Magnetic Field Parameters Research Articles

Changes in and Recovery of the Turbulence Properties in the Magnetosheath for Different Solar Wind Streams

Solar wind is known to have different properties depending on its origin at the Sun. In addition to the differences in plasma and magnetic field parameters, these streams differ due to the properties of turbulent fluctuations involved in the flow. The present study addresses the changes in the turbulence properties in the magnetosheath—the transition region in front of the magnetosphere. This study is based on statistics from the simultaneous measurements of magnetic field fluctuations in the solar wind and in the magnetosheath. Both the dayside and flank magnetosheath regions are focused on to detect the evolution of the turbulent fluctuations during their flow around the magnetosphere. Turbulent cascade is shown to save its properties for fast solar wind streams. Conditions favorable for the preservation of the turbulence properties at the bow shock may correspond to the increased geoefficiency of large-scale solar wind structures.

Evaluating energy transmission characteristics of Non-Newtonian fluid flow in stratified and non-stratified regimes: A comparative study

Considering the natural and industrial importance of flow characterization in stratified media, the current study is articulated. This work highlights the influence of linear stratification as well as convective surfaces in both thermal and solutal fields on the rheological attributes of Williamson fluid flow through an inclined surface. Novel physical aspects of a uniformly provided magnetic field of strength B and chemically reactive species are also included. The concerned transport equations are derived from the associated conservation laws in dimensional forms. Modification in the developed couple system is achieved by using a set of similar variables. Levenberg-Marquardt Scheme (LMS) and Bayesian Regularization Scheme (BRS) are utilized in comparative manner to analyze initial data accessed for quantities of interest. The data used in the generation of MLP was 80 percent for model training and 20 percent for testing and validation. Error histograms, performance plots, fitness curves, and regression plots for training, testing, and validation are presented. Data in the form of tables and graphs are presented, which express an excellent match between the ANN-predicted and targeted values. It is revealed that an artificial neural network approach can provide highly efficient forecasting for such problems by providing accurate data for quantities of interest. It is noticed that Nusselt number and Sherwood number enhances up to 33 % and 29 % versus respective stratification parameters. Velocity profile declines against magnetic field parameter (M) whereas, skin friction coefficient increments up to 25 %. Appliance of convective boundary constraints at the surface of inclined sheet tends to enhance the temperature and concentration fields.

Thermal performance appraisal of hybrid and nanofluid flow between a cone and a disk with variable thermal conductivity, viscous dissipation, and Joule heating

In many engineering systems, hybrid and nanofluids are influenced by their respective thermophysical characteristics. Lately, several models have been envisaged to foresee the hybrid and nanofluid attributes. The properties of hybrid nanofluids (HNFs) as potential heat transfer fluids are controlled by numerous aspects such as solid part size, volume fraction, and temperature. Considering the interesting facts of the hybrid and nanofluid flows, we in this exploration examined the thermal performance comparison of both types of fluid flows. The nanofluid and HNF are composed of molybdenum disulfide (MoS[Formula: see text]/kerosene oil and silicon dioxide–molybdenum disulfide (SiO2–MoS[Formula: see text]/kerosene oil, respectively. The flows are taken in a canonical gap between the cone and the disk. Both the cone and the disk may be rotating or stationary. The novelty of the computational model is enhanced by discussing the effects of viscous dissipation, Joule heating, and the variable thermal conductivity with convective condition. The Tawari and Das model is designed to analyze the heat transfer performance of the assumed fluid flows. The assumed fluid model is transmuted into the set of differential equations that are dealt numerically with the bvp4c MATLAB approach. The results are displayed in tables and graphical forms. For elevating estimations of the Eckert number, the heat transmission rate is found to be more significant in the disk than cone. It is also learned that hybrid nanoliquid heat transfer performance outperforms nanoliquid. The fluid velocity increases by raising the nanoparticle volume fraction [Formula: see text], and is decreasing for a higher magnetic field parameter. With the elevating estimates of thermal conductivity, it is shown that the cone transmits heat more quickly whereas the disc transmits heat more slowly. The thermal conductivity parameter increases the probability of collision of the liquid particles, that ultimately upsurges fluid heat transmission rate.

