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This review reports a critical study on the effect of magnetic fields on the precipitation process of calcium carbonate scale from hard water. Indeed, the harmful consequences of the water scaling phenomenon urged researchers to find effective solutions. One of the interesting antiscaling processes is the magnetic treatment of water, which triggers a reduction in the precipitation of calcium carbonate on the walls when in contact with hard water. In the present review, we discuss selected examples related to this process in a combined analysis of the latest advances and the mechanism of action of the magnetic field. Despite the diversity of studies investigating this phenomenon, the effectiveness of this treatment remains a controversial issue, and it is not possible to obtain a clear explanation of the phenomenon. This review proposes, finally, interesting hypotheses which can effectively explain the effect of magnetic treatment on the behavior of hard waters and the precipitation of calcium carbonate, which include magnetohydrodynamics and the hydration effect. [ABSTRACT FROM AUTHOR]

The mass‐transfer of oxygen in liquid phases (including in the bulk electrolyte and near the electrode surface) is a critical step to deliver oxygen to catalyst sites (especially immersed catalyst sites) and use the full capacity of oxygen reduction reaction (ORR). Despite the extensive efforts of optimizing the complex three‐phase reaction interfaces to enhance the gaseous oxygen transfer, strong limitations remain due to oxygen's poor solubility and slow diffusion in electrolytes. Herein, a magnetic method for boosting the directional hydrodynamic pumping of oxygen toward immersed catalyst sites is demonstrated which allows the ORR to reach otherwise inaccessible catalytic regions where high currents normally would have depleted oxygen. For Pt foil electrodes without forced oxygen saturation in KOH electrolytes, the mass‐transfer‐limited current densities can be improved by 60% under an external magnetic field of 435 mT due to the synergistic effect between bulk‐ and surface‐magnetohydrodynamic (MHD) flows induced by Lorentz forces. The residual magnetic fields are further used at the surface of magnetic materials (such as CoPt alloys and Pt/FeCo heterostructures) to enhance the surface‐MHD effect, which helps to retain part of the ORR enhancement permanently without applying external magnetic fields. [ABSTRACT FROM AUTHOR]

High-precision surface of 201 stainless steel obtained by electrochemical micro-machining without or with magnetic field-assisted was studied by combining experiments and simulations. The results demonstrated that the surface roughness of the samples was reduced to 0.40 μm after 18 min electrochemical micro-machining. Besides, the introduction of the magnetic field further improved the surface accuracy and reduced it to 0.20 μm. At the same machining time, the magnetic field-assisted electrochemical micro-machining provided lower surface roughness, which indicated that the magnetic field had a favorable impact on the improvement of machining efficiency. Additionally, the distribution characteristics of magnetic induction lines in the machining gap were also discussed. When the magnetic induction lines were approximately parallel to the anode surface and perpendicular to the electric field, the processing efficiency was further improved. The simulation results showed that the current density on the anode surface and the mass transfer rate of the electrolyte were enhanced by the existence of the magnetic field, which accelerated the electrochemical reaction behavior. The external permanent magnet contributed magnetohydrodynamic force during electrochemical micro-machining promoting the occurrence of magnetohydrodynamic convection. Consequently, the charge and the mass transfer in electrolyte was expedited, indicating the improvement of processing efficiency. [ABSTRACT FROM AUTHOR]

Methods for enhancing fluid dynamics and thermal mixing in 3D open flow were performed and evaluated numerically in the current study. The impacts of a grouping of active and passive techniques of enhancement, namely: nonuniform magnetic field, complex geometry and nanofluids, on hydrodynamic and thermal behaviors were assessed. Flow characteristics such as degree of mixing, Nusselt number, and secondary flow structure indices were evaluated for various enhancement protocols being considered. An external magnetic field was applied in this project in two ways: over the entire channel or on specific stretches of the complex duct. In addition, mentioned flow features are examined along the channel with the number of Hartmann (Ha) ranging between 0 and 50 and three angles of orientation of the magnetic field (0, π/4 and π/2). The results show that the optimal protocol to achieve good thermal mixing between hot and cold fluids with a degree of mixing exceeds the 90% is for a nonuniform use of magnetic force oriented by π/2 or π/4. Moreover, it was observed that by applying the same optimized protocol, the parietal heat transfer represented by the Nusselt number was increased by more than 45%. [ABSTRACT FROM AUTHOR]

We study the long time asymptotic behavior of the inviscid magnetohydrodynamic equations with magnetic dissipation near a combination of Couette flow and a constant magnetic field. Here we show that there exist nearby explicit global in time low frequency solutions, which we call waves. Moreover, the linearized problem around these waves exhibits resonances under high frequency perturbations, called echoes, which result in norm inflation in Gevrey regularity and infinite time blow-up in Sobolev regularity. [ABSTRACT FROM AUTHOR]

This study examines the flow of an incompressible flow over a linear stretching surface with the inclusion of momentum and thermal slip conditions. A scaling set of alterations is applied to the governing system for both with and without magnetic field situations. The physical system being leftover invariant caused by some associations surrounded by the transformations. Later we find the absolute invariants 3rd -order ODEs for the linear momentum equation and two 2nd order ODEs consistent with the energy and concentration are obtained. The equations that coincide with the boundary circumstances are elucidated mathematically. The physical pertinent parameters as shown in graphs and the friction factor, Nusselt number and Salts 1 and 2 Sherwood numbers are shown in surface plots. We observed that the momentum slip parameter decelerates the skin friction coefficient in the presence of a magnetic field and enhances in the absence of the magnetic field parameter. The thermal slip parameter enhances the Nusselt number in both the presence and absence of magnetic field parameter. Finally, the thermal and concentration buoyancy ratio parameters are shown to upsurge the friction factor, Nusselt and Salts 1 and 2 Sherwood numbers in both cases of M = 0 and M =1. [ABSTRACT FROM AUTHOR]

