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Inspired by significant physiological applications of peristaltic transport, a mathematical model for the peristaltic pumping of a Jeffrey nanofluid containing gyrotactic microorganisms through a flexible and vertical symmetric channel is investigated, along with the effects of thermal radiation, heat source/sink, chemical reaction, porous medium and Hall current. Swimming microorganisms in a model of non-Newtonian fluid has several biological and ecological benefits, including in the pharmaceutical industry, biofertilizers, biofuel technology, biosensors, etc. With these presumptions in mind, a conducting Jeffery fluid flow containing microorganisms via a porous vertical conduit is proposed. The expressions for the flow quantities are established by solving the governing equations of this study analytically using the homotopy perturbation method (HPM). A detailed examination is performed using the tables and graphical representations to comprehend the impact of significant components on this analysis. In addition, the results for Newtonian nanofluid are obtained as a special case and discovered that its velocity is lower than the Jeffrey nanofluid. It is observed that the best velocity distribution can be seen at larger thermal Grashof number and Darcy number. The size of the trapped bolus enhances with the increase of the Hall parameter. Furthermore, the density of the motile microorganism distribution declines for higher bioconvection Peclet number and bioconvection constant. [ABSTRACT FROM AUTHOR]

The influence of conjugate heat transfer based on radiation and magnetohydrodynamic utilization is an attractive research area, with progressive features; it has many applications in thermal engineering, heat exchangers, cooling phenomenon, magnetic cell separation, energy production, hyperthermia, etc. Following the motivating significances of the current research topic, this paper explores the influences of an electrically conducting and radiating fluid with internal friction, heat generation and thermal radiation embedded in a porous medium past a flat permeable plate. The boundary layer equations are dimensionally transformed and solved numerically using implicit finite difference technique called the Keller-box method. The effect of various fluid obeying parameters such as magnetic field, viscous dissipation and heat generation on the flow factors such as velocity and temperature are graphed and discussed in this paper. Growing heat source, energy inside the fluid boosts, thereby increasing the energy of the flow. Increase in generation of energy reduces the viscosity of the flow reduces thereby increasing the velocity of the flow particles. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to explore an oscillatory flow of a magnetohydrodynamics (MHD) couple stress fluid with heat and mass transfer analyses through a porous medium. The modified Darcy–Brinkman couple stress fluid model is employed. There could be many potential applications of this study, such as thermal system, solidification of liquid crystals, cooling of metallic plates in a bath, exotic lubricants and colloidal solutions. In the wake of these potential applications, the study of MHD couple stress fluid flow with additional diffusing components has been found to be innovative and very interesting in the analysis of the influence of combined magnetic effects, couple stress fluid and two solutes. A governing coupled nonlinear partial differential equation with boundary constraints represents the modeled flow problem. In addition, these equations are converted into nondimensional form by employing the suitable nondimensionalizing quantities. It is possible to attain analytic solutions to the dimensionless equations that control the liquid flow, and the consequences of the flow's confines on velocity, temperature, concentration and skin friction profile are examined and also the results are discussed through graphs. It is noteworthy that when the injection level on the heated plate is increased, the skin friction on each channel plate also increases. [ABSTRACT FROM AUTHOR]

An analysis is presented for the stagnation-point two-dimensional fluid flow of hybrid nanofluid towards an expanding surface characterized by the induced magnetic field. Further, the consideration of thermal buoyancy and additional heat source enhances the flow phenomena with various physical parameters involved in it. This work has significant novelty due to the behavior of the convective boundary conditions. Besides, due to the convective term the nonlinear differential equations designed in this problem are incorporated and are resolved numerically by executing the Runge–Kutta–Fehlberg method. Additionally, three different classes of nanosized particle configurations named brick, cylinders, and platelets shapes are examined for the implementation of the Hamilton–Crosser thermal conductivity model. In the end, the influences characterizing the local Nusselt number and the coefficient of skin friction profiles have been discussed for unalike shapes of nanosized particles are discussed. In the above study, it is found that the platelet-shaped nanosized particle is more efficient in comparison to the other shapes considered herein. Further, particle concentration and particle shape are also favorable in enhancing fluid temperature in hybrid nanofluids in contrast to pure fluid. [ABSTRACT FROM AUTHOR]

