MHD Falkner-Skan Boundary Layer Flow past a Moving Wedge with Suction (Injection)

The behaviour of laminar boundary layer flow field over a solid surface moving with constant speed plays a significant role in several applications of science and technology. This paper examines the steady, laminar incompressible boundary-layer flow of a viscous electrically conducting fluid past a moving wedge with suction (injection) in the presence of an applied magnetic field. The set of partial differential equations governing FalknerSkan wedge flow is first transformed into ordinary differential equation using similarity transformations which is later solved numerically, using an implicit finite difference scheme known as the Keller-box method. Numerical results are presented graphically to illustrate the influence of magnetic parameter and suction/injection on local skin friction coefficient and velocity field. Further, it is demonstrated that magnetic field and suction plays a noteworthy role in controlling the laminar boundary layer separation from the moving wedge surface. Introduction The problem of steady, two-dimensional flow of a viscous incompressible fluid past a static wedge shaped bodies constitutes one of the classical results of the Prandtl’s boundary layer theory. With a similarity transformation the governing boundary layer equation is reduced to an ordinary differential equation, which is well known as the Falkner-Skan equation [9]. The variety of applications and the importance of the FalknerSkan equation for the understanding of the physical features of laminar boundary layer flow have motivated many researchers [2,3,4,6,7,8,10,11,12,13,14], employing various analytical and numerical methods acquiescent for different flow situations. Nevertheless, studies reported above related to the Falkner-Skan boundary layer flow over a fixed wedge placed in a moving fluid. Recently, Anuar Ishak et. al [1] have considered the FalknerSkan problem for the flow past a moving wedge with the application of suction or injection. In recent years a great deal of interest has been generated in the study of magneto-hydrodynamic (MHD) boundary layer research due to its extensive practical applications in technological processes; such as MHD power generator designs, design for cooling of nuclear reactors, construction of heat exchangers, installation of nuclear accelerators, blood flow measurement techniques and on the performance of many other systems using electrically conducting fluids. Further, it has been long recognized that surface mass transfer (suction or injection) energetically influences the development of a boundary layer along a surface and, in particular, can prevent or at least delay separation of the viscous region [15]. In view of the above mentioned applications, the present study investigates the Falkner-Skan boundary layer flow past a moving wedge with an applied magnetic field and suction (injection). Using the similarity transformations, the governing equations have been transformed into a third order ordinary differential equation, which is nonlinear in nature and cannot be solved analytically; consequently, Keller box method has been used for solving it.