Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids

•Local self-similar solution for laminar planar jet flow of FENE-P fluids.•Decay of centerline velocity and growth of jet width.•Low elasticity asymptotes for conformation tensor.•Polymer over solvent stress tends to ratio of polymer to solvent viscosities. Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.