The demand for efficient applications of solar energy and nanomaterials has grown significantly in recent years due to industrial needs and the desire to minimize energy consumption and costs. However, the efficiency of photovoltaic cells and solar-powered ships is highly dependent on solar radiation. In this study, a model for the installation of a parabolic trough surface collector (PTSC) was developed to achieve high temperatures on solar-powered ships. The current study analyzed the thermal characterization function in solar-powered ships under the effect of heat radiation, magnetic field, and viscous dissipation by employing hybrid magnetite particles (Fe3O4) and silver (Ag). The Cattaneo–Christov model has been used to assess heat flux in the thermal boundary layer. The Galerkin weighted residual method (GWRM) has been employed to solve the ordinary differential equations using MATHEMATICA 11.3 software. The findings showed that the thermal efficiency of the hybrid nanofluid was significantly enhanced by 56.3% relative percentage. The motto of the current investigation is developing a model for the installation of PTSC on solar-powered ships under various provided assumptions. [ABSTRACT FROM AUTHOR]

This study looks at the numerical results of magnetohydrodynamic liquid flowing across a stretching sheet at its stagnation point while also experiencing chemical reaction, viscous dissipation, thermal radiation and variable magnetic field. The fundamental partial differential equations that regulate physical phenomena are converted into nonlinear ordinary differential equations by using the appropriate similarity transformations. Later, resolved by numerically using Mathematica. The effects of various non-dimensional parameters like velocity ratio parameter (λ), porosity (k), magnetic parameter (M), radiation parameter (R), chemical reaction parameter (γ), etc. on the velocity, temperature and concentration profiles as well as on the local skin-friction and the local Nusselt number are discussed in detail and displayed through graphs. The numerical evaluation of the physical quantities was provided in tabular form for the various values of the relevant stream parameters. It is important to note that magnetic field interaction increases concentration distribution and fluid temperature while decreasing velocities at all domain flow locations. [ABSTRACT FROM AUTHOR]

This paper considers the movement of an incompressible non-Newtonian Walters' B liquid within a rotating annulus. The flow lies within porous media and is magnetized by a uniform normal magnetic field. Mass transmission is included in the arrangements of homogeneous and heterogeneous chemical reactions (HHCR) with a thermal diffusion effect. Heat diffusion is exposed with a temperature- dependent heat source (THS) and an exponential radial-dependent heat source (ERHS), besides Joule heating and viscous dissipations. The mathematical construction is shown by momentum, energy and concentration of chemical materials equations along with time-periodic boundary conditions. The innovation of this study stems from considering mass transfer utilizing HHCR, with thermal diffusion effects in the flow within a rotating annulus, trying to understand the effect of these reactions on the flow and related applications. The principal regulating the structure of nonlinear partial differential equations is transferred by ordinary ones utilizing appropriate similarity analysis. These equations are analyzed by the homotopy perturbation method. Subsequently, the analytical solutions of the main profiles are obtained, and a graphical construction is established to clarify the effects of the relevant physical elements. It is observed that the velocity waves decrease with annulus width enlargement and increase with the wave phase amplitude. With an increase in all significant parameters, heat transmission gets better. Furthermore, as the strength of HHCR is increased, the concentration of molecules decreases. These outcomes are significant in several applications like cancer therapy, biochemical manufacturing purposes through reactors, where biochemical interactions can be regulated by accurate control of various parameters. [ABSTRACT FROM AUTHOR]

The ambipolar diffusion approximation is used to model partially ionized plasma dynamics in a single-fluid setting. To correctly apply the commonly used version of ambipolar diffusion, a set of criteria should be satisfied including the requirement that the difference in velocity between charges and neutral species (known as drift velocity) is much smaller than the thermal velocity, otherwise the drift velocity will drive a non-negligible level of further collisions between the two species. In this paper, we explore the consequences of relaxing this assumption. We show that a new induction equation can be formulated without this assumption. This formulation reduces to the ambipolar induction equation in the case the drift velocity is small. In the large drift velocity limit, the feedback of the drift velocity on the collision frequency results in decreased diffusion of the magnetic field compared with the standard ambipolar diffusion approximation for the same parameters. This has a natural consequence of reducing the frictional heating that can occur. Applying this to results from flux emergence simulations where the expansion of the magnetic field leads to strong adiabatic cooling of the partially ionized chromosphere resulted in a noticeable reduction in the magnitude of the predicted drift velocities. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'. [ABSTRACT FROM AUTHOR]

