On the generalized Falkner–Skan equation governing boundary layer flow of a FENE-P fluid

Abstract

In this work, we consider 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. Assuming that the Reynolds number Re and the Weissenberg number He satisfy the condition Re We 2 ≪ 1 , we will show that the stream function is modeled by a generalized Falkner–Skan equation. Intuitively, this means that 1 / He 2 grows much faster than Re , that is Re = o ( 1 / He 2 ) . Further, it is shown that this extended Falkner–Skan equation can be reduced to the classical Falkner–Skan equation via a function transformation. Finally, a decomposition algorithm is implemented for the numerical solution of the governing equation and an estimate of the skin friction coefficient is obtained.