Research Papers: Forced Convection

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

[+] Author and Article Information
Yanhai Lin

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China;
School of Mechanical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

Liancun Zheng

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China

Xinxin Zhang

School of Mechanical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 21, 2012; final manuscript received January 6, 2013; published online April 11, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(5), 051702 (Apr 11, 2013) (6 pages) Paper No: HT-12-1448; doi: 10.1115/1.4023394 History: Received August 21, 2012; Revised January 06, 2013

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Zheng, L. C., Lin, Y. H., and Zhang, X. X., 2012, “Marangoni Convection of Power Law Fluids Driven by Power-Law Temperature Gradient,” J. Franklin Inst., 349, pp. 2585–2597. [CrossRef]
Zhang, Y., and Zheng, L. C., 2012, “Analysis of MHD Thermosolutal Marangoni Convection With the Heat Generation and a First-Order Chemical Reaction,” Chem. Eng. Sci., 69, pp. 449–455. [CrossRef]
McConaghy, G. A., and Finlayson, B. A., 1969, “Surface Tension Driven Oscillatory Instability in a Rotating Fluid Layer,” J. Fluid Mech., 39, pp. 49–55. [CrossRef]
Cazabat, A. M., Heslot, F., Troian, S. M., and Carles, P., 1990, “Fingering Instability of Thin Spreading Films Driven by Temperature Gradients,” Nature, 346, pp. 824–826. [CrossRef]
Levich, V. G., and Krylov, V. S., 1969, “Surface-Tension-Driven Phenomena,” Annu. Rev. Fluid Mech., 1, pp. 293–317. [CrossRef]
Pearson, J. R. A., 1958, “On Convection Cells Induced by Surface Tension,” J. Fluid Mech., 4(5), pp. 489–500. [CrossRef]
Johnson, D., and Narayanan, R., 1999, “A Tutorial on the Rayleigh-Marangoni-Benard Problem With Multiple Layers and Side Wall Effects,” Chaos, 9(1), pp. 124–140. [CrossRef] [PubMed]
Arafune, K., and Hirata, A., 1999, “Thermal and Solutal Marangoni Convection in In-Ga-Sb System,” J. Cryst. Growth, 197, pp. 811–817. [CrossRef]
Scriven, L. E., and Sternling, C. V., 1960, “The Marangoni Effects,” Nature, 187, pp. 186–188. [CrossRef]
Bergman, T. L., 1986, “Numerical Simulation of Double-Diffusive Marangoni Convection,” Phys. Fluids, 29(7), pp. 2103–2108. [CrossRef]
Bergeon, A., Henry, D., Benhadid, H., and Tuckerman, S., 1998, “Marangoni Convection in Binary Mixtures With Soret Effect,” J. Fluid Mech., 375, pp. 143–177. [CrossRef]
Louchev, O. A., and Otani, S., 1996, “Marangoni Convection and Enhanced Morphological Stability in Float-Zone Traveling Solvent Crystal Growth of LaB6,” J. Appl. Phys., 80(11), pp. 6567–6569. [CrossRef]
Naimi, M., Hasnaoui, M., and Platten, J. K., 2000, “Marangoni Convection of Non-Newtonian Power Law Fluids in a Shallow Rectangular Cavity,” Eng. Comput., 17(6), pp. 638–668. [CrossRef]
Scheid, B., Oron, A., Colinet, P., Thiele, U., and Legros, J. C., 2002, “Nonlinear Evolution of Nonuniformly Heated Falling Liquid Films,” Phys. Fluids, 14(12), pp. 4130–4151. [CrossRef]
Bestehorn, M., Pototsky, A., and Thiele, U., 2003, “3D Large Scale Marangoni Convection in Liquid Films,” Eur. Phys. J. B., 33, pp. 457–467. [CrossRef]
Thiele, U., and Knobloch, E., 2004, “Thin Liquid Films on a Slightly Inclined Heated Plate,” Physica D, 190, pp. 213–248. [CrossRef]
Trevelyan, P. M. J., and Kalliadasis, S., 2004, “Wave Dynamics on a Thin-Liquid Film Falling Down a Heated Wall,” J. Eng. Math., 50, pp. 177–208. [CrossRef]
Ruyer-Quil, B. C., Scheid, B., Kalliadasis, S., Velarde, M. G., and Zeytounian, R. K., 2005, “Thermocapillary Long Waves in a Liquid Film Flow. Part I—Low-Dimensional Formulation,” J. Fluid Mech., 538, pp. 199–222. [CrossRef]
Trevelyan, P. M. J., Scheid, B., Ruyer-Quil, C., and Kalliadasis, S., 2007, “Heated Falling Films,” J. Fluid Mech., 592, pp. 295–334. [CrossRef]
