MHD oblique stagnation-point flow of a Newtonian fluid

Abstract

Abstract. The steady two-dimensional oblique stagnation-point flow of an electrically conducting Newtonian fluid in the presence of a uniform external electromagnetic field (E0, H0) is analyzed, and some physical situations are examined. In particular, if E0 vanishes, H0 lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected, it is proved that the oblique stagnation-point flow exists if, and only if, the external magnetic field is parallel to the dividing streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions, and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analyzed; this depends on the Hartmann number if H0 is parallel to the dividing streamline.

MHD oblique stagnation-point flow of a micropolar fluid

“…As far as |x s | is concerned, if β − α increases from a negative value to zero, |x s | decreases and so x s approaches the origin, otherwise, as β − α increases from zero to a positive value, |x s | increases and so x s departs from the origin. The same results were also found for Newtonian fluids in [3]. Moreover from Table 1 we see that x p and x s lie on the same side of the origin, and m s m i is constant once c 1 , c 2 , c 3 are fixed.…”

“…The consequent values of α, φ We see that η γ is always greater than η φ , as in the Newtonian case ( [3]). Hence the influence of the viscosity on the velocity appears only in a layer of thickness η γ lining the boundary.…”

“…In this paper we extend the results of [3] about Newtonian fluids to incompressible homogeneous micropolar fluids assuming potential flow far from the boundary and prescribing the strict adherence condition on the flat plane boundary. First of all, we summarize the results of [3] concerning an inviscid fluid, and analyze three cases, which are significant from a physical point of view.…”

“…First of all, we summarize the results of [3] concerning an inviscid fluid, and analyze three cases, which are significant from a physical point of view. In the first two cases, an external constant field, either electric or magnetic, is impressed parallel to the rigid wall.…”

“…The paper is organized in this way: In Section 2 we summarize the results in [3] for an inviscid fluid. Section 3 is devoted to treat the same physical problems for a micropolar fluid.…”