Skip to main content
SpringerLink
Log in

Effect of variable viscosity on flow past a porous wedge with suction or injection: new results

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

An analysis is carried out to study the problem of the steady flow and heat transfer of an incompressible fluid over a static wedge in the presence of suction/injection with variable viscosity. The viscosity is assumed to vary as inverse linear function of temperature. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations using similarity transformations, and later solved numerically by using Runge–Kutta–Fehlberg method with shooting technique. The velocity and temperature profiles, the skin friction and the rate of heat transfer are computed and discussed for various values of suction/injection parameter, viscosity parameter and Hartree pressure gradient parameter for gases and liquids.

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

Access this article

Log in via an institution

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

\(a\) :

Constant used in equation (5)

\(C_f \) :

Skin friction coefficient

\(f\) :

Dimensionless stream function

\(f_w \) :

Suction/injection parameter

\(k\) :

Thermal conductivity

\(m\) :

Falkner–Skan power law parameter

Nu :

Local Nusselt number

Pr :

Prandtl number

Re :

Reynolds number

\(T,\, T_w ,\,T_\infty \) :

Temperature of fluid, wall and free stream

\(T_r \) :

Reference temperature

\(u\), v:

Velocity components

\(U_\infty \) :

Free stream velocity

\(V_w \) :

Suction/injection velocity at the wall

\(x,y\) :

Cartesian coordinates

\(\alpha \) :

Thermal diffusivity

\(\beta \) :

Wedge angle parameter

\(\gamma \) :

A constant

\(\tau \) :

Shear stress

\(\eta \) :

Similarity variable

\(\theta \) :

Dimensionless temperature

\(\theta _r \) :

Variable viscosity parameter

\(\mu \) :

Dynamic viscosity

\(\mu _\infty \) :

Viscosity of the free stream

\(\nu \) :

Kinematic viscosity

\(\rho _\infty \) :

Density

\(\psi \) :

Stream function

\(w\) :

Condition at the wall

\(\infty \) :

Free stream condition

\('\) :

Differentiation with respect to \(\eta \)

References

  1. Falkner, V.M., Skan, S.W.: Some approximate solutions of the boundary layer equations. Philos. Mag. 12, 865–896 (1931)

    Article  Google Scholar 

  2. Hartree, D.R.: On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer. Proc. Camb. Philos. Soc. (1937). doi:10.1017/S0305004100019575

  3. Stewartson, K.: Further solutions the Falkner–Skan equation. Proc. Camb. Philos. Soc. (1954). doi:10.1017/S030500410002956X

  4. Cebeci, T., Keller, H.B.: Shooting and parallel shooting methods for solving the Falkner–Skan boundary layer equation. J. Comput. Phys. (1971). doi:10.1016/0021-9991(71)90090-8

  5. Koh, J.C.Y., Harnett, J.P.: Skin friction and heat transfer for incompressible laminar flow over a porous wedge with suction and variable wall temperature. Int. J. Heat Mass Transf. (1961). doi:10.1016/0017-9310(61)90088-6

  6. Chen, K.K., Libby, P.A.: Boundary layers with small departure from the Falkner–Skan profile. J. Fluid Mech. (1968). doi:10.1017/S0022112068001291

  7. Lin, H.T., Lin, L.K.: Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int. J. Heat Mass Transf. (1987). doi:10.1016/0017-9310(87)90041-X

  8. Watanabe, T.: Thermal boundary layer over a wedge with uniform suction and injection in forced flow. Acta Mech. (1990). doi:10.1007/BF01172973

  9. Schlichting, H., Gersten, K.: Boundary Layer Theory, 8th revised edn. Springer-Verlag, Berlin (2000)

  10. Leal, L.G.: Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press, New York (2007)

    Book  Google Scholar 

  11. Ishak, A., Nazar, R., Pop, I.: Falkner–Skan equation for flow past a moving wedge with suction or injection. J. Appl. Math. Comput. (2007). doi:10.1007/BF02832339

  12. Yacob, N.A., Ishak, A., Pop, I.: Falkner–Skan problem for a static or moving wedge in nanofluids. Int. J. Therm. Sci. (2011). doi:10.1016/j.ijthermalsci.2010.10.008

  13. Bararnia, H., Haghparast, N., Miansari, M., Barari, A.: Flow analysis for the Falkner–Skan wedge flow. Curr. Sci. 103(2), 169–177 (2012)