In this paper, we explore the self-similarity time evolution of a hot accretion flow around a compact object in the presence of a toroidal magnetic field. We focus on a simplified model which is axisymmetric, rotating, unsteady viscous-resistive under an advection-dominated stage. In this work, we suppose that both the kinematic viscosity and the magnetic diffusivity to be a result of turbulence in the accretion flow. To describe such a flow, we apply magneto-hydrodynamics equations in spherical coordinates, (r , , φ) and adopt unsteady self-similar solutions. By neglecting the latitudinal dependence of the flow, we obtain a set of one-dimensional differential equations governing the accretion system. In this research, we encounter two parameters related to the magnetic field; one of them is, β , defined as the ratio of the magnetic pressure to the gas pressure and the other one, Γ 0 applied in the magnetic diffusivity definition. Our results show that β is a function of position, and increases towards outer layers. On the other hand, we examine different strength of magnetic field by choosing different value of β 0 which is the value of β at the inner edge of disc. We see that both β 0 and Γ 0 have positive effect on growing the radial infall velocity but density and gas pressure decrease by larger values of these parameters. Moreover, the rotational velocity and temperature of accreting material reduce considerably under the influence of a stronger magnetic field. We also focus on the behavior of the mass accretion rate appearing as a descending function of position. Finally, our solutions confirm that the radial trend of the physical quantities in a dynamical accretion flow is different from the ones in a steady flow. However, the effect of various parameters on the physical quantities in our model is qualitatively consistent with similar steady models. [ABSTRACT FROM AUTHOR]

Supersonic plasma has been widely used. A vacuum arc ion source provides one possible method for generating supersonic plasma. An external magnetic field can effectively avoid the wall loss of the plasma in the ion source and improve the ion yield. In this work, a two-dimensional magnetohydrodynamic model is established, considering different components including ions and electrons. With the help of simulation, we explore the physical characteristics of the supersonic vacuum arc plasma formed from a copper disk cathode. The characteristics that we focus on include plasma composition, current density distribution, plasma velocity, and plasma temperature. These characteristics as well as the ion yield are compared when different magnetic fields generated by solenoids near the cathode are applied, as well as when the arc current is different. The results show that, in the absence of an external magnetic field, ions expand freely with the approximate axial velocity and average ion charge state. With the increase of external magnetic flux density, the wall loss of the plasma will decrease, and the axial velocity and average ion charge state will increase, but the magnetic saturation phenomenon exists. The simulation results are consistent with the experimental results. [ABSTRACT FROM AUTHOR]

Substorm onset is believed to be a fundamental process for magnetic and plasma energy transport in both magnetosphere and ionosphere. In this regard, the ballooning instability is considered to be one of the key trigger mechanism for the substorm onset scenario in the near‐Earth plasma sheet. Here, the kinetic ballooning instability (KBI) in the near‐Earth magnetotail is analyzed using the two‐dimensional (2D) generalized Harris sheet and Voigt equilibrium models. The corresponding kinetic ballooning mode is unstable in the intermediate range of perpendicular wave number (ky) and the equatorial beta (βeq). We further note that the growth rate of the ballooning mode reduces significantly with the increase in electron‐to‐ion temperatures ratio (Te/Ti) and wave number ky. The kinetic ballooning mode is found to be most unstable in a thin current sheet region at the equatorial location xe ∼ (8.5 − 10)RE, where the ballooning drive term (βeq/LpRc) is dominant on stiffening effect due to minimum in normal magnetic field. Because of the stabilizing effect as caused by the field line stiffening and the strong field line stabilization, the ballooning mode is stable (marginally unstable) close (away) from the Earth. The magnitude of the KBI growth rates as a function of the equatorial beta βeq and location xe for a wide and thin current sheets using the Voigt equilibrium model are smaller than the Harris sheet counterpart, which are used for modeling the near‐Earth plasma sheet configuration for the slow and fast substorm growth phases, respectively. The results suggest that the excitation of KBI through the local current sheet thinning may also be an effective trigger mechanism for the substorm onset in the near‐Earth magnetotail. Key Points: The kinetic ballooning instability (KBI) of a general type of 2D current sheet equilibria called generalized Harris sheet equilibria with deep BZ minimum region is analyzedKinetic ballooning mode is unstable in the finite intermediate range of equatorial beta due to dominant term βeq/LpRc on stiffening factorKinetic ballooning mode found most unstable in current sheet region at the equatorial location (8.5 ∼ 10)RE while the effective IM coupling has minor effect on KBI growth rate [ABSTRACT FROM AUTHOR]

The influence of the uniform longitudinal magnetic field on the stability against small disturbances of an electrically conducting Newtonian fluid flow between two parallel horizontal plates is investigated. The sixth‐ order system of disturbance equations is solved by the Chebyshev collocation method, and the critical Reynolds number Rec, the critical wave number αc, and the critical wave speed cc are computed for a wide range of the magnetic Reynolds number Rm and Alfven number A. Curves of wave number against Reynolds number for neutral stability are presented for different values of the parameters. The onset of instability is also discussed in detail using the growth rate curves for various parameters of the problem. It is observed that the effect of both conductivity of the fluid and the strength of the magnetic field is to decay the onset of instability. A comprehensive study is carried out at the critical state of the fluid using the graph of Rec, αc, and cc with respect to Rm for various values of A. The critical values at the onset of instability are also presented for both the Galerkin method and the Chebyshev collocation method. [ABSTRACT FROM AUTHOR]