Study on operational temperature of magneto-rheological fluid and design dimensions of magneto-rheological damper for optimization

This study aims to restrict the upper limit for flow gap and effective length in magnetorheological (MR) damper for optimal performance. Initially, the sedimentation study of in-house MR fluid (25%) shows that an 8% reduction in the sedimentation ratio with the addition of additive and nonlinear Herschel-Bulkley (HB) model fit reflects a 32.5% decrease in average yield stress with increasing currents when the parallel plate gap is increased from 1 mm to 2 mm. Owing to this decrease in yield stress, further study is extended to fabricate two MR dampers with limit values (LV) of flow gap and effective length with a common magnetic outer cylinder. Testing results of MR dampers revealed a 72% reduction in damping force at 0.8 A current when the LV’s is increased from LV-1 to LV-2. Selecting LV-1 over LV-2 as the upper limit for any design optimization will give the MR damper optimal performance. At higher input parameters, amplitude has a 135% greater impact on damping force than frequency and current. It is also demonstrated that saturation magnetization depends on the applied magnetic field and input loading parameters. Finally, gravimetric analysis shows that the effectiveness of the MR fluid and magnetic particle starts to decline after 322 °C and 400 °C.

Numerical scrutinization of heat transfer subject to physical quantities through bioconvective nanofluid flow via stretching permeable surfaces

Background: The mechanics of heat and mass transfer via nanofluid flow across many media are currently being discussed. “Nanofluids” are fluids that include highly heat-conductive nanoparticles, and they are essential for resolving engineering problems. Under the effects of activation energy, thermal radiation, and motile microorganisms, the process of heat and mass transfer through steady nanofluid flow crosses over stretched surfaces in this scenario.Methodology: For mathematical evaluation, the system of partial differential equations (PDEs) is used to describe this physical framework. By introducing suitable similarity variables with a set of boundary conditions, this mathematical system of PDEs has become a system of ordinary differential equations (ODEs). To obtain numerical results, the MATLAB built-in program “bvp4c” is used to solve the system of first-order equations.Results: In the findings and discussion section, the resulting outcomes are thoroughly examined and visually shown. The flow rate in these systems increases due to the erratic movement of microorganisms. The graphical representation shows the impacts of involving physical factors on the microorganism, thermal, concentration, and momentum profiles. Variations/changes in these profiles can be observed by adjusting the parametric values, as depicted in the graphs. Consequently, thermal transport is boosted by 25%. Additionally, the skin friction, Nusselt, Sherwood, and microbe density numbers are determined numerically. The findings demonstrate that increasing the magnetic field parameter causes the velocity profile to decrease, increasing the radiation parameter leads to an increase in temperature description, and increasing the Lewis number causes the microorganism profile’s transport rate to decrease.

Criterial dependencies of the movement of the melt refractory material in the bath of an ore thermal furnace under electromagnetic influence

In this work, for the first time, criterion dependencies of the speed of movement of the melt in the bath of an ore-thermal furnace during electric arc melting of oxide refractory materials under external electromagnetic influence were obtained. The initial quantitative characteristics for generalization in the form of the dependence of the speed in the zone of intense movement of the melt on the currents in the electrodes and the electromagnetic device were taken on the electrolyte and mercury physical models of an ore-smelting furnace with an electromagnetic device. Physical modeling was carried out while maintaining the invariance of the derived similarity criteria: the electrovortex flow parameter πμ and the external magnetic field parameter πl. In order to extend the experimental results obtained to a whole group of similar phenomena, the dependences of the dimensionless speed of melt movement (Reynolds criterion) on the dimensionless parameters of the external magnetic field and electric vortex flow were obtained and constructed. Since for all similar processes the similarity criteria retain the same values, then the criterion dependencies for them will be the same, and the results obtained can be extended to all similar cases.