    Google Scholar 

  14. Parand, K., Rezaei, A., Ghaderi, S.M.: An approximate solution of the MHD Falkner–Skan flow by Hermite functions pseudospectral method. Commun. Nonlinear Sci. Numer. Simul. (2011). doi:10.1016/j.cnsns.2010.03.022

  15. Postelnicu, A., Pop, I.: Falkner–Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl. Math. Comput. (2011). doi:10.1016/j.amc.2010.09.037

  16. Afzal, N.: Falkner–Skan equation for flow past a stretching surface with suction or blowing: analytical solutions. Appl. Math. Comput. (2010). doi:10.1016/j.amc.2010.07.080

  17. Ashwini, G., Eswara, A.T.: MHD Falkner–Skan boundary layer flow with internal heat generation or absorption. World Acad. Sci. Eng. Technol. 65, 662–665 (2012)

  18. Yih, K.A.: Uniform suction/blowing effect on force convection about a wedge: uniform heat flux. Acta Mech. (1998). doi:10.1007/BF01251888

  19. Soundalgekar, V.M., Takhar, H.S., Das, U.N., Deka, R.K., Sarmah, A.: Effect of variable viscosity on boundary layer flow along a continuously moving plate with variable surface temperature. Int. J. Heat Mass Transf. 40, 421–424 (2004)

  20. Pantokratoras, A.: Forced and mixed convection boundary layer flow along a flat plate with variable viscosity and Prandtl number: new results. Heat Mass Transf. 41, 1085–1094 (2005)

    Article  Google Scholar 

  21. Hady, F.M., Bakier, A.Y., Gorla, R.S.R.: Mixed convection boundary layer flow on a continuous flat plate with variable viscosity. Heat Mass Transf. 31, 169–172 (1996)

    Article  Google Scholar 

  22. Mukhopadhyay, S.: Effects of radiation and variable fluid viscosity on flow and heat transfer along a symmetric wedge. J. Appl. Fluid Mech. 2(2), 29–34 (2009)

    Google Scholar 

  23. Salem, A.M.: Temperature-dependent viscosity effects on non-Darcy hydrodynamic free convection heat transfer from a vertical wedge in porous media. Chin. Phys. Lett. (2010). doi:10.1088/0256-307X/27/6/064401

  24. Muhaimin, I., Kandasamy, R., Azme, B.K., Roslan, R.: Effect of thermophoresis particle deposition and chemical reaction on unsteady MHD mixed convective flow over a porous wedge in the presence of temperature-dependent viscosity. Nucl. Eng. Des. (2013). doi:10.1016/j.nucengdes.2013.03.015

  25. Schlichting, H.: Boundary Layer Theory (translated by J. Kestin ). Mc Graw Hill Inc, New York (1979)

    Google Scholar 

  26. Riley, N., Weidman, P.D.: Multiple solutions of the Falkner–Skan equation for flow past a stretching boundary. SIAM J. Appl. Math. (1989). doi:10.1137/0149081

  27. White, F.M.: Viscous Fluid Flow, 3rd edn. Mc Graw-Hill, New York (2006)

    Google Scholar 

  28. Ling, J.X., Dybbs, A.: Forced convection over a flat plate submersed in a porous medium: variable viscosity case. In: ASME winter meeting conference, Boston, 13 December 1987 (1987)

  29. Kumari, M., Takhar, H.S., Nath, G.: Mixed convection flow over a vertical wedge embedded in a highly porous medium. Heat Mass Transf (2001). doi:10.1007/s002310000154

Download references

Acknowledgments

One of the authors (R. K. Deka) acknowledges the support of UGC, New Delhi.

Author information

Authors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, 781014, Assam, India

    Rudra Kanta Deka

  2. Department of Mathematics, Lumding College, Lumding, 782447, Assam, India

    Mwblib Basumatary

Authors
  1. Rudra Kanta Deka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mwblib Basumatary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rudra Kanta Deka.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deka, R.K., Basumatary, M. Effect of variable viscosity on flow past a porous wedge with suction or injection: new results. Afr. Mat. 26, 1263–1279 (2015). https://doi.org/10.1007/s13370-014-0284-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-014-0284-5

Keywords

Mathematics Subject Classification

Search

Navigation