Magnetic Field Boundary Conditions Research Articles

Flux and symmetry effects on quantum tunneling

AbstractMotivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer & Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.

A numerical study on MHD Maxwell fluid with nanoparticles over a stretching surface: Impacts of thermal radiation, convective boundary condition and induced magnetic field

The current study investigates the influence of induced magnetic field and convective boundary condition on the behavior of a magnetohydrodynamic (MHD) Maxwell fluid including nanoparticles flowing through a stretching sheet. Furthermore, the analysis considers the existence of radiation. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The primary conclusions of this study are that increasing the Magnetic parameter decreases the Induced Magnetic field while increasing the Deborah parameter improves the velocity profile. Temperature distribution is growing due to increased estimates of the Radiation, Biot number, and Deborah number values. When the Lewis number values are raised, the concentration profiles get smaller but there is an opposite scenario deployed as the Thermophoresis parameter upsurges. The findings of this study are consistent with those that have been previously reported. The phenomenon of flow induced by a stretched surface finds several applications in various industrial and technological domains, including copper wire production, polymer extrusion, article manufacturing, and fiber synthesis. Induced magnetic fields are extremely prominent in many areas of science and technology, including electromagnetism, magnetic materials, and magnetic resonance imaging (MRI).

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.

Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions

AbstractThis research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Dynamic Behavior Modeling of Natural-Rubber/Polybutadiene-Rubber-Based Hybrid Magnetorheological Elastomer Sandwich Composite Structures.

This study investigates the dynamic characteristics of natural rubber (NR)/polybutadiene rubber (PBR)-based hybrid magnetorheological elastomer (MRE) sandwich composite beams through numerical simulations and finite element analysis, employing Reddy's third-order shear deformation theory. Four distinct hybrid MRE sandwich configurations were examined. The validity of finite element simulations was confirmed by comparing them with results from magnetorheological (MR)-fluid-based composites. Further, parametric analysis explored the influence of magnetic field intensity, boundary conditions, ply orientation, and core thickness on beam vibration responses. The results reveal a notable 10.4% enhancement in natural frequencies in SC4-based beams under a 600 mT magnetic field with clamped-free boundary conditions, attributed to the increased PBR content in MR elastomer cores. However, higher magnetic field intensities result in slight frequency decrements due to filler particle agglomeration. Additionally, augmenting magnetic field intensity and magnetorheological content under clamped-free conditions improves the loss factor by from 66% to 136%, presenting promising prospects for advanced applications. This research contributes to a comprehensive understanding of dynamic behavior and performance enhancement in hybrid MRE sandwich composites, with significant implications for engineering applications. Furthermore, this investigation provides valuable insights into the intricate interplay between magnetic field effects, composite architecture, and vibration response.

A comparative assessment of mono and hybrid magneto nanofluid flow over a stretching cylinder in a permeable medium with generalized Fourier’s law

This study investigates the flow and heat transfer of mono and hybrid nanofluids owing to a stretching cylinder in a porous medium under the influence of a magnetic field and convective boundary condition. The hybrid nanofluid is made up of copper (Cu) and silver (Ag) nanoparticles dispersed in a water-ethylene glycol mixture at a mass ratio of 50:50. The binary mixture of water and ethylene glycol is intermixed with spherical-shaped nanoparticles (copper) to create a mono nanofluid. The study considers the effects of generalized Fourier’s law and heat generation/absorption. The novelty of the study lies in considering the comparison of hybrid and mono nanofluid flows heat transfer efficiency with assumed effects and convective condition at the boundary of the cylinder. A system of ordinary differential equations (ODEs) controlling the flow and heat transport are derived using similarity transformations and are solved numerically using the bvp4c program of MATLAB software. The work explores the ways in which different parameters, such as the shape of the nanoparticles and their volume percentage, affect the pertinent profiles and are depicted in the form of graphical illustrations and numerically tabulated values. The results demonstrate that, in comparison to mono nanofluids, hybrid nanofluids including spherical and blade nanoparticles have a higher heat transfer rate and reduced surface drag when the particle volume fraction is increased in a water-ethylene glycol combination. Furthermore, there is a 0.83% increase in the heat transfer rate for hybrid nanofluids in comparison to mono nanofluids. This is because compared to mono nanofluids, hybrid nanofluids have lower viscosity and better heat conductivity. The results obtained in this study are vetted by making a comparison with published works and an excellent agreement between the values is seen. The study may find use in solar thermal systems, electronic cooling, heat exchangers, and other areas.

