Effect Of Magnetic Field Research Articles

Exact solutions and bifurcations for the (3+1)-dimensional generalized KdV-ZK equation

Abstract In this paper, a class of (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation is studied by utilizing the bifurcation theory of the planar dynamical systems and the Fan sub-function method. This model can be used to explain the effects of magnetic fields on weakly nonlinear ion-acoustic waves investigated in plasma fields composed of cold and hot electrons. Under the different parameter conditions, the phase portraits and bifurcations are derived, and new exact solutions including soliton, periodic, kink and breaking wave solutions for the model are constructed. Moreover, some exact solutions, which contain soliton, kink, trigonometric function, hyperbolic function, Jacobi elliptic function solutions, are derived via the improved Fan sub-function method. The types of solutions obtained completely correspond to the types of the orbits acquired
above, which verifies the validity of the method. Finally, the physical structures of some exact solutions are analyzed in graphical forms.

Propulsive study of blood flow with heat transfer enhancement connection to ferro copper magnetized nanoparticles in converging tapered stenosed arterial surface

To investigate the effects of magnetic fields and variously structured nanoparticles in narrowing, stenosed arteries, an arterial flow model is incorporated. The aim of this study here is to achieve more realistic results by modeling and simulating the arterial blood flow system with the nanoparticles and shape factor of the nanoparticles. The study of blood flow in tapered stenosed arteries with nanoparticles involves understanding the dynamics of blood circulation in vessels having application in drug delivery. Nanoparticles with specific shape factors can enhance imaging modalities like MRI, CT or ultrasound diagnosing tumor. Metallic nanoparticles in various shapes utilizing water as the base fluid have not yet been considered. Imagine a symmetrical radially but axially nonsymmetric constriction for the blood flow. Along with taking into account the regularity in the sequence of distributing the wall shear stress as well as resistance impedance, the study also takes into account a rise in these readings as the stenosis worsens. For speed, resistive impedance, wall shear and shearing forces at the stenosis throat, results have been computed in exact form. For various Cu-water-relevant parameters, the visual results of several types of converging tapering arteries have been assessed.

Numerical simulation of combined effects of a vertical magnetic field and thermal radiation on natural convection of non-Newtonian fluids confined between circular and square concentric cylinders

BackgroundThis study addresses magnetohydrodynamic (MHD) natural convection involving non-Newtonian fluids. Focusing on the annular region between concentric circular and square cylinders, the research examines the impact of a vertical magnetic field and thermal radiation. MethodsThe Multiple Relaxation Time Lattice Boltzmann Method (MRT-LBM) is employed to simulate momentum and energy interactions in non-Newtonian fluid. Control parameters like Rayleigh number, Hartmann number, Radiation parameter, aspect ratio, square cylinder subdivision, and power-law index are systematically varied, while maintaining a constant Prandtl number. Significant findingsUsing shear-thinning fluid (n < 1) significantly improves cooling, particularly in conjunction with radiation effect. Correlations for the mean Nusselt number are established, offering insights. Results emphasize the substantial influence of parameters like Ra, Rd, and AR. High values of the latter promote the flow intensity and heat evacuation. For n < 1, increasing Ra from 103 to 5 × 104 results in a substantial increase in the heat transfer rate reaching 65 %. For shear-thickening fluid, the heat transfer rate is reduced by 25.31 % at Ra = 5 × 104 when Ha is increased from 0 to 50 in the absence of radiation. In addition, radiation enhances the heat transfer rate by 71.41 % by incrementing Rd from 0 to 0.8 for Ha = 0. The most pronounced effect of the radiation parameter is observed in the cases of Newtonian and shear-thickening fluids. Conversely, Ha and n act by reduction effects on the outputs of the problem. The attenuating effect of the magnetic field is more pronounced in the case of shear-thinning fluids. The plot of mean Nusselt number vs. AR shows an hysteresis phenomenon due to the existence of multiple steady solutions in a range of this parameter. In the latter range of AR, heat transfer induced by multicellular flow is higher than that induced by bicellular one. Heat transfer is somewhat enhanced by the RC configuration, compared to SC one.