Effect of magnetic field and key parameters values on natural convection and entropy generation of hybrid nanofluid in a corrugated enclosure

This work enlightens the magnetohydrodynamics (MHD) natural convective hydrothermal scenario and entropy generation analysis in a corrugated enclosure filled with MoS2–SiO2–water hybrid nanofluid. Three discrete uniform heaters are kept fixed to the enclosure bottom wall. The enclosure top wall and the remaining parts of its bottom wall are isothermally cooled. The enclosure has adiabatic vertical walls. A higher-order compact (HOC) finite difference technique is used to determine the solutions to the dimensionless governing equations. To demonstrate the accuracy of the mathematical model, experimental and numerical verifications are accomplished. The numerical investigation is accomplished for Rayleigh number ( Ra = 10 4 − 10 6 ), aspect ratios of heater length ( AR = 0.2 , 0.4 , 0.6 , 0.8 ), nanoparticle volume percentage ( ϕ = 0 − 4 % ), and Hartmann number ( Ha = 0 − 120 ). The numerical outcomes are presented and studied by means of isotherms, streamlines, and the average Nusselt number. Furthermore, local entropy generation resulting from heat transmission, fluidic friction, and magnetic field, along with overall entropy formation and Bejan number are analyzed. This study reveals that the aspect ratio AR = 0.2 enhances the convective flow process at Ra = 10 6 , even when a magnetic field is present. The heat transfer rate increases as a function of the Rayleigh number, while it exhibits a decreasing trend with the aspect ratio of heater length and Hartmann number. Total entropy generation reduces as the Hartmann number and aspect ratio of heater length increase. Bejan number graphs show a reverse pattern as compared to total entropy generation. It has been noted that an increase in the Hartmann number from 0 to 120 decreases the average Nusselt number and total entropy generation by 19.77 and 46.63%, respectively, for AR = 0.2 , Ra = 10 6 , and ϕ = 4 % .

Exploration of thermal radiation and stagnation point in MHD micropolar nanofluid flow over a stretching sheet with Navier slip

The quest to strengthen heat conduction of thermal science base fluid for effective industrial outputs and engineering derives has recently increased. Thus, this study aims to determine how thermal radiation and slip effects affect the flow of a micropolar nanofluid near a stagnation point over an extending sheet. Using similarity transformations, the flow-controlling partial differential equations (PDEs) are turned into a set of non-linear ordinary differential equations (ODEs). The non-linear system of equations has been solved by the numerical technique Runge-Kutta-Fehlberg integration scheme implementing the shooting technique with suitable conditions to generate a numerical solution. The essential factors affecting the flow are depicted graphically and tabularly. Additionally, a comparison is conducted between the present result and previously published data on the Nusselt and Sherwood numbers; it claims that thermophoresis and Brownian motion vary under some restrictive conditions. An increase in the magnetic field parameter was found to boost the velocity of the micropolar nanofluid. In contrast, a rise in the micropolar parameter reduces the angular velocity.

Enhancing Sensitivity of Double-Walled Carbon Nanotubes with Longitudinal Magnetic Field

In this study, the behavior of double-walled carbon nanotubes (DWCNTs) used as mass sensors is explored under various boundary conditions; particular attention is paid to the crucial topic of resonant nanomechanical mass sensors. In the presented approach, nanotubes are subjected to a distributed transverse magnetic force and supported by an elastic foundation. The impacts of the longitudinal magnetic field, elastic medium, and diverse physical parameters on the responsiveness of the sensors are assessed. Using the energy method, governing equations are formulated to determine the frequency shifts of the mass nanosensors. Our findings reveal significant variations in the frequency shifts due to a longitudinal magnetic field, which depends on the applied boundary conditions. This research holds significance in the design of resonant nanomechanical mass sensors and provides valuable insights into the interplay of factors affecting their performance. Through exploring the intricate dynamics of DWCNTs used as mass sensors and thus contributing to the broader understanding of nanoscale systems, the implications for advancements in sensor design are offered and applications are introduced.

Optimization of the Circular Channel Size and the A.C. Magnetic Field Parameters for Application in a Channel-Type Induction-Heating Tundish