Heat and Mass transport analysis for Williamson MHD nanofluid flow over a stretched sheet

This study focuses on analyzing the behavior of a time-varying magnetohydrodynamic (MHD) Williamson nanofluid (WNF) flowing over a stretched plate. The main objective is to understand the heat and mass transport properties of the nanofluid in this scenario. The mathematical model involves a system of partial differential equations (PDEs) that are transformed into a set of ordinary differential equations (ODEs) using a similarity transformation. These ODEs are then solved using the well-established MATLAB BVP4C technique; a part of the finite difference method. To ensure the reliability and accuracy of the approach, the obtained results are compared with previously published literature, serving as a validation step. The numerical findings are presented graphically and in tabular form. The study focuses on examining the impact of various external factors on the friction factor, Nusselt number, and Sherwood number, providing a comprehensive evaluation of heat transfer and mass transport characteristics. Specifically, the study investigates the flow and heat transfer properties near a stretched plate with a permeable layer. Also, takes into account the transverse dispersion, and heat generation effects in MHD WNF moreover with magnetic field and slip boundary conditions. The results of the study indicate that increasing the Brownian motion parameter (Nb) and Thermophoresis parameter (Nt) leads to higher local Nusselt numbers, reflecting the increased rates of transferring the heat. Similarly, an increase in the Nt is associated with higher local Sherwood numbers, indicating enhanced mass transport. Conversely, higher values of the Brownian motion parameter (Nb) result in lower local Sherwood numbers. By analyzing the influence of various external factors, such as nanofluid properties and magnetic fields, a better understanding of heat transfer and mass transport characteristics can be obtained.

Weak solutions to the full MHD system with non-homogeneous boundary conditions

ABSTRACT This paper is devoted to the study of weak solutions for full compressible magnetohydrodynamic flows in a 3D bounded domain, with non-homogeneous boundary condition for the velocity, absolute temperature and density on the inflow part, with Navier-type slip boundary condition for magnetic field. We show the weak–strong uniqueness principle as well as the global existence under a new notion of weak solution.

Magnetic perturbations of the Robin Laplacian in the strong coupling limit

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular limit when the Robin parameter tends to infinity, which is equivalent to a semi-classical limit involving a small positive semi-classical parameter. The main result is a comparison between the spectrum of the Robin Laplacian with an effective operator defined on the boundary of the domain via the Born–Oppenheimer approximation. More precisely, the low-lying eigenvalue of the Robin Laplacian is approximated by those of the effective operator. When the curvature has a unique non-degenerate maximum, we estimate the spectral gap and find that the magnetic field does not contribute to the three-term expansion of the eigenvalues. In the case of the disc domains, the eigenvalue asymptotics displays the contribution of the magnetic field explicitly.

Mechanism of Double-Diffusive Convection on Peristaltic Transport of Thermally Radiative Williamson Nanomaterials with Slip Boundaries and Induced Magnetic Field: A Bio-Nanoengineering Model

The present work has mathematically modeled the peristaltic flow in nanofluid by using thermal radiation, induced a magnetic field, double-diffusive convection, and slip boundary conditions in an asymmetric channel. Peristalsis propagates the flow in an asymmetric channel. Using the linear mathematical link, the rheological equations are translated from fixed to wave frames. Next, the rheological equations are converted to nondimensional forms with the help of dimensionless variables. Further, the flow evaluation is determined under two scientific assumptions: a finite Reynolds number and a long wavelength. Mathematica software is used to solve the numerical value of rheological equations. Lastly, the impact of prominent hydromechanical parameters on trapping, velocity, concentration, magnetic force function, nanoparticle volume fraction, temperature, pressure gradient, and pressure rise are evaluated graphically.

Rheological study of Hall current and slip boundary conditions on fluid-nanoparticle phases in a convergent channel.

Purpose: the purpose of this theoretical study was to analyze the heat transfer in the fluid-particle suspension model under the effects of a porous medium, magnetic field, Hall effects, and slip boundary conditions in a convergent channel with the addition of electrokinetic phenomena. The Darcy-Brinkman (non-Darcy porous medium) model was used to assess the effects of the porous medium. Methodology: the rheological equations of both models were transformed into a dimensionless form to obtain the exact solutions of the fluid and particle phase velocities, pressure gradient, volumetric flow rate, stream function, temperature distribution, and heat-transfer rate. To obtain an exact solution to the models, the physical aspects of the parameters are discussed, analyzed, and reported through graphs, contour plots, and in tabular form. Findings: mixing in hafnium particles in a viscous fluid provide 1.2% more cooling compared to with a regular fluid. A reduction of the streamlines was observed with the contribution of the slip condition. The utilization of the Darcy parameters upgraded both the fluid flow and temperature profiles, while the heat-transfer rate decreased by up to 3.3% and 1.7% with the addition of a magnetic field and porous medium, respectively. Originality: the current study is an original work of the authors and has not been submitted nor published elsewhere.