Magnetic Field Effect on Photocatalytic Dye Degradation: A Review

AbstractIn the present day, photocatalysis has become the primary and most promising technology to generate renewable energy and degrade environmental pollutants. Remarkable efforts have been made to improve photocatalytic efficiency. Among these, introducing an external magnetic field is considered a promising strategy to boost photocatalytic performance. This review explores the dynamic realm of improving photocatalytic efficiency, with a particular emphasis on the strategic integration of external magnetic fields. Examining recent breakthroughs, we reviewed the influence of magnetic fields on diverse catalyst materials, including both magnetic and nonmagnetic variants, 2D materials, and semiconductors. Comprehensive coverage is provided on the mechanisms governing photocatalytic dye degradation, materials utilized for catalysis, and the profound impact of magnetic fields on enhancing reaction kinetics. This review also focuses on recent advances in the application and effect of magnetic fields in the magnetic and nonmagnetic catalysts towards dye degradation. This review provides a forward‐looking view, highlighting the potential of magnetic field‐enhanced photocatalysis to play a central role in sustainable energy and environmental management.

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

Influence of a magnetic field on the frequency of a laser stabilized to molecular iodine

We report on the effect of a weak magnetic field applied on an iodine cell used to frequency stabilize a laser. A 1.5 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}m laser is frequency tripled in order to excite the molecular transitions at 0.51 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}m and frequency locked on a hyperfine line. With this frequency reference, we report short-term stability about 3×10-14τ-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3 \ imes 10^{-14}~\ au ^{-1/2}$$\\end{document}, with a minimum value of 4×10-15\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \ imes 10^{-15}$$\\end{document} at 200 s. The lower part of 10-15\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-15}$$\\end{document} frequency stability domain is reached, in our case, only by adding an efficient magnetic shield around the sealed quartz iodine cell. In order to quantify the Zeeman effect, we applied magnetic fields of several ×10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes 10^{-4}$$\\end{document} T on the cell containing the iodine vapour. The Zeeman effect affects the lineshape transition in such a way that we observe a modification of the laser frequency. We have measured this linear Zeeman shift at (1062±6)×104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1062\\pm 6) \ imes 10^{4}$$\\end{document} Hz/T for the a1 hyperfine component of the R(34) 44-0 transition, near 514 nm by applying a magnetic field along the cell. Thus, in case of uncontrolled magnetic fields of an order of magnitude of 1×10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ imes 10^{-4}$$\\end{document} T, the frequency stability is limited in the upper of the 10-14\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-14}$$\\end{document} domain.

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Impact of heat and mass transfer on the magnetohydrodynamic two-phase flow of couple stress fluids through a porous walled curved channel using Homotopy Analysis Method

The analysis of heat and mass transfer in the movement of immiscible couple stress fluids through a curved channel whose walls are at two different temperatures is the focus of the current work. Immiscible fluids are subjected to an external magnetic field that is taken normal to the fluid’s flow. For suction or injection in the flow, the channel walls are presumed to be porous. The buoyancy force, which is modelled using the Boussinesq approximation, and a constant pressure gradient cause the flow of the couple stress fluids in the curved channel. The highly non-linear coupled differential equations associated with the proposed work are solved with the use of the semi-analytic Homotopy Analysis Method. The semi-analytical expression of the various flow variables such as flow velocity, temperature, concentration, etc. is obtained by solving these non-linear differential equations after they have been non-dimensionalized by taking into account non-dimensional parameters. From the obtained results authors have noted how the two immiscible couple stress fluids’ flow velocity, temperature, and concentration behaviour depend on the flow-effecting parameters, including the couple stress parameter, curvature parameter, Schmidt number, and so on. Further, the authors of the proposed work have analysed the effect of various flow parameters on heat and mass transfer. Since the authors have studied the two-phase flow of couple stress fluids in a porous walled curved channel together with the effect of magnetic field, the current model has various applications in the fields of crude oil extraction, filtration, nuclear reactor, and bio-mechanics.

Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink

Purpose Ferrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions. Design/methodology/approach The leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties. Findings Multiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter. Originality/value The novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.

