Lorentz Force Research Articles

Heat Transportation of 3D Chemically Reactive Flow of Jeffrey Nanofluid over a Porous Frame with Variable Thermal Conductivity

Nanofluids with variable thermal conductivity can potentially bring about a transformative impact in various industries. They offer adaptive and efficient heat transfer solutions that can adjust to changing conditions and specific requirements. The insertion of nanoparticles into the base fluid significantly changes its properties, affecting thermal conductivity and viscosity. The primary objective of this paper is to analyze the heat transfer rate and three-dimensional bio-convective flow of a non-Newtonian Jeffrey nanofluid across a porous surface with variable thermal conductivity. The investigation also considers the impacts of thermophoresis, Brownian motion, and the Lorentz force. The combine impact of thermal radiation and motile microbes also incorporated in the current study. To model these phenomena, we employ the boundary layer approximation to derive a system of partial differential equations (PDEs). These PDEs are subsequently simplified into more manageable ordinary differential equations (ODEs) using the similarity variables. The numerical analysis is performed via the finite difference approach, which consists of a three-stage Lobatto scheme using MATLAB package. Additionally, important engineering parameters under different constraints-like skin friction, Nusselt number, and Sherwood number—are given in a thorough manner using tabular and graphical representations. The results of this study demonstrate significant enhancements in various aspects, including thermophoresis, Brownian motion, and thermal boundary layer thickness are demonstrated through graphically and in the form of tables. As the thermal radiation parameter increases, the temperature profile rises accordingly. This enhancement in the temperature profile is directly attributable to the higher value of the radiation parameter, which results in a physical increase in temperature. These improvements are attributed to a reduction in viscous forces and an increase in the Brownian diffusion coefficient. This research advances the understanding of non-Newtonian thermally radiative flow with variable thermal conductivity, elucidating the complex behavior of such fluids and providing valuable insights for engineering applications.

Dust-evacuated Zones near Massive Stars: Consequences of Dust Dynamics on Star-forming Regions

Stars form within dense cores composed of both gas and dust within molecular clouds. However, despite the crucial role that dust plays in the star formation process, its dynamics is frequently overlooked, with the common assumption being a constant, spatially uniform dust-to-gas ratio and grain size spectrum. In this study, we introduce a set of radiation-dust-magnetohydrodynamic simulations of star-forming molecular clouds from the STARFORGE project. These simulations expand upon the earlier radiation MHD models, which included cooling, individual star formation, and feedback. Notably, they explicitly address the dynamics of dust grains, considering radiation, drag, and Lorentz forces acting on a diverse size spectrum of live dust grains. We find that once stars exceed a certain mass threshold (∼2 M ⊙), their emitted radiation can evacuate dust grains from their vicinity, giving rise to a dust-suppressed zone of size ∼100 au. This removal of dust, which interacts with gas through cooling, chemistry, drag, and radiative transfer, alters the gas properties in the region. Commencing during the early accretion stages and preceding the main-sequence phase, this process results in a mass-dependent depletion in the accreted dust-to-gas (ADG) mass ratio within both the circumstellar disk and the star. We predict that massive stars (≳10 M ⊙) would exhibit ADG ratios that are approximately 1 order of magnitude lower than that of their parent clouds. Consequently, stars, their disks, and circumstellar environments would display notable deviations in the abundances of elements commonly associated with dust grains, such as carbon and oxygen.

Modeling and analysis of non-circumferential symmetric permanent magnet spherical motor using genetic algorithm-based torque map method.

