Journal of Applied Mathematics and Computing

, Volume 25, Issue 1–2, pp 67–83

# Falkner-Skan equation for flow past a moving wedge with suction or injection

Article

## Abstract

The characteristics of steady two-dimensional 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 finite-difference scheme known as the Keller-box method. The effects of Falkner-Skan power-law 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 Falkner-Skan equation for flow past an impermeable stretching boundary.

34B16 34B40

### Key words and phrases

Boundary layer dual solutions mass transfer moving wedge

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### References

1. 1.
V. M. Falkner and S. W. Skan,Some approximate solutions of the boundary-layer equations, Phiols. Mag.12 (1931), 865–896.
2. 2.
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.
3. 3.
K. Stewartson,Further solutions of the Falkner-Skan equation, Proc. Cambridge Phil. Soc.50 (1954), 454–465.
4. 4.
K. K. Chen and P. A. Libby,Boundary layers with small departure from the Falkner-Skan profile, J. Fluid Mech.33 (1968), 273–282.
5. 5.
A. H. Craven and L. A. Peletier,On the uniqueness of solutions of the Falkner-Skan equation, Mathematika19 (1972), 135–138.
6. 6.
S. P. Hastings,Reversed flow solutions of the Falkner-Skan equation, SIAM J. Appl. Math.22 (1972), 329–334.
7. 7.
B. Oskam and A. E. P. Veldman,Branching of the Falkner-Skan solutions for λ < 0, J. Engng. Math.16 (1982), 295–308.
8. 8.
K. R. Rajagopal, A. S. Gupta and T. Y. Nath,A note on the Falkner-Skan flows of a non-Newtonian fluid, Int. J. Non-Linear Mech.18 (1983), 313–320.
9. 9.
E. F. F. Botta, F. J. Hut and A. E. P. Veldman,The role of periodic solutions in the Falkner-Skan problem for λ > 0, J. Engng. Math.20 (1986), 81–93.
10. 10.
P. Brodie and W. H. H. Banks,Further properties of the Falkner-Skan equation, Acta Mechanica65 (1986), 205–211.
11. 11.
N. S. Asaithambi,A numerical method for the solution of the Falkner-Skan equation, Appl. Math. Comp.81 (1997), 259–264.
12. 12.
A. Asaithambi,A finite-difference method for the Falkner-Skan equation, Appl. Math. Comp.92 (1998), 135–141.
13. 13.
R. S. Heeg, D. Dijkstra and P. J. Zandbergen,The stability of Falkner-Skan flows with several inflection points, J. Appl. Math. Phys. (ZAMP)50 (1999), 82–93.
14. 14.
M. B. Zaturska and W. H. H. Banks,A new solution branch of the Falkner-Skan equation, Acta Mechanica152 (2001), 197–201.
15. 15.
S.D. Harris, D. B. Ingham and I. Pop,Unsteady heat transfer in impulsive Falkner-Skan flows: Constant wall temperature case, Eur. J. Mech. B/Fluids21 (2002), 447–468.
16. 16.
B. L. Kuo,Application of the differential transformation method to the solutions of Falkner-Skan wedge flow, Acta Mechanica164 (2003), 161–174.
17. 17.
A. Pantokratoras,The Falkner-Skan flow with constant wall temperature and variable viscosity, Int. J. Thermal Sciences45 (2006) 378–389.
18. 18.
G.C. Yang,On the equation f'"+ff"+λ(1−f2)=0 with λ ≤ -1/2arising in boundary layer theory, J. Appl. Math. & Computing20 (2006), 479–483.
19. 19.
S. J. Liao,A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate, J. Fluid Mech.385 (1999), 101–128.
20. 20.
L. Rosenhead,Laminar Boundary Layers, Oxford University Press, Oxford, 1963.
21. 21.
T. Watanabe,Thermal boundary layers over a wedge with uniform suction or injection in forced flow, Acta Mechanica83 (1990), 119–126.
22. 22.
K. A. Yih,Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux, Acta Mechanica128 (1998), 173–181.
23. 23.
J. C. Y. Koh, and J. P. Hartnett,Skin-friction and heat transfer for incompressible laminar flow over porous wedges with suction and variable wall temperature, Int. J. Heat Mass Transfer2 (1961), 185–198.
24. 24.
W. H. H. Banks,Similarity solutions of the boundary-layer equations for a stretching wall, J. Mec. Theor. Appl.2 (1983), 375–392.
25. 25.
J. Serrin,Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory, Proc. Roy. Soc. A299 (1967), 491–507.
26. 26.
N. Riley and P. D. Weidman,Multiple solutions of the Falkner-Skan equation for flow past a stretching boundary, SIAM J. Applied Mathematics49 (1989), 1350–1358.
27. 27.
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.
28. 28.
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.Google Scholar
29. 29.
B. C. Sakiadis,Boundary layers on continuous solid surfaces, AIChE. J.,7 (1961), 26–28, see also pp. 221–225 and 467–472.
30. 30.
H. Blasius,Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys.56 (1908), 1–37.Google Scholar
31. 31.
E. Magyari and B. Keller,Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Eur. J. Mech. B-Fluids19 (2000), 109–122.
32. 32.
H. Schlichting,Boundary Layer Theory, McGraw-Hill, New York, 1979.
33. 33.
T. Fang,Further study on a moving-wall boundary-layer problem with mass transfer, Acta Mechanica163 (2003), 183–188.
34. 34.
F. M. White,Viscous Fluid Flow, 3rd ed., Mc Graw-Hill, New York, 2006.Google Scholar
35. 35.
T. Cebeci and P. Bradshaw,Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1988.
36. 36.
E. M. Sparrow, E. R. Eckert and W. J. Minkowicz,Transpiration cooling in a magneto-hydrodynamic stagnation-point flow, Appl. Sci. Res. A11 (1962), 125–147.Google Scholar