In this paper, the appropriate channel design and operating conditions for the simultaneous operation of the inclusion removal and the induction heating of the molten steel by imposing the A.C. magnetic field around the circular channel have been studied. (1) The effect of the lift force and the turbulence force on the inclusion in the transition zone of the channel has been computed; the results show that when the diameter of the inclusion is not less than 0.1 mm, both forces can be neglected because they are less than the electromagnetic pinch force, especially when the shielding parameter is not less than 5.0. (2) The minimal channel length to remove the inclusions out of the dead zone was computed without the lift force and the turbulence force; the shielding parameter of 10.0~15.9 is optimal to obtain the shortest channel length. Furthermore, the slow velocity of the molten steel is desirable. (3) The molten steel temperature increase per unit channel length by the induction heating can be controlled by the A.C. magnetic field frequency; a high frequency condition is better for the efficient thermal supply in this calculation condition. (4) When the flow velocity of the molten steel in the channel with a length of 1 m and a radius of 0.075 m is 0.1 m/s, the shielding parameter of 15.9 is the optimal parameter to simultaneously remove the inclusions and heat up the molten steel in the circular channel. And when the non-dimensional magnetic field intensity of the A.C. magnetic field is 31.7, the removal rate of the 0.1 mm inclusion in the channel can reach more than 95% and the molten steel temperature can be heated over 10 K.

METHODOLOGY FOR MATHEMATICAL MODELING OF ELECTRODYNAMIC SUSPENSION SYSTEMS

The report considers the methodology of modeling and analysis of magnetic field parameters as a component of a multi-level system of electrodynamic suspension. Known approaches to determining the parameters of such a system are described, their advantages and disadvantages are discussed.

Non-similar bioconvective analysis of magnetized hybrid nanofluid (Ag + TiO2) flow over exponential stretching surface

Scientists have studied fluid flow over a stretching sheet to explore its potential applications in industries. This study investigates the exponential stretching flow of a bioconvective magnetohydrodynamic (MHD) hybrid nanofluid in porous medium taking into consideration thermal radiations, heat generation, chemical reaction, porosity, and dissipation. Moreover, microorganisms are present in the fluid, so the fluid is more stable, which is crucial in biotechnology, biomicrosystems, and bio-nano coolant systems. Silver and titanium dioxide in a water-based medium are the prototypical nanoparticles. The present study involves a transformation of the governing system into a set of dimensionless, coupled and nonlinear partial differential equations (PDEs) using nonsimilar techniques. The local non-similarity (LNS) technique is used to truncate these equations to ordinary differential equations (ODEs). This technique is also used to estimate transformed equations numerically until the second level of truncation takes place via the bvp4c algorithm, which is a built-in MATLAB solver. Furthermore, tables are provided that presents the drag coefficients, Nusselt numbers, Sherwood numbers, and densities of motile microorganisms. Results show a negative correlation between the velocity and the magnetic field parameter as well as the porosity parameter, as evidenced by a decrease in velocity corresponds to rises in these parameters. The temperature distribution exhibits a positive correlation with the rising values of both radiation parameter and Eckert number. The concentration profiles also exhibit a negative correlation with the increasing values of Lewis and bioconvection Lewis number, chemical reaction parameter, Peclet number and the differences in microbial concentration. This study will improve the future research on hybrid nanofluid regarding industrial applications. There haven't been any previous publications that have investigated the use of this model with the local non-similarity method. The main objective of this article is to enhance the heat transfer performance in a hybrid nanofluid.

Quantum transport of massless Dirac fermions through wormhole-shaped curved graphene in presence of constant axial magnetic flux

In this work, we have studied the spin-dependent quantum transport of charged fermion on (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensional spacetime, whose spatial part is described by a wormhole-type geometry in the presence of constant axial magnetic flux. Choosing the solutions of the Dirac equation associated with real energy and momentum, we explored the spin-dependent transmission probabilities and giant magnetoresistance (GMR) through a single layer of wormhole graphene with an external magnetic field, using the transition matrix (T-Matrix) approach. The spin-up and spin-down components within the A and B sublattices of graphene in the matrix of 4×1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 1$$\\end{document} wave function are coupled to each other due to the wormhole structure and the magnetic field. We have found that transport properties strongly depend on the magnetic field, incident energy, and geometric parameters of the system. We observed that the transmission probability increases as the radius of the wormhole increases, and the length of the wormhole decreases. The higher energies lead to a decrease in the transmission probabilities of particles. Furthermore, we observed that the probability of the spin-flip effect is almost larger than that of the non-spin-flip effect, illustrating that electrons lose their spins during transmission. These findings highlight the complex and interesting behavior of wormhole graphene in the presence of external magnetic fields and suggest that these nano structures can have potential applications in electronic and spintronic devices.