Partially ionized plasmas constitute an essential ingredient of the solar atmosphere, and ground- and space-based observations have pointed out the presence of oscillations in partially ionized solar plasmas such as chromosphere, photosphere, prominences or spicules, which have been interpreted in terms of magnetohydrodynamic waves. Our aim is to study the spatial behaviour of propagating weakly and fully nonlinear Alfvén waves, and the subsequent excitation of field-aligned motions and perturbations, when dissipative mechanisms, such as ambipolar diffusion and radiative losses, together with parametrized heating mechanisms, are taken into account. When only ambipolar diffusion is taken into account, first-order Alfvén waves as well as ponderomotive-driven perturbations are spatially damped, while field-aligned motions and perturbations representing propagating slow waves are undamped. These perturbations are damped when thermal effects are also considered and their damping lengths can be longer or shorter than those of ponderomotive-driven perturbations. Therefore, after the initial excitation, Alfvén waves and ponderomotive-driven perturbations could be quickly damped while slow waves still remain in the plasma, and vice versa. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'. [ABSTRACT FROM AUTHOR]

The purpose of this study is to provide a mathematical model of the process of entropy formation that occurs during the MHD convective transport of Carreau fluid across a curved stretched surface with soret and dufour effects. The energy equation is explored with the combined characteristics of joule heating, viscous dissipation and heat absorption/generation. The modeled governing equations are converted into nonlinear ordinary differential equations using similarity variables, and the results are acquired through the utilization of the built-in command NDSolve. It is revealed that entropy generation and Bejan number increase for higher values of Brinkman number. The impact of the Hartman number increase the entropy generation and reduced the Bejan behavior. The curvature parameter reduced the flow and temperature of fluid but increased the concentration profile. A small change in the heat absorption parameter strengthens the temperature profile. Graphical representations are used to discuss the behavior of Bejan number, entropy generation, velocity, temperature, and concentration profiles for the different values of physical parameters. The results of computations of drag force, the local nusselt number, and the Sherwood number are shown in tabular form for numerous values of the parameters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations. [ABSTRACT FROM AUTHOR]

The hour-long, gradual phase of solar flares is well observed across the electromagnetic spectrum, demonstrating many multiphase aspects, where cold condensations form within the heated post-flare system, but a complete 3D model is lacking. Using a state-of-the-art 3D magnetohydrodynamic simulation, we identify the key role played by the Lorentz force through the entire flare lifespan, and show that slow variations in the post-flare magnetic field achieve the bulk of the energy release. Synthetic images in multiple passbands closely match flare observations, and we quantify the role of conductive, radiative, and Lorentz force work contributions from flare onset to decay. This highlights how the non-force-free nature of the magnetic topology is crucial to trigger Rayleigh–Taylor dynamics, observed as waving coronal rays in extreme ultraviolet observations. Our C-class solar flare reproduces multiphase aspects such as post-flare coronal rain. In agreement with observations, we find strands of cooler plasma forming spontaneously by catastrophic cooling, leading to cool plasma draining down the post-flare loops. As there is force balance between magnetic pressure and tension and the plasma pressure in gradual-phase flare loops, this has potential for coronal seismology to decipher the magnetic field strength variation from observations. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate the dual nature solutions of the triple diffusive magnetohydrodynamic flow due to stretching/shrinking surfaces. The system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations with the help of compatible transforms. Analytical dual solutions are obtained for every unknown velocity, temperature, and concentration profile in terms of known physical parameters. Heat and mass transfer analyses have been carried out in the presence of convective boundary conditions. The graphic interpretation of the possible dual solutions of dimensionless velocity, temperature, concentration, skin‐friction coefficient, and Nusselt and Sherwood numbers is analyzed under the influence of different known physical parameters. The obtained results are validated against previously published results for a special case of the problem. [ABSTRACT FROM AUTHOR]

