THERMAL SCIENCE

International Scientific Journal

Tasawar Hayat

,

Zahid Iqbal

,

Meraj Mustafa

,

Ahmed Alsaedi

UNSTEADY FLOW AND HEAT TRANSFER OF JEFFREY FLUID OVER A STRETCHING SHEET

ABSTRACT
The boundary layer flow and heat transfer of an incompressible Jeffrey fluid have been investigated. The analytic solutions of the arising differential system have been computed by homotopy analysis method (HAM). The dimensionless expressions for wall shear stress and surface heat transfer are also derived. Exact solutions of the momentum equation and numerical solutions of the dimensionless energy equations have been obtained for the steady-state case. The results indicate an increase in the velocity and the boundary layer thickness by increasing the elastic parameter (Deborah number) for a Jeffrey fluid.
KEYWORDS
unsteady flow, heat transfer, analytic solution, viscous dissipation
PAPER SUBMITTED: 2011-09-07
PAPER REVISED: 2012-04-28
PAPER ACCEPTED: 2012-05-08
DOI REFERENCE: https://doi.org/10.2298/TSCI110907092H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE Issue 4, PAGES [1069 - 1078]
REFERENCES
  1. Hayat, T., Ahmad, N., Ali, N., Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid, Comm. Nonlinear Sci. Num. Simul. 13 (2008), pp. 1581-1589.
  2. Kothandapani, M., Srinivas, S., Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel, Int. J. Nonlinear Mech. 43 (2008), pp. 915-924.
  3. Hayat, T., Ali, N., Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube, Comm. Nonlinear Sci. Num. Simul. 13 (2008), pp. 1343-1352.
  4. Nadeem, S., Akbar, N. S., Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel, Z. Naturforsch A. 64a (2009), pp. 713-722.
  5. Crane, L. J., Flow past a stretching plate, Z. Angew. Math. Phys. 21 (1970), pp. 645-647.
  6. Andersson, H. I., Aerseth, J. B., Braud, B. B., Dandapat, B. S., Flow of a power-law fluid film on an unsteady stretching sheet, J. Non-Newtonian Fluid Mech. 62 (1996), pp. 1-8.
  7. Ariel, P. D., MHD flow of a viscoelastic fluid past a stretching sheet with suction, Acta Mech. 105 (1994), pp. 49-56.
  8. Kumari, M., Nath, G., Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface, Comm. Nonlinear Sci. Num. Simul. 14 (2009), pp. 3339-3350.
  9. El-Arabawy, H. A. M., Exact solutions of mass transfer over a stretching surface with chemical reaction and suction/injection, J. Math. Stat. 5 (2009), pp. 159-166.
  10. Andersson, H. I., Slip flow past a stretching surface, Acta Mech., 158 (2002), pp. 121-125.
  11. Ariel, P. D., Axisymmetric flow due to a stretching sheet with partial slip, Comput. Math. Appl. 54 (2007), pp. 1169-1183.
  12. Abbas, Z., Hayat, T., Stagnation slip flow and heat transfer over a nonlinear stretching sheet, Num. Meth. Partial Differential Equations, 27 (2009), pp. 302-314.
  13. Hayat, T., Javed, T., Abbas, Z., Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space, Int. J. Heat Mass Transfer, 51 (2008), pp. 4528-4534.
  14. Wang, C. Y., Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Anal. : RWA., 10 (2009), pp. 375-380.
  15. Liao, S. J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluid over a stretching sheet, J. Fluid Mech., 488 (2003), pp. 189-212.
  16. Devi, C. D. S., Takhar, H. S., Nath, G., Unsteady mixed convection flow in a stagnation region to adjacent to a vertical surface, Heat Mass Transfer, 26 (1991), pp. 71-79.
  17. Andersson, H. I., Aarseth, J. B., Dandapat, B. S., Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Transfer, 43 (2000), pp. 69-74.
  18. Nazar, R., Amin, N., Pop, I., Unsteady boundary layer due to a stretching surface in a rotating fluid, Mech. Res. Comm. 31 (2004), pp. 121-128
  19. Liao, S. J., An Analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Comm. Nonlinear Sci. Num. Simul., 11 (2006), pp. 326-339.
  20. Mukhopadhyay, S., Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in a porous medium, Int. J. Heat Mass Transfer, 52 (2009), pp. 3261-3265.
  21. Liao, S. J., On the relationship between the homotopy analysis method and Euler transform, Comm. Nonlinear Sci. Numer. Simul., 15 (2010), pp. 1421-1431.
  22. Liao, S. J., Notes on the homotopy analysis method: Some definitions and theorems, Comm. Non-linear Sci. Num. Simul. 14 (2009), pp. 983-997.
  23. Abbasbandy, S., Shivanian, E., Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Comm. Nonlinear Sci. Num. Simul., 15 (2010), pp. 3830-3846.
  24. Abbasbandy, S., Shirzadi, A., A new application of the homotopy analysis method: Solving the Sturm--Liouville problems, Comm. Nonlinear Sci. Num. Simul., 16 (2011), pp. 112-126.
  25. Rashidi, M. M., Mohimanian Pour, S. A., Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method, Nonlinear Analysis: Modelling and Control, 15 (2010), 1, pp. 83-95.
  26. Bataineh, A. S., Noorani, M. S. M., Hashim, I., On a new reliable modification of homotopy analysis method, Comm. Nonlinear Sci. Num. Simul., 14 (2009), pp. 409-423.
  27. Hayat, T., Mustafa, M., Obaidat, S., Soret and Dufour effects on the stagnation-point flow of a Micropolar fluid toward a stretching sheet, ASME-J. Fluids Eng., 133 (2011), pp. 021202.
  28. Hayat, T., Mustafa, M., Asghar, S., Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction, Non-Linear Anal. RWA., 11 (2010), pp. 3186-3197.
  29. Hayat, T., Mustafa, M., Hendi, A. A., Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet, Appl. Math. Mech., 32 (2011), pp. 167-178.
  30. Hayat, T., Mustafa, M., Shehzad, S. A., Obaidat, S., Melting heat transfer in the stagnationpoint flow of an upper-convected Maxwell (UCM) fluid past a stretching sheet, Int. J. Num. Meth. Fluids., 68 (2012), pp. 233-243.
PDF VERSION [DOWNLOAD]
Unsteady flow and heat transfer of Jeffrey fluid over a stretching sheet

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence