Narrow Results

The existence of magnetic fields associated with the intracluster medium in clusters of galaxies is now well established through different methods of analysis. Magnetic fields are investigated in the radio band from studies of the rotation measure of polarized radio galaxies and the synchrotron emission of cluster-wide diffuse sources. Other techniques include X-ray studies of the inverse Compton emission and of cold fronts and magneto hydrodynamic simulations. We review the main issues that have led to our knowledge on magnetic fields in clusters of galaxies. Observations show that cluster fields are at the μG level, with values up to tens of μG at the center of cooling core clusters. Estimates obtained from different observational approaches may differ by about an order of magnitude. However, the discrepancy may be alleviated by considering that the magnetic field is not constant throughout the cluster, and shows a complex structure. In particular, the magnetic field intensity declines with the cluster radius with a rough dependence on the thermal gas density. Moreover, cluster magnetic fields are likely to fluctuate over a wide range of spatial scales with values from a few kpc up to hundreds kpc. Important information on the cluster field are obtained by comparing the observational results with the prediction from numerical simulations. The origin of cluster magnetic fields is still debated. They might originate in the early Universe, either before or after the recombination, or they could have been deposited in the intracluster medium by normal galaxies, starburst galaxies, or AGN. In either case, magnetic fields undergo significant amplification during the cluster merger processes.

The importance of non-Newtonian fluid (Casson fluid) in industry is increasingly appreciated. However, little is known about the flow rheology of Casson fluid flowing over a Riga plate. Thus, the purpose of this investigation is to examine the nature of entropy generation (EG) and heat transfer (HT) on Casson hybrid nanofluid flow past a Riga plate by considering the influences of magnetic field and thermal radiation. The Hamilton–Crosser (Model 1) and Xue model (Model 2) of thermal conductivity are incorporated for Casson hybrid nanofluid. The governing equations are solved by numerical methods i.e., bvp4c and shooting techniques. In the current framework, the comparative patterns for both models of temperature, velocities, EG and Bejan number are depicted due to the existing parameters. The domain of the pertinent parameters is taken as thermal radiation, $4\le Ra\le 7$; stretching parameter, $0.6\le \lambda \le 1$; Casson factor, $0.5\le \delta \le 2$; rotation parameter, $1\le {\Re }_t\le 4$and Hartmann number, $2\le Ha\le 11$. The outcomes show that the rise in volume fraction and thermal conductivity profile of Xue model (Model 2) is better than Hamilton–Crosser model (Model 1). Moreover, EG profiles are escalated with augmentation in values of Hartmann number and stretching parameter for both models. The results of the study are useful for predicting the rheology of right fluid, while it also assists in safeguarding the boundary layer (BL) separation, along with establishing a parallel force to the surface in assisting the domain of science and technology.

Hybrid nanofluids have unique characteristics that make them more useful than common heat transfer fluids. The potential applications can be found in applied thermal engineering, chemical engineering, hybrid powered engines, biomedical and mechanical engineering. Therefore, the analysis of SWCNTs–MWCNTs/C₂H₆O₂–H₂O with integrated effects of thermal radiations and perpendicular magnetic field is organized in this research. Thermal conductivity of C₂H₆O₂–H₂O is improved via Xue, Ota and Yamada thermal conductivity correlations. The mathematical problem is designed for two sheets and both the hybrid nanoliquid and the plates rotate in counter clockwise pattern. Mathematical treatment of the model is performed and the results were analyzed through graphical way. Keen observations of the results reveal that the fluid motion controlled by intensifying the magnetic field and higher density of SWCNTs–MWCNTs leads to optimum decrement. Further, the fluid movement is investigated optimum and slow for outward and inward plate movement, respectively. The temperature results for the parameters, especially the thermal radiations, showed that hybrid nanoliquid has the ability to store high thermal energy than common mono-nanoliquid, hence it would be suitable for future industrial applications. The parametric ranges are selected as $A_1=0.1$–1.7, ${\alpha }_1=0.1$–0.9, $M=1.0$–9.0 and $\mathrm{\Omega }=0.0$–20.0 for the study.