A permanent magnet spherical motor (PMSpM) is a typical multiple-degree-of-freedom apparatus. This paper proposes a torque map-based torque model and its counterpart using a genetic algorithm for the PMSpM with non-circumferential symmetric permanent magnets. The basic structure and operating principle of the PMSpM under study are presented. The analytic model of the 3D magnetic field is researched using the spherical harmonic method. The magnetic field model is verified via finite element method (FEM) analysis and an experiment of radial magnetic flux density. The analytic torque model is formulated using the Lorentz force method. The torque maps are established according to the principle, and the torque map-based torque model originates from the maps. FEM and the experimental results prove the correctness of the torque map-based torque model, and real-time performance of the torque model is also estimated. To solve the coil current calculation difficulty, the genetic algorithm is introduced for establishing the reversal torque model; MATLAB simulation is conducted for the convergence speed of the reversal torque model; and the real-time performance is studied on Qt 5.14/C++ upper software.

Microstructure and mechanical properties of CP780 steel - 7075 aluminum alloy laser welded joint assisted by rotating magnetic field

Abstract This study uses a rotating magnetic field for laser welding on 1 mm thick CP780 high-strength steel and 1.5 mm thick 7075 aluminum alloy. The effects of different welding parameters (B = 0 mT, B = 65 mT with V = 0°/s, B = 65 mT with V = 10°/s) on the morphology, microstructure, and tensile properties of welded joints are analyzed. At B = 0 mT, the weld shape is V-shaped, with the intermetallic compounds primarily consisting of needle-like brittle Al-rich (Fe, Si)Al2 phase and fewer granular ductile Fe-rich (Fe, Si)Al phase, resulting in poor mechanical properties. With the application of the rotating magnetic field, the laser energy becomes more concentrated, forming a ‘T’ shape weld. The rotating magnetic field (B = 65 mT with V = 10°/s) generates a constantly changing Lorentz force, promoting molten pool flow and enhancing Fe diffusion within the weld. This process reduces needle-like brittle Al-rich (Fe, Si)Al2 phase and increases granular ductile Fe-rich (Fe, Si)Al phase. It also accelerates the weld cooling rate and inhibits the reaction time and grain growth of intermetallic compounds, thereby reducing the thickness and content of the intermediate transition layer and significantly improving mechanical properties. A comprehensive comparison shows that the best mechanical properties are achieved at B = 65 mT with V = 10°/s. This study offers new insights and a theoretical foundation for achieving cost-effective, high-performance welded joints in advanced high-strength steel and high-strength aluminum alloy for automobiles, thereby facilitating lightweight vehicle development.

Role of two isothermal cylinders towards three-dimensional flow and melting of phase-change materials

Recently, investigators focused on examining the melting of phase change materials (PCM) in regular two-dimensional or three-dimensional flow domains. At the same time, this topic still needs more study to get a better understanding of it. Also, such problems should be reported using the local thermal non-equilibrium (LTNE) model because the latent heat substances and the included porous elements have different temperatures. Therefore, this study examines the three-dimensional flow and melting process of phase change materials (PCM) within cubic enclosures filled with copper foam, using a local thermal non-equilibrium model (LTNE). The system includes two isothermal cylinders with different temperature conditions, varying distances, and radii, placed within the flow domain. The enthalpy-porosity approach is applied to model the PCM behavior, while the Brinkman-extended non-Darcy model accounts for high-velocity flow situations. A magnetic field is introduced to control the flow, with the Lorentz force acting opposite to gravity. The governing equations are solved using a home-developed code based on the finite volume method with the SIMPLE algorithm. Key parameters investigated include cylinder radii, Fourier number, Hartmann number, horizontal and vertical distances between cylinders, and Darcy number. The results are presented through streamlines, temperature distributions for fluid and solid phases, and profiles of the Nusselt number and average liquid fraction.

A Rydberg-Bohr-de Broglie Algebraic Model of Hydrogen Atoms

Bohr ignored the electromagnetic interaction of moving charges in atoms and only considered Coulomb forces, thus encountering half frequency difficulties. This article considers the Lorentz force to make the classical Bohr model consistent with modern quantum theory, uses de Broglie's standing wave principle instead of Bohr's quantization assumption, derives the energy level formula for hydrogen atoms, and explains the radiation mechanism of hydrogen atomic spectra. The hydrogen atom in a spectral tube emits a photon wave train during one free path, and the wavelength of the photon is the eigen wavelength of its wave train. The head wavelength of the wave train is four thirds of its eigen wavelength, and the tail wavelength of the wave train is two-thirds of its eigen wavelength.

