Transverse Magnetic Flux Research Articles

Stagnation point slip flow of Al2O3/γ-Al2O3 nanofluids subject to Lorentz force and nonlinear thermal radiation over a stretching sheet

The flow analysis of Al 2 O 3 and γ ‐Al 2 O 3 nanofluids near a stagnating point over a stretching sheet having velocity slip at the solid–liquid interface is presented. There is a quadratic surface temperature and a linear deformation acting on the wall boundary. Due to the uniformly applied transverse magnetic flux, the Lorentz force has an impact on the flow. The effect of nonlinear TR is integrated into the heat equation. Further, water H2O and EG C2H6O2 are base fluids. The governing boundary equations are translated into dimensionless ODEs using relevant similarity variables and solved numerically using the Runge-Kutta algorithm scheme (fourth-order) and the shooting algorithm. The impacts of the parameters, that is, velocity ratio ε , velocity slip δ , nonlinear TR Rd, the temperature ratio parameter θ w , and magnetohydrodynamics M are observed for the velocity h 2 ≤ y ≤ 0 and temperature θ ( η ) fields graphically. The results of local skin friction and local Nusselt number are shown in the table. A comparative analysis of the present results and the results of previous studies has also been made in tabular form. The research indicates that water as a base fluid gives better thermal conductivity than ethylene glycol. The consequence of TR enhances the heat transfer rate of both Al 2 O 3 / γ ‐Al 2 O 3 with H2O and C2H6O2.

STUDY OF DOUBLE SLIP BOUNDARY CONDITION ON THE OSCILLATORY FLOW OF DUSTY FERROFLUID CONFINED IN A PERMEABLE CHANNEL

The effects of slips and porosity on the channel walls in the flow of a heat-absorbing/generating dusty ferrofluid streaming through a porous medium are investigated in this article. The channel is upright and subjected to a transverse magnetic flux along with thermal radiation. Kerosene with magnetite is used as the base fluid. The basic equations of the channel flow, which seem dimensional, are redesigned in a dimensionless manner utilizing non-dimensional variables. The variable separable method approach is used to solve the obtained equations analytically. The graphs demonstrate the behavior of these parameters on the flow fields, skin friction, and heat transmission rate, and are explained briefly. Results reveal that the flow velocity for heat-generating fluids is greater than the heat-absorbing liquids. The fluid velocity upsurges with the improved values of the velocity slip parameter. The heat-generating dusty liquid has a higher heat transmission rate as compared to heat-absorbing dusty liquid.

Analysis of the energy efficiency and control ability under different magnetic flux forms in RPECT

Roll profile electromagnetic control technology (RPECT), which has the flexible control ability of the roll profile, is a new roll gap control technology that can be applied in the cold rolling process. The electromagnetic stick (ES) is generally used as the main bulging driving to adjust the roll profile. However, the ES structure can be changed with the variation of the electromagnetic flux forms, which further results in the difference of the energy efficiency and control ability. In this paper, the transverse magnetic flux form (TMF) and longitudinal magnetic flux form (LMF) of RPECT are proposed, and the principles of TMF and LMF are analyzed, and their advantages in the heat transfer paths are discussed. To conduct the parameterized impact analysis, the electromagnetic-thermal-structural coupled model matching the two electromagnetic flux forms are established and verified. Through the analysis of the current density, the current frequency, the external cooling and the initial roll temperature, the results show that the variation of the current densities, the current frequencies or the initial roll temperatures can change the control ability of RPECT, while changing the external cooling can not affect that of RPECT. The energy efficiency intersection of TMF and LMF can be achieved by changing the current density or current frequency separately. However, compared with changing the current frequency, increasing the current density of TMF to two times of LMF at different initial roll temperatures can realize the energy efficiency intersection of TMF and LMF, which is the best way to achieve this goal.

