FLOW OF AN ERYING-POWELL FLUID OVER A STRETCHING SHEET IN PRESENCE OF CHEMICAL REACTION

Abstract

In this paper we study the flow of an incompressible Erying-Powell fluid bounded by a linear stretching surface. The mass transfer analysis in the presence of destructive /generative chemical reactions is also analyzed. A similarity transformation is used to transform the governing partial differential equations into ordinary differential equations. Computations for dimensionless velocity and concentration fields are performed by an efficient approach namely the homotopy analysis method (HAM) and numerical solution is obtained by shooting technique along with Runge-Kutta-Fehlberg integration scheme. Graphical results are prepared to illustrate the details of flow and mass transfer characteristics and their dependence upon the physical parameters. The values for gradient of mass transfer are also evaluated and analyzed. A comparison of the present solutions with published results in the literature is performed and the results are found to be in excellent agreement.

Keywords

Dates

  • Submission Date2013-11-29
  • Revision Date2014-07-15
  • Acceptance Date2014-07-27
  • Online Date2014-10-05

DOI Reference

10.2298/TSCI131129111K

References

  1. Ishak, A., et al., Heat Transfer over a Stretching Surface with Variable Heat Flux in Micropolar Fluids, Phys Lett A 372 (2008) pp. 559-561.
  2. Fetecau, C., et al., On the Oscillating Motion of an Oldroyd-B Fluid Between Two Infinite Circular Cylinders, Comput Math Appl 59 (2010) pp. 2836-2845.
  3. Fetecau, C., et al., A Note on the Second Problem of Stokes for Maxwell Fluids, Int J Non-Linear Mech 44 (2009) pp. 085-1090.
  4. Fetecau, C., et al., On the First Problem of Stokes for Burgers' Fluid, I: Nonlinear Anal.: Real World Appl 10 (2009) pp. 2183-2194.
  5. Vieru D., Rauf A., Stokes Flows of a Maxwell Fluid with Wall Slip Condition, Can J Phys 89 (2011) pp. 1-12.
  6. Vieru D., Zafar A. A., Some Couette Flows of a Maxwell Fluid with Wall Slip Condition, Appl Math InfSci 7 (2013) pp. 209-219.
  7. Imran M.A., et al., Exact Solutions for Oscillating Motion of a Second Grade Fluid along an Edge with Mixed Boundary Conditions, Chem Eng Comm 199 (2012) pp. 1085-1101.
  8. Qasim M., Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink, Alexandria Engineering Journal, 52 (2013) pp. 571-575.
  9. Khan I., et al., Stokes' Second Problem for Magnetohydrodynamics Flow in a Burgers' Fluid: Cases γ = λ(2)/4 and γ > λ(2)/4, PLoS ONE 8(5) (2013) pp. e61531.
  10. Qasim M., et al., Heat Transfer in a Micropolar Fluid over a Stretching Sheet with Newtonian Heating, PLoS ONE 8(4) (2013) pp. e59393.
  11. Powell R. E., Eyring H, Nature, London 427 (1944).
  12. Javed T., et al., Flow of an Eyring-powell Non-Newtonian Fluid over a Stretching Sheet, Chem Eng Comm 200 (2013) pp. 327-336.
  13. Hayat T., et al., Flow of an Eyring-Powell Fluid with Convective Boundary Conditions. J Mech 29 (2009) pp. 217-224.
  14. Patel M., Timol M. G., Numerical Treatment of Powell-Eyring Fluid Flow Using Method of Satisfaction of Asymptotic Boundary Conditions (MSABC), Appl Num Math (2009) pp. 2584-2592.
  15. Eldabe N. T. M., et al., Effect of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates, Z. Naturforsch. (2003) pp. 204 - 210.
  16. Crane L. J., Flow Past a Stretching Plate. Z Angew Math Mech (1970) pp.645-647.
  17. Andersson H. I., et al. Diffusion of Chemically Reactive Species from a Stretching Sheet, Int J Heat Mass Transferpp.659-664.
  18. Takhar H. S., et al., Flow and Mass Transfer on a Stretching Sheet with Magnetic Field and Chemical Reactive Species, Int J EngSci pp. 1303-1314.
  19. Akyilidiz F. T., et al., Diffusion of Chemical Reactive Species in Porous Medium over a Stretching Sheet, J Math Anal Appl (2006) pp. 322-339.
  20. Hayat T., et al., MHD Flow and Mass Transfer of Upper-Convected Maxwell Fluid past a Porous Shrinking Sheet with Chemical Reaction Species. PhysLettA (2008) pp. 4698- 4704.
  21. Liao S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method. Chapman and Hall, CRC Press, Boca Reton (2003).
  22. Liao S. J., Homotopy Analysis Method in Nonlinear Differential Equations, Springer (2011).
  23. Butt A S., Ali A., A computational study of entropy generation in magnetohydrodynamic flow and heat transfer over an unsteady stretching permeable sheet, The European Physical Journal Plus, 129 (2014) pp. 1-13.
  24. Qasim M., Khan Z H., Khan W A., Shah A A., MHD boundary layer slip flow and heat transfer of Ferrofluid along a stretching cylinder with prescribed heat flux, Plos One, 9(1), (2014), pp-e83930.
  25. Mabood F., Khan W A., Homotopy analysis method for boundary layer flow and heat transfer over a permeable flat plate in a Darcian porous medium with radiation effects, Journal of the Taiwan Institute of Chemical Engineers, (2014) pp. 1217-1224.
  26. Nadeem et al., Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet, Alexandria Engineering Journal, (2014) pp. 219-224.