Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-06T14:23:58.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Soret and Dufour Effects on the Unsteady Mixed Convection Flow Over a Stretching Surface

Published online by Cambridge University Press:  07 August 2013

F. E. Alsaadi ,
S. A. Shehzad ,
T. Hayat  and
S. J. Monaquel
F. E. Alsaadi
Affiliation:
Department of Electrical and Computer Engineering, King Abdulaziz University, Saudi Arabia
S. A. Shehzad*
Affiliation:
Department of Mathematics, Quaid-i-Azam University, Pakistan
T. Hayat
Affiliation:
Department of Electrical and Computer Engineering, King Abdulaziz University , Saudi Arabia Department of Mathematics, Quaid-i-Azam University, Pakistan
S. J. Monaquel
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University , Saudi Arabia
*
*ali_qau70@yahoo.com
Get access

Abstract

Mixed convection flow of second grade fluid bounded by a permeable stretching surface is discussed. Soret and Dufour effects are also present. Series solutions for the resulting problems are made using homotopy analysis method (HAM). Analysis has been carried out for the effects of embedded parameters on the velocity, temperature and concentration fields. Numerical values of Nusselt and Sherwood numbers are computed and discussed.

Keywords

Soret and Dufour effectsSecond grade fluidNonlinear analysis
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 623 - 632
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Altan, T. S. Oh and Gegel, H., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, Ohio (1979).Google Scholar
2.Fisher, E. G., Extrusion of Plastics, Wiley, New York (1976).Google Scholar
3.Tadmor, Z. and Klein, I., Engineering Principles of Plasticating Extrusion, in: Polymer Science and Engineering Series, Van Nostrand Reinhold, New York (1970).Google Scholar
4.Karwe, M. V. and Jaluria, Y., “Fluid Flow and Mixed Convection Transport from a Moving Plate in Rolling and Extrusion Processes,” Journal of Heat Transfer Transactions, ASME, 110, pp. 655–661 (1988).Google Scholar
5.Karwe, M. V. and Jaluria, Y., “Numerical Simulation of Thermal Transport Associated with a Continuously Moving Flat Sheet in Materials Processing,” Journal of Heat Transfer Transactions, ASME, 113, pp. 612–619 (1991).CrossRefGoogle Scholar
6.Sakiadis, B. C., “Boundary Layer Behaviour on Continuous Solid Surfaces: I Boundary Layer Equations for Two Dimensional and Axisymmetric Flow,” Journal of American Institute of Chemical Engineering, 7, pp. 26–28 (1961).Google Scholar
7.Sakiadis, B. C., “Boundary Layer Behaviour on Continuous Solid Surfaces: II Boundary Layer on a Continuous Flat Surface,” Journal of American Institute of Chemical Engineering, 7, pp. 221–225 (1961).Google Scholar
8.Crane, L. J., “Flow Past a Stretching Plate,” Zeitschrift Für Angewandte Mathematik Und Physik, 21, pp. 645–647 (1970).CrossRefGoogle Scholar
9.Cortell, R., “A Note on Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, 41, pp. 78–85 (2006).Google Scholar
10.Ariel, P. D., “A Numerical Algorithm for Computing the Stagnation Point Flow of a Second Grade Fluid With/Without Suction,” Journal of Communications Applied Mathematical, 59, pp. 9–24 (1995).Google Scholar
11.Cortell, R., “MHD Flow and Mass Transfer of an Electrically Conducting Fluid of a Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species,” Chemical Engineers Proceedings, 46, pp. 721–728 (2007).Google Scholar
12.Ariel, P. D., “Axisymmetric Flow of a Second Grade Fluid Past a Stretching Sheet,” International Journal of Engineering Science, 39, pp. 529–553 (2001).Google Scholar