Higher order topology in a Creutz ladder

A Creutz ladder, is a quasi one dimensional system hosting robust topological phases with localized edge modes protected by different symmetries such as inversion, chiral and particle-hole symmetries. Non-trivial topology is observed in a large region of the parameter space defined by the horizontal, diagonal and vertical hopping amplitudes and a transverse magnetic flux that threads through the ladder. In this work, we investigate higher order topology in a two dimensional extrapolated version of the Creutz ladder. To explore the topological phases, we consider two different configurations, namely a torus (periodic boundary) and a ribbon (open boundary) to look for hints of gap closing phase transitions. We also associate suitable topological invariants to characterize the non-trivial sectors. Further, we find that the resultant phase diagram hosts two different topological phases, one where the higher order topological excitations are realized in the form of robust corner modes, along with (usual) first order excitations demonstrated via the presence of edge modes in a finite lattice, for the other.

Mathematical modeling of nanolayer on biological fluids flow through porous surfaces in the presence of CNT

Because of their unique intrinsic physical and chemical properties, carbon nanotubes (CNT) are being used in biological and biomedical applications. The current study proposes a mathematical model to analyze the effect of interfacial nanolayers on heat and mass transfer processes for nanofluid flow. Furthermore, the presence of carbon nanotubes (CNT) in a biological fluid (non-Newtonian fluid) with a reaction effect is investigated using porous surfaces. The uniform transverse magnetic flux was also included in the current study. Using a similarity transformation, the nonlinear partial differential equation is reduced to a set of ordinary differential equations. A phase simulation based on Brownian and thermophoresis factors have been developed for this problem. Optimal nanoparticles in the range of 2–8% have a significant effect on thermal conductivity as well as the thermal performance of the blood flow system. The numerical procedure supported the shooting method, resulting in the desired accuracy. Utilization of the Cason parameter under the effect of nanolayer thermal conductivity has horrendous results. The increase in nanolayer thickness, h = 3–9 nm, enhanced the effective thermal conductivity and thermal performance significantly.

Visualization of thermo-magnetic natural convective heat flow in a square enclosure partially filled with a porous medium using bejan heatlines and Hooman energy flux vectors: Hybrid fuel cell simulation

The aim of the article is to study the magneto-convective laminar incompressible flow within a differentially heated square enclosure partly filled with porous medium saturated with ionized helium gas in the presence of a transverse magnetic flux, as a model for emerging fuel cell designs. A Darcy model is utilized for porous medium bulk drag effects. Visualization of heat line and energy flux vectors is computed via Bejan's heat line approach and the Hooman energy flux vector method. The horizontal (i.e., bottom and top) wall boundaries are considered adiabatic and impermeable, while the side walls (cold and hot walls) are maintained at different but constant temperatures. The nonlinear coupled conservation equations under prescribed boundary conditions are solved with a finite difference-based vorticity-stream function approach. Appropriate convergence criteria factors are deployed. Furthermore, validation with earlier studies for the purely fluid, non-magnetic case i. e. in the absence of porous medium (Da) and Hartmann number (Ha) effects, is included. A parametric examination of the impact of Rayleigh number (Ra), Darcy number (Da) and Hartmann number (Ha) on temperature contours, heat lines, energy flux vectors and streamline patterns for ionized helium gas (Prandtl number, Pr = 0.71) is conducted. An increment in Hartmann magnetic number decreases the magnitudes of heat lines, suppresses heat transmission in the enclosure and curtails flow circulation. Enhancing the magnetic parameter and Rayleigh number however boosts the average heat transfer rate. Average Nusselt number at the left hot wall is elevated with increasing permeability of the porous medium and Rayleigh number. Mid-section velocities are enhanced in the porous layer but depleted in the non-porous layer of the enclosure with greater Rayleigh number. The simulations find provide some insight into applications in emerging hybrid electromagnetic fuel cells enabling better visualization of the thermal/fluid characteristics via the novel heat flow visualization heat-function and energy flux vectors analogy.