Electric and magnetic waveguides in graphene: quantum and classical

Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. We have assumed the displacement symmetry of the system along the y-direction, whose associated constant is k. We have also examined other symmetries relevant to each type of waveguide, magnetic or electric. Waveguides with square profile have been worked out in detail to show up explicitly some of the most interesting features. For example, the classical region of confined motion of the electric case, for a fixed intensity, is bounded between k and −k, while in the magnetic case that region is symmetric in the energy and presents a gap (−k, k). Besides, in the quantum systems we have shown that there are edge states in the magnetic systems but they are missing in electric waveguides. We have also analysed scattering states and resonances which match with bound states for both waveguides. The classical scattering properties are also quite different in both types of waveguides. While the electric system has essentially one type of refraction of the incident electron, the magnetic system is much richer due to the Lorentz force.

Two branches solutions for mixed convection flow of thermally Williamson nanofluid flow with heat transfer due to magnetized shrinking sheet

AbstractThe study of magnetohydrodynamics (MHD) and thermal radiation over‐stretching and shrinking sheets has significant applications in a wide range of fields, from chemical manufacturing to transport engine cooling systems, electronic chip cooling, plasma, the nuclear‐powered sector, saltwater, etc. The present study aims to numerically and theoretically analyze the movement of thermally magnetized Williamson nanofluid owing to an extended/contracting sheet. The regulating flow equations are converted to self‐similar equations through similarity transformation, and then numerically solved by bvp4c using MATLAB software. A comparison of the present numerical study with the published study is quite impressive. The investigation demonstrates that the self‐similar equations disclose the two branches for the limited shrinking factor range. For the stretching case, only one solution exists. As a result, the most fundamentally feasible solution has been determined by the linear assessment of temporal stability. For the aim of stability analysis, the lowest eigenvalue sign indicates the stability or instability of a solution. Through stability analysis, it is witnessed that the first solution (first branch) is stable. Due to the presence of the Lorentz force effect, it is perceived that the velocity curves decline in the whole channel. The point to be noted here is that the velocity of the lower branch compared to the upper branch is higher. The reduced Skin Friction is increased in the first branch and declines in the second branch for the two different values of magnetic factor.

Optical force and torque in near-field excitation of C3H6: A first-principles study using RT-TDDFT.

Optical trapping is an effective tool for manipulating micrometer-sized particles, although its application to nanometer-sized particles remains difficult. The field of optical trapping has advanced significantly, incorporating more advanced techniques such as plasmonic structures. However, single-molecule trapping remains a challenge. To achieve a deeper understanding of optical forces acting on molecular systems, a first-principles approach to analyze the optical force on molecules interacting with a plasmonic field is crucial. In our study, the optical force and torque induced by the near-field excitation of C3H6 were investigated using real-time time-dependent density functional theory calculations on real-space grids. The near field from the scanning tunneling probe was adopted as the excitation source for the molecule. The optical force was calculated using the polarization charges induced in the molecule based on Lorentz force. While the optical force and torque calculated as functions of the light energy were in moderate agreement with the oscillator strengths obtained from the far-field excitation of C3H6, a closer correspondence was achieved with the power spectrum of the induced dipole moment using near-field excitation. Time-domain analysis of the optical force suggests that the simultaneous excitation of multiple excited states generally weakens the force because of mismatches between the directions of the induced polarization and the electric field. This study revealed a subtle damping mechanism for the optical force arising from intrinsic electronic states and the influence of beating.

