Research Article Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder Antonio Mastroberardino 1,2 and J. I. Siddique 1,2 1 School of Science, Penn State Erie, he Behrend College, Erie, PA 16563-0203, USA 2 Department of Mathematics, Penn State University, York Campus, York, PA 17403-3326, USA Correspondence should be addressed to Antonio Mastroberardino; axm62@psu.edu Received 12 April 2014; Accepted 9 June 2014; Published 29 June 2014 Academic Editor: Jinjia Wei Copyright © 2014 A. Mastroberardino and J. I. Siddique. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We perform an analysis of MHD low and heat transfer on a stretching, permeable cylinder. We prove existence of solutions for all values of the relevant parameters and provide uniqueness results in the case of a monotonic solution. he nonlinear boundary value problem that is derived from a similarity transformation of the governing system of nonlinear partial diferential equations is solved numerically and the results are presented with graphs and tables. 1. Introduction he study of axisymmetric stagnation low on a sheet or a cylinder is an important aspect in various industrial applications. Exact solutions were obtained by Homann [1] for axisymmetric stagnation point low on a sheet and by Wang [2] for axisymmetric stagnation low on a circular cylinder. he work of Wang was later extended by Gorla [3] who included an analysis of the heat transfer and by Crane [4] and Wang [5] who considered a stretching cylinder in their studies. A recent study of axisymmetric stagnation low by Ishak et al. [6] included the efects of suction or injection of the luid for low toward a stretching cylinder. Wang and Ng [7] investigated the efects of a partial slip boundary condition. Studies of magnetohydrodynamic low and heat transfer due to a stretching cylinder were performed by Ishak et al. [8] who obtained numerical solutions using the Keller- box method, Joneidi et al. [9] who obtained solutions using the homotopy analysis method, and Butt and Ali [10] who included the efects of entropy generation. Chauhan et al. [11] generalized the results of Joneidi et al. by considering the cylinder to be embedded in a porous medium along with a partial slip boundary condition. Munawar et al. [12] examined unsteady low and heat transfer due to a stretching cylinder in consideration of two general types of thermal boundary conditions. In this paper, we extend the work of Ishak et al. [8] by including the efects of suction/injection and by obtaining existence and uniqueness results for the nonlinear boundary value problem governing the luid low. We provide igures of the velocity and temperature proiles for various values of the system parameters and tables of the relevant boundary derivatives. In addition, we compare our results with the aforementioned studies. 2. Mathematical Formulation Consider the steady laminar low and heat transfer of an incompressible electrically conducting luid induced by an axially stretching cylinder of radius  as depicted in Figure 1. We assume that the low is subject to a uniform magnetic ield of intensity  0 that is perpendicular to the cylinder’s axis of symmetry and that the temperature at the cylinder and the ambient luid temperature are   and  ∞ , respectively. he governing system of nonlinear partial diferential equations for the luid low and heat transfer in terms of the cylindrical coordinate system (,,) is given by [8]   ()+   () = 0, Hindawi Publishing Corporation Advances in Mechanical Engineering Volume 2014, Article ID 419568, 5 pages http://dx.doi.org/10.1155/2014/419568