We study the global well‐posedness and existence of uniform attractor for magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity and pressure coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no‐slip boundary condition, while the magnetic field is subject to a time‐dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to Equations (1.1)‐(1.4). And at this stage, we further derive the existence of a uniform attractor for Equations (1.1)‐(1.4). [ABSTRACT FROM AUTHOR]

Numerical study of natural convection and melting in a corrugated square cavity filled with CNT-water nanofluid under the influence of inclined magnetic field was performed. The left and right walls of the cavity are kept at constant temperatures while the horizontal wall is adiabatic. Galerkin weighted residual finite element was used. The effects of Hartmann number (between 0 and 40), magnetic inclination angle (between 0° and 90°), nanoparticle volume fraction (between 0 and 4%), number (between 1 and 20) and height (between 0.002 H and 0.16 H) of the corrugation on the convective heat transfer features and melting in the square cavity were examined. Magnetic field was found to dampen the fluid motion, and less movement of the melt front in the upper part of the cavity is observed. By using the CNT nanoparticles in the base fluid, significant enhancement in the heat transfer and faster propagation of the melt front is observed in the absence and presence of magnetic field. Average heat transfer enhancements are around 118% and 95% when nanofluid at the highest particle volume fraction is compared with water in the absence and presence of magnetic field. The heat transfer is reduced and melt front curve characteristics are affected when the number and height of corrugation waves are increased. [ABSTRACT FROM AUTHOR]

In this study, the behavior of Cu–water nano-fluid in a pipe has been investigated numerically. The pipe is under the external magnetic field, and the magnetic field is applied perpendicularly to the pipe. The temperature of pipe is higher than the temperature of fluid. The study was carried out for three different Reynolds numbers. The magnetic field forces and nano-fluid volume fractions were chosen as Ha = 0, 10, 20 and φ = 0, 0.02, 0.04, respectively. Analysis was carried out with the ANSYS Fluent commercial software. Fluid velocity curves, local Nusselt (NuX) and average Nusselt (Nu) values are presented graphically. In all Re numbers, the fluid velocity decreases with magnetic field strength and nanoparticle effect. Local Nu number has increased with magnetic field, nanoparticle volume fraction (Re = 500) and Re number. However, this increase is less for the nano-fluid volume fraction, and then decreases at Re = 5 and 50. At all magnetic field strengths, the mean Nu number for Re = 5 and 50 is reduced with the addition of nanoparticles, but has increased for Re = 500. At all nano-volume fraction, the average Nu number is increased with the magnetic field for Re = 50 and 500. For Re = 5, the average Nu number increases up to Ha = 10, but it decreases at Ha = 20. As a result, magnetic field strength, nano-fluid volume fraction and Re number have found to be effective on heat transfer, and nano-fluid motion can be controlled by magnetic field. [ABSTRACT FROM AUTHOR]

The design of efficient stable and noble metal-free catalysts for the hydrogen evolution reaction is an important and challenging global task. In this work, high catalytic activity NiCoP braided rope was prepared by magneto-electrodeposition strategy for the first time. Notably, the magnetic field-induced magnetohydrodynamic effect serves multiple purposes. COMSOL numerical simulations reveal the formation mechanism of a braided rope structure. Density functional theory (DFT) calculations confirm that NiCoP has superior activity, attributed to Co active sites. In 1.0 M KOH and 0.5 M H 2 SO 4 , respectively, the overpotential of NiCoP prepared under 600 mT magnetic field (NiCoP-600) is only 48 and 34 mV at a current density of 10 mA cm−2. Additionally, the TOF of NiCoP-600 was 36 times as high as that of NiCoP at an overpotential of 100 mV. Furthermore, NiCoP-600 can be used as the cathode and anode for overall water splitting in an alkaline electrolyzer. [Display omitted] • Under magnetic field, not only a dense braided rope structure was prepared, but also the ratio of Ni to Co was controlled. • NiCoP prepared under 600mT exhibits excellent HER performance over a wide pH range. • The motion trajectories of particles in the magnetic field were determined by COMSOL simulation. • DFT calculations revealed the reason for the excellent catalytic performance of NiCoP. [ABSTRACT FROM AUTHOR]

A new mathematical model for a flexible blade coater is proposed and analysed for slip and magnetohydrodynamic (MHD) effects in blade coating process. The slip is considered at the blade surface and magnetic field is imposed normal to the flow. To obtain the velocity profile, pressure, pressure gradient, volumetric flow rate and maximum pressure both exact and numerical solutions are utilized. In order to obtain the numerical solution shooting technique is applied. The interesting physical quantities like load and deflection are calculated and presented in graphical and tabulated form. The influence of the Hartman number the slip parameter and normalized coating thickness parameter on the flow and deflection are discussed graphically. In the presence of magnetic field and slip the fluid velocity and hence blade deflection can be controlled. [ABSTRACT FROM AUTHOR]

