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This research utilizes the bvp4c method to conduct a detailed numerical analysis of the hydrothermal behavior of magnetized hybrid nanofluids flowing across a permeable curved surface. The study explores the impact of crucial parameters such as curvature, magnetic field strength, viscosity and suction/injection, alongside the heat absorption coefficient, on the transport properties of copper (Cu) and ferric oxide (Fe₃O₄) nanomaterial’s suspended in water. Results reveal that as the curvature parameter increases, velocity profiles exhibit a decrease under suction conditions and an increase under injection conditions for both conventional and hybrid nanofluids. Furthermore, higher magnetic parameters are found to decrease velocities in general. Hybrid nanofluids display enhanced velocity and thermal performance compared to conventional nanofluids, manifesting higher skin friction and heat transfer rates. Temperature profiles exhibit a complex interplay with curvature, magnetic parameters and the injection/suction scenario, where injection conditions intensify thermal effects. The incorporation of the heat absorption coefficient further amplifies the thermal efficiency of hybrid nanofluids. These findings, supported by previous research, offer valuable insights for optimizing industrial processes, especially in sectors like ceramics, plastics and polymers, where efficient heat management is paramount.

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}$ particles suspended in $\mathrm{\text{EG}}$. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}/\mathrm{\text{EG}}$-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

The aim of this study is to analyze heat transfer over two horizontal concentric cylinders in the influence of MHD, internal heat source containing porous nanofluids and thermal radiation are considered. The novelty of this work is internal heat source and porous media of H₂O–Cu nanofluids with the Lorentz effect are investigated and its applications are cooling systems, and heat exchangers. In addition, transformation for the momentum and energy equation is applied to obtain a set of ODEs for governing equations in the heat transfer flows. Further, the numerical technique BVP4C is used to solve the resulting system of nonlinear, coupled equations with boundary conditions. The influence of Hartmann number, volume fraction, radiation parameter, internal heat source parameter, Darcy number and different nanoparticles are examined in velocity and temperature profiles. The results show good agreement with the existing work of velocity and temperature graphs. Moreover, they reveal that thermal radiation significantly influences temperature distribution within the annulus, leading to a higher heat transfer rate. Furthermore, the presence of a porous medium and internal heat source modulates the flow patterns. This study provides optimizing MHD nanofluid systems for engineering applications such as thermal management systems, hyperthermia treatment in cancer therapy, food processing, rotating machinery and cooling systems.

The objective of this study is to conduct a numerical examination of the influence of nonlinear chemical reaction and heat source or sink on magnetohydrodynamic (MHD) heat and mass transmission nanofluid flow through a shrinking permeable surface. In addition, the investigation considers thermal radiation and the occurrence of viscous dissipation. Ethylene glycol (EG) is used as the primary fluid medium, whilst the nanoparticles consist of nickel–zinc ferrite. The use of nanofluid flow has garnered significant interest as a result of its potential applications across several sectors. Nanofluids possess a notable benefit in comparison to traditional fluids as a consequence of their enhanced heat transfer capabilities. This advantage may be ascribed to the inclusion of nanoparticles, which augment thermal conductivity and therefore lead to enhanced heat dissipation and efficiency. The mathematical flow model, which is formulated using nonlinear partial differential equations (PDEs), may be transformed into a set of ordinary differential equations (ODEs) by the application of suitable similarity conversions. In order to address the complexities of the nonlinear system, the bvp4c and shooting techniques are used inside the MATLAB program, a widely utilized commercial platform, to effectively solve the associated ODEs by numerical means. This study presents a graphical analysis of the effects of flow parameters on several variables of interest.

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because of hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. We have derived equations for the vertical profiles of stationary accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Our recent analysis in Ref. 1 shows that the inward or outward advection of the large-scale magnetic field depends on the ratio of the accretion power going into magnetic disk winds to the viscous power dissipation and the plasma-β which is the ratio of the midplane plasma pressure to the magnetic pressure.

Recent radio emission, polarization, and Faraday rotation maps of the radio jet of the galaxy 3C303 have been obtained in Ref. 2 and show that one component of this jet has a galactic-scale electric current of ~ 3 × 10¹⁸ A flowing along the jet axis. We show that this current can be used to calculate the electromagnetic energy flow in this magnetically dominated jet.

