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Application of Crocco-Wang equation to the Blasius problem
language: English
received 04.12.2006, published 22.01.2007
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ABSTRACT
Navier-Stokes problem for a boundary layer can be transformed, by a similarity transformation, into the Blasius problem which is governed by a non-linear ordinary differential equation of order three. Since it is simpler to solve an ordinary differential equation, this transformation leads to an easy evaluation of physical parameters such as the drag and the thickness of the boundary layer. Crocco and independently Wang further transformed this problem to one which is governed by a second order differential equation. In this paper this problem is solved by a classical method and the solution is used to derive two sequences, the first an increasing sequence and the second a decreasing sequence, both converging to the unknown second derivative, at the origin, of the solution to the Blasius equation. Also an asymptotic expression for the solution is obtained.
Keywords: Blasius equation, Crocco-Wang equation, Adomian decomposition method, Newton's method, asymptotic solution.
11 pages
Сitation: Faiz Ahmad. Application of Crocco-Wang equation to the Blasius problem. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2007, 2.
REFERENCES
1. B. J. Cantwell. Introduction to Symmetry Analysis. Cambridge University Press, 2002.
2. H. Blasius. Grenzschichten in Flussigkeiten mit kleiner Reibung. Z. Math. u. Phys. 56 (1908) 1-37.
3. L. Howarth. On the solution of the laminar boundary layer equations. Proc. London Math. Soc. A 164 (1938) 547-579.
4. Asai Asaithambi. Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients. J. Comput. Appl. Math. 176 (2005) 203-214.
5. T. Fang, F. Guo, C. F. Lee. A note on the extended Blasius problem. Applied Mathematics Letters 19 (2006) 613-617.
6. S. J. Liao. An explicit, totally analytic approximate solution for Blasius' viscous flow problems. International Journal of Non-Linear Mechanics 34 (1999) 759-778.
7. J. H. He. A simple perturbation approach to Blasius equation. Appl. Math. Comput. 140 (2003) 217-222.
8. S. Abbasbandy. A numerical solution of Blasius equation by Adomian decomposition method and comparison with homotopy perturbation method. Chaos, Solitons and Fractals 31 (2007) 257-260.
9. R. Cortell. Numerical solutions of the classical Blasius flat-plate problem. Appl. Math. Comput. 170 (2005) 706-710.
10. Chia-Shun Yih. Fluid Mechanics - A Concise Introduction to the Theory, McGraw-Hill, New York, 1969.
11. L. Wang. A new algorithm for solving classical Blasius equation. Appl. Math. Comput. 157 (2004) 1-9.
12. I. Hashim. Comments on A new algorithm for solving classical Blasius equation by L. Wang. Appl. Math. Comput. 176 (2006), 700-703.
13. F. Ahmad. Degeneracy in the Blasius problem, submitted for publication to the Electronic Journal of Differential Equations.
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Faiz Ahmad was born in Pakistan on 15 March, 1946. He received his education at the University of Punjab (Pakistan) and the University of Manchester (England). He received his Ph.D. in 1972. He has taught at the Quaid-i-Azam University, Islamabad (Pakistan), Al-Fateh University, Tripoli (Libya) and King Abdulaziz University, Jeddah (Saudi Arabia). |