15] L. B. Younis, A. A. Mohamad, A. K. Mojtabi, Double diffusion natural
convection in open lid enclosure filled with binary fluids, Int. J. Thermal
Sciences, Vol. 46, p. 112-117, 2007.
[16] S. Chen, J. Tolke, M. Krafczyk, Numerical investigation of doublediffusive
(natural) convection in vertical annuluses with opposing
temperature and concentration gradients, Int. J. Heat and Fluid Flow,
Vol. 31, p. 217-226, 2010.