Abstract
The thermal-diffusion and diffusion-thermo effects on magnetohydrodynamic viscoelastic flow of second grade fluid over porous oscillatory stretching sheet with thermal radiation are analyzed. The dimensionless nonlinear partial differential equations are solved by means of homotopy analysis method. The effects of various parameters on velocity, temperature and concentration distributions are investigated and discussed in detail. It is found that temperature increases by increasing Dufour number. The concentration field is enhanced by increasing Soret number while it decreases with Schmidt number. Moreover, the numerical values of effective local Nusselt number and local Sherwood number are calculated and illustrated through tables.
Similar content being viewed by others
References
Vajravelu K, Rollins D (1991) Heat transfer in a viscoelastic fluid over a stretching sheet. J Math Anal Appl 158:241–255
Subhas AM, Veena PH (1998) Visco-elastic fluid flow and heat transfer in a porous medium over a stretching sheet. Int J Non-Linear Mech 33:531
Vajravelu K, Roper T (1999) Flow and heat transfer in a second grade fluid over a stretching sheet. Int J Non-Linear Mech 34:1031–1036
Massoudi M, Maneschy CE (2004) Numerical solution to the flow of a second grade fluid over a stretching sheet using the method of quasi-linearization. Appl Math Comput 149:165–173
Hayat T, Sajid M (2007) Analytic solution of axisymmetric flow and heat transfer of second grade fluid past a stretching sheet. Int J Heat mass Transfer 50:75–84
Abel SM, Nandeppanavar MM, Malipatil SB (2010) Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink. Int J Heat Mass Transf 53:1788–1795
Cortell R (2006) Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and a transverse magnetic field. Int J Heat Mass Transf 49:1851–1856
Siddheshwar PG, Mahabaleshwar US (2005) Effects of radiation and heat transfer on MHD flow of visco-elastic liquid and heat transfer over a stretching sheet. Int J Nonlinear Mech 40:807–820
Sajid M, Ahmad I, Hayat T, Ayub M (2009) Unsteady flow and heat transfer of a second grade fluid over a stretching sheet. Commun Non-Linear Sci Numer Simul 14:96–108
Hayat T, Nawaz M (2010) Effect of heat transfer on magnetohydrodynamic axisymmetric flow between two stretching sheets. Z Naturforsch 65a:961–968
Alharbi SM, Bazid MAA, Gendy MSE (2010) Heat and mass transfer in MHD viscoelastic fluid flow through a porous medium over a stretching sheet with chemical reaction. Appl Math 1:446–455
Hayat T, Abbas Z, Sajid M (2008) Heat and mass transfer analysis on the flow of a second grade fluid in presence of chemical reaction. Phys Lett A 372:2400–2408
Veena PH, Pravin VK, Shahjahan SM, Hippargi VB (2007) Non-similar solutions for heat and mass transfer flow in an electrically conducting visco-elastic fluid over a stretching sheet embedded in a porous medium. Int J Mod Math 2(1):9–26
Rashidi MM, Rostami B, Freidoonimehr N, Abbasbandy S (2014) Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects. Ain Shams Eng J 5(3):901–912
Sanjayanand E, Khan SK (2006) On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet. Int J Therm Sci 45(8):819–828
Turkyilmazoglu M (2011) Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet. Int J Therm Sci 50:2264–2276
Layek GC, Mukhopadhyay S, Samad SA (2007) Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int Commun Heat Mass Transf 34(3):347–356
Shateyi S, Motsa SS, Sibanda P (2010) Homotopy analysis of heat and mass transfer boundary layer flow through a non-porous channel with chemical reaction and heat generation. Can J Chem Eng 88(6):975–982
Anghel M, Takhar HS, Pop I (2000) Dufour and soret effects on free convection boundary layer over a vertical surface embedded in a porous medium, Studia Universitatis Babes-Bolyai, Mathematica, XLV(4), 11–21