In this study, we explore the analysis of peristaltic flow with heat transfer occurring within the gap between coaxial inclined tubes. The inner tube’s wall is rigid, while the outer tube’s wall features a sinusoidal wave propagating through it. The cylindrical system is employed to formulate the problem. The flow is characterized using continuity, momentum, and energy equations. We apply the assumption of long wavelength and the low Reynolds number approximation to simplify the nonlinear governing equation, subsequently solving it through perturbation techniques. We investigate the impact of crucial parameters, such as the magnetic field, porous media, slipping conditions, and others, on the peristaltic flow of a couple stress fluid. Our focus lies on assessing their influence on axial velocity, pressure gradient, and flow streamlines. The outcomes are visually presented through graphical representations. Notably, an increase in the slipping parameter results in a reduction of fluid velocity, attributed to the reverse slipping of the flow. The introduction of a magnetic field leads to an augmentation of the pressure gradient. Moreover, elevating the peristaltic amplitude and heat source induces the formation of a vortex within the flow. The presence of porous media leads to an increase in the pressure difference of the fluid flow. The primary objective of this research is to enhance our understanding of the peristaltic motion of non-Newtonian fluid dynamics, specifically incorporating a couple stress fluid. This contributes to a deeper understanding of crucial fluids, such as blood, within the human circulatory system. The implications extend to biological and industrial applications like magnetic resonance imaging (MRI) and radiosurgery, advancing our scholarly understanding of fluid behavior, especially in non-Newtonian scenarios.

Practical Applications: Numerous technical applications, including as polymer deposition, electrolysis control, medication delivery, spin-stabilized missile cooling and cooling of rotating machinery slices have sparked considerable interest in studying stagnation point flow. Nuclear power plants, photovoltaic panels and heat exchangers as well as microfluidic heating devices use them.

Purpose: To better understand the unsteady $(\mathrm{\text{Cu}}$–${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–$\mathrm{\text{Si}}{\mathrm{\text{O}}}_2\mathrm{\text{/polymer}})$ ternary hybrid nanofluid stream at the stagnation zone with Joule heating, this research examines the unique prospective applicative properties.

Methodology: The flow equations will be modeled. By using similarity transformation, it is possible to transform nonlinear partial differential equations (PDEs) that are not precisely solvable into ordinary differential equations (ODEs) that can be numerically resolved. Runge–Kutta-IV and the shooting technique in MATHEMATICA have been demonstrated to have a significant effect on the predominance of heat exchange and the mobility features of ternary hybrid nanofluids.

Findings: Results show that the unsteadiness parameter influences the $x$-direction velocity and mono nanofluid has a larger velocity than other nanofluids, while the opposite is true for the $z$-direction velocity. Nanoparticle concentrations, magnetic and Eckert number characteristics increase the thermal distribution, whereas the unsteadiness and rotation parameter decreases it. Unsteadiness, rotation and magnetic factors all improve heat transfer, while the Eckert number parameter has the reverse effect. The ternary hybrid nanofluid also has a greater heat transfer rate than the hybrid and normal nanofluids.

Originality: Unsteady $(\mathrm{\text{Cu}}$–${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–$\mathrm{\text{Si}}{\mathrm{\text{O}}}_2\mathrm{\text{/polymer}})$ ternary nanofluid stream generated by magneto hydrodynamic (MHD) in the stagnation zone was studied in detail in this study. To avoid any errors in heat transfer, it may assist other researchers in selecting critical parameters for modern industrial heat transfer and the right parameters for developing nonunique solutions.