An overview of ion-acoustic solitary and shock waves in a magnetized nonthermal plasma: influence of trapped positrons and electrons

A magnetized nonthermal electron–positron-ion (e-p-i) plasma is considered to study the propagation properties of ion-acoustic solitary and shock waves in the presence of trapped positrons and electrons for the first time. The Schamel-κ (kappa) distribution function that describes plasma nonthermality and particle trapping is assumed to consider electrons and positrons. The diffusive effect of ion plasma fluid, which is responsible for shock dynamics, is taken into account. A nonlinear Schamel-Korteweg–de Vries-Burgers’ (SKdVB) equation is derived by employing the reductive perturbation approach, and the solitary and shock wave solutions of the SKdVB equation have also been derived for different limiting cases. It is found that only positive potential nonlinear structures (for both solitary and shock waves) are formed in the proposed plasma system. The condition for stable solitons in the absence of dissipation is analyzed, and the nature of arbitrary amplitude solitary waves (obtained via the Sagdeev potential approach) is discussed. It is found through theoretical and numerical investigation that different plasma compositional parameters (such as the trapping effect of electrons (β e ) and positrons (β p ), the obliquity effect (θ), electron-to-ion number density ratio (µ e ), the magnetic field effect (via Ω) and the viscous effect (via η)) have a significant influence on the dynamics of ion-acoustic solitary and shock waves. The theoretical and numerical investigations in this study may be helpful in describing the nature of localized structures in different plasma contexts, e.g. space and astrophysical plasmas and experimental plasmas where electron–positron-ion plasmas exist.

In vitro assessment of the effect of magnetic fields on efficacy of biosynthesized selenium nanoparticles by Alborzia kermanshahica

Cyanobacteria represent a rich resource of a wide array of unique bioactive compounds that are proving to be potent sources of anticancer drugs. Selenium nanoparticles (SeNPs) have shown an increasing potential as major therapeutic platforms and led to the production of higher levels of ROS that can present desirable anticancer properties. Chitosan–SeNPs have also presented antitumor properties against hepatic cancer cell lines, especially the Cht-NP (Chitosan–NPs), promoting ROS generation and mitochondria dysfunction. It is proposed that magnetic fields can add new dimensions to nanoparticle applications. Hence, in this study, the biosynthesis of SeNPs using Alborzia kermanshahica and chitosan (CS) as stabilizers has been developed. The SeNPs synthesis was performed at different cyanobacterial cultivation conditions, including control (without magnetic field) and magnetic fields of 30 mT and 60 mT. The SeNPs were characterized by uv-visible spectroscopy, Fourier-transform infrared spectroscopy (FT-IR), Dynamic light scattering (DLS), zeta potential, and TEM. In addition, the antibacterial activity, inhibition of bacterial growth, minimum inhibitory concentration (MIC), and minimum bactericidal concentration (MBC), as well as the antifungal activity and cytotoxicity of SeNPs, were performed. The results of uv-visible spectrometry, DLS, and zeta potential showed that 60 mT had the highest value regarding the adsorption, size, and stabilization in compared to the control. FTIR spectroscopy results showed consistent spectra, but the increased intensity of peaks indicates an increase in bond number after exposure to 30 mT and 60 mT. The results of the antibacterial activity and the inhibition zone diameter of synthesized nanoparticles showed that Staphylococcus aureus was more sensitive to nanoparticles produced under 60 mT. Se-NPs produced by Alborzia kermanshahica cultured under a 60 mT magnetic field exhibit potent antimicrobial and anticancer properties, making them a promising natural agent for use in the pharmaceutical and biomedical industries.

Computational Fluid Dynamics-Based Analysis of Magnetic Field Effect on Improvement the Performance of Stepped Solar Still

Computational Fluid Dynamics-Based Analysis of Magnetic Field Effect on Improvement the Performance of Stepped Solar Still

The Influence and Mechanism Analysis of the Longitudinal Magnetic Field on the Microstructure Evolution and Properties of AZ40 Welds

This paper studied the effect of the longitudinal magnetic field (LMF) on the microstructure evolution and mechanical properties of AZ40 argon tungsten arc welding joints. Magnetic field-assisted argon tungsten arc welding technology was used to achieve butt welding of an AZ40 Mg alloy sheet with a thickness of 1.5 mm. The microstructure of the Mg alloy weld was studied by using metallographic microscopy and scanning electron microscopy. Mechanical performance of the Mg alloy weld was evaluated by using a hardness tester and universal tensile machine. The experimental results revealed that the average crystallite dimension of the weld zone of the Mg alloy joint reached 43 μm without an LMF. By introducing LMF-assisted technology, the weld structure was significantly refined and the average crystallite dimension of the weld seam was reduced by 39.5% to 26 μm with a coil current of 1.2 A. For the joint without magnetic field assistance, the optimum tensile strength of the AZ40 weldment was 225 MPa under a welding current of 80 A, and fracture occurred in the center of joint welding seam. Under an LMF coil current of 1.2 A, the joint strength increased from the initial 225 MPa to 254 MPa, and fracture occurred at the weld edge with obvious plastic fracture characteristics. It can be confirmed that the LMF-assisted welding process effectively improved the microstructure characteristics of the weld seam and strengthened the microhardness and mechanical performance of the AZ40 joint.

