Enhanced and reduced natural convection using magnetic fluid in a square cavity

Natural convection using a magnetic fluid was studied in a square cavity under the influence of a permanent magnet. The aim was to explore the degree by which heat transfer may be controlled, enhanced or reduced, by investigating a set of different distances of a permanent magnet to the cavity. These distances of the magnet were set such that the cavity was in some cases fully dominated by buoyancy or by the magnetic body force and in other cases partly dominated by either of both body forces in different parts of the fluid. The effect on heat transfer was characterised by an averaged Nusselt number, Rayleigh and magnetic Rayleigh number. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Locomotion based on the control of the shape of magnetic fluid surfaces and of magnetizable media

The realization of locomotion based on the deformation of a free surface of a magnetic fluid layer in a traveling magnetic field is studied. A plane flow of an incompressible viscous magnetic fluid layer on a horizontal surface in a nonuniform magnetic field and a plane two-layers flow of incompressible viscous magnetic fluids between two parallel solid planes in a magnetic field is considered. Also the flow of an incompressible viscous magnetic fluid layer on a cylinder in a nonuniform magnetic field is an object of investigation. The deformation and the motion of a body made by a magnetizable polymer in an alternating magnetic field are experimentally studied. The cylindrical body (worm) which is located in a cylindrical tube is analyzed. These effects can be used in designing autonomous mobile robots without a hard cover. Such robots can be employed in clinical practice and biological investigations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic field in a turbulent conducting fluid

The problem of magnetic field in conducting turbulent, incompressible fluid is considered. The velocity of the fluid is taken to be independent of the magnetic field and is described by a Gaussian field, ‘white noise’ in time with smooth space correlation. The main result is that no fast dynamo (by which is meant almost sure exponential growth of magnetic field) can exist for an incompressible fluid when the magnetic viscosity is positive. For d = 2, sharper results are obtained; the magnetic field dies out when the magnetic viscosity is strictly positive. Furthermore, when d = 2, existence and characterization of invariant measure are given for d = 2 when the magnetic viscosity is zero. The results are compared to those discussed by Baxendale and Rosovskii in [2]     

Propagation of harmonic waves in prestressed fiber viscoelastic thick tubes filled with a viscous dusty fluid

In this work, propagation of harmonic waves in initially stressed cylindrical viscoelastic thick tubes filled with a Newtonian fluid is studied. The tube, subjected to a static inner pressure P_i and a positive axial stretch λ, will be considered as an incompressible viscoelastic and fibrous material. The fluid is assumed as an incompressible, viscous and dusty fluid. The field equations for the fluid are obtained in the cylindrical coordinates. The governing differential equations of the tube’s viscoelastic material are obtained also in the cylindrical coordinates utilizing the theory of small deformations superimposed on large initial static deformations. For the axially symmetric motion the field equations are solved by assuming harmonic wave solutions. A closed form solution can be obtained for equations governing the fluid body, but due to the variability of the coefficients of resulting differential equations of the solid body, such a closed form solution is not possible to obtain. For that reason, equations for the solid body and the boundary conditions are treated numerically by the finite-difference method to obtain the effects of the thickness of the tube on the wave characteristics. Dispersion relation is obtained using the long wave approximation and, the wave velocities and the transmission coefficients are computed.     

NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity

The effects of dependence on temperature of the viscosity and electric conductivity, Reynolds number and particle concentration on the unsteady MHD flow and heat transfer of a dusty, electrically conducting fluid between parallel plates in the presence of an external uniform magnetic field have been investigated using the network simulation method (NSM) and the electric circuit simulation program Pspice. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field perpendicular is applied to the plates. We solved the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. With this method, only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. Velocity and temperature are studied for different values of the viscosity and magnetic field parameters and for different particle concentration and upper wall velocity.     

Study of magnetohydrodynamic pulsatile flow in a constricted channel

The present work reports the study of steady and pulsatile flows of an electrically conducting fluid in a differently shaped locally constricted channel in presence of an external transverse uniform magnetic field. The governing nonlinear magnetohydrodynamic equations simplified for low conducting fluids are solved numerically by finite difference method using stream function-vorticity formulation. The analysis reveals that the flow separation region is diminished with increasing values of magnetic parameter. It is noticed that the increase in the magnetic field strength results in the progressive flattening of axial velocity. The variations of wall shear stress with increasing values of the magnetic parameter are shown for both steady and pulsatile flow conditions. The streamline and vorticity distributions in magnetohydrodynamic flow are also shown graphically and discussed.     

Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.     

