MHD THREE-DIMENSIONAL STAGNATION-POINT FLOW OF A MICROPOLAR FLUID

The steady three-dimensional stagnation-point flow of an electrically conducting micropolar fluid in the absence and in the presence of a uniform external electromagnetic field (E0,H0) is analyzed and some physical situations are examined. In particular, we proved that if we impress an external magnetic field H0, and we neglect the induced magnetic field, then the steady MHD three-dimensional stagnation-point flow of such a fluid is possible if, and only if, H0 has the direction parallel to one of the axes. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions. Moreover in the presence of an external magnetic field H0, it is found that the flow of a micropolar fluid has to satisfy an ordinary differential problem whose solution depend on H0 through the Hartmann number M. Finally, the skin-friction components along the axes are computed

MHD OBLIQUE STAGNATION-POINT FLOW OF A MICROPOLAR FLUID

The steady two-dimensional oblique stagnation-point flow of an electrically conducting micropolar 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 stagnationpoint 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 three dimensionless material parameters, and also on the Hartmann number if H0 is parallel to the dividing streamline

MHD oblique stagnation-point flow of a Newtonian fluid

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 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

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

Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

Purpose – This paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated. Design/methodology/approach – The governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB. Findings – If the temperature of the obstacle Tw coincides with the environment temperature T0, then the motion reduces to the usual orthogonal stagnation-point flow; if Tw=T0, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies. Originality/value – The present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature

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

An exact solution for the 3D MHD stagnation-point flow of a micropolar fluid

The influence of a non-uniform external magnetic field on the steady three dimensional stagnation-point flow of a micropolar fluid over a rigid uncharged dielectric at rest is studied. The total magnetic field is parallel to the velocity at infinity. It is proved that this flow is possible only in the axisymmetric case. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations by a similarity transformation, before being solved numerically. The effects of the governing parameters on the fluid flow and on the magnetic field are illustrated graphically and iscussed

Poiseuille-Couette flow of a hybrid nanofluid in a vertical channel: Mixed magneto-convection

The study of mutual interaction between flow and external magnetic field, as well as the influence of temperature on the motion, is crucial for new classes of materials involved in nanotechnologies. This paper considers a very common situation where a hybrid nanofluid fills a vertical plane channel with a moving wall. Since the nanofluid is Boussinesquian the flow is induced by the buoyancy and Lorentz forces together with a constant pressure gradient. This problem has many industrial applications so that it is of relevant interest. Using a steady and laminar flow, an exact solution for the ODEs which govern the motion has been found. This is the first time an analytical solution is developed for the problem here considered. Analytical expressions for velocity profile and magnetic field are exhibited graphically. Effect of parameters on the flow characteristics has been discussed also in the case of some real hybrid nanofluids (H2O with Al2O3 and Cu, H2O with Ag and MgO, C2H6O2 with TiO2 and Fe3O4). We also find that the presence of two different types of particles determines an increase in the velocity of the nanofluid in accordance with experimental studies. As usual the presence of the external magnetic field causes a decrease in the velocity. Finally, the reverse flow phenomenon is discussed