Applied Mathematics, 2015, 6, 466-475 Published Online March 2015 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2015.63044 How to cite this paper: Mat, N.A.A., Arifin, N.Md., Nazar, R. and Bachok, N. (2015) Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface. Applied Mathematics, 6, 466- 475. http://dx.doi.org/10.4236/am.2015.63044 Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface Nor Azian Aini Mat 1 , Norihan Md. Arifin 2* , Roslinda Nazar 3 , Norfifah Bachok 4 1 Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak, Malaysia 2 Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia 3 School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Selangor, Malaysia 4 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia Email: * norihanarifin@yahoo.com Received 14 February 2015; accepted 4 March 2015; published 10 March 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrink- ing/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter ( ) δ , the thermal slip parameter ( ) β , the curva- ture parameter ( ) γ and the velocity ratio parameter ( ) ca . The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by () ′′ 0 f and () ′ 0 θ − , re- spectively. The numerical results show that the velocity slip parameter δ increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter δ causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder ( ) 0 ca < are non-unique with dual solutions, which is different from a stretching cylinder ( ) 0 ca > case. Finally, it is also found that the values of () ′′ 0 f and () ′ 0 θ − increase as the curvature parameter γ increases. * Corresponding author.