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

Ray‐Tracing Analysis for the Propagation of Saturn Narrowband Emission Within the Saturnian Magnetosphere

AbstractThis study investigates the propagation characteristics of Saturn's Narrowband (NB) emissions using a 3D ray‐tracing code incorporating Saturn's magnetic field and electron density parameters. The potential source regions and propagation zones of the L‐O mode, Z mode and whistler mode NB emissions are distinguished. The L‐O mode NB emissions, generated along local electron plasma frequency surfaces through mode conversion, exhibit straight‐line propagation but undergo reflections between the ionosphere, the plasma torus, and the magnetosheath. The slot region, characterized by a lower electron density distributed around the plasma torus boundary, significantly influences emission propagation, potentially leading to trapping and depolarization. The 5 kHz Z mode NB emissions propagate and fill the trapping region delineated by lower cut‐off and upper hybrid resonance frequencies. In contrast, the 20 kHz Z mode NB emissions are primarily confined near source regions at the north and south edges of the plasma torus, with the possibility of escaping under variable plasma conditions.

Aligned Magnetohydrodynamics and Thermal Radiation Effects on Ternary Hybrid Nanofluids Over Vertical Plate with Nanoparticles Shape Containing Gyrotactic Microorganisms

Nowadays, challenges in development of heat transfer for various engineering fields including heat exchangers, electronics, chemical and bio-industry and others are crucial. Ternary hybrid nanofluids (THNF) as a new heat transfer liquids can be considered as effective medium for increment of heat and energy transport. In the case of THNF when three nanoparticles are added in the based fluid to enhance the transport processes. Dissimilar to the nanofluids (NF) and hybrid nanofluids (HNF) model that considers two types of nanoparticles, this studied consider the three types of nanoparticles in this work which are Aluminium Oxide (AI2O3), Copper (Cu), and Carbon Nanotube (CNT) with different shapes containing gyrotactic microorganisms. The objective is to find the effect of magnetohydrodynamics (MHD) and radiation to the steady of THNF flow past the vertical plate. The mathematical model has been formulated based on a combination Tiwari-Das and Buongiorno nanofluids model. The governing flow and heat transfer equations are simplified to the ordinary differential equations (ODEs) with the adaptation of conventional similarity transformations which are then evaluated by the bvp4c solver (MATLAB) to generate the numerical solutions. The solutions are visually represented through graphs and table to be easily observed. The results indicated that the effect of magnetic field parameter decrease the velocity and contrary in concentration, and microorganism profile while the temperature is increased in magnetic but contrary in radiation parameter . The concentration and density microorganism of THNF is increase with higher value in and but decrease in velocity and temperature. The spherical nanoparticle shape has a higher density, causing the skin friction of THNF to be lower compared to NF and HNF.

Multi-scale magnetic field investigation of the M-dwarf eclipsing binary CU Cancri

Aims.We aim to characterise the magnetic field of the eclipsing binary CU Cancri, which consists of two M-dwarf components. The determination of the magnetic field parameters of this target enables comparisons with both observations of similar stars and theoretical predictions of the magnetic field strength in CU Cnc. The target therefore provides an excellent opportunity to test our understanding of the generation of magnetic fields in low-mass stars and its impact on stellar structure.Methods.We used spectropolarimetric observations obtained with ESPaDOnS at the CFHT to investigate the magnetic properties of CU Cnc. To improve the signal, we used least-squares deconvolution (LSD) to create average line profiles. From these LSD profiles, we extracted information about the radial velocities of the components, significantly expanding the number of radial velocity measurements available and allowing for a determination of the orbital parameters. StokesVLSD profiles were used with Zeeman Doppler imaging to obtain the large-scale magnetic field structures of the two components. We also used detailed polarised radiative transfer modelling to investigate the small-scale fields, by Zeeman-splitting magnetically sensitive Ti Ilines in non-polarised spectra.Results.We obtain both the small- and large-scale magnetic field properties of the two components. The large-scale fields are dominantly poloidal, and both components have an average strength of approximately 100 G. This analysis of the large-scale fields likely suffers from some amount of hemisphere degeneracy due to the high inclination of the target, which would cause the large-scale field strength of the components to be underestimated. Both components also show unusual magnetic field configurations compared to stars with similar parameters: the primary is weakly axisymmetric (∼10%), and the secondary has a strong toroidal contribution (∼20%). The small-scale fields are significantly stronger, 3.1 and 3.6 kG for the primary and secondary, respectively. This measurement is in excellent agreement with surface field strength predictions for CU Cnc from magneto-convective stellar evolution models. These results indicate that magnetic fields could play a significant role in the radius inflation due to convective inhibition.