Finite element solutions of non-Newtonian dissipative Casson fluid flow past a vertically inclined surface surrounded by porous medium including constant heat flux, thermal diffusion, and diffusion thermo

This research investigates the simultaneous effects of thermal diffusion and diffusion thermo on incompressible, viscous, electrically conducting non-Newtonian Casson fluid flow past a vertically inclined surface through a porous medium in the presence of the uniform transverse magnetic field, chemical reaction, viscous dissipation, and constant heat flux. The action of thermal radiation and viscous dissipation is scrutinized. The fundamental governing equations determining the flow condition are transfigured as nonlinear coupled partial differential equations through self-similarity transmutations. The finite element technique is implemented to acquire the solution to the problem. Graphs are plotted to inspect the influence of sundry physical quantities on the three routine profiles of the flow field. Further, expressions are procured for friction factor and the rate of heat and mass transfers and discussed comprehensively through tabular forms. Favorable comparisons with previously published work on various exceptional cases of the problem are obtained. This research shows that the Soret number increases both the velocity and concentration fields, and the Dufour number increases the velocity and temperature fields. It is also observed that concentration and velocity fields reduce toward chemical reaction parameter. Furthermore, the Schmidt number decreases the velocity and concentration profiles. It is also noteworthy that velocity decays for the magnetic variable. An improvement in radiation declines the velocity and temperature profiles.

Finding the Optimal Size of Permanent Magnets for a Transverse Magnetic Flux Generator with a Disk Rotor

Based on the analysis of the transverse flux machine designs, they were found to have a relative design simplicity and a high-power density. The purpose of this work is to determine the optimal height of a permanent magnet and to define its effect on the induced EMF value in the stator coils and the cogging torque, as well as to define the picture of the magnetic flux leakage between the stator poles. To achieve these goals, the 3D model of a low speed generator was studied. The electromagnetic analysis was carried out using a modern software, which allows us to determine the magnetic field distribution in the 3D, as well as the induced EMF value and the rotor cogging torque. The criterion for the optimal calculation is the highest EMF value at the minimum value of the rotor cogging torque. The parameters of the permanent magnets, such as the width and length, remained unchanged, whereas, the height varied from 1 to 8 mm at a 1-mm step. The corresponding dependencies are obtained for each height. The most significant result of the work is the conclusion that the height of the permanent magnet should not exceed the 3-mm value. The significance of the obtained results is that the used methodology allowed finding the optimal height of the permanent magnet, since a further increase in its height leads to no growth in the EMF value, but rather significantly enhances the negative effect from the rotor cogging torque. In addition, the simulation results were supported experimentally.

Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls

Abstract The flow of Casson fluid streaming through a porous zone in a permeable channel with homogeneously distributed dust particles is studied. The flow is oscillatory and exposed to thermal radiation. With non-uniform temperature and velocity slip at the wall, the channel is put under transverse magnetic flux control. The variable separation approach is used to obtain the exact analytic solution for the flow fields of fluid and dust particles. Physical insights of collective effects of suction/injection, magnetic field, thermal radiation, and buoyance force on the fluid velocity, temperature, rate of heat transport and friction at the wall surface are examined and analysed graphically. Results reveal that surface friction increases on both channel plates as an injection on the hot plate rises.

An optimization method based on the Legendre wavelets for 3D rotating, squeezing and stretching magnetohydrodymanic flow in a channel with porous wall

In this paper, the 3D flow in a rotating channel with the lower permeable stretching wall is investigated. The unsteady squeezing flow in the presence of transverse magnetic flux is mathematically modeled by utilizing Navier-Stokes equations. A new optimal wavelet method based on coupling the Legendre wavelets and the hat functions with some auxiliary convergence-control parameters is proposed to solve the obtained fourth-order system of nonlinear differential equations. In the proposed method, the residual function and its error of norm two are employed for converting the main problem into an optimization one to optimally choose the auxiliary convergence-control parameters. The main idea behind this approach is to reduce solving such problems to those of solving optimization ones which greatly simplifies the problem and also leads to obtaining a good approximate solution for the problem under consideration.

