Thermal instability of a boundary layer subjected to external electric and magnetic fields

This paper presents a numerical study of the electrical and magnetic fields on thermal instability in a boundary layer. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the electric field parameter, and the Hartmann number. The flow becomes more stable as the magnetic field increases. However, the destabilizing effect is found on the flow when the negative electric field parameter is applied. The results of the present numerical prediction show reasonable agreement with the experimental data in the case of zero Hartmann number and zero electric field parameter in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

磁场和Hall电流对狭窄动脉中血液流动的影响

A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis （stenosis throat）, have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hail parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.     

Combined influence of Hall effect,ion slip,viscous dissipation and Joule heating on MHD heat transfer in a channel

To investigate the combined influence of Hall effect, ion slip, viscous dissipation and Joule heating on the fully developed laminar MHD channel heat transfer, the exact solution of the energy equation is derived assuming a constant wall heat flux, finely segmented electrodes and a small magnetic Reynolds number. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field intensity and Brinkman number, between the Nusselt number considering the Hall effect and that neglecting it. Representative results are presented in diagrams and in tables.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

Effect of magnetic field on thermal instability in mixed convection flow over a rotating boundary layer

Effect of magnetic field on the formation of longitudinal vortices in mixed convection flow over a rotating heated flat plate is presented. The onset position is characterized by the Grashof number, the rotational number, the Prandtl number, the Eckert number, the magnetic field parameter, and the wave number. Negative rotation (clockwise) and external magnetic field stabilize the boundary layer flow. On the contrary, positive rotation (anti-clockwise), the Eckert number, and the Prandtl number destabilize the flow. The numerical data show agreement with the experimental data with the case of zero Hartmann number in the literature.     

MHD duct flows under hydrodynamic “slip” condition

Three classic MHD problems are revisited assuming hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating wall: (1) Hartmann flow; (2) fully developed flow in a rectangular duct; and (3) quasi-two-dimensional (Q2D) turbulent flow. The first two problems have been solved analytically. Additionally to the Hartmann number (Ha), a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions of the paper is that the duct flows with the slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha >> 1 by factor (1+ S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers.     

A computational solution of hydromagnetic‐free convective flow past a vertical plate in a rotating heat‐generating fluid with Hall and ion‐slip currents

Taking Hall and ion‐slip current into account, the unsteady magnetohydrodynamic heat‐generating free convective flow of a partially ionized gas past an infinite vertical plate in a rotating frame of reference is investigated theoretically. A computer program using finite elements is employed to solve the coupled non‐linear differential equations for velocity and temperature fields. The effects of Hall and ion‐slip currents as well as the other parameters entering into the problem are discussed extensively and shown graphically. Copyright © 2006 John Wiley & Sons, Ltd.     

Hydromagnetic flow through uniform channel bounded by porous media

The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible,and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability,Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.     

Hall and ion slip effects on peristaltic flow and heat transfer analysis with Ohmic heating

The peristaltic transport of a magnetohydrodynamic （MHD） fluid is exam- ined for both symmetric and asymmetric channels. Hall and ion slip effects are taken into account. The heat transfer is analyzed by considering the effects of viscous and Ohmic dissipations. The relevant flow problems are first modeled, and then the closed form solutions are constructed under the assumptions of long wavelength and low Reynolds number. The solutions are analyzed through graphical illustration. It is noted that the velocity increases but the temperature decreases with the increases in the Hall and ion slip parameters. The axial pressure gradient is less in magnitude in the presence of Hall and ion slip currents. The Hall and ion slip effects are to decrease the maximum pres- sure against which peristalsis works as a pump. The free pumping flux decreases with the increases in the Hall and ion slip parameters. The increases in the Hall and ion slip parameters result in an increase in the size of the trapped bolus.     

Thermal instability in natural convection flow over a boundary layer subject to external electrical and magnetic fields

This paper presents a numerical study of external electrical and magnetic effects on the formation of longitudinal vortices in natural convection flow over a heated horizontal plate. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The onset position characterized by the Grashof number depends on the Prandtl number, the wave number, the electric field parameter, and the magnetic field parameter. The flow is found more stable as the value of the magnetic field parameter increases. Moreover, the stabilizing effect is also found on the flow when the positive electric field parameter Ec is applied. The results of the present numerical prediction show reasonable agreement with the experimental data with zero magnetic field and electric field parameters in literature.     

Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM–FDM

Unsteady turbulent magnetohydrodynamic nanofluid hydrothermal treatment is studied. The zero-equation turbulence model is used to simulate turbulent flow. The modeling results obtained by applying the hybrid differential transformation method–finite difference method to solve this problem confirm its viability. An analytical procedure is used for finding the effects of the problem parameters. Results indicate that the average Nusselt number over the lower plate depends linearly on volume fraction of nanofluid, Hall parameter, turbulent Eckert number, and Reynolds number whereas it is inversely proportional on the Hartmann number and the turbulent parameter.     