We have investigated the influence of velocity shear on the linear and non-linear development of the CD kink instability. We follow temporal development of the instability within a periodic computational box. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the location of the velocity shear relative to the characteristic radius of the helically twisted force-free magnetic field. At small radius the plasma flows through the kink. The kink propagation speed increases as the radius increases and the kink becomes more embedded in the plasma flow. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than occurs for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and non-linear development become more similar to the development of a static plasma column.

Gamma Ray Bursts (GRB) are the extremely energetic transient events, visible from the most distant parts of the Universe. They are most likely powered by accretion on the hyper-Eddington rates that proceeds onto a newly born stellar mass black hole. This central engine gives rise to the most powerful, high Lorentz factor jets that are responsible for energetic gamma ray emission. We investigate the accretion flow evolution in GRB central engine, using the 2D MHD simulations in General Relativity. We compute the structure and evolution of the extremely hot and dense torus accreting onto the fast spinning black hole, which launches the magnetized jets. We calculate the chemical structure of the disk and account for neutrino cooling. Our preliminary runs apply to the short GRB case (remnant torus accreted after NS-NS or NS-BH merger). We estimate the neutrino luminosity of such an event for chosen disk and central BH mass.

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that the so-called small-scale dynamo is occurring in the postshock region. We also find that the amplitude of magnetic-field amplification depends on the direction of the mean preshock magnetic field.

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability was excited by a small initial velocity perturbation and developed turbulent structure inside the hot plasma column. We demonstrated that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter "σ", the ratio of the magnetic energy to the thermal energy for a hot plasma, declined from an initial value of 0.3 to about 0.01 when the CD kink instability saturated. Our simulations demonstrated that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.

Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in the energy space with the Fokker-Planck equation. In this paper, a time-dependent numerical code is used to solve the reduced Fokker-Planck equation involving only time and energy variables with general forms of the diffusion coefficients. We also propose a self-similar model for particle acceleration in Sedov explosions and use the TeV SNR RX J1713.7-3946 as an example to demonstrate the model characteristics. Markov Chain Monte Carlo method is utilized to constrain model parameters with observations.

I will review the current status of our theoretical understanding of Pulsar Winds and associated nebulae (PWNe). In recent years, axisymmetric models of pulsar winds with a latitude dependent energy flux have proved very successful at explaining the morphology of PWNe as seen in the X-rays. This success has prompted developments aimed at using multi-wavelength observations of these nebulae as a diagnostics of the hidden physics of the pulsar wind and of the mechanism(s) through which particles are accelerated in these sources.

I will discuss these most recent developments in terms of the information that we infer from detailed comparison of simulated non-thermal emission with current observations.

Pulsar wind nebulae (PWN) provide a unique test-bed for the study of highly relativistic processes right at our astronomical doorstep. In this contribution we will show results from the first 3D RMHD simulations of PWN. Of key interest to our study is the long standing "sigma-problem" that challenges MHD models of Pulsars and their nebulae now for 3 decades. Earlier 2D MHD models were very successful in reproducing the morphology of the inner Crab nebula showing a jet, torus, concentric wisps and a variable knot. However, these models are limited to a purely toroidal field geometry which leads to an exaggerated compression of the termination shock and polar jet — in contrast to the observations. In three dimensions, the toroidal field structure is susceptible to current driven instabilities; hence kink instability and magnetic dissipation govern the dynamics of the nebula flow. This leads to a resolution of the sigma-problem once also the pulsar's obliqueness (striped wind) is taken into account. In addition, we present polarized synchrotron maps constructed from the 3D simulations, showing the wealth of morphological features reproduced in 2D is preserved in the 3D case.

We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. In the rotating relativistic jet case, developing helical kink structure propagates along jet as it grows in amplitude. The growth rate of the CD kink instability does not depend on the jet rotation. The coupling of multiple unstable wavelengths is crucial to determining whether the jet is eventually disrupted in the nonlinear stage. The CD kink instability deformed magnetic field may trigger magnetic reconnection in the jet.