IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X. Volume 10, Issue 3 Ver. III (May-Jun. 2014), PP 49-54 www.iosrjournals.org www.iosrjournals.org 49 | Page Hydromagnetic Effects on Fluid Flow and Internal Flow Separation in a Linearly Diverging Channel M. Saiful Islam Mallik 1 , Tahmina Begum 2 , Md. Minarul Haque 3 , Rebeya Akter 4 1 Assistant Professor, Department of Arts and Sciences, Ahsanullah University of Science and Technology, Dhaka. 2 Assistant Professor, Department of Mathematics, Dhaka City College, Dhaka. 3 Lecturer, Department of Mathematics, Dhaka City College, Dhaka. 4 Lecturer, Department of Mathematics, Jagannath University, Dhaka. Abstract: In this paper, we investigated the hydromagnetic steady flow of a viscous conducting fluid in a two- dimensional uniform width linearly diverging channel. For this investigation the effect of an externally applied homogeneous magnetic field on the development of velocity profiles and internal flow separation in the diverging channel are observed. The solution for the flow governing non-linear differential equation is found using perturbation method together with Pade´ approximation technique. The investigation results reveal that the requirement of flow Reynolds number for the development of internal flow separation increases with an increase in magnetic field intensity. Furthermore, the behavior of velocity profiles under the effect of magnetic field is discussed. Keywords: Linear diverging channel, internal flow separation, magnetic field, Pade´ approximants. I. Introduction The study of electrically conducting viscous fluid flowing through diverging channels under the influence of an external magnetic field is not only fascinating theoretically, but also finds applications in mathematical modeling of several industrial and biological systems such as magnetohydrodynamics (MHD) generators, plasma studies, nuclear reactors, industrial metal casting, controlling of molten metal flows, etc. The theoretical study also finds application in the area of motion of liquid metals or alloys in the cooling systems of advanced nuclear reactors. In the past few years, several simple flow problems associated with classical hydrodynamics have received new attention within the more general context of MHD. A survey of MHD studies in the technological fields can be found in (Moreau 1990). In modern times the theory of flow convergent-divergent channels has many applications in aerospace, chemical, civil, environmental, mechanical and bio-mechanical engineering as well as in understanding rivers and canals. A numerical investigation of the study of hydromagnetic flows in a slowly varying exponentially diverging channel under the effect of an externally applied homogeneous magnetic field was performed by Makinde and Mhone (2006). For this they have used perturbation method and Pade´ approximation technique (Baker Jr. 1975). The mathematical investigations of this type of problem have been studied by Rao and Deshikachar (1986) and (Makinde 1995). In the present paper, the steady hydromagnetic flows in a two-dimensional uniform width linearly diverging channel under the influence of an externally applied homogeneous magnetic field have been investigated. The objective of this study is to analyze the fluid velocity profiles and to determine numerically the effect of the externally applied homogeneous magnetic field on the development of internal flow separation as flow Reynolds number increases using perturbation method together with Pade´ approximation technique. II. Mathematical Formulation Consider the steady flow of an incompressible viscous conducting fluid through an uniform width linearly diverging channel under the influence of an externally applied homogeneous magnetic field as shown in Fig. 1.