Articles

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

Expand
  • 1. Department of Humanities and Sciences, Institute of Space Technology, Islamabad 44000, Pakistan;
    2. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;
    3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received date: 2011-12-23

  Revised date: 2012-07-23

  Online published: 2012-11-10

Supported by

Project supported by the Deanship of Scientific Research (DSR) of King Abdulaziz University of Saudi Arabia (No.HiCi/40-3/1432H)

Abstract

The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.

Cite this article

M. NAWAZ;T. HAYAT;A.ALSAEDI . Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium[J]. Applied Mathematics and Mechanics, 2012 , 33(11) : 1403 -1418 . DOI: 10.1007/s10483-012-1632-6

References

[1] Sakiadis, B. S. Boundary layer behavior on continuous solid surface: I. AIChE Journal, 7, 26-28(1961)
[2] Sakiadis, B. S. Boundary layer behavior on continuous solid surface: II. AIChE Journal, 7, 221-225(1961)
[3] Wang, C. Y. Analysis of viscous flow due to a stretching sheet with surface slip and suction.Nonlinear Analysis: Real World Applications, 10, 375-380 (2009)
[4] Ishak, A., Nazar, R., and Pop, I. Heat transfer over an unsteady stretching permeable surface withprescribed wall temperature. Nonlinear Analysis: Real World Applications, 10, 2909-2913 (2009)
[5] Wang, C. Y. Natural convection on a vertical radially stretching sheet. Journal of MathematicalAnalysis and Applications, 332, 877-883 (2007)
[6] Hayat, T. and Awais, M. Three-dimensional flow of upper-convected Maxwell (UCM) fluid. InternationalJournal for Numerical Methods in Fluids, 66(7), 875-884 (2011)
[7] Ariel, P. D. Axisymmetric flow of a second grade fluid past a stretching sheet. International Journalof Engineering and Science, 39, 529-553 (2001)
[8] Salem, A. M. and Abd El-Aziz, M. Effect of Hall currents and chemical reaction on hydromagneticflow of a stretching vertical surface with internal heat generation/absorption. Applied Mathematicsand Modelling, 32, 1236-1254 (2008)
[9] Ishak, A., Nazar, R., and Pop, I. Magnetohydrodynamic (MHD) flow and heat transfer due to astretching cylinder. Energy Conversion and Managemant, 49, 3265-3269 (2008)
[10] Cortell, R. Effects of viscous dissipation and work done by deformation on the MHD flow and heattransfer of a viscoelastic fluid over a stretching sheet. Physics Letters A, 357, 298-305 (2006)
[11] Mukhopadhyay, S. Effect of thermal radiation on unsteady mixed convection flow and heat transferover a porous stretching surface in porous medium. International Journal of Heat and MassTransfer, 52, 3261-3265 (2009)
[12] Bataller, R. C. Effects of heat source/sink, radiation and work done by deformation on flow andheat transfer of a viscoelastic fluid over a stretching sheet. Computers and Mathematics withApplications, 53, 305-316 (2007)
[13] Tsai, R., Huang, K. H., and Huang, J. S. Flow and heat transfer over an unsteady stretching surfacewith non-uniform heat source. International Journal of Heat and Mass Transfer, 35, 1340-1343(2008)
[14] Osalusi, E., Side, J., and Harris, R. Thermal-diffusion and diffusion-thermo effects on combinedheat and mass transfer of a steady MHD convective and slip flow due to a rotating disk withviscous dissipation and Ohmic heating. International Journal of Heat and Mass Transfer, 35,908-915 (2008)
[15] B?eg, O. A., Bakier, A. Y., and Prasad, V. R. Numerical study of free convection magnetohydrodynamicheat and mass transfer from a stretching surface to a saturated porous medium with Soretand Dufour effects. Computational Materials Science, 46, 57-65 (2009)
[16] Tsai, R. and Huang, J. S. Heat and mass transfer for Soret and Dufour’s effects on Hiemenzflow through porous medium onto a stretching surface. International Journal of Heat and MassTransfer, 52, 2399-2406 (2009)
[17] Afify, A. A. Similarity solution in MHD: effects of thermal diffusion and diffusion thermo effectson free convective heat and mass transfer over a stretching surface considering suction or injection.Communications in Nonlinear Science and Numerical Simulation, 14, 2202-2214 (2009)
[18] El-Arabawy, H. A. M. Exact solutions of mass transfer over a stretching surface with chemicalreaction and suction/injection. Journal of Mathematics and Statistics, 5, 159-166 (2009)
[19] Hayat, T., Abbas, Z., and Ali, N.MHD flow and mass transfer of an upper-convectedMaxwell fluidpast a porous shrinking sheet with chemical reaction species. Physics Letters A, 372, 4698-4704(2008)
[20] Mohamed, R. A., Abbas, I. A., and Abo-Dahab, S. M. Finite element analysis of hydromagneticflow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porousmedium in the presence of chemical reaction. Communications in Nonlinear Science and NumericalSimulation, 14, 1385-1395 (2009)
[21] Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, CRC Press, Florida(2003)
[22] Liao, S. J. Notes on the homotopy analysis method: some definitions and theorems. Communicationsin Nonlinear Science and Numerical Simulation, 14(4), 983-997 (2009)
[23] Liao, S. J. A new branch of solutions of unsteady boundary layer flows over an impermeablestretched plate. International Journal of Heat and Mass Transfer, 48(12), 2529-2539 (2005)
[24] Abbasbandy, S. and Hayat, T. Solution of the MHD Falkner-Skan flow by homotopy analysismethod. Communications in Nonlinear Science and Numerical Simulation, 14(9-10), 3591-3598(2009)
[25] Abbasbandy, S. and Shirzadi, A. A new application of the homotopy analysis method: solvingthe Sturm-Liouville problems. Communications in Nonlinear Science and Numerical Simulation,16(1), 112-126 (2011)
[26] Hashim, I., Abdulaziz, O., and Momani, S. Homotopy analysis method for fractional IVPs. Communicationsin Nonlinear Science and Numerical Simulation, 14(3), 674-684 (2009)
[27] Bataineh, A. S., Noorani, M. S. M., and Hashim, I. Modified homotopy analysis method for solvingsystems of second-order BVPs. Communications in Nonlinear Science and Numerical Simulation,14(2), 430-442 (2009)
[28] Allan, F. M. Derivation of the Adomian decomposition method using the homotopy analysismethod. Applied Mathematics and Computation, 190(1), 6-14 (2007)
[29] Hayat, T. and Nawaz, M. Soret and Dufour effects on the mixed convection flow of a second gradefluid subject to Hall and ion-slip currents. International Journal for Numerical Methods in Fluids,67(9), 1073-1099 (2011)
[30] Hayat, T. and Nawaz, M. Magnetohydrodynamic three-dimensional flow of a second-grade fluidwith heat transfer. Zeitschrift für Naturforschung A, 65a(8), 683-691 (2010)
[31] Hayat, T. and Nawaz, M. Hall and ion-slip effects on three-dimensional flow of a second gradefluid. International Journal for Numerical Methods in Fluids, 66, 183-193 (2011)
[32] Hayat, T., Nawaz, M., and Obaidat, S. Axisymmetric magnetohydrodynamic flow of micropolarfluid between unsteady stretching surfaces. Applied Mathematics and Mechanics (English Edition),32(3), 361-374 (2011) DOI 10.1007/s10483-011-1421-8

Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals