Solutions of Falkner–Skan equation with heat transfer by Fourier series ☆

Abstract In this paper, we solve the Falkner–Skan equation with heat transfer through an expansion in Fourier series, results are improved by incorporating an asymptotic analysis for the Fourier series coefficients. The results show that the classical expansion in Fourier series together with the incorporation of an asymptotic analysis for coefficients of the series delivers a solution with very good accuracy and rapid convergence when it is compared with other methods of solution found in the literature as finite difference and shooting method.

[1]  Asai Asaithambi,et al.  A finite-difference method for the Falkner-Skan equation , 1998, Appl. Math. Comput..

[2]  F. White.  Viscous Fluid Flow , 1974 .

[3]  Asai Asaithambi.  Numerical solution of the Falkner-Skan equation using piecewise linear functions , 2004, Appl. Math. Comput..

[4]  V. M. F. B.Sc.,et al.  LXXXV. Solutions of the boundary-layer equations , 1931 .

[5]  Claudio Canuto,et al.  Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation) , 2007 .

[6]  Weiwei Sun,et al.  Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains , 2005, SIAM J. Numer. Anal..

[7]  S. Liao.  A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.

[8]  Elsayed M. A. Elbashbeshy,et al.  Effect of radiation on the flow and heat transfer over a wedge with variable viscosity , 2002, Appl. Math. Comput..

[9]  N. S. Asaithambi,et al.  A numerical method for the solution of the Falkner-Skan equation , 1997 .

[10]  Jiawei Zhang,et al.  An iterative method for solving the Falkner-Skan equation , 2009, Appl. Math. Comput..

[11]  D. Meksyn.  New Methods In Laminar Boundary-Layer Theory , 1961 .

[12]  D. Summers,et al.  The use of generalized Laguerre polynomials in spectral methods for nonlinear differential equations , 1998 .

[13]  H. B. Keller,et al.  Shooting and parallel shooting methods for solving the Falkner-Skan boundary-layer equation , 1971 .

[14]  D. R. Hartree,et al.  On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer , 1937, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  A. Salama,et al.  HIGHER-ORDER METHOD FOR SOLVING FREE BOUNDARY-VALUE PROBLEMS , 2004 .

[16]  Internal separated flows at large Reynolds number , 1980 .

[17]  John P. Boyd,et al.  The Blasius Function in the Complex Plane , 1999, Exp. Math..

[18]  R. M. Cotta,et al.  Benchmark results for internal forced convection through integral transformation , 1996 .

[19]  H. Schlichting.  Boundary Layer Theory , 1955 .