Two-term Boltzmann approximation versus Monte-Carlo simulation: effect of magnetic field

In this paper, we investigate the spatial-local electron energy distribution function (eEDF) interacting with a background gas at the sub-atmospheric pressure in a wide range of applied crossed electric and magnetic fields using the Boltzmann kinetic equation. We compare solutions obtained using two numerical approaches (deterministic two-term approximation and stochastic Monte Carlo method) to identify their applicability in the context of determining drift velocity and reaction constants for electrons. For argon and helium, the upper limit of the reduced electric field applicability of the two-term approximation is discussed. It has been shown that the presence of a magnetic field can reduce this limit. Two explanations are given, one is based on the math of two-term formalism, and the other is based on velocity-space analysis. Two-term approximation fails due to it’s inability to resolve underlying cyclotron oscillation (it should result in an energy variation along the electron’s trajectory). The absence of this feature causes an incorrect estimation of momentum-transfer rate. This results an inaccuracy in the estimation of the angle between electric field and drift velocity.

Analytical solution to boundary layer flow and convective heat transfer for low Prandtl number fluids under the magnetic field effect over a flat plate

AbstractThe present study aims to quantify the flow field, flow velocity, and heat transfer features over a horizontal flat plate under the influence of an applied magnetic field, with a particular emphasis on low Prandtl number fluids. Nonlinear partial differential expressions can be incorporated into the ordinary differential framework with the use of appropriate transformations. This research utilizes the variational iteration method (VIM) to approximate solutions for the system of nonlinear differential equations that define the problem. The objective is to demonstrate superior flexibility and broader application of the VIM in addressing heat transfer issues, compared to alternative approaches. The results obtained from the VIM are compared with numerical solutions, revealing a significant level of accuracy in the approximation. The numerical findings strongly suggest that the VIM is effective in providing precise numerical solutions for nonlinear differential equations. The analysis includes an examination of the flow field, velocity, and temperature distribution across various parameters. The study found that improving temperature patterns, velocity distribution, and flow dynamics were all positively impacted by increasing the Prandtl numbers. As a result, this leads to the thickness of the boundary layer to decrease and improves heat transfer at the moving surface. Thus, the convection process becomes more efficient. When the strength of the magnetic field is increased, the velocity of the fluid decreases. This observation aligns with expectations since the magnetic field hampers the natural flow of convection. Notably, the convection process can be precisely controlled by carefully applying magnetic force.

Magnetic field assisted centrifugal acceleration thin-layer chromatography: An approach to investigate the magnetic field effects on separation parameters including retention factor difference, selectivity factor, and resolution

The effect of internal and external magnetic fields on the separation of antifungal drugs by centrifugal acceleration thin-layer chromatography was reported for the first time. External and internal magnetic fields were applied using neodymium magnets and CoFe2O4@SiO2 ferromagnetic nanoparticles. Separation of ketoconazole and clotrimazole was performed using a mobile phase consisting of n-hexane, ethyl acetate, ethanol, and ammonia (2.0:2.0:0.5:0.2, v/v). The influence of the magnetic field on the entire chromatographic system led to changes in the properties of the stationary and mobile phases and the analytes affecting the retention factor, shape, and width of the separated rings. The extent of this impact depended on the structure of the analyte and the type and intensity of the magnetic field. In the presence of the external magnetic field, there were more significant changes in the chromatographic parameters of the drugs, especially the width of the separated rings, and ketoconazole was more affected than clotrimazole. The changes are conceivably due to the effect of the magnetic field on the analyte distribution between the stationary and mobile phases, which is also caused by the possibility of the magnetic field affecting the viscosity, surface tension, and surface free energy between the stationary and mobile phases.