Electro-magneto-hydrodynamic flow of couple stress nanofluids in micro-peristaltic channel with slip and convective conditions

This study explores the effects of electro-magneto-hydrodynamics,Hall currents,and convective and slip boundary conditions on the peristaltic propulsion of nanofluids(considered as couple stress nanofluids)through porous symmetric microchannels.The phenomena of energy and mass transfer are considered under thermal radiation and heat source/sink.The governing equations are modeled and non-dimensionalized under appropriate dimensionless quantities.The resulting system is solved numerically with MATHEMATICA(with an in-built function,namely the Runge-Kutta scheme).Graphical results are presented for various fluid flow quantities,such as the velocity,the nanoparticle temperature,the nanoparticle concentration,the skin friction,the nanoparticle heat transfer coefficient,the nanoparticle concentration coefficient,and the trapping phenomena.The results indicate that the nanoparticle heat transfer coefficient is enhanced for the larger values of thermophoresis parameters.Furthermore,an intriguing phenomenon is observed in trapping:the trapped bolus is expanded with an increase in the Hartmann number.However,the bolus size decreases with the increasing values of both the Darcy number and the electroosmotic parameter.     

Magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer

This paper presents a numerical study of magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer. The criterion for the position marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the rotational Goertler number G_δ,rot, depends on the local rotation number, Reynolds number, the magnetic field parameter, the Prandtl number and the wave number. The results show that positive rotation destabilizes the flow. The flow is found to become more unstable to the vortex mode of instability as the value of magnetic field parameter M increases. The numerical data shows good agreement with the experimental results. Copyright © 2005 John Wiley & Sons, Ltd.     

Hall and ion‐slip effects on three‐dimensional flow of a second grade fluid

This investigation pursues the study of Hall and ion‐slip effects on steady three‐dimensional flow of an incompressible second grade fluid. The partial differential equations are reduced to ordinary differential equations by using similarity variables. The resulting problems are solved by employing homotopy analysis method (HAM). The convergence of derived solutions is ensured. The influence of different physical parameters on the dimensionless velocities is examined by sketching plots. Variation of skin friction coefficients for different involved parameters is seen through tabulated values. Copyright © 2010 John Wiley & Sons, Ltd.     

Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions

The effect of flow slip on the nanofluid boundary layer over a stretching surface is studied. The present results provide a basic understanding on the effects of the slip boundary condition on heat and mass transfer of nanofluids past stretching sheets subject to a convective boundary condition from below. The results show that an increase of thermophoresis parameter or slip factor would decrease the reduced Nusselt number in some cases.     

Magnetic control of natural convection in the horizontal Bridgman configuration using a spectral method: transversal plan

The present study investigates the electromagnetic braking of buoyancy convective flows occurring in differentially heated cavities, filled with low Prandtl, dilute, incompressible and electrically conducting alloys, and subjected to a constant horizontal temperature gradient. In practice, such flows known as ‘Hadley circulation’ are relevant in material processing technologies, such as the horizontal Bridgman configuration. A collocation spectral numerical method is developed to solve the two-dimensional Navier–Stokes equations, modelling the flow phenomena occurring in such configurations, using a vorticity–stream function formulation. The two components of the velocity are deduced from the stream function and the temperature distribution is obtained through the resolution of the energy conservation equation. The results in terms of velocity and temperature distributions for a given Grashof number are obtained for various Hartmann numbers and show that as the Hartmann number increases, the electromagnetic braking of the flow is observed. Moreover, the results illustrate the changes affecting the flow structure which becomes quasi-parallel in the core region of the cavity for sufficiently high values of Ha and the onset of the Hartmann and parallel layers along the boundaries. Also, with increasing Ha, the isotherms are less affected by the convective flow and become parallel to the vertical walls indicating that heat transfer is mainly achieved by conduction.     

Peristaltic transport and heat transfer of a MHD Newtonian fluid with variable viscosity

The influence of temperature‐dependent viscosity and magnetic field on the peristaltic flow of an incompressible, viscous Newtonian fluid is investigated. The governing equations are derived under the assumptions of long wavelength approximation. A regular perturbation expansion method is used to obtain the analytical solutions for the velocity and temperature fields. The expressions for the pressure rise, friction force and the relation between the flow rate and pressure gradient are obtain. In addition to analytical solutions, numerical results are also computed and compared with the analytical results with good agreement. The results are plotted for different values of variable viscosity parameter β, Hartmann number M, and amplitude ratio ?. It is found that the pressure rise decreases as the viscosity parameter β increases and it increases as the Hartmann number M increases. Finally, the maximum pressure rise (σ=0) increases as M increases and β decreases. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions

The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.     

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.     

Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid (blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model. The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function (UDF). Numerical solutions are obtained by the finite volume method based on a nonuniform grid structure. The accuracy and efficiency of the solver are verified through a comparison with the literature. The results are presented graphically for different parameter values, and the effects of the magnetic number, the magnetic source position, the vascular obstruction ratio, the slip parameter, and the power-law index on the flow and temperature fields are illustrated.