Thermal enhancement remains a critical requirement in different engineering applications. Many factors can affect the efficiency of the techniques used for this aim. The purpose of this study is to investigate the impact of particle‐fluid suspensions with heat transfer through porous annular‐sector duct on enhancement techniques and address the potential application of deep learning to suspension problems. The analysis is focused on the fully developed region of the forced convection flow. Thermal and rheological properties of particle‐fluid suspensions were studied using physics‐informed neural networks exploiting transfer learning capabilities for making parameter analysis. Another finite element solution was introduced as a measure of accuracy and to support our findings. Results were prepared in a comparative manner for both solvers including contour plots, tabular, and two dimensional figures. The average Nusselt number and friction factors were calculated for different cases to investigate the value of the thermal performance factor. Our results indicate the downside of suspensions on thermal enhancement and their negative impact on other techniques. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to focus on the transient flow and heat transfer of a non-newtonian fluid (Casson fluid) between parallel disks in the presence of an external magnetic field. The bottom disk is considered to be porous and fixed, whereas the upper disk moves down. Also, the influence of the heat source/sink and viscous dissipation is taken into account. The conservative partial differential equations have been transformed into dimensionless ones and are solved semi-analytically using Least Square Method. Besides, applying a numerical solution, the accuracy of analytical results is verified using the fourth-order Runge–Kutta method. The effects of various physical parameters such as suction/injection, heat source/sink, Prandtl number, magnetic field, slip condition, and Casson fluid parameter on velocity and temperature distribution as well as skin-friction coefficient and Nusselt number are examined and discussed. The results have shown that higher values of the Casson fluid parameter decrease the Nusselt number and shear stress. Also, it is observed that the Hartmann number augmentation decreases the heat transfer rate. What is more, it is shown that the intensity of injection/suction affects how streamlines behave against the central vertical axis. [ABSTRACT FROM AUTHOR]

We investigate the global existence of classical solutions for two‐dimensional incompressible, inviscid, and resistive magnetohydrodynamics (MHD) system. Assuming that the initial magnetic field is close to an equilibrium state of constant magnetic vorticity, the global existence result could be obtained using a time‐weighted energy estimate. [ABSTRACT FROM AUTHOR]

AbstractChemical reaction and ohmic heating can significantly influence the flow behavior and heat transfer characteristics in industrial processes involving non-Newtonian fluids. These processes include polymer processing, food processing, and manufacturing processes where non-Newtonian fluids are commonly encountered. Therefore, the impacts of chemical reaction and ohmic heating on the unsteady flow of an incompressible magnetized non-Newtonian Casson liquid through a rectangular pipe with a variable pressure gradient is scrutinized in this article. The impacts of heat generation/absorption and viscous dissipation are also incorporated through the energy equation. The numerical simulations of partial differential equations (PDEs) are acquired utilizing the finite difference method with the incorporating relaxation (SOR) algorithm. The impacts of dissimilar imperative parameters on various flow fields are scrutinized through graphs. Outcomes indicate that liquid velocity decreases with enhancing values of the Casson parameter. Furthermore, the liquid temperature has an enhancing behavior with the impact of the heat source/sink parameter. Comparisons of numerical results with previously published results show an excellent agreement. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc. [ABSTRACT FROM AUTHOR]

An essential factor for determining the characteristics of an accretion flow is its angular momentum. According to the angular momentum of the flow, semi-analytical analysis suggests various types of accretion solutions. It is critical to test these with numerical simulations, using the most advanced framework available (general relativistic magnetohydrodynamics), to understand how the flow changes with different angular momentum. By changing the initial condition of the accretion torus minimally, we can simulate a steady, low-angular-momentum accretion flow around a Kerr black hole. We focus primarily on the lower limits of angular momentum and find that an accretion flow with an intermediate range of angular momentum differs significantly from high- or very-low-angular-momentum flows. The intermediate-angular-momentum accretion flow has the highest density, pressure, and temperature near the black hole, making it easier to observe. We find that the density and pressure have power-law scalings ρ ∝ r n −3/2 and p g ∝ r n −5/2, which only hold for very-low-angular-momentum cases. With the increase in flow angular momentum, it develops a nonaxisymmetric nature. In this case, simple self-similarity does not hold. We also find that the sonic surface moves away from the innermost stable circular orbit as the angular momentum decreases. Finally, we emphasize that an intermediate-angular-momentum flow could provide a possible solution to explaining the complex observation features of the supermassive black hole Sgr A* at our galactic center. [ABSTRACT FROM AUTHOR]

