FalknerSkan equation for flow past a moving wedge with suction or injection
 Anuar Ishak,
 Roslinda Nazar,
 Ioan Pop
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The characteristics of steady twodimensional laminar boundary layer flow of a viscous and incompressible fluid past a moving wedge with suction or injection are theoretically investigated. The transformed boundary layer equations are solved numerically using an implicit finitedifference scheme known as the Kellerbox method. The effects of FalknerSkan powerlaw parameter (m), suction/injection parameter (f0) and the ratio of free stream velocity to boundary velocity parameter (λ) are discussed in detail. The numerical results for velocity distribution and skin friction coefficient are given for several values of these parameters. Comparisons with the existing results obtained by other researchers under certain conditions are made. The critical values off _{0},m and λ are obtained numerically and their significance on the skin friction and velocity profiles is discussed. The numerical evidence would seem to indicate the onset of reverse flow as it has been found by Riley and Weidman in 1989 for the FalknerSkan equation for flow past an impermeable stretching boundary.
 V. M. Falkner and S. W. Skan,Some approximate solutions of the boundarylayer equations, Phiols. Mag.12 (1931), 865–896.
 D. R. Hartree,On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer, Proc. Cambridge Phil. Soc.33 (1937), 223–239.
 K. Stewartson,Further solutions of the FalknerSkan equation, Proc. Cambridge Phil. Soc.50 (1954), 454–465.
 K. K. Chen and P. A. Libby,Boundary layers with small departure from the FalknerSkan profile, J. Fluid Mech.33 (1968), 273–282. CrossRef
 A. H. Craven and L. A. Peletier,On the uniqueness of solutions of the FalknerSkan equation, Mathematika19 (1972), 135–138. CrossRef
 S. P. Hastings,Reversed flow solutions of the FalknerSkan equation, SIAM J. Appl. Math.22 (1972), 329–334. CrossRef
 B. Oskam and A. E. P. Veldman,Branching of the FalknerSkan solutions for λ < 0, J. Engng. Math.16 (1982), 295–308. CrossRef
 K. R. Rajagopal, A. S. Gupta and T. Y. Nath,A note on the FalknerSkan flows of a nonNewtonian fluid, Int. J. NonLinear Mech.18 (1983), 313–320. CrossRef
 E. F. F. Botta, F. J. Hut and A. E. P. Veldman,The role of periodic solutions in the FalknerSkan problem for λ > 0, J. Engng. Math.20 (1986), 81–93. CrossRef
 P. Brodie and W. H. H. Banks,Further properties of the FalknerSkan equation, Acta Mechanica65 (1986), 205–211. CrossRef
 N. S. Asaithambi,A numerical method for the solution of the FalknerSkan equation, Appl. Math. Comp.81 (1997), 259–264. CrossRef
 A. Asaithambi,A finitedifference method for the FalknerSkan equation, Appl. Math. Comp.92 (1998), 135–141. CrossRef
 R. S. Heeg, D. Dijkstra and P. J. Zandbergen,The stability of FalknerSkan flows with several inflection points, J. Appl. Math. Phys. (ZAMP)50 (1999), 82–93. CrossRef
 M. B. Zaturska and W. H. H. Banks,A new solution branch of the FalknerSkan equation, Acta Mechanica152 (2001), 197–201. CrossRef
 S.D. Harris, D. B. Ingham and I. Pop,Unsteady heat transfer in impulsive FalknerSkan flows: Constant wall temperature case, Eur. J. Mech. B/Fluids21 (2002), 447–468. CrossRef
 B. L. Kuo,Application of the differential transformation method to the solutions of FalknerSkan wedge flow, Acta Mechanica164 (2003), 161–174. CrossRef
 A. Pantokratoras,The FalknerSkan flow with constant wall temperature and variable viscosity, Int. J. Thermal Sciences45 (2006) 378–389. CrossRef
 G.C. Yang,On the equation f'"+ff"+λ(1−f′^{2})=0 with λ ≤ 1/2arising in boundary layer theory, J. Appl. Math. & Computing20 (2006), 479–483.
 S. J. Liao,A uniformly valid analytic solution of twodimensional viscous flow over a semiinfinite flat plate, J. Fluid Mech.385 (1999), 101–128. CrossRef
 L. Rosenhead,Laminar Boundary Layers, Oxford University Press, Oxford, 1963.
 T. Watanabe,Thermal boundary layers over a wedge with uniform suction or injection in forced flow, Acta Mechanica83 (1990), 119–126. CrossRef
 K. A. Yih,Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux, Acta Mechanica128 (1998), 173–181. CrossRef
 J. C. Y. Koh, and J. P. Hartnett,Skinfriction and heat transfer for incompressible laminar flow over porous wedges with suction and variable wall temperature, Int. J. Heat Mass Transfer2 (1961), 185–198. CrossRef
 W. H. H. Banks,Similarity solutions of the boundarylayer equations for a stretching wall, J. Mec. Theor. Appl.2 (1983), 375–392.
 J. Serrin,Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory, Proc. Roy. Soc. A299 (1967), 491–507.
 N. Riley and P. D. Weidman,Multiple solutions of the FalknerSkan equation for flow past a stretching boundary, SIAM J. Applied Mathematics49 (1989), 1350–1358. CrossRef
 J. P. Abraham and E. M. Sparrow,Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface, Int. J. Heat Fluid Flow26 (2005), 289–295. CrossRef
 E. M. Sparrow and J. P. Abraham,Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid, Int. J. Heat Mass Transfer48 (2005), 3047–3056.
 B. C. Sakiadis,Boundary layers on continuous solid surfaces, AIChE. J.,7 (1961), 26–28, see also pp. 221–225 and 467–472. CrossRef
 H. Blasius,Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys.56 (1908), 1–37.
 E. Magyari and B. Keller,Exact solutions for selfsimilar boundarylayer flows induced by permeable stretching walls, Eur. J. Mech. BFluids19 (2000), 109–122. CrossRef
 H. Schlichting,Boundary Layer Theory, McGrawHill, New York, 1979.
 T. Fang,Further study on a movingwall boundarylayer problem with mass transfer, Acta Mechanica163 (2003), 183–188. CrossRef
 F. M. White,Viscous Fluid Flow, 3rd ed., Mc GrawHill, New York, 2006.
 T. Cebeci and P. Bradshaw,Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1988.
 E. M. Sparrow, E. R. Eckert and W. J. Minkowicz,Transpiration cooling in a magnetohydrodynamic stagnationpoint flow, Appl. Sci. Res. A11 (1962), 125–147.
 Title
 FalknerSkan equation for flow past a moving wedge with suction or injection
 Journal

Journal of Applied Mathematics and Computing
Volume 25, Issue 12 , pp 6783
 Cover Date
 20070901
 DOI
 10.1007/BF02832339
 Print ISSN
 15985865
 Online ISSN
 18652085
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 34B16
 34B40
 Boundary layer
 dual solutions
 mass transfer
 moving wedge
 Authors

 Anuar Ishak ^{(1)}
 Roslinda Nazar ^{(1)}
 Ioan Pop ^{(2)}
 Author Affiliations

 1. School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia, 43600, UKM Bangi, Malaysia
 2. Faculty of Mathematics, University of Cluj, CP 253, R3400, Cluj, Romania