Application of Crocco - Wang equation to the Blasius problem

Автор: Faiz Ahmad

Журнал: Техническая акустика @ejta

Статья в выпуске: т.7, 2007 года.

Бесплатный доступ

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.

Еще

Blasius equation, crocco-wang equation, adomian decomposition method, newton's method, asymptotic solution

Короткий адрес: https://readera.ru/14316076

IDR: 14316076

Список литературы Application of Crocco - Wang equation to the Blasius problem

  • B. J. Cantwell. Introduction to Symmetry Analysis. Cambridge University Press, 2002.
  • H. Blasius. Grenzschichten in Flussigkeiten mit kleiner Reibung. Z. Math. u. Phys. 56 (1908) 1-37.
  • L. Howarth. On the solution of the laminar boundary layer equations. Proc. London Math. Soc. A 164 (1938) 547-579.
  • Asai Asaithambi. Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients. J. Comput. Appl. Math. 176 (2005) 203-214.
  • T. Fang, F. Guo, C. F. Lee. A note on the extended Blasius problem. Applied Mathematics Letters 19 (2006) 613-617.
  • S. J. Liao. An explicit, totally analytic approximate solution for Blasius' viscous flow problems. International Journal of Non-Linear Mechanics 34 (1999) 759-778.
  • J. H. He. A simple perturbation approach to Blasius equation. Appl. Math. Comput. 140 (2003) 217-222.
  • 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.
  • R. Cortell. Numerical solutions of the classical Blasius flat-plate problem. Appl. Math. Comput. 170 (2005) 706-710.
  • Chia-Shun Yih. Fluid Mechanics -A Concise Introduction to the Theory, McGraw-Hill, New York, 1969.
  • L. Wang. A new algorithm for solving classical Blasius equation. Appl. Math. Comput. 157 (2004) 1-9.
  • I. Hashim. Comments on A new algorithm for solving classical Blasius equation by L. Wang. Appl. Math. Comput. 176 (2006), 700-703.
  • F. Ahmad. Degeneracy in the Blasius problem, submitted for publication to the Electronic Journal of Differential Equations.
Еще
Статья научная