Due to its superior insulating qualities, SF6 gas is extensively used in the power sector. However, because of its poor environmental protection properties, finding ecologically acceptable insulating gas has become a critical challenge in the power sector in the context of pursuing green electricity. This work simulates the arc-quenching performance of a gas mixture of CF3I and CO2, which is thought to be a workable substitute for SF6 gas. The COMSOL software is used to build a two-dimensional model of a single-pipe arc-quenching chamber based on the concepts of magnetohydrodynamics (MHD) theory. The lightning impulse current is made by applying electrical stimulation to pure CO2 gas, gas mixtures with 10% CF3I and 90% CO2, and gas mixtures with 30% CF3I and 70% CO2 in the single-pipe arc-quenching chamber. During the first stage of arc formation, the results show that CF3I/CO2 gas mixtures with 10% and 30% CF3I have lower electrical conductivity than pure CO2 gas. An 8/20 μs lightning impulse current waveform with a magnitude of 4 kA is used for this observation. The highest airflow velocity for pure CO2 is 1744 m/s, but the mixture of 10%/90% CF3I/CO2 has a maximum airflow velocity of 1593 m/s. The 30%/70% CF3I/CO2 mixture has the highest maximum airflow velocity at 1840 m/s. Airflow velocity increases and the overpressure in the arc-quenching chamber is prolonged when there is a greater concentration of CF3I gas in the gas mixture. Consequently, these factors greatly reduce the duration of the arc-extinguishing time. The arc-quenching chamber's overpressure is extended when the amount of CF3I gas in the gas mixture is increased, which increases the velocity of the airflow. As a result, these factors significantly decrease the duration of the arc-extinguishing time. [ABSTRACT FROM AUTHOR]

This study investigates the steady, incompressible MHD flow of a hybrid nanofluid over a vertical solid cone embedded in a porous medium under suction effect. The research explores the effects of various factors, such as thermal radiation, chemical reactions, heat generation, viscous dissipation, and Joule heating on heat and mass transfer phenomena. To investigate the effects of hybrid nanoparticles, we consider single-walled carbon nanotubes (SWCNT) and alumina (Al2O3) along with water (H2O) as the base fluid. After a suitable similarity transformation, the governing equations are reconstructed and solved using the Keller-box numerical scheme. We present graphical and tabular analyses of various parameter impacts on heat transfer profiles and coefficients. This study provides valuable insights into the control of fluid dynamics and heat transfer in porous media, which have significant implications for industrial and engineering applications. The findings of the current article are in excellent agreement with previously published works. [ABSTRACT FROM AUTHOR]

Observed spectral profiles of emission lines from the corona are found to have widths exceeding the thermal line width. To investigate the physical mechanism, we run a 3D magnetohydrodynamics model of a single, straightened loop in which we partially resolve turbulent motions that form in response to the driving by self-consistently evolving magneto-convection in the photosphere. The convective motions shear and twist the magnetic field lines, leading to heating. From the model, we synthesize spectral profiles of emission lines forming at temperatures around and above 1 MK. The coronal heating process generates a range of velocity amplitudes and directions structured on a scale much smaller than the resolving power of current instruments, leading to a broadening of the spectral lines. Our model includes the mass exchange between corona and chromosphere, thus we also capture flows parallel to the loop axis. We find that the spectral lines show a non-thermal line broadening roughly consistent with observations for a viewing angle perpendicular to the axis. The broadening through field-parallel flows is comparable, although slightly smaller. The line broadening is independent of the instrument resolution for a perpendicular line of sight (LOS). We can connect the non-thermal line broadening to heating events and flows. While small-scale velocities along the LOS are mainly responsible for the broadening observed perpendicular to the loop, chromospheric evaporation is important for the line broadening observed along the loop. The model reproduces observed values for non-thermal line widths. In the model, these result from continuous driving by magnetoconvection, without imposing driving motions or starting from an already braided field. [ABSTRACT FROM AUTHOR]

In this paper, inscribed non-Newtonian Williamson fluid relaxation and contraction phenomena due to the effect of magnetohydrodynamics (MHD) is taken into account. This issue is modeled, and precise solutions are handled using a low Reynolds number and long wavelength approximation. Graphical depiction of the consequences of various parameters on temperature and velocity are provided. It becomes clear that the temperature reactions to increases in Biot numbers are decreased. Considering a cylindrical coordinate system, the impact of various physical parameters on the temperature distribution, velocity, the pressure gradient, and frictional force are secured from the flow for non-Newtonian Williamson fluid exposed from MATLAB. Additionally, it has been discovered that the velocity profile at the tube's center increases for shear-thinning a fluid and decreases for thickening a fluid. Furthermore, the peristaltic walls show the opposite behavior. [ABSTRACT FROM AUTHOR]

