International Journal of Ocean System Engineering

Korean Society of Ocean Engineers (한국해양공학회)
권호 표지
DOI QR코드

DOI QR Code

A Method of Moments Approach for Laminar Boundary Layer Flows

  • Kinaci, Omer Kemal (Yildiz Technical University, Faculty of Naval Architecture and Maritime) ;
  • Usta, Onur (Istanbul Technical University, Faculty of Naval Architecture and Ocean Engineering)
  • Received : 2013.06.12
  • Accepted : 2013.08.12
  • Published : 2013.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

Blasius equation describes the boundary layer formed over a flat plate inside a fluid and this equation is solved numerically by the method of moments which is a type of weighted residual methods. Compared to the traditionally used Runge - Kutta Method, Method of Moments propose a direct solution to Blasius Equation which makes it easier to solve. The obtained solutions show good agreement with the results found in literature and this study aims to demonstrate the power of the method.

Keywords

References

  1. I. Tani, History of boundary-layer theory, Ann. Rev. Fluid Mech. 9 (1977) 87-111. https://doi.org/10.1146/annurev.fl.09.010177.000511
  2. H. Aminikhah, An analytical approximation for solving nonlinear Blasius equation by NHPM, Numerical Methods for Partial Differential Equations, 26 (6) (2010) 1291-1299
  3. J. H. He, Approximate analytical solution of Blasius' equation, Communications in Nonlinear Science & Numerical Simulation, 4 (1) (1999) 75-78 https://doi.org/10.1016/S1007-5704(99)90063-1
  4. B. K. Datta, Analytic solution for the Blasius equation, Indian Journal of Pure and Applied Mathematics, 34 (2) (2003) 237-240
  5. L. Wang, A new algorithm for solving classical Blasius equation, Appl. Math. Comput. 157 (2004) 1-9 https://doi.org/10.1016/j.amc.2003.06.011
  6. L. Howarth, On the solution of the laminar boundary layer equations, Proc. Roy. Soc. London A 164 (1938) 547-579. https://doi.org/10.1098/rspa.1938.0037
  7. U. Filobello-Nino, H. Vazquez-Leal, R. Castaneda- Sheissa, A. Yildirim, L. Hernandez- Martinez, D. Pereyra-Diaz, A. Perez-Sesma, C Hoyos-Reyes, An approximate solution of Blasius equation by using HPM method, Asian Journal of Mathematics & Statistics, 5 (2) (2012) 50-59 https://doi.org/10.3923/ajms.2012.50.59
  8. K. Parand, M. Dehghan, A. Pirkhedri, Sinccollocation method for solving the Blasius equation, Physics Letters A, 373 (44) (2009) 4060-4065 https://doi.org/10.1016/j.physleta.2009.09.005
  9. J. H. He, A simple perturbation approach to Blasius equation, Applied Mathematics and Computation, 140 (2-3) (2003) 217-222 https://doi.org/10.1016/S0096-3003(02)00189-3
  10. M. Benlahsen, M. Guedda, R. Kersner, The generalized Blasius equation revisited, Mathematical and Computer Modelling, 47 (9-10) (2008) 1063-1076 https://doi.org/10.1016/j.mcm.2007.06.019
  11. R. Cortell, Numerical solutions of the classical Blasius flat-plate problem, Appl. Math. Comput. 170 (1) (2005) 706-710 https://doi.org/10.1016/j.amc.2004.12.037
  12. T. Fang, F. Guob, C. F. Leea, A note on the extended Blasius equation, Applied Mathematics Letters, 19 (7) (2006) 613-617 https://doi.org/10.1016/j.aml.2005.08.010
  13. Hartree, D. R., On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer, Proc. Cambridge Philos. Society 33 (1937) 223-239. https://doi.org/10.1017/S0305004100019575
  14. G.V. Rao, Least square and galerkin finite element solution of flow past a flat plate, Int. J. for Numer. Meth. Engng. 11 (1) (1975) 185-190.
  15. A. Asaithambi, A finite-difference method for the Falkner Skan equation, Appl. Math. Comput. 92 (1998) 135-141. https://doi.org/10.1016/S0377-0427(97)00235-5
  16. A. Asaithambi, A second-order finitedifference method for the Falkner Skan equation, Appl. Math. Comput. 156 (2004) 779-786. https://doi.org/10.1016/j.amc.2003.06.020
  17. A. Asaithambi, Numerical solution of the Falkner- Skan equation using piecewise linear equation, Appl. Math. Comput. 159 (2004) 267-273. https://doi.org/10.1016/j.amc.2003.10.047
  18. A. Asaithambi, A solution of the Falkner-Skan equation by recursive Taylor coefficients, Journal of Computational and Applied Mathematics, 176 (2005) 203-214. https://doi.org/10.1016/j.cam.2004.07.013
  19. H. Schlichting, K. Gersten, Boundary Layer Theory, eighth rev.ed., McGraw-Hill, New York, 1999.
  20. B. A. Finlayson, Nonlinear Analysis in Chemical Engineering, McGraw Hill, New York, 1980