Numerical simulation of two‐phase flow towards a stagnation point in the Jeffrey nanofluid across a porous deformable disc with zero mass flux condition and Lorentz forces

Numerical simulation of two‐phase flow towards a stagnation point in the Jeffrey nanofluid across a porous deformable disc with zero mass flux condition and Lorentz forces

Effect of nanofluid cooling on electrical power of solar panel system in existence of TEG implementing magnetic force

This study investigates the efficacy of applying a Lorentz force to improve the efficiency of a photovoltaic-thermal (PVT) system featuring a finned duct, while also addressing challenges associated with dust accumulation. The magnetic field helps to prevent nanoparticle aggregation, enhancing the cooling process. The use of a finned duct combined with a nanofluid as the cooling medium efficiently dissipates excess heat from the silicon layer. Dust accumulation on the glass layer reduces transmissivity, negatively impacting system performance. The magnetic field's interaction with the nanoparticles enhances convective cooling of the upper layer, leading to an overall improvement in performance. Increased pumping power results in higher cooling rates, with improvements of approximately 3.48 % in thermal efficiency (ηth), 75.01 % in thermoelectric generator efficiency (ηTEG), and 39.37 % in photovoltaic efficiency (ηPV). An increase in the Hartmann number (Ha) improves ηth by about 1.87 %, with corresponding enhancements in electrical performance components. A higher concentration of ferrofluid further boosts performance, with the effect being roughly 1.7 times more significant in the absence of MHD compared to when Ha = 97. Dust presence decreases ηth, ηTEG, and ηPV by approximately 9.39 %, 8.55 %, and 25.77 %, respectively. Furthermore, the presence of Ha diminishes the influence of Vin on ηth by around 1.33 %.

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication of rough Triangular plates

In this study, Christensen's stochastic theory is utilized on rough surfaces' hydrodynamic lubricating effect to examine how surface roughness, couple stress fluid, slip velocity, magnetohydrodynamic (MHD), and the triangular surface interact. Modified Reynolds equation is derived analytically using combining theories of Stokes couple stresses, Lorentz forces, and Christensen's stochastic hypothesis about hydrodynamic lubrication. Pressure, load carrying capacity and squeeze film time expression is derived mathematically using Reynolds equation that accounts for surface roughness and coupling stress. For various parameters including rough parameter, slip velocity, Hartmann number, and couple stress, the lubricating characteristics are analysed graphically. Squeeze film time, load carrying capacity, and pressure are enhanced by an increase in slip velocity, couplestress and magnetic field. The lubrication characteristics decreases (increases) on squeeze film pressure, load carrying capacity and squeeze film time through increasing values of the longitudinal (transverse) roughness parameter.

Twist analysis of the spin-orbit correlation in QCD

We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} case, the result is partially related to the kinematical twist-three part of the gT (x) distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.

A Decoupled Feedback and Fast Norm Optimal Control approach for Normal and Superconducting RF Cavity disturbances compensation

Iterative learning controller (ILC)s of different types have been used in various engineering applications for system control in presence of repetitive disturbance, often encountered in batch control systems. A particle accelerator usually comprising of Radiofrequnecy (RF) cavities, when operated in pulsed mode processes particle beam similar to that in batch systems. However, an injected particle beam disturbs electric field inside RF cavity. In additions to beam loading disturbance encountered in all types of RF cavities, a superconducting cavity also encounters disturbance due to Lorentz force detuning. Under presence of such persisting disturbance/s, a Fast Norm Optimal ILC (FNOILC), helps achieve specified amplitude and phase stability of electric field, which results in beam of specified quality. A sophisticated control system helps achieve this objective. In this paper, FNOILC technique is explored for this purpose. Though, it has been reported for few accelerator facilities, in this work, a decoupling strategy is used in a feedback control loop, resulting into overall enhancement of control performance. Behavioral model of RF cavity is represented as dual input dual output system exhibiting two loops, found interacting due to nonzero cavity detuning. A decoupler is designed based on well known technique/s used in process control applications. Relative gain array element values are used to quantify interaction. In presence of beam loading disturbance, a FNOILC demonstrates an excellent control performance. A standard performance index has been used to assess control performance. It is found that use of decoupler in main feedback loop of RF cavity, enhances the resulting performance index. Besides, an ILC performance needs assessment with practical issues like model uncertainty, sensing delays, high detuning and observation noise. In this paper, most of conclusions are drawn based on large number of modeling and simulation studies carried out for lab prototype 650MHz cavity. Interesting studies like effects of low controller sampling frequency, feedback controller gain tuning, severe detuning, etc. are presented using a novel state plane representation. A zero phase filtering is simulated and proposed as an effective strategy when measurements have noise. This paper forms a case study which can be applied to any general system encountering repetitive disturbance. Additionally, paper also elaborates on FNOILC algorithm application for Lorentz force detuning compensation often encountered in superconducting cavity during pulse mode of operation.