Significance of Free Convection Flow over an Oscillating Inclined Plate Induced by Nanofluid with Porous Medium: The Case of the Prabhakar Fractional Approach.

Given the importance and use of electrically conducted nanofluids, this work aims to examine an engine-oil-based nanofluid including various nanoparticles. In the current study, a fractional model for inspecting the thermal aspect of a Brinkman-type nanofluid, composed of (molybdenum disulfide (MOS2) and graphene oxide (GO) nanoparticles flows on an oscillating infinite inclined plate, which characterizes an asymmetrical fluid flow, heat, and mass transfer. Furthermore, the Newtonian heating effect, magnetic field, and slip boundary conditions were taken into account. The objectives for implementing the Prabhakar-like fractional model are justified because this fractional algorithm has contemporary definitions with no singularity restrictions. Furthermore, the guided fractional model was solved using the Laplace transform and several inverse methods. The obtained symmetrical solutions have been visually analyzed to investigate the physics of several relevant flow parameters on the governed equations. Some exceptional cases for the momentum field are compiled to see the physical analysis of the flowing fluid symmetry. The results show that the thermal enhancement can be progressively improved with the interaction of the molybdenum disulfide-engine oil-based nanofluid suspension, rather than with the graphene oxide mixed nanoparticle fluid. Furthermore, the temperature and momentum profiles enhance due to the factional parameters for molybdenum disulfide and the graphene oxide-engine oil-based nanofluid suspension. This study's graphical and numerical comparison with the existing literature has shown a very close resemblance with the present work, which provides confidence that the unavailable results are accurate. The results show that an increase improved the heat transmission in the solid nanoparticle volume fractions. In addition, the increment in the mass and heat transfer was analyzed in the numerical evaluation, while the shear stress was enhanced with the enhancement in the Prabhakar fractional parameter α.

Global Existence of Bounded Solutions for Eyring–Powell Flow in a Semi-Infinite Rectangular Conduct

The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial velocity profiles (u10,u20) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u10,u20)∈L2(Ω), Ω=[0,L]×[0,H]×(0,∞). Afterward, the results are extended for (u10,u20)∈Lp(Ω), p>2. Lastly, the existence criteria are obtained when (u10,u20)∈H1(Ω). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids.

Hydromagnetic mixed convection unsteady radiative Casson fluid flow towards a stagnation‐point with chemical reaction, induced magnetic field, Soret effect, and convective boundary conditions

AbstractThis article presents the two‐dimensional mixed convective MHD unsteady stagnation‐point flow with heat and mass transfer on chemically reactive Casson fluid towards a vertical stretching surface. This fluid flow model is influenced by the induced magnetic field, thermal radiation, viscous dissipation, heat absorption, and Soret effect with convective boundary conditions and solved numerically by shooting technique. The calculations are accomplished by MATLAB bvp4c. The velocity, induced magnetic field, temperature, and concentration distributions are displayed by graphs for pertinent influential parameters. The numerical results for skin friction coefficient, rate of heat, and mass transfer are analyzed via tables for different influential parameters for both assisting and opposing flows. The results reveal that the enhancement of the unsteadiness parameter diminishes velocity and induced magnetic field but it rises temperature and concentration distributions. Moreover, higher values of magnetic Prandtl number enhance Nusselt number and skin friction coefficient, but it has the opposite impact on Sherwood number. We observe that the amplitude is higher in assisting flow compared to opposing flow for skin friction coefficient and Nusselt number whereas opposite trends are noticed for Sherwood number. Our model will be applicable to various magnetohydrodynamic devices and medical sciences.

Tangent-hyperbolic nanoliquid flow in a microchannel, thermal and irreversibility rate analysis

ABSTRACT The objective of the current investigation is to examine the influence of buoyancy force, heat source, Brownian motion, thermophoresis, chemical reaction, transverse magnetic field and convective boundary condition on flow of tangent-hyperbolic nanofluid through an upright microchannel. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations. The RKF45 method along with the shooting technique is used to solve the fluidic system numerically. The Buongiorno model is considered to observe the influence of thermophoresis, Brownian motion and chemical reaction with mixed convection. Graphical and numerical illustrations are presented to visualize the behavior of different parameters of interest on velocity, temperature, concentration and entropy generation of the flow system. The substantial findings of this study have been recorded as the amplification in the thermal and solutal Grashof number causes an increment in the flow rate in a channel, the thermal energy builds up with Brinkman number and heat source parameter, another significant outcome of the present analysis is that there is a downfall in the concentration field with the strengthening of thermophoresis parameter.