Coherence and decoherence in the Harper-Hofstadter model

We quantum-simulated the 2D Harper-Hofstadter (HH) lattice model in a highly elongated tube geometry -- three sites in circumference -- using an atomic Bose-Einstein condensate. In addition to the usual transverse (out-of-plane) magnetic flux, piercing the surface of the tube, we threaded a longitudinal flux $\Phi_{\rm L}$ down the axis of the tube This geometry evokes an Aharonov-Bohm interferometer, where noise in $\Phi_{\rm L}$ would readily decohere the interference present in trajectories encircling the tube. We observe this behavior only when transverse flux is a rational fraction of the flux-quantum, and remarkably find that for irrational fractions the decoherence is absent. Furthermore, at rational values of transverse flux, we show that the time evolution averaged over the noisy longitudinal flux matches the time evolution at nearby irrational fluxes. Thus, the appealing intuitive picture of an Aharonov-Bohm interferometer is insufficient. Instead, we quantitatively explain our observations by transforming the HH model into a collection of momentum-space Aubry-Andr\'{e} models.

Stability model of bulk HTS field pole of a synchronous rotating machine under load conditions

High-temperature superconducting (HTS) bulks act as magnets with trapped magnetic flux and potentially exhibit high magnetic field performance, superior to that of permanent magnets. In the fourth industrial revolution, HTS magnets could potentially facilitate the development of highly efficient and lightweight motors and generators for propulsion. To evaluate and verify the durability of HTS rotating machines, we developed a radial-gap-type rotating machine whose field-pole modules comprised HTS bulks. We examined the stability of the trapped magnetic flux of the field poles during the machine’s operation. The rotating machine was operated with different loads, and the magnetic field associated with the trapped flux of the HTS bulks was analyzed. The analysis was performed for different loads and revolution speeds, and the long-term operation for a constant load was investigated. The trapped flux of the bulk field poles and the output power were observed to be almost constant for over 360 h, and the HTS bulk magnet’s surface temperature hardly changed below 40 K during the machine’s operation. Furthermore, the magnetic flux decay determined from magnetic flux measurements before and after a load test was less than 1%. An analysis of the magnetic field distribution around the HTS bulk revealed that the transverse magnetic flux flowed through the magnetic guide of the rotor core. These results indicate the potential synchronous machine application of the high trapped magnetic flux of the field-pole modules accumulated by the appropriate positioning the HTS bulks three-dimensionally.

A nonlinear solar magnetic field calibration method for the filter-based magnetograph by the residual network

Context. The method of solar magnetic field calibration for the filter-based magnetograph is normally the linear calibration method under weak-field approximation that cannot generate the strong magnetic field region well due to the magnetic saturation effect. Aims. We try to provide a new method to carry out the nonlinear magnetic calibration with the help of neural networks to obtain more accurate magnetic fields. Methods. We employed the data from Hinode/SP to construct a training, validation and test dataset. The narrow-band Stokes I, Q, U, and V maps at one wavelength point were selected from all the 112 wavelength points observed by SP so as to simulate the single-wavelength observations of the filter-based magnetograph. We used the residual network to model the nonlinear relationship between the Stokes maps and the vector magnetic fields. Results. After an extensive performance analysis, it is found that the trained models could infer the longitudinal magnetic flux density, the transverse magnetic flux density, and the azimuth angle from the narrow-band Stokes maps with a precision comparable to the inversion results using 112 wavelength points. Moreover, the maps that were produced are much cleaner than the inversion results. The method can effectively overcome the magnetic saturation effect and infer the strong magnetic region much better than the linear calibration method. The residual errors of test samples to standard data are mostly about 50 G for both the longitudinal and transverse magnetic flux density. The values are about 100 G with our previous method of multilayer perceptron, indicating that the new method is more accurate in magnetic calibration.