Postelnicu A (2004) Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Int J Heat Mass Transfer 47:1467–1472
Srinivasacharya D, RamReddy Ch (2011) Soret and Dufour effects on mixed convection from an exponentially stretching surface. Int J Nonlinear Sci 12:60–68
Bég A, Bakier AY, Prasad VR (2009) Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Comp Mater Sci 46:57–65
Tsai R, Huang JS (2009) Heat and mass transfer for a Soret and Dufour’s effects on Hiemenz flow through porous medium onto a stretching surface. Int J Heat Mass Transf 52:2399–2406
Ahmed AA (2009) Simlarty solution in MHD effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction and injuction. Commun Nonlinear Sci Numer Simul 14:2202–2214
Hayat T, Mustafa M, Pop I (2010) 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. Commun Nonlinear Sci Numer Simul 15:1183–1196
Hayat T, Shehzad SA, Alsaedi A (2012) Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid. Appl Math Mech Engl Ed 33(10):1301–1312
Bazid MAA, Gharsseldien ZM, Seddeek MA, Alharbi M (2012) Soret and Dufour Numbers effect on heat and mass transfer in stagnation point flow twards a stretching surface in the presence of Buoyancy force and variable thermal conductivity. J Comp Model 2:25
Pal D, Mondal H (2012) Soret and Dufour effects on MHD non-Darcian mixed convection heat and mass transfer over a stretching sheet with non-uniform heat source/sink. Phys B Condens Matter 407:642–651
Nayak A, Panda S, Phukan DK (2014) Soret and Dufour effects on mixed convective unsteady MHD boundary layer flow over stretching sheet in porous medium with chemical spacies. Appl Math Mech 35:849–862
Wang CY (1988) Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid. Acta Mech 72:261–268
Zheng LC, Jin X, Zhang XX, Zhang JH (2013) Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects. Acta Mech Sin 29(5):667–675
Liao SJ (2003) Beyond perturbation: introduction to homotopy analysis method. Chapman & Hall/CRC, Boca Raton
Liao SJ (2003) On the analytic solution of magnetohydrodynamic flow of non-Newtonian fluid over a stretching sheet. J Fluid Mech 488:189–212
Liao SJ (2009) A general to get series solution of non similarity boundary laeyer flows. Commun Nonlinear Sci Numer Simul 14:2144–2159
Liao SJ (2004) On the homotopy analysis method for nonlinear problems. Appl Math Comput 147:499–513
Abbasbandy S (2006) The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 360:109–113
Chaudhury TK (1979) On swimming in a visco-elastic liquid. J Fluid Mech 95:189–197
Hayat T, Mamboudou HM, Mahmed FM (2008) Unsteady solutions in a third-grade fluid filling the porous space. Math Probl Eng 1–13
Schichting H (1964) Boundary Layer Theory, 6th edn. McGraw-Hill, New York
Raptis A, Perdikisc C, Takhar HS (2004) Effects of radiation on MHD flow. Appl Math Comput 153:645–649
Rajagopal KR, Na TY, Gupta AS (1984) Flow of a visco-elastic fluid over a stretching sheet. Rheol Acta 23:213–215
Magyari E, Pantokratoras A (2011) Note on the effect of thermal radiation in the linearized Roseland approximation on the heat transfer characteristics of various boundary layer flows. Int Commun Heat Mass Transf 38:554–556
Acknowledgments
We are thankful to the anonymous reviewer for his/her useful comments to improve the earlier version of the paper. The second author is grateful to the Higher Education Commission of Pakistan for financial assistance.
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Roney Leon Thompson.
Rights and permissions
About this article
Cite this article
Ali, N., Khan, S.U., Abbas, Z. et al. Soret and Dufour effects on hydromagnetic flow of viscoelastic fluid over porous oscillatory stretching sheet with thermal radiation. J Braz. Soc. Mech. Sci. Eng. 38, 2533–2546 (2016). https://doi.org/10.1007/s40430-016-0506-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40430-016-0506-x