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Lie Group Analysis for a Mixed Convective Flow and Heat Mass Transfer Over a Permeable Stretching Surface with Soret and Dufour Effects

Published online by Cambridge University Press:  14 November 2013

Reda G. Abdel-Rahman  and
Ahmed M. Megahed
Reda G. Abdel-Rahman
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Egypt
Ahmed M. Megahed*
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Egypt
*
ah_mg_sh@yahoo.com
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Abstract

The Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

Keywords

Lie group analysisSoret and dufour effectsStretching surface
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 1 , February 2014 , pp. 67 - 75
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Sparrow, E. M. and Yu, H. S., “Local Nonsimilarity Thermal Boundary-Layer Solutions,” Journal of Heat Transfer, ASME, 93, pp. 328–332 (1971).Google Scholar
2.Lai, F. C. and Kulacki, F. A., “The Influence of Lateral Mass Flux on Mixed Convection over Inclined Surfaces in Saturated Porous Media,” Journal of Heat Transfer, 112, pp. 515–518 (1990).Google Scholar
3.Hooper, W. B., Chen, T. S. and Armaly, B. F., “Mixed Convection from a Vertical Plate in Porous Media with Surface Injection or Suction,” Numerical Heat Transfer, 25, pp. 317–329 (1993).CrossRefGoogle Scholar
4.Hossain, M. A and Takhar, H. S., “Radiation Effect on Mixed Convection Along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, 31, pp. 243–248 (1996).Google Scholar
5.Chen, C.-H., “Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets,” Heat and Mass Transfer, 33, pp. 471–476 (1998).Google Scholar
6.Eckert, E. R. G. and Drake, R. M., Analysis of Heat and Mass Transfer, McGraw Hill, New York (1972).Google Scholar
7.Ibrahim, F.S., Abdel-Gaid, S. M. and Gorla, R. S. R., “Non-Darcy Mixed Convection Flow Along a Vertical Plate Embedded in a Non-Newtonian Fluid Saturated Porous Medium with Surface Mass Transfer,” International Journal of Numerical Methods for Heat and Fluid Flow, 10, pp. 397–408 (2000).Google Scholar
8.Postelnicu, A., “Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects,” International Journal Heat and Mass Transfer, 47, pp. 1467–1472 (2004).Google Scholar
9.Eldabe, N. T., El-Saka, A. G. and Fouad, A., “Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Free-Forced Convection and Mass Transfer Boundary Layer Flow for Non-Newtonian Fluid with Temperature Dependent Viscosity,” Applied Mathematics and Computation, 152, pp. 867–883 (2004).Google Scholar
10.Postelnicu, A., “Influence of Chemical Reaction on Heat and Mass Transfer by Natural Convection From Vertical Surfaces in Porous Media Considering Soret and Dufour Effects,” Heat and Mass Transfer, 43, pp. 595–602 (2007).CrossRefGoogle Scholar
11.Ishak, A., Nazar, R. and Pop, I., “Mixed Convection Stagnation Point Flow of a Micropolar Fluid Towards a Stretching Sheet,” Meccanica, 34, pp. 411–418 (2008).Google Scholar
12.Lakshmi, P. A. and Murthy, P. V. S. N., “Soret and Dufour Effects on Free Convection Heat and Mass Transfer from a Horizontal Flat Plate in a Darcy Porous Medium,” Journal of Heat Transfer, 130, pp. 104504–1–5 (2008).Google Scholar
13.Ishak, A., Nazar, R. and Pop, I., “Mixed Convection Boundary Layer Flow Adjacent to a Vertical Surface Embedded in a Stable Stratified Medium,” Heat Mass Transfer, 51, pp. 3693–3695 (2008).Google Scholar
14.Hayat, T., Mustafa, M. and Pop, I., “Heat and Mass Transfer for Soret and Dufour's Effect on Mixed Convection Boundary Layer Flow over a Stretching Vertical Surface in a Porous Medium Filled with a Viscoelastic Fluid,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 1183–1196 (2010).CrossRefGoogle Scholar
15.Anwar Bég, O., Bakier, A. Y. and Prasad, V. R., “Numerical Study of Free Convection Magnetohy-drodynamic Heat and Mass Transfer from a Stretching Surface to a Saturated Porous Medium with Soret and Dufour Effects,” Computational Materials Science, 46, pp. 57–65 (2009).Google Scholar
16.Saied, E. A. and Abdel-Rahman, R. G., “On the Porous Medium Equation with Modified Fourier's Law: Symmetries and Integrability,” Journal of the Physical Society of Japan, 68, pp. 360–368 (1998).Google Scholar
17.Abdel-Rahman, R. G., “Group Classification of Dispersion Equation of Gaseous Pollutants in Presence of a Temperature Inversion,” Journal of Quantitative Spectroscopy and Radiative Transfer, 98, pp. 1–17 (2006).Google Scholar
18.Ibragimov, N. H., Handbook of Lie Group Analysis of Differential Equations, II. Applications in Engineering and Physical Sciences, CRC Press, Boca Raton (1994).Google Scholar
19.Olver, P. J., Application of Lie Group to Differential Equations, Graduate Text in Mathematics, 107, Springer, New York (1993).Google Scholar
20.Bluman, G. W. and Kumei, S., Symmetries and Differential Equations. Springer-Varlag, New York, USA (1989).Google Scholar