title: Dual Solutions for Nonlinear Flow Using Lie Group Analysis.
abstract: `The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered.
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Awais
authors.affiliation: Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan.
authors.forename: Tasawar
authors.initials: T
authors.lastname: Hayat
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.
authors.forename: Sania
authors.initials: S
authors.lastname: Irum
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.
authors.forename: Salman
authors.initials: S
authors.lastname: Saleem
mesh_terms: D018481:Convection; D057446:Hydrodynamics; D008962:Models, Theoretical; D016062:Porosity; D012996:Solutions / Q000737:chemistry*
chemical_list: D012996:Solutions