MHD stagnation‐point flow towards a shrinking sheet

Abstract

Purpose -The purpose of this paper is to theoretically investigate the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied. Design/methodology/approach -A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller-box method. Findings -The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non-aligned and a reverse flow is formed near the surface due to shrinking effect. Practical implications -The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface. Originality/value -The present results are original and new for the MHD flow near the stagnation-point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier–Stokes equations

“…The stagnation flow over a shrinking sheet was investigated by Wang [32]. Finally, we mention the papers by Hayat et al [33] on the magnetohydrodynamic and rotating flow over a permeable shrinking sheet and by Lok et al [34] on the MHD stagnation-point flow towards a shrinking sheet.…”

MHD Mixed Convection Flow of a Non-Newtonian Powell-Erying Fluid Over a Permeable Exponentially Shrinking Sheet

“…The existence and uniqueness of the similarity solution for the flow past a shrinking surface were investigated by Miklavčič and Wang (2006). The flow patterns of various Newtonian and non-Newtonian fluids on a shrinking sheet are discussed by many researchers Fang and Zhang, 2009;Lok et al, 2011;. On the other 2 hand, very limited attention has been given to study the flow over an exponentially stretching/shrinking sheet though it is very significant in numerous engineering problems.…”

Stagnation-Point Flow towards a Stretching Vertical Sheet with Slip Effects

“…On the other hand, Chiam [3] reported the analytical and numerical solutions of the stagnation-point flow over a flat stretching sheet with variable thermal conductivity. Since then, many researchers, such as Mahapatra and Gupta [4,5], Ishak et al [6,7], Layek et al [8], Nadeem et al [9], Bachok et al [10], Bhattacharyya and Layek [11], and Lok et al [12] have investigated the behavior of stagnation-point flow with different aspects and conditions such as considering magnetic field effect, homogeneous-heterogeneous reactions effect, thermal radiation effect, suction/blowing, and micropolar fluid.…”