Numerical and asymptotic study of non‐axisymmetric magnetohydrodynamic boundary layer stagnation‐point flows

Abstract

Both numerical and asymptotic analyses are performed to study the similarity solutions of three‐dimensional boundary‐layer viscous stagnation point flow in the presence of a uniform magnetic field. The three‐dimensional boundary‐layer is analyzed in a non‐axisymmetric stagnation point flow, in which the flow is developed because of influence of both applied magnetic field and external mainstream flow. Two approaches for the governing equations are employed: the Keller‐box numerical simulations solving full nonlinear coupled system and a corresponding linearized system that is obtained under a far‐field behavior and in the limit of large shear‐to‐strain‐rate parameter (λ). From these two approaches, the flow phenomena reveals a rich structure of new family of solutions for various values of the magnetic number and λ. The various results for the wall stresses and the displacement thicknesses are presented along with some velocity profiles in both directions. The analysis discovered that the flow separation occurs in the secondary flow direction in the absence of magnetic field, and the flow separation disappears when the applied magnetic field is increased. The flow field is divided into a near‐field (due to viscous forces) and far‐field (due to mainstream flows), and the velocity profiles form because of an interaction between two regions. The magnetic field plays an important role in reducing the thickness of the boundary‐layer. A physical explanation for all observed phenomena is discussed. Copyright © 2017 John Wiley & Sons, Ltd.

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

“…for the above streamfunctions given in (5). Plugging the ansatz defined in (5) and (6) in the momentum boundary-layer equations (3), we get the coupled nonlinear ordinary differential equations as…”

“…The solutions exist only in the range −1≤ α ≤0. However, the flow in the 3‐dimensional boundary‐layers is mainly dominated by the mainstream flows U = U ∞ x and V = V ∞ y , which are further superposed onto U ( x , y )= U ∞ x + V ∞ y and V ( x , y )= V ∞ x + U ∞ y so that the constraint on α can be removed (Weidman), and also further extended for the applied magnetic field in the boundary‐layer flow (Kudenatti and Kirsur). Note that in these studies, the shear flows form an irrotational flow outside the boundary layer.…”

Numerical and perturbative analysis on non-axisymmetric Homann stagnation-point flow of Maxwell fluid

“…The analysis of heat transfer in the unsteady case on Homann nonaxisymmetric stagnation-point flow over a rigid surface was made by Mahapatra and Sidui [25]. The asymptotic and numerical explanation of non-axisymmetric MHD boundary-layer stagnation-point flow was obtained by Kudenatti and Kirsur [26]. They found out that viscous fluid flow is due to the applied magnetic field and the effects of the outer stream.…”

Computational and asymptotic methods for three-dimensional boundary-layer flow and heat transfer over a wedge

“…Previously, Davey [8] and Davey and Schofield [9] have considered self similar solutions for the three-dimensional boundary-layer flow where outer mainstream irrotational flows are assumed in linear forms U ¼ U 1 x and V ¼ V 1 y, where U 1 and V 1 are strain rates and x and y are distances from leading edge, and the solutions exist in the range À1 c 0. The flow in three-dimensional flow is mainly dominated by potential flows U ¼ U 1 x and V ¼ V 1 y, which are further superposed into Uðx; yÞ ¼ U 1 x þ V 1 y, so that the condition on c can be removed [10], and was extended for the applied magnetic field in the boundary-layer flow [11]. Furthermore, that the outer mainstream flows were approximated by a power of distances from the leading boundary-layer edge, in the form Uðx; yÞ ¼ U 1 ðx þ yÞ m and V ¼ V 1 ðx þ yÞ m , where m is a constant [12] which will provoke significantly a different flow structure.…”