A mathematical study on entropy analysis in MHD forced convective flow through a circular channel

In this paper, we study the effect of the flow of a viscous incompressible fluid within a circular channel filled with a hyper porous medium saturated with a rarefied gas amid a transverse magnetic field, thermal radiation and uniform heat flux on the walls. The velocity and heat equations of the fluid flow are solved analytically using the Homotopy Analysis Method (HAM). Approximate analytical expressions are determined for the velocity and temperature profiles and these profiles together with the entropy generation rate are discussed graphically. The results are compared with the previous study and found to be in consensus.

Dissipative Power-law fluid flow using spectral quasi linearization method over an exponentially stretchable surface with Hall current and power-law slip velocity

The present article aims to reports laminar, incompressible, electrically conducting two-dimensional non-Newtonian (power-law) liquid flow via exponentially stretching sheet with power-law slip velocity conditions. Transverse magnetic field, Hall current, viscous dissipation and radiative flux effects are incorporated in the formulation. Rosseland's diffusion model is defined for the radiation heat transfer. The non-linear partial derivation formulations satisfying the flow are transformed to the non-linear derivative equations by employing the local similarity quantities and then solved analytically through spectral quasi-linearization method (SQLM). The resultant solution is computed for different parameters in tables and graphical representation for clear understanding of the thermo-physical terms. Extensive visualization of primary and secondary velocities, temperature distributions for various emerging parameters presented for n = 0.7 (pseudo-plastic fluid) and n = 1,3 (dilatant fluid). The results are verified for limiting cases by comparing with various investigations and found excellent accuracy for Newtonian case. It is interesting to note that secondary flow rate is more dominant for both the cases of pseudo plastic and dilatant fluids for Hall parameter and Eckert number. Increasing Hall current leads suppress the fluid temperature but as Eckert number grows it leads grow the fluid temperature. Further, it is observed that as Hall parameter increases local Nusselt number strongly elevates.

A 3-D Simulation of a Single-Sided Linear Induction Motor with Transverse and Longitudinal Magnetic Flux

This paper presents a novel and improved configuration of a single-sided linear induction motor. The geometry of the motor has been modified to be able to operate with a mixed magnetic flux configuration and with a new configuration of paths for the eddy currents induced inside the aluminum plate. To this end, two slots of dielectric have been introduced into the aluminum layer of the moving part with a dimension of 1 mm, an iron yoke into the primary part, and lastly, the width of the transversal slots has been optimized. Specifically, in the enhanced motor, there are two magnetic fluxes inside the motor that circulate across two different planes: a longitudinal magnetic flux which goes along the direction of the movement and a transversal magnetic flux which is closed through a perpendicular plane with respect to that direction. With this new configuration, the motor achieves a great increment of the thrust force without increasing the electrical supply. In addition, the proposed model creates a new spatial configuration of the eddy currents and an improvement of the main magnetic circuit. These novelties are relevant because they represent a great improvement in the efficiency of the linear induction motor for low velocities at a very low cost. All simulations have been made with the finite elements method—3D, both in standstill conditions and in motion in order to obtain the characteristic curves of the main forces developed by the linear induction motor.

Hall current, viscous and Joule heating effects on steady radiative 2-D magneto-power-law polymer dynamics from an exponentially stretching sheet with power-law slip velocity: A numerical study