A Study of Differential Topology on the Magnetically Induced Isotropically Averaged Lorentz Force Density of a Few Simple Molecules.

Quantum chemical topology addresses the study of the chemical structure by applying the tools of differential topology to scalar and vector fields obtained by quantum mechanics. Here, the magnetically induced isotropically averaged Lorentz force density was computed and topologically analyzed for 11 small molecules. Critical points (attractors, repellers, and saddles) were determined and trajectories connecting the attractors computed. It is shown that kinds and numbers of the critical points are to some extent transferable in similar molecules. CC bonds of different orders are endowed with critical points of different kinds close to their center. The sum of topological indices of the isolated critical points is influenced by the presence of repellers on the outer part of the molecules.

Study on the influence mechanism of electromagnetic field on multifield coupling during the laser cladding Fe60 process

During laser cladding, microdefects such as pores, cracks, and segregation inevitably occur. Practical experience has shown that applying an electromagnetic field is an effective method for eliminating these microdefects during the cladding process. In the study, a multifield coupling three-dimensional numerical model was established for the electromagnetic field-assisted laser cladding Fe60 process. The instantaneous evolution law in the temperature field, flow field, and stress field under the influence of a magnetic field and without magnetic influence was calculated and revealed. At the same time, the two were compared and analyzed, focusing on the influence of an external electromagnetic field on the flow of molten pool Marangoni and its action mechanism. The results show that under the electromagnetic conditions applied in the study, the maximum magnetic induction intensity and the maximum Lorentz force density in the molten pool reach 0.13 T and 6.84 × 103 N/m3. Under the influence of magnetic force, the “double vortex” flow of Marangoni convection is asymmetrically distributed in the center of the molten pool. The fluid flow line has irregular flow and the circulation area generated at the front of the molten pool is larger in the corresponding scanning direction. Under the magnetic field influence, the overall flow velocity of the molten pool obviously increases, and the maximum flow velocity of the molten pool reaches 0.28 m/s. The study lays a significant theoretical foundation for revealing the mechanism of laser cladding assisted by a magnetic field.

Thermal performance of nanofluid natural convection magneto-hydrodynamics within a chamber equipped with a hot block

In this study, flow and free convection thermal performance within a chamber in the presence of a permanent magnetic field are simulated. Boussinesq approximation and the Lorentz force equation are used for the density variation in free convection, and the magnetic field, respectively. The steady-state, two-dimensional, and incompressible governing equations are simulated using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE). The present study is simulated for different Rayleigh numbers (Ra) corresponding to the situation where the conduction mechanism was predominant (Ra = 100) and the convection heat transfer was predominant (Ra = 105). Also, different intensities of the magnetic field (0 ≤ Ha ≤ 40) and different directions of the magnetic field along with the effects of three different nanoparticles Ag, Cu, and Al2O3 are given. The present study showed that in the case of the dominant convection mechanism, the presence of the magnetohydrodynamics (MHD) condition decreases the Nusselt number (Nu). However, if the conduction is predominant, the applied magnetic field improves the average Nu number. The optimum state for the magnetic field strength was found in the low Rayleigh number. The presence of nanoparticles also intensifies the magnetic field effects. In the high Rayleigh number, the heat transfer rate reduces by 13.5% with the increase of the Hartmann number.

