%0 Journal Article
%T Numerical solution of general boundary layer problems by the method of differential quadrature
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Eftekhari, S. A.
%A Jafari, A. A.
%D 2013
%\ 08/01/2013
%V 20
%N 4
%P 1278-1301
%! Numerical solution of general boundary layer problems by the method of differential quadrature
%K Differential quadrature method (DQM)
%K Blasius flow
%K Sakiadis flow
%K Falkner-Skan flow
%K MHD Falkner-Skan flow
%K Jeffery-Hamel flow
%K Unsteady two-dimensional flow
%K Unsteady three-dimensional MHD flow
%R
%X Accurate numerical solutions to some boundary layer equations are presented for boundary layer flows of incompressible Newtonian fluid over a semi-infinite plate. The differential quadrature method (DQM) is first used to reduce the governing nonlinear differential equations to a set of nonlinear algebraic equations. The Newton-Raphson method is then employed to solve the resulting system of nonlinear algebraic equations. The proposed formulation is applied here to solve some boundary layer problems including Blasius,Sakiadis, Falkner-Skan, magnetohydrodynamic (MHD) Falkner-Skan, Jeffery-Hamel, unsteady two-dimensional and three-dimensional MHD flows. A simple scheme is also presented for solving Blasius boundary layer equation. In this techniques, Blasius boundary value problem is first converted to a pair of nonlinear initial-value problems and then solved by a step-by-step DQM. The accuracy and efficiency of the proposed formulations are demonstrated by comparing the calculated results with those of other numerical and semi-analytical methods. Accurate numerical solutions are achieved using both formulations via a small number of grid points for all the cases considered
%U https://scientiairanica.sharif.edu/article_3400_05b566331cf622c390e0c1e3df87dcf8.pdf