Analysis of the magnetohydrodynamic parameters of S-8BM (S-8B) electrolyzers in the modernization of aluminum smelters

The article aims to determine the magnetohydrodynamic parameters of an aluminum electrolyzer in order to compare different types of bus arrangements used in baths with a Soderberg anode. The electrical parameters of the electrolyzer (current distribution across blooms and anode studs) and magnetic field parameters were computed using the Blums V5.07 program (Polyfem, Russia). Data on circulation rates and skew of the metal in the electrolyzer were obtained using the MHD-Valdis program (developed by V. Boyarevich, University of Greenwich, UK). In the course of the studies, mathematical models of the C-8BM (C-8B) electrolyzer with various bus arrangements were built. Three bus arrangements were selected for testing the installation of a bridge designed to close the current distribution in the anode bus arrangement of the electrolyzer. These types of bus arrangements were realized in two variants: with and without a bridge. The obtained circulation rates and skew of the metal were used to evaluate the possibility of modernizing baths with a Soderberg anode without significant capital costs. When using the first type of bus arrangement, the best current distribution was achieved for the blooms with limits of ~757 A (for the variant without a bridge) and ~656 A (for the modernized variant with closed series), as well as for the anode studs having limits of ~1754 A and ~1609 A, respectively. With the use of the third bus arrangement variant, the current distribution was shown to slightly decrease following the installation of a bridge between the anode bus bars. The obtained results suggest that in the modernization of a C-8BM (C-8B) electrolyzer with different types of bus arrangements, current distribution across blooms and anode studs, magnetic field characteristics (By and Bz components), as well as circulation rates and skew of the metal, have no significant impact on the efficiency of this electrolyzer, which contributes to a faster transition to EcoSoderberg bath electrolysis without significant economic costs.

Effects of Hall, ion slip, viscous dissipation and nonlinear thermal radiation on MHD Williamson nanofluid flow past a stretching sheet

This work aims to explore the effects of ion slip and Hall current on the flow of MHD Williamson nanofluid over a stretching plate in the presence of chemical reaction, viscous dissipation, ohmic (Joule) heating, nonlinear thermal radiation, and heat generation/absorption. After using appropriate similarity transformations, the highly nonlinear governing partial differential equations are transformed to a system of ordinary differential equations. The subsequent non-linear problems are treated to numerical results by reducing the converted nonlinear ODE in to first order. The fifth-order Runge–Kutta method along with the shooting approach is implemented using the python programming tool to analyze the problem. Graphical representations have been used to investigate the impacts of the derived physical parameters on the temperature, velocity, and concentration distributions of nanoparticles with the goal of giving each parameter a physical interpretation. The study of the effects of various physical parameters on the skin friction coefficient, the local Nusselt number and the Sherwood number was finally explained with the help of graphs and tables. It is discovered that when the Williamson parameter increases, both the principal and secondary velocity profiles decline but the temperature and concentration profiles rise. Both the Hall parameter and ion slip effect produce similar results with increasing principal velocity profile and decreasing secondary velocity, temperature and concentration profiles. Furthermore, it is seen that the temperature and concentration profiles increase in response to an increase in the nonlinear thermal radiation parameter. The increment in Eckert number (viscous dissipation term) also showed enhancements in temperature and concentration profiles. Additionally, the primary skin friction coefficient and rate of mass transfer are accelerated by raising the magnetic field parameter, Williamson parameter, or Darcy number, but the heat transfer rates are slowed down in the boundary layer. Lastly, the obtained results were cross-referenced with earlier findings, considering specific assumptions, to establish the credibility of the results. The comparison revealed that the new results provided valuable and profound insights into the studied phenomenon.