13.Liao, S. J., “On the Analytic Solution of Magneto-hydrodynamic Flows of Non-Newtonian Fluid over a Stretching Sheet,” Fluid Mechanics, 488, pp. 189–212 (2003).Google Scholar
14.Hayat, T., Shehzad, S. A., Qasim, M. and Obaidat, S., “Radiative Flow of Jeffery Fluid in a Porous Medium with Power Law Heat Flux and Heat Source,” Nuclear Engineering and Design, 243, pp. 15–19 (2012).Google Scholar
15.Hayat, T., Shehzad, S. A. and Qasim, M., “Mixed Convection Flow of a Micropolar Fluid with Radiation and Chemical Reaction,” International Journal for Numerical Methods in Fluids, 67, pp. 1418–1436 (2011).Google Scholar
16.Cortell, R., “Flow and Heat Transfer of an Electrically Conducting Fluid of a Second Grade over a Stretching Sheet Subject to Suction and to a Transverse Magnetic Field,” International Journal Heat and Mass Transfer, 49, pp. 1851–1856 (2006).Google Scholar
17.Hayat, T., Abbas, Z., Pop, I. and Asghar, S., “Effects of Radiation and Magnetic Field on the Mixed Convection Stagnation-Point Flow over a Vertical Stretching Sheet in a Porous Medium,” International Journal Heat and Mass Transfer, 53, pp. 466–474 (2010).Google Scholar
18.Yurusoy, M. and Pakdemirli, M., “Exact Solutions of Boundary Layer Equations of a Special Non-Newtonian Fluid over a Stretching Sheet,” Mechanics Research Communications, 26, pp. 171–175 (1999).CrossRefGoogle Scholar
19.Cortell, R., “Toward an Understanding of the Motion and Mass Transfer with Chemically Reactive Species for Two Classes of Viscoelastic Fluid over a Porous Stretching Sheet,” Chemical Engineers Proceedings, 46, pp. 982–989 (2007).Google Scholar
20.Cortell, R., “Effects of Viscous Dissipation and Work Done by Deformation on the MHD Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” Physics Letters A, 357, pp. 298–305 (2006).CrossRefGoogle Scholar
21.Andersson, H. I., Aarseth, J. B. and Dandapat, B. S., “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface,” International Journal Heat and Mass Transfer, 43, pp. 69–74 (2003).Google Scholar
22.Ishak, A., Nazar, R. and Pop, I., “Heat Transfer over an Unsteady Stretching Permeable Surface with Prescribed Wall Temperature,” Nonlinear Analysis: Real World Applications, 10, pp. 2909–2913 (2009).Google Scholar
23.Hayat, T., Qasim, M. and Abbas, Z., “Radiation and Mass Transfer Effects on the Magnetohydrody-namic Unsteady Flow Induced by a Stretching Sheet,” Zeitschrift Naturforschung A, 65, pp. 231–239 (2010).Google Scholar
24.Mukhopadhyay, S., “Effect of Thermal Radiation on Unsteady Mixed Convection Flow and Heat Transfer over a Stretching Surface in a Porous Medium,” International Journal Heat and Mass Transfer, 52, pp. 3261–3265 (2009).CrossRefGoogle Scholar
25.Hayat, T. and Qasim, M., “Radiation and Magnetic Field Effects on the Unsteady Mixed Convection Flow of a Second Grade Fluid over a Vertical Stretching Sheet,” International Journal for Numerical Methods in Fluids, 66, pp. 820–832 (2011).CrossRefGoogle Scholar
26.Eckert, E. K. G. and Drake, R. M., Analysis of Heat and Mass Transfer, Mcgraw-Hill, New York (1972).Google Scholar
27.Tsai, R. and Huang, J. S., “Heat and Mass Transfer for Soret and Dufour's Effects on Heimenz Flow Through Porous Medium Onto a Stretching Surface,” International Journal Heat and Mass Transfer, 52, pp. 2399–2406 (2009).Google Scholar
28.Hayat, T., Mustafa, M. and Pop, I., “Heat and Mass Transfer for Soret and Dufour's Effects 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