An analytical power frequency reactance calculation method of the triaxial high temperature superconducting cables

Using the triaxial high temperature superconducting cables (HTSC) for high density load supply in modern cities is a new development direction. Since the triaxial HTSCs have a different structure from the common cables, their reactance cannot be calculated by conventional methods. In order to establish a basis for further research on operation control, it is important to study the analytical power frequency reactance calculation method of the triaxial HTSC. In this paper, the mathematical model of the triaxial HTSC is established based on the branch parameter method. Based on the model, the analytical calculation method of the three-phase reactance and sequence reactance parameters is established considering the magnetic field coupling and boundary conditions. The calculated values are compared with the measured sequence reactance values of the triaxial HTSC in a pilot project, and the comparison results verify the accuracy and validity of the proposed method. Furthermore, considering the asymmetrical three-phase parameters of the triaxial HTSCs, the impact on the power system operation is tested through the simulation model based on the pilot project network. Simulation results show that the impact is small and does not endanger the system stability.

Runaway electron deconfinement in SPARC and DIII-D by a passive 3D coil

The operation of a 3D coil—passively driven by the current quench (CQ) loop voltage—for the deconfinement of runaway electrons (REs) is modeled for disruption scenarios in the SPARC and DIII-D tokamaks. Nonlinear magnetohydrodynamic (MHD) modeling is carried out with the NIMROD code including time-dependent magnetic field boundary conditions to simulate the effect of the coil. Further modeling in some cases uses the ASCOT5 code to calculate advection and diffusion coefficients for REs based on the NIMROD-calculated fields, and the DREAM code to compute the runaway evolution in the presence of these transport coefficients. Compared with similar modeling in Tinguely et al (2021 Nucl. Fusion 61 124003), considerably more conservative assumptions are made with the ASCOT5 results, zeroing low levels of transport, particularly in regions in which closed flux surfaces have reformed. Of three coil geometries considered in SPARC, only the n = 1 coil is found to have sufficient resonant components to suppress the runaway current growth. Without the new conservative transport assumptions, full suppression of the RE current is maintained when the thermal quench MHD is included in the simulation or when the RE current is limited to 250kA, but when transport in closed flux regions is fully suppressed, these scenarios allow RE beams on the order of 1–2 MA to appear. Additional modeling is performed to consider the effects of the close ideal wall. In DIII-D, the CQ is modeled for both limited and diverted equilibrium shapes. In the limited shape, the onset of stochasticity is found to be insensitive to the coil current amplitude and governed largely by the evolution of the safety-factor profile. In both devices, prediction of the q-profile evolution is seen to be critical to predicting the later time effects of the coil.

Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions

We investigate the linear instability of a fully developed pressure-driven flow of an electrically conducting fluid in a porous channel using the Brinkman-Darcy model and the additional effects of a uniform magnetic field and slip boundary conditions. Two Chebyshev collocation techniques are used to solve the ordinary eigenvalue system governing the onset of convection. The critical Reynolds number, Rec, wavenumber, ac, and wave speed cc are found in terms of the porous parameter M, the dimensionless slip length, N0, and the Hartmann number Ha.

Existence of a solution to the steady Magnetohydrodynamics‐Boussinesq system with mixed boundary conditions

In this paper, we are concerned with the steady magnetohydrodynamics (MHD)‐Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include the stick, Tresca slip, leak, one‐sided leaks, pressure, vorticity, and stress conditions together, and the conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. For the electromagnetic field, mixed boundary conditions are given. Also, the viscosity, magnetic permeability, electrical conductivity, thermal conductivity, and specific heat of the fluid depend on the temperature. Special attention is paid to the meaning of non‐homogeneous mixed boundary conditions for magnetic field. For the problem involving the static pressure and stress boundary conditions for fluid, it is proven that if the data of problem are small enough, then there exists a solution and the solution with small norm is unique when the viscosity, magnetic permeability, electrical conductivity, thermal conductivity, and specific heat are independent of the temperature. For the problem involving the total pressure and total stress boundary conditions for fluid, the existence of a solution is proven when a datum concerned with non‐homogeneous boundary conditions for magnetic field is small, but without smallness of other data.