Abstract
The stagnation-point flow of an incompressible non-Newtonian Casson fluid over a stretching sheet in the presence of Soret and Dufour effects is investigated. The resulting partial differential equations are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved using the Matlab bvp4c package. A comparison is made with the results available in the literature and found to be in good agreement. Dual solutions for the velocity, temperature, concentration and skin friction were obtained for some special cases when the stretching parameter is negative. The effect of the Casson parameter on the skin friction, heat transfer and mass transfer rates is discussed.
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Bhattacharyya K 2011 Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet. Int. Commun. Heat Mass Transf. 38: 917–922
Bhattacharyya K, Hayat T and Alsaedi A 2013a Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet. ZAMM Z. Angew. Math. Mech. 1–7 doi: 10.1002/zamm.201200031
Bhattacharyya K, Hayat T and Alsaedi A 2013b Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer. Chin. Phys. B. 22: 024702
Casson M 1959 A flow equation for pigment-oil suspensions of the printing ink type. In: C.C.Mills (ed.), Rheology of disperse systems, Newyork, Oxford: Pergamon, 84–104
Chamkha A J and Aly A M 2010 Heat and mass transfer in stagnation point flow of a polar fluid towards a stretching surface in porous media in the presence of Soret, Dufour and chemical reaction effects. Chem. Eng. Comm. 198: 214–234
Crane L J 1970 Flow past a stretching plate. J. Appl. Math. Phys. 21: 645–647
Dutta B K, Roy P and Gupta A S 1985 Temperature field in flow over a stretching sheet with uniform heat flux. Int. Commun. Heat Mass Transf. 12: 89–94
Hayat T, Javed T and Sajid M 2008 Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface. Phys. Lett. A 372: 3264–3273
Hayat T, Shehzad S A and Alsaedi A 2012a Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid. Appl. Math. Mech. Engl. Ed. 33: 1301–1312
Hayat T, Shehzad S A, Alsaedi A and Alhothuali M S 2012b Mixed convection stagnation point flow of casson fluid with convective boundary conditions. Chin. Phys. Lett. 29: 114704
Ishak A, Lok Y Y and Pop I 2010 Stagnation-point flow over a shrinking sheet in a micropolar fluid. Chem. Eng. Comm. 197: 1417–1427
Ishak A, Lok Y Y and Pop I 2012 Non-Newtonian power-law fluid flow past a shrinking sheet with suction. Chem. Eng. Commun. 199: 142–150
Kameswaran P K, Narayana M, Sibanda P and Murthy P V S N 2012 Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects. Int. J. Heat Mass Transf. 55: 7587–7595
Kameswaran P K, Shaw S, Sibanda P and Murthy P V S N 2013 Homogeneous – heterogeneous reactions in a nanofluid flow due to a porous stretching sheet. Int. J. Heat Mass Transf. 57: 465–472
Liao S J 2003 On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488: 189–212
Mahapatra T R and Gupta A S 2001 Magnetohydrodynamic stagnation-point flow towards a stretching sheet. Acta Mechanica. 152: 191–196
McDonald D A 1974 Blood flows in arteries. 2nd Edition, Chap. 2., London: Arnold
Merkin J H 1985 On dual solutions occurring in mixed convection in a porous media. J. Eng Math. 20: 171–179
Merrill K, Beauchesne M, Previte J, Paullet J and Weidman P 2006 Final steady flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 49: 4681–4686
Mukhopadhyayay S 2013 Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chin. Phys. B 22: 7 074701
Mustafa M, Hayat T, Pop I and Hendi A A 2012 Stagnation-point flow and heat transfer of a Casson fluid towards a stretching sheet. Z. Naturforsch 67: 70–76
Nakamura M and Sawada T 1988 Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis. J. Biomech Eng. 110: 137–143
Nawaz M, Hayat T and Alsaed A 2012 Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium. Appl. Math. Mech. 33: 1403–1418
Paullet J and Weidman P 2007 Analysis of stagnation point flow toward a stretching sheet. Int. J. Non-Linear Mech. 42: 1084–1091
Postelnicu A and Pop I 2011 Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl. Math. Comput. 217: 4359–4368
Shaw S, Gorla R S R, Murthy P V S N and Ng C O 2009 Pulsatile Casson fluid flow through a stenosed bifurcated artery. Int. J. Fluid Mech. Res. 36: 43–63
Shehzad S A, Hayat T, Qasim M and Asghar S 2013 Efects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction. Brazilian J. Chem. Eng. 30: 187–195
Srinivasacharya D and RamReddy C. 2011 Soret and Dufour effects on mixed convection in a non-Darcy porous medium saturated with micropolar fluid. Nonlinear Analysis: Modelling and Control 16: 100–115
Wang C Y 2008 Stagnation flow towards a shrinking sheet. Int. J. Non-Linear Mech. 43: 377–382
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KAMESWARAN, P.K., SHAW, S. & SIBANDA, P. Dual solutions of Casson fluid flow over a stretching or shrinking sheet. Sadhana 39, 1573–1583 (2014). https://doi.org/10.1007/s12046-014-0289-7
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DOI: https://doi.org/10.1007/s12046-014-0289-7