×

Falkner-Skan equation for flow past a moving wedge with suction or injection. (English) Zbl 1290.34040

Consider the boundary value problem \[ \begin{gathered} f'''+ ff''+\beta(1- f^{\prime 2})= 0,\\ f(0)= f_0,\;f'(0)= -\lambda,\;f'(\infty)= 1,\end{gathered}\tag{\(*\)} \] for \(0\leq \beta\leq 2\), \(\lambda< 0\) and \(|\lambda|\) large. The authors use an implicit finite difference scheme to study the solution of \((*)\).

MSC:

34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
Full Text: DOI

References:

[1] V. M. Falkner and S. W. Skan,Some approximate solutions of the boundary-layer equations, Phiols. Mag.12 (1931), 865–896. · Zbl 0003.17401
[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. · JFM 63.0432.03 · doi:10.1017/S0305004100019575
[3] K. Stewartson,Further solutions of the Falkner-Skan equation, Proc. Cambridge Phil. Soc.50 (1954), 454–465. · Zbl 0058.20104 · doi:10.1017/S030500410002956X
[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. · Zbl 0159.27905 · doi:10.1017/S0022112068001291
[5] A. H. Craven and L. A. Peletier,On the uniqueness of solutions of the Falkner-Skan equation, Mathematika19 (1972), 135–138. · Zbl 0259.34024 · doi:10.1112/S0025579300005064
[6] S. P. Hastings,Reversed flow solutions of the Falkner-Skan equation, SIAM J. Appl. Math.22 (1972), 329–334. · Zbl 0243.34026 · doi:10.1137/0122031
[7] B. Oskam and A. E. P. Veldman,Branching of the Falkner-Skan solutions for {\(\lambda\)} < 0, J. Engng. Math.16 (1982), 295–308. · Zbl 0497.76049 · doi:10.1007/BF00037732
[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. · Zbl 0527.76010 · doi:10.1016/0020-7462(83)90028-8
[9] E. F. F. Botta, F. J. Hut and A. E. P. Veldman,The role of periodic solutions in the Falkner-Skan problem for {\(\lambda\)} > 0, J. Engng. Math.20 (1986), 81–93. · Zbl 0594.34036 · doi:10.1007/BF00039325
[10] P. Brodie and W. H. H. Banks,Further properties of the Falkner-Skan equation, Acta Mechanica65 (1986), 205–211. · Zbl 0609.76027 · doi:10.1007/BF01176882
[11] N. S. Asaithambi,A numerical method for the solution of the Falkner-Skan equation, Appl. Math. Comp.81 (1997), 259–264. · Zbl 0873.76049 · doi:10.1016/S0096-3003(95)00325-8
[12] A. Asaithambi,A finite-difference method for the Falkner-Skan equation, Appl. Math. Comp.92 (1998), 135–141. · Zbl 0973.76581 · doi:10.1016/S0096-3003(97)10042-X
[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. · Zbl 0928.76037 · doi:10.1007/s000330050140
[14] M. B. Zaturska and W. H. H. Banks,A new solution branch of the Falkner-Skan equation, Acta Mechanica152 (2001), 197–201. · Zbl 0992.76027 · doi:10.1007/BF01176954
[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. · Zbl 1051.76543 · doi:10.1016/S0997-7546(02)01193-7
[16] B. L. Kuo,Application of the differential transformation method to the solutions of Falkner-Skan wedge flow, Acta Mechanica164 (2003), 161–174. · Zbl 1064.76034 · doi:10.1007/s00707-003-0019-4
[17] A. Pantokratoras,The Falkner-Skan flow with constant wall temperature and variable viscosity, Int. J. Thermal Sciences45 (2006) 378–389. · doi:10.1016/j.ijthermalsci.2005.06.004
[18] G.C. Yang,On the equation f”’+ff”+{\(\lambda\)}(1’2)=0 with {\(\lambda\)} -1/2arising in boundary layer theory, J. Appl. Math. & Computing20 (2006), 479–483. · Zbl 1093.34519 · doi:10.1007/BF02831954
[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. · Zbl 0931.76017 · doi:10.1017/S0022112099004292
[20] L. Rosenhead,Laminar Boundary Layers, Oxford University Press, Oxford, 1963. · Zbl 0115.20705
[21] T. Watanabe,Thermal boundary layers over a wedge with uniform suction or injection in forced flow, Acta Mechanica83 (1990), 119–126. · doi:10.1007/BF01172973
[22] K. A. Yih,Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux, Acta Mechanica128 (1998), 173–181. · Zbl 0926.76108 · doi:10.1007/BF01251888
[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. · doi:10.1016/0017-9310(61)90088-6
[24] W. H. H. Banks,Similarity solutions of the boundary-layer equations for a stretching wall, J. Mec. Theor. Appl.2 (1983), 375–392. · Zbl 0538.76039
[25] J. Serrin,Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory, Proc. Roy. Soc. A299 (1967), 491–507. · Zbl 0149.44901
[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. · Zbl 0682.76026 · doi:10.1137/0149081
[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. · doi:10.1016/j.ijheatfluidflow.2004.08.007
[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. · Zbl 1189.76143 · doi:10.1016/j.ijheatmasstransfer.2005.02.028
[29] B. C. Sakiadis,Boundary layers on continuous solid surfaces, AIChE. J.,7 (1961), 26–28, see also pp. 221–225 and 467–472. · doi:10.1002/aic.690070108
[30] H. Blasius,Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys.56 (1908), 1–37. · JFM 39.0803.02
[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. · Zbl 0976.76021 · doi:10.1016/S0997-7546(00)00104-7
[32] H. Schlichting,Boundary Layer Theory, McGraw-Hill, New York, 1979. · Zbl 0434.76027
[33] T. Fang,Further study on a moving-wall boundary-layer problem with mass transfer, Acta Mechanica163 (2003), 183–188. · Zbl 1064.76032 · doi:10.1007/s00707-002-0979-9
[34] F. M. White,Viscous Fluid Flow, 3rd ed., Mc Graw-Hill, New York, 2006.
[35] T. Cebeci and P. Bradshaw,Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1988. · Zbl 0702.76003
[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. · Zbl 0117.43403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.