International Scientific Journal

Authors of this Paper

External Links


The foremost aspiration of the present endeavor is to investigate the boundary-layer flow of a generalized Newtonian Carreau fluid model past a static/moving wedge. In addition, the effects of heat transfer on the flow field are also taken into account. The governing equations of the problem based on the boundary-layer approximation are changed into a non-dimensional structure by introducing the local similarity transformations. The subsequent system of ODE has been numerically integrated with fifth-order Runge-Kutta method. Influence of the velocity ratio parameter, the wedge angle parameter, the Weissenberg number, the power law index, and the Prandtl number on the skin friction and Nusselt number are analyzed. The variation of the skin friction as well as other flow characteristics has been presented graphically to capture the influence of these parameters. The results indicate that the increasing value of the wedge angle substantially accelerates the fluid velocity while an opposite behavior is noticed in the temperature field. Moreover, the skin friction coefficient for the growing Weissenberg number significantly enhances for the shear thickening fluid and show the opposite behavior of shear thinning fluid. However, the local Nusselt number has greater values in the case of moving wedge. An excellent comparison with previously published works in various special cases has been made.
PAPER REVISED: 2016-06-27
PAPER ACCEPTED: 2016-06-30
CITATION EXPORT: view in browser or download as text file
  1. Falkner, V. M., Skan, S. W., Some approximate solutions of the boundary-layer equations, Philos. Mag., 12 (1931), pp. 865-896.
  2. Hartree, D. H., On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer, Proc. Camb. Philos. Soc., 33 (1937), pp. 223-239.
  3. Riley, N., Weidman, P. D., Multiple solutions of the Falkner-Skan equation for flow past a stretching boundary, SIAM J. Apple. Math., 49 (1989), pp. 1350-1358.
  4. Watanabe, T., Thermal boundary layer over a wedge with uniform suction or injection in force flow, Acta Mech., 83 (1990), pp. 119-126.
  5. Ishak, A., Nazar, R., Pop, I., MHD boundary layer flow past a moving wedge, Magnetohydrodynamics, 45 (2009), pp. 3-10.
  6. Schlichting, H., Gersten, K., Boundary Layer Theory, Springer, Berlin, 2000.
  7. Hayat, T., Khan, M, I., Farooq, M., Alsaedi, A., Waqas, M., Yasmeen, T., Impact of Cattaneo-Christov heat flux model in flow of variable thermal conductivity fluid flow over a variable thicked surface, Int. J. Heat Mass transf., 99 (2016), pp. 702-710.
  8. Hayat, T., Khan, M, I., Farooq, Yasmeen, T., Alsaedi, A., Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, J. Mol. Liq., 220 (2016), pp 49-55.
  9. Hayat, T., Imtiaz, M., Alsaedi, A., Unsteady flow of nanofluid with double stratification and magnetohydrodynamics, Int. J. Heat Mass transf., 92 (2016) pp. 100-109.
  10. Hayat, T., Shafiq, A., Imtiaz, M., Alsaedi, A., Impact of melting phenomenon in the Falkner-Skan wedge flow of second grade nanofluid: A revised model, J. Mol. Liq., 215 (2016), pp. 664-670.
  11. Bird, R. B., Curtiss, C. F., Armstrong, R. C., Hassager, O., Dynamics of Polymeric Liquids, John Wiley and Sons Inc., New York, USA, 1987.
  12. Slattery, J. C., Advanced Transport Phenomena, Cambridge University Press, Cambridge, USA, (1999).
  13. Carreau, P. J., Rheological equations from molecular network theories, Trans. Soc. Rheol., 16 (1972), pp. 99-127
  14. Chapkove, A. D., Bair, S., Cann, P., Lubrecht, A. A., Film thickness in point contacts under generalized Newtonian EHL conditions: numerical and experimental analysis, Tribol. Int., pp.
  15. Jang, J. Y., Khonsari, M, M., Bair, S., On the elastohydrodynamic analysis of shear-thinning fluids, Proc. R. Soc. A., pp. 3271-3290.
  16. Khellaf, K., Lauriat, G., Numerical study of heat transfer in a non-Newtonian Carreau-fluid between rotating concentric vertical cylinders, J. Non-Newtonian Fluid Mech., 89 (2000), pp. 45-61.
  17. Olajuwon, B. K., Convection heat and mass transfer in a hydromagnetic Carreau fluid past a vertical porous plate in presence of thermal radiation and thermal diffusion, Thermal Sci., 15 (2011), pp. 241-252.
  18. Martins, R. R., Silveira, F. S., Martins-Costa, M. L., Frey, S., Numerical investigation of Inertia and shear-thinning effects on axisymmetric flows of Carreau fluids by a Galerkin least-squares method, Latin American Appl. Research, 38 (2008), pp. 321-328.
  19. Khan. M., Hashim, Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet, AIP Advances 5, 107203 (2015), doi: 10.1063/1.4932627.
  20. Rajagopal, K. R., Gupta, A. S., Nath, T. Y., A note on the Falkner-Skan flows of a non-Newtonian fluid, Int. J. Nonlinear Mech., 18 (1983), pp. 313-320.
  21. Kuo, B. L., Application of the differential transformation method to the solutions of Falkner-Skan wedge flow, Acta Mech., 164 (2003), pp. 161-174.
  22. Ishak, A., Nazar, R., Pop, I., Moving wedge and flat plate in a micropolar fluid, Int. J. Eng. Sci., 44 (2006), pp. 1225-1236.
  23. White, F. M., Viscous Fluid Flow, McGraw-Hill, New York, USA, 1991.

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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