An Iteration Method to Solve the Boundary Layer Flow past a Flat Plate

Ken-ichi Kusukawa, Shigeaki Suwa, Takeo R. M. Nakagawa

Jusup Balasagyn Kyrgyz National University, Frunze Str. Bishkek, Kyrgyz Republic.
National Defense Academy, Yokosuka, Japan.
Tokyo Metropolitan University, Hachiohji, Japan.

DOI: 10.4236/jamp.2014.24005                

Abstract

An iteration method similar to the thin-wing-expansion method for the compressible flow has been proposed to solve the boundary layer flow past a flat plate. Using such an iteration, the first step of which is Oseen’s approximation, the boundary layer past a flat plate is studied. As proceeding from the first approximation to the second and third approximations, it is realized that our solution approaches to a well known Howarth’s bench mark one gradually. Hence, it is concluded that the usefulness of the present method has been confirmed.

Keywords

Boundary Layer Flow; Mathematical Analysis; Iteration Method; Approximate Solution; Navier-Stokes Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Prandtl, L. (1904) über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandl Ⅲ, Intern. Math. Kongr. Heidelberg, Auch: Gesammelte Abhandlungen, 2, 484-491.
[2]	Blasius, H. (1908) Grenzschichten in Flüssigkeiten mit kleiner Reibung. Zeits. f. Math. u. Phys, 56, 1-37.
[3]	von Kámán, Th. (1921) über laminare und turbulente Reibung. ZAMM, 1, 233-252. http://dx.doi.org/10.1002/zamm.19210010401
[4]	Howarth, L. (1938) On the Solution of the Laminar Boundary Layer Equations. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 164, 547-579. http://dx.doi.org/10.1098/rspa.1938.0037
[5]	Imai, I. (1957) Second Approximation to the Laminar Boundary Layer Flow over a Flat Plate. Journal of the Aeronautical Sciences, 24, 155-156.
[6]	Pohlhausen, K. (1921) Zur naherungsweisen Integration der Differentialgleichung der Grenzschicht. ZAMM, 1, 252-268. http://dx.doi.org/10.1002/zamm.19210010402
[7]	Tani, I. (1954) On the Approximate Solution of the Laminar Boundary Layer Equations. Journal of the Aeronautical Sciences, 21, 487-495. http://dx.doi.org/10.2514/8.3092
[8]	Meksyn, D. (1961) New Methods in Laminar Boundary Layer Theory. Pergamon Press, 65-81.
[9]	Imai, I. (1944) Two-Dimensional Aero-Foil Theory for Compressible Fluids. Rep. Aero. Research Institute, Tokyo Imperial University, No. 294.
[10]	Schlichting, H. (1960) Boundary Layer Theory. New York, McGraw-Hill, 125-134.