MHD orthogonal stagnation-point flow of a micropolar fluid with the magnetic field parallel to the velocity at infinity

An exact solution is obtained for the steady MHD plane orthogonal stagnation-point flow of a homogeneous, incompressible, electrically conducting micropolar fluid over a rigid uncharged dielectric at rest. The space is permeated by a not uniform external magnetic field He and the total magnetic field H in the fluid is parallel to the velocity at infinity. The results obtained reveal many interesting behaviours of the flow and of the total magnetic field in the fluid and in the dielectric. In particular, the thickness of the layer where the viscosity appears depends on the strength of the magnetic field. The effects of the magnetic field on the velocity and on the microrotation profiles are presented graphically and discussed

MHD micropolar nanofluid flow over an exponentially stretching/shrinking surface: triple solutions

In this study, the problem of MHD micropolar nanofluid boundary layer flows over an exponentially stretching/shrinking sheet with radiation and suction effect is considered. The Buongiorno’s nanofluid model is applied to the problem. The governing equations are first transformed to the coupled nonlinear similarity equations by using similarity transformations. The resulting equations which is in ordinary differential equations form are then solved numerically by using shooting method.Triple solutions are observed to exist for the flows. A comparison with existing solutions in literature for specific case are made to assess the accuracy of the present results. Further, the flows profiles are examined, and it is found that the presence of suction parameter will contribute the occurrences of triple solutions

MHD stagnation-point flow over a stretching/shrinking sheet in a micropolar fluid with a slip boundary

The problem of stagnation point flow over a stretching/shrinking sheet immersed in a micropolar fluid is analyzed numerically. The governing partial differential equations are transformed into a system of ordinary (similarity) differential equation and are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The effects of various parameters on the velocity and the angular velocity as well as the skin friction coefficient and the couple stress are shown in tables and graphs. The noticeable results are found that the micropolar and the slip parameters decrease the skin friction coefficient and the couple stress in the existence of magnetic field. Dual solutions appear for certain range of the shrinking strength. A stability analysis is performed to determine which one of the solutions is stable. Practical applications include polymer extrusion, where one deals with stretching of plastic sheets and in metallurgy that involves the cooling of continuous strips

Rotating unsteady multi-physico-chemical magneto-micropolar transport in porous media : Galerkin finite element study

In this paper, a mathematical model is developed for magnetohydrodynamic (MHD), incompressible, dissipative and chemically reacting micropolar fluid flow, heat and mass transfer through a porous medium from a vertical plate with Hall current, Soret and Dufour effects. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations for momentum, heat, angular momentum and species conservation are transformed into dimensionless form under the assumption of low Reynolds number with appropriate dimensionless quantities. The emerging boundary value problem is then solved numerically with a Galerkin finite element method employing the weighted residual approach. The evolution of translational velocity, micro-rotation (angular velocity), temperature and concentration are studied in detail. The influence of many multi-physical parameters in these variables is illustrated graphically. Finally, the friction factor, surface heat transfer and mass transfer rate dependency on the emerging thermo-physical parameters are also tabulated. The finite element code is benchmarked with the results reported in the literature to check the validity and accuracy under some limiting cases and an excellent agreement with published solutions is achieved. The study is relevant to rotating MHD energy generators utilizing non-Newtonian working fluids and also magnetic rheo-dynamic materials processing systems

MHD orthogonal stagnation-point flow of a micropolar fluid with the magnetic field parallel to the velocity at infinity

An exact solution is obtained for the steady MHD plane orthogonal stagnation-point flow of a homogeneous, incompressible, electrically conducting micropolar fluid over a rigid uncharged dielectric at rest. The space is permeated by a not uniform external magnetic field He and the total magnetic field H in the fluid is parallel to the velocity at infinity. The results obtained reveal many interesting behaviours of the flow and of the total magnetic field in the fluid and in the dielectric. In particular, the thickness of the layer where the viscosity appears depends on the strength of the magnetic field. The effects of the magnetic field on the velocity and on the microrotation profiles are presented graphically and discussed

MHD stagnation-point flow

The flow near a stagnation-point is a fundamental topic in fluid dynamics and it has been studied by several researches during the past decades because of its relevant applications. In this Thesis we investigate the influence of the electromagnetic field on the stagnation-point flow of a Newtonian or a micropolar fluid. To this end we consider three types of such a motion: plane orthogonal, plane oblique and three-dimensional. We take into consideration a fluid which moves towards a flat surface. We descrive several situations which are relevant from a physical point of view when an external uniform or not uniform electromagnetic field is impressed. Actually, we have prove that if the external magnetic field is uniform and the induced magnetic field is neglected, then the stagnation-point flow exists if, and only, if the external magnetic field has some suitable directions. Further, we compute the induced magnetic field in the other cases. We prove also that if the external magnetic field is not uniform and it is parallel to the velocity at infinity then the three-dimensional stagnation-point flow is possible if and only if it is axisymmetric. In all the cases here considered, the MHD PDEs which govern the motion are reduced to a system of nonlinear ODEs. These boundary values problems are then integrated numerically and some graphics and tables are furnished in order to show the behaviour of the solution near the obstacle