Abstract
The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.
Similar content being viewed by others
References
Andersson HI (2002) Slip flow past a stretching surface. Acta Mech 158: 121–125
Andersson HI, Kumaran V (2006) On sheet-driven motion of power-law fluids. Int J Non-linear Mech 41:1228–1234
Ariel PD (2002) On the flow of power law fluid over a stretching sheet-techniques and solutions. Acta Mech 156:13–27
Ariel PD, Hayat T, Asghar S (2006) The flow of an elastico-viscous fluid past a stretching sheet with partial slip. Acta Mech 187:29–35
Bataller RC (2007) Viscoelastic fluid flow and heat transfer over a stretching sheet under the effects of a non-uniform heat source, viscous dissipation and thermal radiation. Int J Heat Mass Transfer 50:3152–3162
Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. In: Fluid mechanics, 2nd edn, vol 1. Wiley, New York
Buscall R (2010) Letter to the editor: wall slip in dispersion rheometry. J Rheol 54:1177–1184
Dandapat BS, Santra B, Vajravelu K (2007) The effects of variable fluid properties and thermo-capillarity on the flow of a thin film on an unsteady stretching sheet. Int J Heat Mass Transfer 50:991–996
Ece MC, Büyük E (2002) Similarity solutions for free convection to power-law fluids from a heated vertical plate. Appl Math Lett 15:1–5
Hassanien IA (1996) Flow and heat transfer on a continuous flat surface moving in a parallel free stream of power-law fluid. Appl Math Model 20:779–784
Hassanien IA, Abdullah AA, Gorla RSR (1998) Flow and heat transfer in a power-law fluid over a non-isothermal stretching sheet. Math Comput Model 28:105–116
Hayat T, Javed T, Abbas Z (2008) Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space. Int J Heat Mass Transfer 51:4528–4534
Kapur JN, Srivastava RC (1963) Similar solutions of the boundary layer equations for power-law fluids. ZAMP 14:383–389
Lee SY, Ames WF (1966) Similarity solutions for non-Newtonian fluids. AIChE J 12:700–708
Mahmoud MAA (2011) Variable viscosity effect on free convection of a non-Newtonian power-law fluid over a vertical cone in a porous medium with variable heat flux. Eur Phys J Plus 126:1–6
Megahed AM (2011) HPM for slip velocity effect on a liquid film over an unsteady stretching surface with variable heat flux. Eur Phys J Plus 126(9):1–8
Pontrelli G (1995) Flow of a fluid of second grade over a stretching sheet. Int J Non-linear Mech 30:287–293
Rajagopal KR, Na Tk, Gupta AS (1984) Flow of a viscoelastic fluid over a stretching sheet. Rheol Acta 23:213–215
Rao IJ, Rajagopal KR (1999) The effect of the slip boundary condition on the flow of fluids in a channel. Acta Mech 135:113–126
Raptis A (1998) Flow of a micropolar fluid past a continuously moving plate by the presence of radiation. Int J Heat Mass Transfer 41:2865–2866
Raptis A (1999) Radiation and viscoelastic flow. Int Commun Heat Mass Transf 26:889–895
Sahoo B (2010) Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip. Commun Nonlinear Sci Numer Simulat 15:602–615
Sahoo B, Poncet S (2011) Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition. Int J Heat Mass Transfer 54:5010–5019
Schowalter WR (1960) The application of boundary layer theory to power-law pseudoplastic fluids: similar solution. AIChE J 6:24–28
Wang CY (2002) Flow due to a stretching boundary with partial slip-an exact solution of the Navier–Stokes equation. Chem Eng Sci 57:3745–3747
Wang CY (2009) Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlinear Anal Real World Appl 10:375–380
Acknowledgements
The author is indebted to the referees for their suggestions and comments which led to the improvement of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Megahed, A.M. Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation. Rheol Acta 51, 841–847 (2012). https://doi.org/10.1007/s00397-012-0644-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-012-0644-8