29.Alam, M. S. and Rahman, M. M., “Dufour and So-ret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction,” Nonlinear Analysis: Modelling Control, 11, pp. 3–12 (2006).Google Scholar
30.Hayat, T., Mustafa, M. and Mesloub, S., “Mixed Convection Boundary Layer Flow over a Stretching Surface Filled with a Maxwell Fluid In Presence of Soret and Dufour Effects,” Zeitschrift Naturforschung A, 65, pp. 401–410 (2010).Google Scholar
31.Pal, D. and Mondal, H., “Effects of Soret Dufour, Chemical Reaction and Thermal Radiation on MHD Non-Darcy Unsteady Mixed Convective Heat and Mass Transfer over a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 1942–1958 (2011).CrossRefGoogle Scholar
32.Liao, S. J., Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall, CRC Press, Boca Raton (2003).Google Scholar
33.Bataineh, A. S., Noorani, M. S. M. and Hashim, I., “On a New Reliable Modification of Homotopy Analysis Method,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 409–423 (2009).Google Scholar
34.Hayat, T., Shehzad, S. A., Alsaedi, A. and Alhothuali, M. S., “Mixed Convection Stagnation Point Flow of Casson Fluid with Convective Boundary Conditions,” Chinese Physics Letters, 29, p. 114704 (2012).Google Scholar
35.Shehzad, S. A., Hayat, T., Qaism, M. and Asghar, S., “Effects of Mass Transfer on MHD Flow of Casson Fluid with Chemical Reaction and Suction,” Brazilian Journal of Chemical Engineering, 30, pp. 187–195 (2013).CrossRefGoogle Scholar
36.Abbasbandy, S., “Soliton Solutions for the 5th-Order Kdv Equation with the Homotopy Analysis Method,” Nonlinear Dynamics, 51, pp. 83–87 (2008).Google Scholar
37.Hayat, T., Qasim, M. and Abbas, Z., “Three-Dimensional Flow of an Elastico-Viscous Fluid with Mass Transfer,” International Journal for Numerical Methods in Fluids, 66, pp. 194–211 (2011).Google Scholar
38.Rashidi, M. M. and Pour, S. A. M., “Analytic Approximate Solutions for Unsteady Boundary-Layer Flow and Heat Transfer Due to a Stretching Sheet by Homotopy Analysis Method,” Nonlinear Analysis: Modelling and Control, 15, pp. 83–95 (2010).Google Scholar
39.Liao, S. J., “Notes on the Homotopy Analysis Method: Some Definitions and Theorems,” Communications in Nonlinear Science and Numerical >Simulation, 14, pp. 983–997 (2009).Google Scholar
40.Liao, S. J., “A General Approach to Get Series Solution of Non-Similarity Boundary-Layer Flows,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 2144–2159 (2009).Google Scholar
41.Hayat, T., Shehzad, S. A., Qasim, M. and Obaidat, S., “Steady Flow of Maxwell Fluid with Convec-tive Boundary Conditions,” Zeitschrift Naturforschung A, 66, pp. 417–422 (2011).Google Scholar
42.Hayat, T., Maqbool, K. and Asghar, S., “Hall and Heat Transfer Effects on the Steady Flow of a Sis-ko Fluid,” Zeitschrift Naturforschung A, 64, pp. 769–782 (2009).Google Scholar
43.Hayat, T., Shehzad, S. A. and Alsaedi, A., “Soret and Dufour Effects on Magnetohydrodynamic (MHD) Flow of Casson Fluid,” Applied Mathematics and Mechanics - English Edition, 33, pp. 1301–1312 (2012).Google Scholar
44.Hayat, T., Qasim, M., Abbas, Z. and Hendi, A. A., “Magnetohydrodynamic Flow and Mass Transfer of a Jeffery Fluid over a Nonlinear Stretching Surface,” Zeitschrift Naturforschung A, 64, pp. 1111–1120 (2010).Google Scholar
45.Grubka, L. J. and Bobba, K. M., “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Journal of Heat Transfer Transactions, ASME, 107, pp. 248–250 (1985).Google Scholar
46.Chen, C. H., “Laminar Mixed Convection Adjacent to Vertical, Continuously Stretching Sheets,” Heat Mass Transfer, 33, pp. 471–476 (1998).CrossRefGoogle Scholar