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

Mathematical modeling of coupled turbulent flow and solidification in a single belt caster with electromagnetic brake

A mathematical model has been developed to simulate turbulent fluid flow and solidification in the presence of a DC magnetic field in an extended nozzle for metal delivery to a single belt caster. This paper reports on predicted effects of DC magnetic field conditions in modifying flows and solidification behavior in the metal delivery system. It is shown that the application of a DC magnetic brake to the proposed system can result in a reasonably uniform feeding of melt onto the cooled moving belt. This, in turn, optimises the rate of even shell growth along the chilled substrate. In order to account for the effects of turbulence, a revised low-Reynolds k–ε turbulent model was employed. A Darcy-porosity approach was used to simulate fluid flow within the mushy solidification region. Simulations were carried out for plain carbon steel strip casting. The fully coupled transport equations were numerically solved using the finite volume method. The computed flow patterns were compared with those reported in the literature. The performance of the magnetic flow control device proposed in this work is evaluated and compared with flow modifications obtained by inserting a ceramic filter within the reservoir.     

Rayleigh problem for a MHD Sisko fluid

The problem of unsteady unidirectional flow of an incompressible Sisko fluid bounded by a suddenly moved plate is studied. The fluid is magnetohydrodynamic (MHD) in the presence of a time-dependent magnetic field applied transversely to the flow. The non-linear flow problem arising from the laws of momentum, mass and suitable boundary and initial conditions is solved analytically using Lie symmetry method. The manner in which the various emerging parameters affect the structure of the velocity is delineated.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Nonaxisymmetric Free Convection Flow over a Rotating Disk in a Viscoelastic fluid with Magnetic Field

The non axisymmetric motion produced by a buoyancy-induced secondary flow of a viscoelastic fluid over an infinite rotating disk in a verticalplane with a magnetic field applied normal to the disk has been studied.The governing Navier Stokes equations and the energy equation admit a self similar solution. The system of ordinary differential equations has been solved numerically using Runge-Kutta Gill subroutine.The turning moment for the viscoelastic fluid is found to be less than that of the Newtonian fluid but the turning moment is increased due to the magnetic parameter. The resultant force due to the buoyancy-induced secondary flow increases with the magnetic parameter but reduces as the viscoelastic parameter increases. The quantity of fluid, which is pumped outwards due to the centrifuging action of the disk, for the viscoelastic fluid is more than that of the Newtonian fluid. The buoyancy-induced secondary flow boundary layer is much thicker than the primary boundary layer thickness. The thermal boundary layer due to the primary flow increases with the magnetic parameter decreases as the viscoelastic parameter increases. The heat transfer increases with the viscoelastic parameter but decreases as the magnetic parameter increases. The effect of the viscoelastic parameter is more pronounced on the secondary flow than on the primary flow.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Note on the fall of an axisymmetric body in a perfect fluid over a horizontal ramp

In this note, we consider the fall of an axisymmetric body in a perfect fluid over a ramp. It was shown in [12] that the possibility of a collision between the body and the ramp is related to the asymptotics of the so-called added mass when the distance between the ramp and the body goes to 0. We propose here a new method to compute this added mass, which provides simultaneously an approximation of an associated fluid velocity field in the gap between the ramp and the body.     

Dynamo Action of Isotropically Driven Motions of a Rotating Fluid

Fluid motions are driven by a random isotropic body force in a rotating system. The fluid is incompressible and infinite in extent. The dynamo action of the resulting fluid motions is investigated by Fourier decomposition. The global effects of the turbulent motions are expressed in terms of gradients of the local mean magnetic field, Bo . Two aspects of the problem are novel. The spectral approach is used to solve for the turbulent quantities while gradients of Bo are retained, and secondly a non-zero mean emf. is obtained from an entirely isotropic forcing.     

Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M , the Hartmann number and N_ratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of [6]. It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.     

An estimate of the time of a direct-axis collision of a body of finite mass and a semiinfinite cylindrical shell with fluid

The problem of a direct-axis collision of a body affinite mass and a semi-infinite cylindrical shell with fluid is considered, and is solved using an analytic-numerical method, which is based on an application of the Laplace-Carson transform with its subsequent numerical inverse. An expression is found for the interaction force for the body and the hydro-elastic system, which allows us to determine the time of collision. Numerical results of calculations of the interaction force and the time of collision are given.Translated from Dinamicheskie Sistemy, No. 7, pp. 29–32, 1988.     

Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction

An analysis is carried out to study the flow, chemical reaction and mass transfer of a steady laminar boundary layer of an electrically conducting and heat generating fluid driven by a continuously moving porous surface embedded in a non-Darcian porous medium in the presence of a transfer magnetic field. The governing partial differential equations are converted into ordinary differential equations by similarity transformation and are solved numerically by using the finite element method. The results obtained are presented graphically for velocity, temperature and concentration profiles, as well as the Sherwood number for various parameters entering into the problem.     

Effect of magnetic field on the flow of a fourth order fluid

A study is made of the flow engendered in a semi-infinite expanse of an incompressible non-Newtonian fluid by an infinite rigid plate moving with an arbitrary velocity in its own plane. The fluid is considered to be fourth order and electrically conducting. A magnetic field is applied in the transverse direction to the flow. The nonlinear problem is solved for constant magnetic field analytically using reduction methods as well as numerically and expressions for the velocity field are obtained. Limiting cases of interest can be deduced by choosing suitable parametric values.