Skip to main content
Log in

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

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Andersson HI (2002) Slip flow past a stretching surface. Acta Mech 158: 121–125

    Article  Google Scholar 

  • Andersson HI, Kumaran V (2006) On sheet-driven motion of power-law fluids. Int J Non-linear Mech 41:1228–1234

    Article  Google Scholar 

  • Ariel PD (2002) On the flow of power law fluid over a stretching sheet-techniques and solutions. Acta Mech 156:13–27

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. In: Fluid mechanics, 2nd edn, vol 1. Wiley, New York

    Google Scholar 

  • Buscall R (2010) Letter to the editor: wall slip in dispersion rheometry. J Rheol 54:1177–1184

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Kapur JN, Srivastava RC (1963) Similar solutions of the boundary layer equations for power-law fluids. ZAMP 14:383–389

    Article  Google Scholar 

  • Lee SY, Ames WF (1966) Similarity solutions for non-Newtonian fluids. AIChE J 12:700–708

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Pontrelli G (1995) Flow of a fluid of second grade over a stretching sheet. Int J Non-linear Mech 30:287–293

    Article  Google Scholar 

  • Rajagopal KR, Na Tk, Gupta AS (1984) Flow of a viscoelastic fluid over a stretching sheet. Rheol Acta 23:213–215

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Raptis A (1999) Radiation and viscoelastic flow. Int Commun Heat Mass Transf 26:889–895

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Schowalter WR (1960) The application of boundary layer theory to power-law pseudoplastic fluids: similar solution. AIChE J 6:24–28

    Article  CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Ahmed M. Megahed.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-012-0644-8

Keywords

Navigation