This paper describes the theoretical analysis of unsteady non-linear convection of magnetic field effect on Burgers’ fluid flow in the presence of Buongiorno nano model. The flow is created by stretching the surface. Diffusion of thermal, concentration levels and heat absorption/generation are examined. Suitable similarity transformations are used to convert the nonlinear partial differential system into the nonlinear ordinary differential system. The solutions of nonlinear systems are obtained from the convergent approach. The profiles temperature, concentration and velocity are elaborated by various physical flow parameters and these are investigated through the graphs. Local Nusselt and Sherwood numbers numerical values are interpreted and discussed for various values of physical parameters in the form of the table. In the following research we determine the velocity, temperature, and concentration are extremely clear with the flow in non-linear unsteady convection than in the non-linear steady convection and also observe that the cooling process of non-linear unsteady convection is exceedingly beneficial. [ABSTRACT FROM AUTHOR]

Abstract We measured the concentration boundary layer during copper electrodeposition in a copper sulfate solution under an applied magnetic field. Using a holographic laser interference microscope, we demonstrated the formation of the diffusion layer near the cathode. In the initial stage of electrodeposition, the diffusion layer was distorted in a magnetic field. An analysis of the electrode surface concentration supported the following assertions: without a magnetic field, dendrites formed when the surface concentration of Cu2+ was depleted; with a magnetic field, the unique convection phenomena of the field gradient force and localized Lorentz force promoted Cu2+ mass transport in the diffusion layer, producing large crystal grains. [ABSTRACT FROM AUTHOR]

We study the evolution of magnetized quark gluon plasma (QGP) in the magneto hydrodynamic (MHD) framework. The fluid under investigation has a non-zero magnetization with infinite electrical conductivity. We solve the coupled Maxwell and conservation equations in (1+1D) transverse flow. We assume that the motion of fluid is longitudinally boost-invariant along beam line. In this study, we consider two different scenarios. First, we consider an ideal relativistic plasma with massless particles and infinite electrical conductivity with a constant magnetic susceptibility (χ m). Thus, we solve the coupled Maxwell and conservation equations, and obtain the transverse fluid velocity, the energy density and the magnetic field as functions of both space and time. We investigate the effects of magnetic susceptibility (χ m) on the evolution of thermodynamic quantities. Then, we solve the coupled Maxwell and conservation equations with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data [43,44]. We find the evaluation of temperature, energy density, the magnetic field, and the transverse fluid velocity. We improve our previous study [21] to include a nonzero magnetization, the transverse relativistic velocity u x 2 ≠ 0 , and a realistic equation of state. We realize the effects of non-zero magnetization on the fluid quantities are rather small. Besides, our work shows a fluid with a realistic equation and a temperature-dependent magnetic susceptibility behaves like a conformal fluid with a small constant magnetic susceptibility. [ABSTRACT FROM AUTHOR]

The present analysis discusses the effects of thermal-diffusion with thermal radiation, Joule heating and internal heat generation on peristaltic flow of a non-Newtonian fluid obeying Jeffery model. Heat and mass transfer are also taken into consideration, the flow is between two co-axial tubes under the effect of radially varying magnetic field. The inner tube is uniform and at rest, while the outer tube is flexible with sinusoidal wave traveling. The problem is modulated mathematically by a system of partial differential equations which describes the equations of momentum, heat, and mass transfer. These equations are solved analytically under the assumptions of long wave length and low-Reynolds number in non-dimensional form. The solutions are obtained as a functions of physical parameters of the problem. The radially varying magnetic field effect on the temperature and concentration distributions is analyzed and it is shown that the increase of Hartman number tends to reduce the temperature, while it increases the concentration. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A bigger rotation leads to the exertion of drag force. • High intensity of magnetic field causes a resistance in the fluid flow. • An upsurge of nanoparticles concentration deteriorates the heat transfer rate. • Dual solutions exist and stability analysis shows that the first solution is stable. Abstract This study accentuates the magnetohydrodynamic effect on three dimensional rotating flow and heat transfer of ferrofluid over an exponentially permeable stretching/shrinking sheet with suction effect. The flow and heat transfer model in partial differential equations are simplified by employing the suitable similarity transformations to a system of ordinary differential equations. Numerical results are generated by using the Matlab solver bvp4c function. The computational outcomes give significant insight into the rotating flow. The influence of three different types of base fluids are also considered, namely water, methanol and kerosene. The skin friction coefficients and the rate of heat transfer are prominently affected by the intensity of suction, magnetic field, rotating scale, concentration of nanoparticles and Prandtl number. It is found that a rise in the rotation parameter causes the ferrofluid to exert a drag force on the surface of the shrinking sheet. High intensity of the magnetic field induces higher Lorentz force and leads to the increment of the skin friction. A large concentration of nanoparticles degenerates the rate of heat transfer. On the other hand, the presence of dual solutions within the shrinking region is observed for certain values of the governing parameters. The execution of stability analysis affirms the reliability and stability of the first solution while the second solution is unstable. [ABSTRACT FROM AUTHOR]

Analytically, velocity field solutions for the magnetohydrodynamic (MHD) oscillating and rotating flows of Maxwell fluids in a porous plane have been set up with the help of Laplace transform technique. A fine uniform magnetic field of strength B0 has been employed in normal direction to the angular velocity Ω of fluid flow. Expressions for the Dimensionless velocity field have been given for electrically conducing, oscillating and rotating flows in a porous plane. A couple of analytical solutions have been acquired separately for two types of oscillations i.e for sine and cosine oscillations. In addition these solutions fulfil all proposed initial and boundary conditions. Graphical illustrations are also considered to find out the steady-state time for oscillating and rotating flows as well as influence of magnetic field parameter on velocity of Maxwell fluid has observed. [ABSTRACT FROM AUTHOR]