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, $\mathrm{\text{Ha}}=0-20$, Rayleigh number, $\mathrm{\text{Ra}}=10^4-10^6$, PL indices, $n=0.6$–1.4, Prandtl number, $\mathrm{\text{Pr}}=6.2\mathrm{\text{(water)}}$, to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio $\mathrm{\text{AR}}=2.0$. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, $\mathrm{\text{Ra}}$ and decreasing the PL index, $n$. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, $\mathrm{\text{Ha}}=0$, fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing $n$ and $\mathrm{\text{Ra}}$, respectively. In the presence of the magnetic field, $\mathrm{\text{Ha}}>0$, the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field ${ℬ}$ defined on a 3D Riemannian manifold. First, we consider a moving charged particle under the action of a frictional force, $f$, in the magnetic field ${ℬ}$. Then, we assume that trajectories of the particle associated with the magnetic field ${ℬ}$ correspond to frictional magnetic curves ($f$-magnetic curves$)$ of magnetic vector field ${ℬ}$ on the 3D Riemannian manifold. Thus, we are able to investigate some geometrical properties and physical consequences of the particle under the action of frictional force in the magnetic field ${ℬ}$ on the 3D Riemannian manifold.

In this paper, we study a special type of magnetic trajectories associated with a magnetic field ${ℬ}$ defined on a 3D Riemannian manifold. First, we assume that we have a moving charged particle which is supposed to be under the action of a gravitational force $G$ in the magnetic field ${ℬ}$ on the 3D Riemannian manifold. Then, we determine trajectories of the charged particle associated with the magnetic field ${ℬ}$ and we define gravitational magnetic curves ($G$-magnetic curves) of the magnetic vector field ${ℬ}$ on the 3D Riemannian manifold. Finally, we investigate some geometrical and physical features of the moving charged particle corresponding to the $G$-magnetic curve. Namely, we compute the energy, magnetic force, and uniformity of the $G$-magnetic curve.

This study aims to investigate the thermodynamic analysis for electroosmotic flow of ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{Cu/H}}}_2\mathrm{\text{O}}$ hybrid nanofluid in the presence of peristaltic propulsion. Hybrid nanofluid is an aqueous solution of copper and iron oxide nanoparticles. Effects of electric field, Ohmic heating, magnetic field, viscous dissipation, heat sink/source and mixed convection are also considered. The Debye–Hückel and lubrication approach has been adopted to perform mathematical modeling. The resulting differential equations are numerically solved by employing the Shooting method. Analysis has been presented for irreversibility rate and heat transfer for the flow of hybrid nanoliquid. Results reveal that the addition of nanoparticles reduces the temperature and entropy generation of hybrid nanoliquid. Heat transfer rate enhances by improving Joule heating and electroosmotic parameters. An increase in Helmholtz–Smoluchowski velocity and Hartmann number decrease the velocity of fluid. Thermal performance of hybrid nanofluid (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{Cu/H}}}_2\mathrm{\text{O}}$) is more noticeable in comparison with conventional mono nanofluid (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$–${\mathrm{\text{H}}}_2\mathrm{\text{O}}$) and base fluid (${\mathrm{\text{H}}}_2\mathrm{\text{O}}$).

In this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or longitudinal magnetic field which is also exposed to both the hygroscopic as well as thermal environments. The thermal environment is considered as nonlinear thermal stress field based on the Murnaghan’s model whereas the hygroscopic environment is assumed as a linear stress field. The size effect of the SWCNT has been captured by both the nonlocal and gradient parameters by employing the Nonlocal Strain Gradient Theory (NSGT). Governing equation of motion of the proposed model has been developed by utilizing the extended Hamilton’s principle and the non-dimensional frequency parameters have been computed by incorporating the Navier’s approach for Hinged–Hinged (HH) boundary condition. The proposed model is validated with the existing model in special cases, by comparing the non-dimensional frequency parameters, displaying an excellent agreement. Further, a parametric study has been conducted to analyze the impact of nonlocal parameter, gradient parameter, thermal environment, hygroscopic environment, and magnetic field intensity on the non-dimensional frequency parameters. Also, results for some other theories like Classical Elasticity Theory (CET), Nonlocal Elasticity Theory (NET), and Strain Gradient Theory (SGT) have been presented along with the NSGT.