Christopher, D. M., and Wang, B. X., 2001, “Similarity Simulation for Marangoni Convection Around a Vapor Bubble During Nucleation and Growth,” Int. J. Heat Mass Transfer, 44, pp. 799–810. [CrossRef]
Zheng, L. C., Sheng, X. Y., and Zhang, X. X., 2006, “Analytical Approximate Solutions for Marangoni Convection Boundary Layer Equations,” Acta Phys. Sin., 55(10), pp. 5298–5304. Available at http://wulixb.iphy.ac.cn/CN/Y2006/V55/I10/5298
Zheng, L. C., Zhang, X. X., and Gao, Y. T., 2008, “Analytical Solution for Marangoni Over a Liquid-Vapor Surface Due to an Imposed Temperature Gradient,” Math. Comput. Modell., 48, pp. 1787–1795. [CrossRef]
Savino, R., and Fico, S., 2004, “Transient Marangoni Convection in Hanging Evaporating Drops,” Phys. Fluids, 16(10), pp. 3738–3754. [CrossRef]
Chen, C. H., 2003, “Heat Transfer in a Power-Law Film Over an Unsteady Stretching Sheet,” Heat Mass Transfer, 39, pp. 791–796. [CrossRef]
Chen, C. H., 2007, “Marangoni Effects on Forced Convection of Power-Law Liquids in a Thin Film Over a Stretching Surface,” Phys. Lett. A, 370, pp. 51–57. [CrossRef]
Demekhin, E. A., Kalliadasis, S., and Velarde, M. G., 2006, “Suppressing Falling Film Instabilities by Marangoni Forces,” Phys. Fluids, 18(4), p. 042111. [CrossRef]
Nepomnyashchy, A. A., and Simanovskii, I. B., 2007, “Marangoni Instability in Ultrathin Two-Layer Films,” Phys. Fluids, 19(12), p. 122103. [CrossRef]
Hamid, R. A., Arifin, N. M., Nazar, R., and Ali, F. M., 2011, “Radiation Effects on Marangoni Convection Over a Flat Surface With Suction and Injection,” J. Math. Sci., 5(1), pp. 13–25. Available at http://psasir.upm.edu.my/12541/
Mudhaf, A. A., and Chamkha, A. J., 2005, “Similarity Solutions for MHD Themosolutal Marangoni Convection Over a Flat Surface in the Presence of Heat Generation or Absorption Effects,” Heat Mass Transfer, 42, pp. 112–121. [CrossRef]
Magyari, E., and Chamkha, A. J., 2007, “Exact Analytical Solutions for the Thermosolutal Convection in the Presence of Heat and Mass Generation or Consumption,” Heat Mass Transfer, 43, pp. 965–974. [CrossRef]
Magyari, E., and Chamkha, A. J., 2008, “Exact Analytical Results for the Themosolutal MHD Marangoni Boundary Layers,” Int. J. Therm. Sci., 47, pp. 848–857. [CrossRef]
Rongy, L., and De Wit, A., 2006, “Steady Marangoni Flow Traveling With Chemical Fronts,” J. Chem. Phys., 124(16), p. 164705. [CrossRef] [PubMed]
Rongy, L., De Wit, A., and Homsy, G. M., 2008, “Asymptotic Structure of Steady Nonlinear Reaction-Diffusion-Marangoni Convection Fronts,” Phys. Fluids, 20(7), p. 072103. [CrossRef]
Pop, I., Rashidi, M., Gorla, R. S. R., 1991, “Mixed Convection to Power-Law Type Non-Newtonian Fluids From a Vertical Wall,” Polym.-Plast. Technol. Eng., 30, pp. 47–66. [CrossRef]
Subba, R., Gorla, R., Dakappagari, V., and Pop, I., 1993, “Boundary Layer Flow at a Three-Dimensional Stagnation Point in Power-Law Non-Newtonian Fluids,” Int. J. Heat Fluid Flow, 14(4), pp. 408–412. [CrossRef]
Andersson, H. I., and Kumaran, V., 2006, “On Sheet-Driven Motion of Power-Law Fluids,” Int. J. Non-Linear Mech., 41, pp. 1228–1234. [CrossRef]
Chen, C. H., 2009, “Magneto-Hydrodynamic Mixed Convection of a Power-Law Fluid Past a Stretching Surface in the Presence of Thermal Radiation and Internal Heat Generation/Absorption,” Int. J. Non-Linear Mech., 44, pp. 596–603. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic of the physical system

Grahic Jump Location
Fig. 2

Effects of the Hartmann number on the velocity for n = 0.8

Grahic Jump Location
Fig. 3

Effects of the Hartmann number on the temperature for n = 0.8

Grahic Jump Location
Fig. 4

Effects of the power-law index on the velocity

Grahic Jump Location
Fig. 5

Effects of the power-law index on f(η)

Grahic Jump Location
Fig. 6

Effects of the power-law index on the shear tension

Grahic Jump Location
Fig. 7

Effects of the Marangoni number on the temperature for n = 1.2




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In