The present paper focuses on the investigation of the surface wave of liquid GaInSn film which flows along a non-electric conductivity surface in the presence of a spanwise magnetic field. Using the high-speed camera with frame rate 1000 1/s, we experimentally observed the time-varying surface waves at different Reynolds number and Hartmann number. Furthermore, we also extracted the gray value from two fixed lines in photos to show the wave information quantitatively along the streamwise direction and spanwise direction. Experimental results show that the present spanwise direction magnetic field plays an important role in the regularization of film surface waves, namely when gradually increasing the strength of magnetic field, the random surface waves can be firstly damped along the direction of magnetic field and then strongly inhibited due to the induced Lorentz force. The decreasing of wave velocity also indicates that the spanwise magnetic field has a stabilizing effect on the film flow. [ABSTRACT FROM AUTHOR]

The present paper aims to establish the MHD module of Anupravaha-1, a general purpose solver for fluid-flow, developed by our research group as a versatile computational tool for simulating MHD flows through complex geometric configurations. The code is capable of handling non-orthogonal, multi-block, structured grids and treats a coupled fluid–wall (conjugate) modeling to include thermal and electro-magnetic effects in the presence of duct walls and electro-thermally coupled manifolds. The solver module is thoroughly validated using various benchmark numerical and analytical results, which include, but not limited to the following variety of problems: (a) 2-D analytical and numerical reference cases of pressure driven flows in straight and curved channels, and natural convection in a rectangular enclosure, for Hartmann numbers Ha  ≤ 300. (b) Fully-developed flow through a rectangular duct for Hartmann numbers up to Ha  = 15,000, considering the duct walls to be all insulating (the Shercliff's case) and also with only the Hartmann walls partially conducting (Hunt's case II). (c) For the 3-D solver validation, comparative results for (1) the flow through a straight duct in the presence of a non-uniform magnetic field, (2) free convection in a cubical enclosure under a uniform magnetic field, and (3) an electro-magnetically driven flow in a toroidal duct for low Hartmann numbers ( Ha  ≤ 100), are obtained and discussed. (d) In addition, the implementation of a simple wall treatment method for computing high Hartmann number flows, as typically encountered in liquid metal cooled fusion-blanket applications, is tested using the case of flow through a rectangular duct in the presence of a homogeneous magnetic field for Ha  = 10,000–30,000. The performance of the code in the cases considered ranged from good to excellent. Lastly, comparison with the ALEX (Argonne Liquid metal EXperiment), for the case of flow through a rectangular duct in a fringing magnetic field is presented, that revealed the sensitivity of the results to the precise description of the magnetic field. [ABSTRACT FROM AUTHOR]

• An electrode-normal magnetic field is applied during water electrolysis process. • Bubble detachment diameter is larger in magnetic field at low current density. • The induced MHD convection reduces bubble growth rate. • Magnetic field makes most oxygen bubbles experience a sliding motion. The effect of magnetohydrodynamic (MHD) convection on the behavior of oxygen bubbles generated by alkaline water electrolysis is investigated in this paper. In order to avoid mutual obstruction of bubbles and get clear images, a special electrolytic cell with a wire anode is designed to conduct the experiments. The current densities in our experiments are between 0.15 and 0.35 A/cm2, which are relatively low but common values in ordinary industrial electrolyzers. The results show that external magnetic field can reduce the cell voltage slightly and change the distribution of bubble detachment size. The induced MHD convection is found to be able to accelerate the diffusion of gas components in to the bulk electrolyte, resulting in a low comprehensive current efficiency, and further leading to longer growth cycle and larger separation diameter of oxygen bubbles. In addition, different from the "coalesce-and-bounce" detachment pattern, bubbles generated in magnetic field will undergo a sliding motion on the electrode surface during their growth process, which shows a lower coalescence frequency and a smoother detachment. Our work suggests that the driving effect of magnetic field on oxygen bubbles may be positive only at high current densities. [ABSTRACT FROM AUTHOR]

The effect of magnetic field on the flow of the UCMF (Upper-Convected-Maxwell Fluid) with the property of a heat source/sink immersed in a porous medium is explored. A shrinking phenomenon along with the permeability of the wall are considered. The governing equations for the motion and transfer of heat of the UCMF along with boundary conditions are converted into a set of coupled nonlinear mathematical equations. Appropriate similarity transformations are used to convert the set of nonlinear partial differential equations into nonlinear ordinary differential equations. The modeled ordinary differential equations have been solved by the Homotopy Analysis Method (HAM). The convergence of the series solution is established. For the sake of comparison, numerical (ND-Solve method) solutions are also obtained. Special attention is given to how the non-dimensional physical parameters of interest affect the flow of the UCMF. It is observed that with the increasing Deborah number the velocity decreases and the temperature inside the fluid increases. The results show that the velocity and temperature distribution increases with a porous medium. It is also observed that the magnetic parameter has a decelerating effect on velocity while the temperature profiles increases in the entire domain. Due to the increase in Prandtl number the temperature profile increases. It is also observed that the heat source enhance the thermal conductivity and increases the fluid temperature while the heat sink provides a decrease in the fluid temperature. [ABSTRACT FROM AUTHOR]

