Skip to main content
SpringerLink
Log in

Effect of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and a convective surface boundary condition

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this paper, the combined effects of radiation, temperature dependent viscosity, suction and injection on thermal boundary layer over a permeable flat plate with a convective heat exchange at the surface are investigated. By taking suitable similarity variables, the governing boundary layer equations are transformed into a boundary value problem of coupled nonlinear ordinary differential equations and solved numerically using the shooting technique with sixth-order Runge-Kutta integration scheme. The solutions for the velocity and temperature distributions together with the skin friction coefficient and Nusselt number depend on six parameters; Prandtl number Pr, Brinkmann number Br, the radiation parameter Ra, the viscosity variation parameter a, suction/injection parameter f w and convection Biot number Bi. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal boundary layer. The thermal boundary layer thickens with a rise in the local temperature as the viscous dissipation, wall injection, and convective heating each intensifies, but decreases with increasing suction and thermal radiation. For fixed Pr, Ra, Br and Bi, both the skin friction coefficient and the Nusselt number increase with a decrease in fluid viscosity and an increase in suction. A comparison with previously published results on special case of the problem shows excellent agreement.

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

Similar content being viewed by others

References

  1. H. Blasius, Grenzschichten in flussigkeiten mit kleiner reibung, Z. math. Phys., 56 (1908) 1–37.

    Google Scholar 

  2. V. M. Falkner and S. W. Skan, Some approximate solutions of the boundary layer equations, Philos. Mag., 12 (1930) 865–896.

    Google Scholar 

  3. J. H. He, A simple perturbation approach to Blasius equation, Appl. Math. Comput., 140 (2003) 217–222.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. V. Prasad, S. Abel and P. S. Datti, Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, Int. J. Non-linear Mech., 38 (2003) 651–657.

    Article  MATH  Google Scholar 

  5. T. Fang, Similarity solutions for a moving-flat plate thermal boundary layer, Acta Mech., 163 (2003) 161–172.

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. A. Y. Ghaly and M. A. Seddeek, Chebyshev finite difference method for the effect of chemical reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate with temperature dependent viscosity, Choas Soltions Fractals, 19 (2004) 61–70.

    Article  MATH  Google Scholar 

  8. F. C. Lai and F. A. Kulacki, The effect of variable viscosity on convective heat and mass transfer in saturated porous media, Int J Heat and Mass Transfer, 33 (1991) 1028–1031.

    Article  Google Scholar 

  9. E. M. Sparrow and R. D. Cess, Radiation heat transfer. Augmented edu Hemi- sphere publication Washington DC, 7–10 (1978).

  10. O. D. Makinde and A. Ogulu, The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, 195(12) (2008) 1575–584.

    Article  Google Scholar 

  11. M. A. Hossain and H. S. Takhar, Radiation effects on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Transfer, 31 (1996) 243–248.

    Article  Google Scholar 

  12. E. M. Abo-Eldahab and M. S. Elgendy, Radiation effect on convective heat transfer in an ellectrically conducting fluid at a stretching surface with variable viscosity and uniform free stream, Physica Scripta, 62 (2000) 321–325.

    Article  Google Scholar 

  13. R. C. Bataller, Radiation effects in the Blasius flow, Appl. Math. Comput., 198 (2008) 333–338.

    Article  MathSciNet  MATH  Google Scholar 

  14. O. D. Makinde, Free-convection flow with thermal radiation and mass transfer past a moving vertical porous plate, International Communications in Heat and Mass transfer, 32 (2005) 1411–1419.

    Article  Google Scholar 

  15. R. C. Bataller, Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition, Applied Mathematics and Computation, 206 (2008) 832–840.

    Article  MathSciNet  MATH  Google Scholar 

  16. O. D. Makinde and A. Aziz, MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition, International Journal of Thermal Sciences, 49 (2010) 1813–1820.

    Article  Google Scholar 

  17. A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun Nonlinear Sci Numer Simulat, 14 (2009) 1064–1068.

    Article  MathSciNet  Google Scholar 

  18. A. Ishak, Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition, Applied Mathematics and Computation, 217 (2010) 837–842.

    Article  MathSciNet  MATH  Google Scholar 

  19. O. D. Makinde, On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition, Canadian Journal of Chemical Engineering, 88 (2010) 983–990.

    Article  Google Scholar 

  20. P. R. Nachtsheim and P. Swigert, Satisfaction of the asymptotic boundary conditions in numerical solution of the system of nonlinear equations of boundary layer type, NASA TND-3004 (1965).

Download references

Author information

Authors and Affiliations

  1. Institute for Advance Research in Mathematical Modelling and Computations, P. O. Box 1906, Bellville, 7535, South Africa

    Oluwole Daniel Makinde

Authors
  1. Oluwole Daniel Makinde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oluwole Daniel Makinde.

Additional information

Recommended by Associate Editor Man-Yeong Ha.

Oluwole Daniel Makinde is currently a Senior Professor and Director of Postgraduate Studies at Cape-Peninsula University of Technology (CPUT) in South Africa. He is also the founder and Director of Institute for Advance Research in Mathematical Modelling and Computations at CPUT. He received his B.Sc. (Hons) First Class and M.Sc. from Obafemi Awolowo University, Ile-Ife, Nigeria and Ph.D at University Bristol, England all in Computational and Applied Mathematics. Professor Makinde has taught and supervised graduate students and served as an external examiner at many universities within and outside African continent. He has co-authored two applied mathematics textbooks, two Open University monographs on Particle Mechanics and Incompressible Flow Theory and published numerous research articles in several reputable international journals. He is presently the Secretary General of African Mathematical Union, Editor and editorial board member of several international journals. Professor Makinde received several research excellence awards, among them are: South African NSTF/National Research Foundation award and African Union Kwame Nkrumah Continental Scientific Award for outstanding contribution to Science, Engineering, Technology and Innovation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makinde, O.D. Effect of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and a convective surface boundary condition. J Mech Sci Technol 26, 1615–1622 (2012). https://doi.org/10.1007/s12206-012-0302-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-012-0302-1

Keywords

Search

Navigation