This article concerns with free vibration analysis of spinning sandwich cylindrical shells with functionally graded (FG) graphene/aluminum (Al) face sheets and honeycomb core exposed to an axial magnetic field. Lorentz magnetic force is derived by using Maxwell’s relations. The face layers are made of multi-nanocomposite sheets. Each sheet is composed of an Al matrix reinforced with graphene platelets (GPLs) that are uniformly distributed through the sheet thickness. The effective material properties of the face layers of the spinning sandwich cylindrical shells are derived employing the modified Halpin–Tsai model. The honeycomb core layer is made of hexagonal aluminum cells. According to the first-order shear deformation theory and Hamilton’s principle, five governing equations are obtained involving Lorentz force. Frequencies of the present model are analytically derived from the equations of motion. The present outcomes are examined by introducing some comparison examples. The effects of the geometric parameters, magnetic field parameter, GPLs weight fraction, core-to-face thickness ratio, circumferential wave number, axial wave number and spinning speed on the vibration of spinning sandwich honeycomb cylindrical shells are numerically discussed.

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius a at the equatorial plane.

In the weak field approximation, we study the gravitational lensing by spherical symmetric compact object immersed in magnetic field in the presence of magnetized plasma. The external magnetic field causes the split of the deflection angle of the photon, Einstein ring and Einstein cross as the counterpart of the Zeeman effect. In particular, the magnetic field affects the magnification of images, creating additional components. We also study the time delay of an electromagnetic signal due to the geometry and the gravitational field around the lensing source. We show that the time delay of the electromagnetic signal strongly depends on the plasma parameters, and it slightly decreases in the plasma in comparison with that in vacuum.

An analysis is carried out for the free convection of magneto-micropolar liquid via a stretching surface for the inclusion of thermal radiation and chemical reaction. The transverse magnetic field is employed on the normal direction of flow with the impact of Peclet number relating to thermal and solutal transfer profiles. Referring to the current applications in several engineering problems, industrial applications, and more importantly the peristaltic pumping processes, blood flow phenomena, etc. the role of micropolar fluid is significant. Therefore, the objective of thismodel is to develop by incorporating thermal radiation which has several applications in aforesaid areas. However, the proposed model is solved analytically using the differential transform method (DTM) and prior to that transformation to ordinary system is obtained by using similarity transformations. The characteristic of various physical components associated with the governing equations is deployed graphically. The analysis of these parameters is described briefly in the discussion section. Further, a statistical approach response surface methodology (RSM) is used to optimize the heat transfer rate for the factors such as magnetic parameter, thermal radiation, and Peclet number.

This study comprehensively investigates the effect of magnetic fields and thermal radiation on mixed convection in a hybrid alumina–copper/water nanofluid flowing over a permeable vertical flat plate. The study aims to model conventional nanofluid behavior accurately by considering the hybridization of two types of nanoparticles. Conventional similarity transformations and Akbari–Ganji’s method are employed to simplify the governing equations, resulting in ordinary differential equations. Among the dual solutions obtained, only one stable solution is identified. The key findings reveal that boundary layer separation can be avoided by reducing the copper concentration volume and increasing the magnetic and radiation parameters. The mixed convection parameters induce counter-flow, enhancing heat transfer when the magnetic and radiation parameters increase and the copper concentration volume decreases. Conversely, increasing the concentration volume of copper leads to accelerated boundary layer separation and reduced measured physical quantities. Overall, the mixed convection parameter enhances skin friction and heat transfer rates, particularly in the achievable solution. The accuracy of the proposed method is validated through a comparison with the finite element method (FEM). The graphical presentation of the results facilitates a clearer interpretation of the study’s findings.

We examine the motion of a charged particle in the vicinity of a weakly magnetized naked singularity. The escape velocity and energy of the particle moving around the naked singularity after being kicked by another particle or photon are investigated. Also at innermost stable circular orbit (ISCO) escape velocity and energy are examined. Effective potential and angular momentum of the particle are also discussed. We discuss the center-of-mass energy after collision between two particles having same mass and opposite charges moving along the same circular orbit in the opposite direction. It is investigated that under what conditions maximum energy can be produced as a result of collision.