In this research, influence of melting heat transfer on magnetohydrodynamic nanofluid free convection is analyzed by means of CVFEM. KKL model is taken into account to obtain viscosity and thermal conductivity of CuO-water nanofluid. Roles of melting parameter ( δ ) , CuO-water volume fraction ( ϕ ) , Hartmann ( Ha ) and Rayleigh ( Ra ) numbers are illustrated in outputs. Results depict that temperature gradient enhances with rise of Rayleigh and melting parameter. Nusselt number decreases with increase of Lorentz forces. [ABSTRACT FROM AUTHOR]

Nanofluid heat transfer intensification in a porous enclosure in existence of magnetic field is studied numerically using Non-Darcy model. Simulation has been done by means of CVFEM. Viscosity of Fe 3 O 4 -water is considered as a function of magnetic field. Roles of Darcy number ( D a ) , inclination angle ( ξ ) , Fe 3 O 4 -water volume fraction ( ϕ ) , Hartmann ( H a ) and Rayleigh ( R a ) numbers are demonstrated in outputs. Results illustrate that Nu ave increases with increase of Ra and Darcy numbers. Isotherms become denser near the hot surface with augment of inclination angle and Darcy number. Temperature gradient reduces with augment of Habut it enhances with rise of inclination angle. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the magneto hydrodynamic flow of conducting Walter's visco-elastic fluid in a long uniform straight channel of rectangular cross-section under the influence of time varying pressure gradient and uniform magnetic field applied perpendicularly to the flow of fluid. The exact solution for the velocity of fluid has been obtained by using integral transform technique. Some particular cases of pressure gradient have been discussed in detail. Also we have discussed the case when magnetic field is withdrawn. Besides, the corresponding viscous flow problem has been derived as a limiting case when the relaxation time parameter tends to become zero. [ABSTRACT FROM AUTHOR]

This work investigates mainly the magnetic field and the thermophoresis effects on the heat and mass transfer in steady laminar boundary layer flow of an incompressible viscous micropolar fluid over a moving vertical and permeable plate subjected to a magnetic field without neglecting the resulting dissipation. The governing differential equations are transformed into the ordinary differential equations which are solved numerically. Results are displayed graphically to illustrate the influence of Magnetic parameter, Thermophoretic parameter, and suction/injection parameter on velocity, microrotation, temperature and species concentration profiles. The rate of mass transfer is affected strongly by Thermophoretic parameter while the local skin-friction coefficient and the local wall couple stress are sensitive to the variations of the magnetic field and to the suction case. The micropolarity controls the shear stress but plays a limited role for the others quantities. Heat and mass transfer rate can be regulated principally by the use of a permeable plate with suction. [ABSTRACT FROM AUTHOR]

In the present study an unsteady mixed convection boundary layer flow of an electrically conduct- ing fluid over an stretching permeable sheet in the presence of transverse magnetic field, thermal radiation and non-uniform heat source/sink effects is investigated. The unsteadiness in the flow and temperature fields is due to the time-dependent nature of the stretching velocity and the surface temperature. Both opposing and assisting flows are considered. The dimensionless governing or- dinary non-linear differential equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. The effects of unsteadiness parameter, buoyancy parameter, thermal radiation, Eckert number, Prandtl number and non-uniform heat source/sink parameter on the flow and heat transfer characteristics are thoroughly examined. Comparisons of the present results with previously published results for the steady case are found to be excellent. [ABSTRACT FROM AUTHOR]

In this paper, the effect of non-uniform magnetic field on nanofluid forced convection heat transfer in a lid driven semi-annulus is studied. The effects of Brownian motion and thermophoresis are taken into account. Control volume based finite element method is used to solve the governing equations in the form of stream function–vorticity formulation. The calculations were performed for different governing parameters namely; the Reynolds number, Lewis number, and Hartmann number. Results show that the Nusselt number has a direct relationship with the Reynolds number while it has a reverse relationship with the Hartmann number and Lewis number. [ABSTRACT FROM AUTHOR]

In this paper force convection heat transfer in a lid driven semi annulus enclosure is studied in presence of non-uniform magnetic field. The enclosure is filled with Fe 3 O 4 –water nanofluid. It is assumed that the magnetization of the fluid is varying linearly with temperature and magnetic field intensity. Control volume based finite element method is used to solve the governing equations in the form of vorticity–stream function formulation. The calculations were performed for different governing parameters namely, the Reynolds number, nanoparticle volume fraction and Hartmann number. Results show that Nusselt number has direct relationship with Reynolds number, nanoparticle volume fraction while it has reverse relationship with Hartmann number. [ABSTRACT FROM AUTHOR]

In this paper magnetohydrodynamic free convection flow of CuO–water nanofluid in a square enclosure with a rectangular heated body is investigated numerically using Lattice Boltzmann Method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction and Rayleigh number on the flow, heat transfer and entropy generation have been examined. The results show that the heat transfer rate and Dimensionless entropy generation number increase with increase of the Rayleigh number and nanoparticle volume fraction but it decreases with increase of the Hartmann number. [ABSTRACT FROM AUTHOR]

Abstract: A numerical study of laminar natural convection in a square cavity with a thin fin that is under the influence of a uniform magnetic field is presented. The side walls of the cavity are kept at different temperatures and the horizontal walls are thermally insulated. An Adaptive Network-based Fuzzy Inference System (ANFIS) approach and an Artificial Neural Network (ANN) approach are developed, trained and validated using the results of Computational Fluid Dynamics (CFD) analysis. The effects of pertinent parameters on fluid flow and heat transfer characteristics are studied. Among these parameters are the Rayleigh number , the Hartmann number , the position of the thin fin and the length of the thin fin . The results show that ANFIS and ANN can successfully predict the fluid flow and heat transfer behaviour within the cavity in less time without compromising accuracy. In most cases, ANFIS can predict the results more accurately than ANN. [Copyright &y& Elsevier]