Confinement and magnetic-field effect on chiral ferroelectric nematic liquid crystals in Grandjean-Cano wedge cells

Confinement and magnetic-field effect on chiral ferroelectric nematic liquid crystals in Grandjean-Cano wedge cells

Exploring travelling wave solutions, bifurcation, chaos, and sensitivity analysis in the (3+1)-dimensional gKdV-ZK model: A comprehensive study using Lie symmetry methodology

This article presents a study on the generalized Korteweg-de Vries-Zakharov-Kuznetsov (gKdV-ZK) model, which is a nonlinear system that demonstrates the effect of magnetic fields on weak ion-acoustic waves in plasma consisting of cold and hot electrons. The research entails investigating the reduction of symmetry through Lie group analysis, scrutinizing the characteristics of the dynamic structure using bifurcation phase diagrams, and examining the dynamic behaviour of the perturbed dynamical system employing chaos theory. Methods such as 3D and 2D phase portraits, time series analysis, Poincaré maps, exploration of multistability in the autonomous structure across various initial conditions, Lyapunov exponents, and bifurcation diagrams are exercised to demonstrate chaotic behaviour. Additionally, the research establishes general forms of solitary wave solutions, encompassing hyperbolic, trigonometric, and rational soliton solutions, through the utilization of a modified auxiliary equation approach to analytically address the examined problem. These findings are visually depicted as 2D and 3D graphs with carefully selected parameters, accompanied by their corresponding constraint conditions. Furthermore, the sensitivity analysis of the studied equation is deliberated upon and visually illustrated. The uncovered findings are captivating, innovative, and potentially beneficial for comprehending various physical phenomena in engineering and science.

Analytical Solution for MHD Casson Nanofluid Flow and Heat Transfer due to Stretching Sheet in Porous Medium

The feature of having a surface that can stretch has garnered attention in numerous industrial and engineering fields because of its advantages. Nevertheless, most fluid mechanics simulations for stretchable surfaces have predominantly relied on numerical solutions, with a notable lack of theoretical investigations into this matter. Consequently, the current research aims to contribute a theoretical exploration of heat transfer and boundary layer flow for Casson nanofluid on a linearly stretching sheet, considering the existence of porosity and magnetic field effects. Two distinct types of water-based nanofluids containing aluminium oxide and silicon dioxide are examined. By employing similarity transformations, the governing momentum and energy equations undergo transformation and subsequent analytical resolution using Laplace transformations. The resulting solutions are graphically presented to examine the influence of key parameters on temperature and velocity distribution. The analysis indicates that heat transfer is improved by the inclusion of nanoparticles, porosity, and a magnetic field. However, the velocity distribution slows down as a result of higher nanoparticle volume fraction, porosity, and magnetic field imposition.

Numerical simulations of a coaxial bubble pair rising in a liquid metal column under horizontal magnetic fields

The motion and coalescence of a coaxial bubble pair rising in a liquid metal column under horizontal magnetic fields were numerically examined using the VOF method in this present paper. The MHD (Magnetohydrodynamics) effects on the characteristics of rise velocity, flow field, and coalescence process of bubble pair by considering various wall confinement ratios (Cr) were analyzed. The results indicate that the effects of magnetic field and wall confinement on the coalescence of the coaxial bubbles are non-monotonic. For smaller Cr, a higher initial rise velocity of the bubbles is generated by strengthening the counter-rotating toroidal vortices around bubbles in the initial stage, but the terminal rise velocity decreases in the stable stage. In the presence of the magnetic field, both the initial rise velocity and terminal rise velocity decrease. A horizontal magnetic field makes the flow field around the bubbles be anisotropic by weakening the toroidal vortices on both sides of the bubbles along the magnetic field direction, which also dampens the wake vortices of the leading bubble and thus reduces the attractive force of wake effect acting on the tailing bubble. On the other hand, the downward Lorentz force induced by the magnetic field on the top of the leading bubble suppresses its upward motion, which makes the tailing bubble collide with the leading bubble earlier. As the competition between the above two mechanisms varies with the magnetic field strength, the coalescence time of the bubble pair also changes accordingly. Particularly, a strong horizontal magnetic field tends to promote the bubbles coalescence under the wall effects and delay that when the wall effects are minor or negligible. For Ha=771, bubbles coalescence at Cr=2 is about 32 % earlier than that at Cr=4.