A mathematical model is developed for 2-D laminar, incompressible, electrically conducting non-Newtonian (Power-law) fluid boundary layer flow along an exponentially stretching sheet with power-law slip velocity conditions in the presence of Hall currents, transverse magnetic field and radiative flux. The secondary flow has been induced with appliance of Hall current. The distinguish features of Joule heating and viscous dissipation are included in the model since they are known to arise in thermal magnetic polymeric processing. Rosseland’s diffusion model is employed for radiation heat transfer. The non-linear partial differential equations describing the flow (mass, primary momentum, secondary momentum and energy conservation) are transformed into non-linear ordinary differential equations by employing local similarity transformations. The non-dimensional nonlinear formulated set of equations is numerically evaluated with famous shooting algorithm by using MATLAB software. The validation of simulated numerical results has been completed with generalized differential quadrature (GDQ). Extensive visualization of primary and secondary velocities and temperature distributions for the effects of the emerging parameters is presented for both pseudo-plastic fluids (n = 0.8) and dilatant fluids (n = 1.2). The study is relevant to the manufacturing transport phenomena in electro-conductive polymers (ECPs).

Proposal of two‐dimensional magnetic field analysis model for transverse magnetic flux type linear synchronous motor

AbstractA three‐dimensional model is necessary for the magnetic field analysis of transverse magnetic flux type linear synchronous motors. However, it is unsuitable for design calculation because of the high calculation costs. In order to virtually represent the magnetic path of a three‐dimensional arm on a two‐dimensional model, we propose the use of virtual arms, which are provided above and below the armature core teeth. In the proposed two‐dimensional model, almost the same thrust waveform is obtained with a calculation time of less than 1/30 compared with the threedimensional analysis. The proposed model is also applicable to transverse magnetic flux and longitudinal magnetic flux hybrid type linear synchronous motors.

Effective Metal Mixing at a Low Melt Level in a Furnace or Mixer

The problem of increasing the efficiency of melt mixing in a furnace bath or mixer at low melt levels using an electromagnetic mixer installed on the furnace or mixer side is considered. It is proposed to use a transverse magnetic flux mixer as an electromagnetic mixer. A comparative analysis of devices with a longitudinal and transverse running magnetic field is performed. To perform the comparative analysis, mathematical modeling is carried out using the ANSYS software. By means of parametric mathematical models of electromagnetic mixers with a longitudinal and transverse magnetic field installed on the mixer side, it is possible to accurately reflect electromagnetic processes and obtain dependences of electromagnetic forces in the melt, to determine the release of thermal power in the melt and inductor, and power consumption and cosφ for different linear current load and different melt levels in the mixer. Based on the results of mathematical modeling, two types of electromagnetic mixers are compared and best practice advices are provided for choosing the mixer type depending on the initial metallurgical process conditions.

The magnetic circuit analysis of the transverse magnetic flux generator in no-load mode

Purpose. The transversal flux generators are very perspective machine type. They can use low wind or water flow to transform their energy into the electricity with good efficiency value. Obtaining the dependence of the length of the permanent magnet on its magnetizing force on both radii of the rotor. This ratio allows us to correctly select the dimensions of the standardized permanent magnets to excite the generator. This dependence of permanent magnet length allows us to better analyze the electromagnetic processes in transverse magnetic field generator. Methodology. Analytic and computer calculation of magnetic field of the transversal magnetic flux generator in no-load mode. The analytical methodology must be proved by finiteelement method using the 3D simulation in the modern and powerful software such as Ansys Maxwell. It allows us to compare methodology of TFM design and find the most optimal method for TFM design in accordance with fast and accuracy design process. Results. An equivalent circuit is presented for the magnetic system of the transverse magnetic flux generator, which is characterized by a disk design of the rotor and excitation from permanent magnets in no-load mode. On the example of TFM-32-180, the principle of its solution using the working diagram of a permanent magnet is presented. Originality. The analytical calculation of the correct selection of the standardized permanent magnets dimensions to excite the transversal magnetic flux generator in no-load mode. Practical value. This generators work as a low speed machine and have a rather simple construction. It can be used as high effective machine in low speed rivers or wind turbines installations. Therefore, quality and accurate design process is a practically evaluated. Getting the possibility to analytically design the transversal magnetic flux generator more accurately is a good practical value of this perspective type of the machine.