Heat transfer of Cu-water nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The group method of data handling (GMDH) type neural networks (NNs) is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge-Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. The effects of nanoparticle volume fraction, magnetic parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles while it is a decreasing function of magnetic parameter. As volume fraction of nanoparticles increases, the effect of this parameter on Nusselt number also increases, but opposite behavior is obtained for magnetic parameter and Reynolds number. [ABSTRACT FROM AUTHOR]

Abstract: The steady two-dimensional stagnation-point flow over a linearly stretching/shrinking sheet in a viscous and incompressible fluid in the presence of a magnetic field is studied. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. Results show that the skin friction coefficient decreases, but the heat transfer rate at the surface increases when the effect of slip at the boundary is taken into consideration. Dual solutions are found to exist for the shrinking sheet, while for the stretching sheet, the solution is unique. [Copyright &y& Elsevier]

The steady laminar two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid impinging normal to a nonlinearly stretching/shrinking flat sheet in the presence of a nonuniform magnetic field applied in the positive normal to the flat sheet is considered. The governing system of partial differential equations is first transformed into ordinary differential equations and solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the magnetic parameter , the velocity exponent parameter , and the stretching/shrinking parameter on the flow field are discussed. It is found that the magnitude of the skin friction coefficient increases with both the magnetic parameter and the velocity exponent parameter , when the stretching velocity differs from the free-stream velocity (), and is zero when . For a fixed value of the magnetic parameter , a unique or dual solutions are found for the shrinking sheet, depending on the values of the parameters and . [ABSTRACT FROM AUTHOR]

Abstract: The main goal of the present study is to show the procedure, application and main features of the hybrid numerical/analytical approach known as GITT (Generalized Integral Transform Technique) by solving a magnetohydrodynamic channel flow with heat transfer, sustained by a pressure gradient and subjected to a uniformly applied and undisturbed transversal magnetic field. Although not the primary objective, application of this novel method provides a critical review of previously published numerical results on developing channel flows with uniform or non-uniform velocity and temperature profiles at the channel inlet. This is bounded by non-conducting horizontal walls at constant temperature and lateral walls that are electrically perfect conductors (open or short-circuited). Transport properties, namely, fluid viscosity, thermal and electrical conductivities, are taken as either constant or thermally-dependent, exponential-type, functions. Due to the hybrid numerical-analytical nature of the integral transform approach, benchmark results for velocity and temperature fields and the main correlated potentials are produced as a function of the primary dimensionless governing parameters, such as Hartmann, Prandtl and Eckert numbers, as well as the electrical parameter, for typical situations. [Copyright &y& Elsevier]

Abstract: Liquid metal flow in a rectangular duct subjected to a strong external magnetic field is numerically simulated by three-dimensional SIMPLE algorithm on a finite volume structured staggered grid. The current density and the Lorentz force are calculated by solving the electrical potential equation at low magnetic Reynolds numbers and high Hartmann numbers with consistent and conservative scheme. The Crank–Nicolson scheme is used to update the convective and diffusion terms to get a second-order temporal accuracy. The diffusion and convective term is discretised by a second order central difference scheme. The code is verified by simulating Shercliff''s case and Hunt''s case II with different Hartmann number and Reynolds number. Numerical results have a good agreement with the analytical solution. [Copyright &y& Elsevier]

Abstract: Forced convective heat transfer and friction factor for air flowing inside rectangular horizontal duct over a set of pin–fins, is experimentally studied under uniform heat flux. Experiments are conducted with air subjected to a magnetic body force through a magnetic gradient field. Experiments are carried out for two different fin geometries. An experimental test loop equipped with the required measuring instruments is designed and constructed to assess the effects of magnetic field, mass flow rate, and applied heat flux on convection heat transfer process and pressure drop. The measurements of temperature, flow rate, applied voltage to the heater and pressure drop in the duct are recorded and manipulated to evaluate Nusselt number and friction factor. The obtained experimental results show that, both Nusselt number and pressure drop increases in case of using pin–fin in a staggered arrangement. Higher rates of heat transfer and pressure drop are obtained from the duct provided by a pin–fin set compared to flow in a plain duct under similar conditions. The turbulence structures are markedly elongated in the direction of the applied magnetic field when it is strong enough. The performance factor of the pin–fin inserts for both inline and staggered is evaluated. Comparison with the previous work shows good agreement. A correlation that best fits the experimental data is developed to predict the Nusselt number with presence of the magnetic field for pin–fin array inserts. The duct with staggered arrangement of fins produces a higher value of the heat transfer coefficient compared to in-line arrangement at all range of Reynolds number. [Copyright &y& Elsevier]

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated. [ABSTRACT FROM AUTHOR]

Abstract: An analysis is made of Hall effects on the steady shear flow of a viscous incompressible electrically conducting fluid past an infinite porous plate in the presence of a uniform transverse magnetic field. It is shown that for suction at the plate, steady shear flow solution exists only when , where S and Q are the suction and magnetic parameters, respectively. The primary flow velocity decreases with increase in Hall parameter m. But the cross-flow velocity first increases and then decreases with increase in m. Similar results are obtained for variation of the induced magnetic field with m. It is further found that for blowing at the plate, steady shear flow solution exists only when , where S 1 is the blowing parameter. [Copyright &y& Elsevier]

