Title:
|
On similarity solution of a boundary layer problem for power-law fluids (English) |
Author:
|
Bognár, Gabriella |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
137 |
Issue:
|
2 |
Year:
|
2012 |
Pages:
|
139-148 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The boundary layer equations for the non-Newtonian power law fluid are examined under the classical conditions of uniform flow past a semi infinite flat plate. We investigate the behavior of the similarity solution and employing the Crocco-like transformation we establish the power series representation of the solution near the plate. (English) |
Keyword:
|
similarity solution |
Keyword:
|
boundary layer problem |
Keyword:
|
power series solution |
MSC:
|
34B40 |
MSC:
|
35C06 |
MSC:
|
35Q35 |
MSC:
|
76A05 |
idZBL:
|
Zbl 1265.35258 |
idMR:
|
MR2978260 |
DOI:
|
10.21136/MB.2012.142860 |
. |
Date available:
|
2012-06-08T10:07:31Z |
Last updated:
|
2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142860 |
. |
Reference:
|
[1] Abbasbandy, S.: A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method.Chaos Solitons Fractals 31 (2007), 257-260. MR 2262129, 10.1016/j.chaos.2005.10.071 |
Reference:
|
[2] Acrivos, A., Shah, A., Petersen, E. E.: Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces.AIChE J. 6 (1960), 312-317. 10.1002/aic.690060227 |
Reference:
|
[3] Blasius, H.: Grenzschichten in Flüssigkeiten mit kleiner Reibung.Z. Math. Phys. 56 (1908), 1-37. |
Reference:
|
[4] Briot, Ch., Bouquet, J. K.: Étude des fonctions d'une variable imaginaire.Journal de l'École Polytechnique, Cashier 36 (1856), 85-131. |
Reference:
|
[5] Guedda, M.: Similarity and pseudosimilarity soutions of degenerate boundary-layer equations.M. Chipot Handbook of Differential Equations, Stationary Partial Differential Equation vol. 4, North Holland (2007), 117-202. MR 2569332, 10.1016/S1874-5733(07)80006-4 |
Reference:
|
[6] He, J-H.: Comparison of homotopy perturbation method and homotopy analysis method.Appl. Math. Comput. 156 (2004), 527-539. Zbl 1062.65074, MR 2087530, 10.1016/j.amc.2003.08.008 |
Reference:
|
[7] Henrici, P.: Applied and Computational Complex Analysis. Vol. 1.Power Series---Integration---Conformal Mappings---Location of Zeros. Wiley, New York (1974). Zbl 0313.30001, MR 0372162 |
Reference:
|
[8] Hille, E.: Ordinary Differential Equations in the Complex Domain.John Wiley, New York (1976). Zbl 0343.34007, MR 0499382 |
Reference:
|
[9] Howarth, L.: On the solution of the laminar boundary layer equations.Proc. R. Soc. Lond. A 164 (1938), 547-579. 10.1098/rspa.1938.0037 |
Reference:
|
[10] Liao, S.-J.: An explicit, totally analytic, solution for Blasius viscous flow problems.Int. J. Non-Lin. Mech. 34 (1999), 758-778. MR 1688603 |
Reference:
|
[11] Ince, E. L.: Ordinary Differential Equations.Dover Publ., New York (1956). MR 0010757 |
Reference:
|
[12] Nachman, A., Callegari, A.: A nonlinear singular boundary value problem in the theory of pseudoplastic fluids.SIAM J. Appl. Math. 38 (1980), 275-281. Zbl 0453.76002, MR 0564014, 10.1137/0138024 |
Reference:
|
[13] Schlichting, H., Gersten, K.: Boundary Layer Theory (8th revised and enlarged edition).Springer, Berlin (2000). MR 1765242 |
Reference:
|
[14] Schowalter, W. R.: The application of boundary-layer theory to power-law pseudoplastic fluids: Similar solutions.AIChE J. 6 (1960), 24-28. 10.1002/aic.690060105 |
Reference:
|
[15] Töpfer, K.: Bemerkung zu dem Aufsatz von H. Blasius: Grenzschichten in Flüssigkeiten mit kleiner Reibung.Z. Math. Phys. 60 (1912), 397-398. |
. |