title: Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet.
abstract: In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.
authors.affiliation: School of Mathematical Sciences, Faculty of Science &Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.
authors.forename: Kohilavani
authors.initials: K
authors.lastname: Naganthran
authors.affiliation: School of Mathematical Sciences, Faculty of Science &Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.
authors.forename: Roslinda
authors.initials: R
authors.lastname: Nazar
authors.affiliation: Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania.
authors.forename: Ioan
authors.initials: I
authors.lastname: Pop