Numerical solution of a generalized Falkner–Skan flow of a FENE-P fluid

Abstract

The purpose of this article is to introduce a novel strategy for the numerical solution of a viscous boundary layer flow past a flat plate at a non-zero pressure gradient for a viscoelastic fluid governed by the FENE-P model. The stream function of this problem obeys a generalized Falkner–Skan equation. The fundamental method is based on embedding an integral operator, expressed in terms of Green's function of the corresponding linear differential operator, into well-known fixed-point iterative procedures, including Picard's and Mann's. Estimates of the skin friction coefficient are computed. The numerical solutions obtained from the proposed method are compared with the analytical and numerical solutions that exist in the literature. The convergence of the iterative scheme is proved via manipulation of the contraction principle. Numerical experiments and calculations ascertain that the introduced scheme handles the governing equation very efficiently, provides rapid convergence, and yields highly accurate results.

Keywords:

• Falkner–Skan equation
• boundary layer
• FENE-P fluid
• skin friction
• Green's functions
• fixed-point iterative schemes

2010 Mathematics Subject Classifications:

• 65L10
• 76G25

Disclosure statement

No potential conflict of interest was reported by the author(s).