Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Hydromagnetic convection in a rotating annulus with an azimuthal magnetic field

The problem of convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus (angular frequency, ) in the presence of a homogeneous magnetic field (B) in the azimuthal direction is considered. The small gap approximation is used together with rigid cylindrical boundaries. The onset of convection occurs in the form of axial, axisymmetric or oblique rolls. The angle between the roll axis and the axis of rotation depends of the ratio between the Chandrasekhar number, QB², and the Coriolis number, . Fully three-dimensional numerical simulations as well as Galerkin representations for roll patterns including the subsequent stability analysis are used in the theoretical investigation. At finite amplitudes, secondary transitions to 3D-hexarolls and to spatio-temporal chaos are found. Overlapping regions of pattern stability exist such that the asymptotically realized state may depend on the initial conditions. PACS 47.27.-i, 47.65.+a     

Unsteady free convection flow under the influence of a magnetic field

Summary The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, andx-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer andx-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer andx-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction andx-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.

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Instationäre freie Konvektionsströmung unter dem Einfluß eines magnetischen Feldes

Übersicht Untersucht wurde die instationäre freie Konvektionsgrenzschicht am Ruhepunkt eines zweidimensionalen und achsensymmetrischen umströmten Körpers bei vorgegebenem Wärmefluß bzw. bei vorgegebener Temperatur an der Oberfläche. Das magnetische Feld wird parallel zur Oberfläche angelegt, und der Einfluß des induzierten magnetischen Feldes wurde berücksichtigt. Es stellt sich heraus, daß bei bestimmter, zeitlicher Potenzgesetzverteilung des Wärmeflusses bzw. der Temperatur und des magnetischen Feldes an der Oberfläche die geltenden Grenzschichtgleichungen örtlich eine selbstähnliche Lösung erlauben. Die sich ergebenden nichtlinearen gewöhnlichen Differentialgleichungen wurden mittels einer Finite-Element-Methode und einer Shooting-Methode mit Newtonschen Korrekturen für fehlende Anfangsbedingungen gelöst. Die Ergebnisse zeigen, daß die Oberflächenreibung und die Wärmeübergangskoeffizienten sowie diex-Komponente des induzierten magnetischen Feldes an der Oberfläche mit dem angelegten magnetischen Feld zunehmen. Im allgemeinen sind die Oberflächenreibung, der Wärmeübergang und diex-Komponente des induzierten magnetischen Feldes im achsensymmetrischen Fall größer als die entsprechenden Werte im zweidimensionalen Fall. Außerdem verändern sich diese Werte beim zeitlichen Abfallen des Wärmeflusses an der Oberfläche bzw. der Temperatur in höherem Maße als bei der zeitlichen Zunahme dieser Werte. Die Oberflächenreibung, der Wärmeübergang und diex-Komponente des induzierten magnetischen Feldes werden durch die magnetische Prandtl-Zahl erheblich beeinflußt; sie nehmen mit abfallender magnetischer Prandtl-Zahl zu. Die Oberflächenreibung und diex-Komponente des magnetischen Feldes nehmen mit dem Wärmeableitungsparameter zu, der Wärmeübergang jedoch fällt ab.

     

On hydromagnetic free convection in the presence of induced magnetic field

Free convection in an electrically conducting fluid in a vertical channel under the action of an applied magnetic field has been discussed. The induced magnetic field has been included in the flow analysis. The equations describing the transport processes have been solved numerically. The effects of these processes, parameterized by a number of non-dimensional parameters have been discussed on the developing velocity and induced magnetic field profiles.     

Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.     

Hydromagnetic flow near an accelerated plate in the presence of a magnetic field

Summary Hydromagnetic flow of a viscous incompressible fluid due to uniformly accelerated motion of an infinite flat plate in the presence of a magnetic field fixed relative to the plate, is discussed. It is assumed that the induced magnetic field is negligible compared to the imposed magnetic field. It is observed under these conditions that the velocity at any point and at any instant decreases when the strength of the magnetic field is increased.     

Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field

The problem of steady laminar magnetohydrodynamic （MHD） mixed con- vection stagnation-point flow of an incompressible viscous fluid over a vertical stretch- ing sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an exter- nally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A 〉 1 and A ~ 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow.     

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.     

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion, induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.     

Magnetic effects on the flow with a great magnetic reynolds number by the presence free convection and mass transfer

An analysis of the effects of a magnetic field on the flow past an infinite plate by the presence free-convection and mass transfer is considered when the magnetic Reynolds number of the flow is not small. The influence of magnetic parameterM on the velocity and the skin-friction is discussed with the help of graphs, when the plate is being cooled by the free convection currents.

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Magnetische Einflüsse auf eine Strömung mit großen magnetischen Reynolds-Zahlen unter Anwesenheit freier Konvektion und Stoffübertragung

Zusammenfassung Es werden die Einflüsse eines magnetischen Feldes auf die Strömung an einer unendlichen Platte mit freier Konvektion und Stofftransport analysiert, wobei die magnetische Reynolds-Zahl der Strömung nicht klein ist. Diskutiert wird der Einfluß des magnetischen ParametersM auf die Geschwindigkeit und die Oberflächenreibung mit Hilfe graphischer Methoden, wobei die Platte durch die freie Konvektion gekühlt wird.

     

Nonstationary conducting free flow in a transverse magnetic field

In magnetohydrodynamic flow the viscous friction at the walls can be substantial. The role of viscous friction can be considerably reduced by using a free or a semirestricted flow of the conducting fluid. Nonstationary phenomena in one-dimensional motion of a free plane incompressible fluid flow in a transverse magnetic field are examined. The narrow sides of the flow come into contact with the sectional electrodes connected through external circuits with an active-inductive load. The magnetic Reynolds number and the magnetody-dynamic interaction parameter are assumed to be large. When the electric field due to electromagnetic induction in the channel is much smaller than the field due to the external circuits, the problem can be reduced to the characteristic Cauchy problem for a quasilinear hyperbolic system of first-order equations which can be solved by the method of characteristics using a computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 34–39, July–August, 1970.     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

Dissipation effects on MHD free convection flow past a semi-infinite vertical plate

Viscous and Joule dissipation effects are considered on MHD free convection flow past a semi-infinite isothermal vertical plate under a uniform transverse magnetic field. Series solutions in powers of a dissipation number (=gx/c _p) have been employed and the resulting ordinary differential equations have been solved numerically. The velocity and temperature profiles are shown on graphs and the numerical values of ₁(0)/₀(0) (, temperature function) have been tabulated. It is observed that the dissipation effects in the MHD case become more dominant with increasing values of the magnetic field parameter (=M ²/(Gr _x /4)^1/2) and the Prandtl number.     

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion,magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.     

The influence of a magnetic field on free convection in a finite vertical channel

An approximate analytical solution is presented for developing free convection flows of electrically conducting fluids between finite vertical channels which are subjected to a uniformly applied transverse magnetic field. Specifically, the basic approximation lies in the linearization of the governing boundary layer type of equations. It is demonstrated that the application of a transverse magnetic field reduces the induced flow rate in the channel and the heat transfer to the fluid.     

Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier–Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (, ). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.     

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.     

Energy stability of modulation driven porous convection with magnetic field

Meccanica - Free convective onset in a bottom heated porous medium under the influence of transverse magnetic field is studied within the framework of nonlinear theory. Simple harmonic time...