The influences of magnetic field on thermodynamic, mechanical and electromagnetic properties of water including the specific heat, surface tension force, soaking effect or angle of contact, refraction index and electric conductivity are studied. From these investigations we know that the magnetic fields reduce the specific heat of water, increase the soaking degree and hydrophobicity of water to materials, depress its surface tension force and increase refractive index and electric conductivity of water relative to those of pure water. We can predict that these changes are caused by the changes of microscopic structures and distribution of water molecules under the action of a magnetic field. Therefore, our studies have important significations in science and has practical value of application of magnetized water.

We investigate particle motion and collisions in the vicinity of rotating black holes immersed in combined cosmological quintessential scalar field and external magnetic field. The quintessential dark-energy field governing the spacetime structure is characterized by the quintessential state parameter ${\omega }_q\in (-1;-1/3)$ characterizing its equation of state, and the quintessential field-intensity parameter $c$ determining the static radius where the black hole attraction is just balanced by the quintessential repulsion. The magnetic field is assumed to be test field that is uniform close to the static radius, where the spacetime is nearly flat, being characterized by strength $B$ there. Deformations of the test magnetic field in vicinity of the black hole, caused by the Ricci non-flat spacetime structure are determined. General expression of the center-of-mass energy of the colliding charged or uncharged particles near the black hole is given and discussed in several special cases. In the case of nonrotating black holes, we discuss collisions of two particles freely falling from vicinity of the static radius, or one such a particle colliding with charged particle revolving at the innermost stable circular orbit. In the case of rotating black holes, we discuss briefly particles falling in the equatorial plane and colliding in close vicinity of the black hole horizon, concentrating attention to the interplay of the effects of the quintessential field and the external magnetic field. We demonstrate that the ultra-high center-of-mass energy can be obtained for black holes placed in an external magnetic field for an infinitesimally small quintessential field-intensity parameter $c$; the center-of-mass energy decreases if the quintessential field-intensity parameter $c$ increases.

In this paper, the two-phase flow of non-Newtonian fluid is investigated. The main source of the flow is metachronal waves which are caused by the back and forth motion of cilia attached to the opposite walls of the channel. Magnetohydrodynamics (MHD) of Casson fluid experience the effects of transverse magnetic fields incorporated with the slippery walls of the channel. Thermal effects are examined by taking Roseland’s approximation and application of thermal radiation into account. The heat transfer through the multiphase flow of non-Newtonian fluid is further, compared with Newtonian bi-phase flow. Since the main objective of the current study is to analyze heat transfer through an MHD multiphase flow of Casson fluid. The two-phase heated flow of non-Newtonian fluid is driven by cilia motion results in nonlinear and coupled differential equations which are transformed and subsequently, integrated subject to slip boundary conditions. A closed-form solution is eventually obtained form that effectively describes the flow dynamics of multiphase flow. A comprehensive parametric study is carried out which highlights the significant contribution of pertinent parameters of the heat transfer of Casson multiphase flow. It is inferred that lubricated walls and magnetic fields hamper the movement of multiphase flow. It is noted that a sufficient amount of additional thermal energy moves into the system, due to the Eckert number and Prandtl number. While thermal radiation acts differently by expunging the heat transfer. Moreover, Casson multiphase flow is a more suitable source of heat transfer than Newtonian multiphase flow.

The effect of surface roughness, magnetic field, and couple stress on the performance of secant slider bearing is studied in this paper. The effectiveness of the bearing is assessed by using a couple stress liquid as the lubricant in the process. Because of microstructural impacts, couple stress fluids have distinctive rheological characteristics. These features have the potential to make a major impact on the bearing’s performance. The novel aspect of this study is that the roughness of the secant slider is taken into consideration. The modified Reynolds equation is derived using Christensen’s stochastic theory for roughness. Here, both transverse and longitudinal roughness patterns are considered. The analytical solutions are obtained for steady-state pressure, load-carrying capacity, film stiffness, and damping coefficient. The results are presented for various parameters through graphs and tables. The combined effect of the magnetic field and couple stress is significant on bearing characteristics. It is noticed that the bearing features increase with the longitudinal roughness parameter, and the reverse phenomenon is observed with the transverse roughness parameter. When a transverse roughness pattern is assumed on a secant slider bearing, characteristics like pressure, load, stiffness of the film, and damping coefficient increase significantly.