Enhancing fatigue performance of AA6063-T6 fasteners through novel electromagnetic cold expansion using a double-frequency discharge

Non-contact electromagnetic cold expansion process (EMCE) represents a highly promising way to enhance the fatigue performance of fasteners. However, within the current technological framework, the necessity for dual power supplies and an accurate discharge control system has constrained the development and application of this technique. To address this, a novel EMCE process utilizing a double-frequency discharge is proposed. This process is accompanied by the development of an electromagnetic system with only one set of power supply to generate a current composed of a gradual-ascending and rapid-descending stage. This current induces a significant radially outward Lorentz force, facilitating hole expansion and introducing residual compressive stress around the hole, thus increasing the fatigue life of the fasteners. The experimental results demonstrate a remarkable enhancement in fatigue life for samples treated with the EMCE process when compared to untreated ones, showing an impressive 6.8-fold, 4.9-fold, and 1.6-fold increase at stress loads of 120 MPa, 130 MPa, and 150 MPa, respectively. Microstructural analysis reveals that the processed components exhibit favorable surface integrity, and there is no significant grain refinement near the hole. Moreover, it is found that there existed optimal current waveform to maximize fatigue life. These findings hold significance in understanding the EMCE process and advancing its practical applicability.

Numerical modeling of electromagnetic field spatiotemporal evolution to evaluate the effects on calcium carbonate crystallization

Calcium carbonate (CaCO3) scaling is a significant impediment to water systems. Electromagnetic field (EMF) treatment is a promising approach to control scaling owing to its simplicity and low or no energy requirements. However, the underlying mechanisms by which EMF impacts CaCO3 crystallization remain unclear due to the challenges in measuring the EMFs in feed solutions and the lack of a fundamental understanding of the applied EMFs and the observed physicochemical phenomena. To fill this knowledge gap, a high-fidelity COMSOL model was first developed to simulate EMFs in bulk solutions for three alternating current-induced EMF devices with different configurations and properties. These were then integrated with experimental data to unveil the underlying mechanism by which applied EMFs alter the physicochemical processes. The study revealed that even low-strength EMFs (e.g., electric fields <0.15 V/m and magnetic fields <0.03 mT) promoted CaCO3 precipitation in bulk solutions. The electric fields created by these EMF devices resulted in higher Lorentz force compared to their induced magnetic fields. The methodology of this study offers the capability to predict the effectiveness of different EMF devices in facilitating crystallization processes, and these mechanistic insights lay the foundation for the smart design of EMF devices for diverse water treatment applications.

Equivalence of magnetic flux and energy

Magnetic flux and energy equivalence is the principle that everything that has magnetic flux has an equivalent amount of energy, and vice versa. The main methods used: transformation of natural units, algebra, analogy. The equivalence of magnetic flux and energy, despite its widespread use in describing the principles of physics, has not yet been formulated. This paper presents the formula for this equivalence. This is done based on known measurement systems, parameters and principles of physics. Five examples (Stoney units, Planck units, standard gravitational parameter, Lorentz force, and Ampere force) of the algebraic representation of this principle show its universality. Five examples should justify the universality of the new principle and its use in physics and astrophysics. Using the equivalence of magnetic flux and energy, new physical units of mass and magnetic flux are proposed, each of which is suitable for measuring both mass and magnetic flux. Natural values of electric current and voltage, linear density of electric capacitance and inductance, linear density of magnetic flux, linear density of electric charge, as well as natural units of electric voltage and current, electrical resistance, magnetic flux, electrical capacitance and inductance are also described. The article presents the Einstein field equation (additional magnetic stress–energy–momentum tensor) and a standard astrophysical parameter for refining the orbits of celestial bodies.