Application of magnetic fields to medical science is growing rapidly, with the development of novel magnetic pumps, hydromagnetic separation devices, etc. In this paper, we study the dual control mechanisms of transverse magnetic field and porous media filtration on viscous convection heat transfer in a buoyancy-driven blood flow regime in a vertical pipe, as a model of a blood separation configuration. Non-Newtonian characteristics of the blood are modeled with the well-tested, thermodynamically rigorous micropolar model introduced by Eringen. Porous media effects are simulated with a Darcy-Forchheimer drag force model. The two-point boundary value problem is normalized and the resulting dimensionless linear momentum, angular momentum (Eringen micro-rotation) and energy conservation equations are solved by the Differential Transform M ethod ( DTM). The convergence analysis elucidates that the DTM yields exceedingly accurate results, which are validated with a comparison with optimized fourth-order Runge-Kutta numerical quadrature. The influence of micropolar vortex viscosity parameter (Eringen parameter (Er), Hartmann magnetohydrodynamic number ( Ha), aspect ratio ( A), Darcy number ( Da), heat generation/absorption parameter (α) and Grashof number on the flow variables are studied in detail. The present study has important applications in magnetic field control of biotechnological (hemodynamic) processes, biomagnetic device technology, etc. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Due to the magnetohydrodynamic (MHD) effect on the flow, which degrades heat transfer coefficients by pulsation suppression of external magnetic field on the flow, a hemispherical protrusion wall is applied to free surface MHD-flow system as a heat transfer enhancement, because the hemispherical protrusion wall has some excellent characteristics including high heat transfer coefficients, low friction factors and high overall thermal performances. So, the characteristics of the fluid flow and heat transfer of the free surface MHD-flow with hemispherical protrusion wall are simulated numerically and the influence of some parameters, such as protrusion height δ/D, and Hartmann number, are also discussed in this paper. It is found that, in the range of Hartmann number 30≤ Ha ≤70, the protrusion wall assemblies can achieve heat transfer enhancements (Nu/Nu 0) of about 1.3–2.3 relative to the smooth channel, while the friction loss (f/f 0) increases by about 1.34–1.45. Thus, the high Nusselt number can be obtained when the protrusion wall with a radically lower friction loss increase, which may help get much higher overall thermal performances. [ABSTRACT FROM AUTHOR]

Due to the Magnetohydrodynamic (MHD) effect, which degrades heat transfer coefficients by pulsation suppression of external magnetic field, on the electrically conducting flow, the wall with non-uniform electrical conductivity is employed in a free surface MHD-flow system for heat transfer enhancement. The non-uniform electrical conductivity distribution of the channel wall may create alternate Lorentz forces along spanwise direction, which can effectively produce flow disturbance, promote mixture, reduce the thickness of boundary layer, and enhance heat transfer. So the heat transfer performances enhanced by some conducting strips aligned with the mean flow direction on the insulating wall of free surface MHD-flow are simulated numerically in this paper. The flow behaviors, heat transfer coefficients, friction factors and pressure drops are presented under different Hartmann numbers. Results show that, in the range of Hartmann numbers 30≤Ha≤100, the wall with non-uniform conductivity can achieve heat transfer enhancements (Nu/Nu0) of about 1.2 to 1.6 relative to the insulating wall, with negligible friction augmentation. This research indicates that the modules with three or five conducting strips can obtain better enhancement effect in our research. Particularly, the heat transfer augmentation increases monotonically with increasing Hartmann numbers. Therefore, the enhancement purpose for high Hartman number MHD-flow is marked, which may remedy the depressing heat transfer coefficients by MHD effect. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we provide a detailed investigation of the problem of existence of solutions to the stochastic magnetohydrodynamic equations which describe the motion of turbulent particles of fluids in a magnetic field. The results are proved through a delicate combination of Galerkin approximation scheme with some deep compactness results of analytic and probabilistic nature. [Copyright &y& Elsevier]

The effect of different directional magnetic fields on critical temperature differences of oscillatory thermocapillary convection in a rectangular cavity with differentially heated side walls filled with two viscous, immiscible, incompressible fluids is simulated in the absence of gravity. In this two-layer fluid system, the upper layer fluid is the electrically non-conducting encapsulant boron oxide (B2O3), while the lower one is the electrically conducting molten indium phosphide (InP). The interface between the two fluids is assumed to be flat and non-deformable. The computational results show that all the magnetic fields along the x, y and z directions can delay the transition from steady convection to oscillatory convection, and critical temperature differences increase with an increasing Hartmann number. Furthermore, the effect of a magnetic field along the z direction is strongest, followed by that along the y direction, and that along the x direction is the weakest for the same intensity of the magnetic field. [ABSTRACT FROM AUTHOR]

Abstract: The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed. [Copyright &y& Elsevier]

To understand the effects of magnetic fields on the evolution behaviours of thermocapillary convection in a two-layer fluid system under the absence of gravity, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary flows in a rectangular cavity. The results show that the convective cell merging process under x direction magnetic field is decelerated in the encapsulant, but that in the melt is accelerated; magnetic field in z direction decelerates the convective cells merging in the melt and encapsulant greatly; the effect of magnetic field in y direction on the convective cell merging is weak. The maximum vorticity magnitude of thermocapillary convection 58.3 s−1 at fully developed without magnetic field is reduced to 53.4, 54.4 and 20.7 s−1 under magnetic fields in x, y and z directions, respectively. [ABSTRACT FROM PUBLISHER]