The primary purpose of this work is to investigate the influence of a magnetic field on a micropolar fluid, which is rotating between two horizontally arranged parallel plates. A uniform magnetic field acts perpendicularly to the porous plate, which consumes fluid with a steady suction velocity. The obtained higher-order nonlinear partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) by using similarity transformation. A semi-analytical methodology has been applied to obtain the result to the problem. The influence of various flow parameters of the flow field like coupling parameter, viscosity parameter, Reynolds number, porosity parameter, rotation parameter and magnetic field parameter has been examined and explained by graphs. A resemblance between the results obtained by solving by the differential transform method (DTM) and the outcomes of the former research works has also been displayed which shows the correctness and efficiency of the used analytical method. The numerical values of the coefficient of skin friction at the lower plate are also displayed in tabular form and compared with the literature. [ABSTRACT FROM AUTHOR]

This article investigates the nonlinear convection transport of heat transfer in a nanoparticle laden two-layer flow in a vertical channel under the additional effects of magneto hydrodynamic (MHD) and radiation. Water and compressed air are chosen as the fluids in two-layer flow. This type of flow is commonly seen in the transportation of oil and gas in pipelines, therefore, correct understanding of flow dynamics including convective transport phenomenon, layers interaction, and graphical interpretation of flow variables is important for better designing of equipments. Titanium dioxide (Ti O 2 ) nanoparticles are added into the air to magnify the transport mechanism. The mathematical model incorporating buoyancy, nonlinear convection, MHD, viscous dissipation, and radiation effects is presented in the form of nonlinear Ordinary Differential Equation (ODE's). Then utilizing homotopy analysis method, these interconnected differential equations are resolved. A visual illustration shows how different physical factors affect fluid rate and temperature. Tabulated values of Nusselt number at both walls are presented to discuss the numerical data of convection and found that it decreases toward the left boundary but rises toward the right wall by increasing Eckert number and Prandtl number. The results of this two-layer flow will help in understanding this complex flow which has practical applications in various engineering processes and further enhance the scientific knowledge related to multilayer problems. [ABSTRACT FROM AUTHOR]

AbstractCarbon nanotubes have gained significant attention due to their unique properties like small dimensions, high thermal conductivity, and unique architecture. These nanotubes have enormous potential in various fields such as nanomedicine, mechanical compound materials, sensor devices, bio-sensors, and many other applications. The present study investigates the impact of adding nanoparticles such as iron oxide (Fe3O4), single-walled carbon nanotubes (SWCNT), and multi-walled carbon nanotubes (MWCNT) on magnetohydrodynamics (MHD) oscillatory water-based flow over a porous medium. The aim is to examine the effect of heat and mass transfer rate and radiative viscous dissipation that interacts with Fe3O4 nanoparticles and carbon nanotubes. The governing equations of the dynamic nanofluid systems are transformed into a set of coupled nonlinear partial differential equations through suitable dimensionless transformations and further converted into ordinary differential equations by taking appropriate solutions for oscillatory-type nanofluid flow. The homotopy perturbation method is applied to solve the governing equations with oscillatory boundary conditions and the solution is also compared with the numerical solver bvp4c. The rate of increase in the temperature and Heat Transfer are computed by the linear slope regression method and results are computed for nanoparticles SWCNT, MWCNT, and Ferro. Also, Skin friction and rate of heat transfer are computed and compared for the nanoparticles with varying Peclet and Eckert numbers. The velocity profile and temperature profile of SWCNT/MWCNT/Ferro nanofluids are being compared. The heat transfer rate is observed to be high for Ferro nanoparticles compared to SWCNT and MWCNT. [ABSTRACT FROM AUTHOR]

High-speed flows over a 34° compression corner subjected to several types of applied electromagnetic fields are numerically investigated. A coupled model for the turbulent flow field and the externally applied electromagnetic field is established based on the low magnetic Reynolds number assumption. The advection upstream splitting method with pressure-based weight function (AUSMPW) scheme and the lower upper symmetric Gauss Seidel (LUSGS) method are implemented to solve turbulent magnetohydrodynamic (MHD) flow equations. Numerical results demonstrate that the performance of MHD separation flow control is determined mainly by the Lorentz force in the turbulent boundary layer. For the counter-flow Lorentz force, the velocity fluid in the boundary layer can be retarded, and a significant temperature increase was observed. The decelerating Lorentz force significantly brings negative effects on the turbulent skin friction coefficients and increases the static pressure locally. Furthermore, the position of the MHD zone has a significant impact on the control efficiency of the ramp-induced separation. With an external electric and magnetic field applied, the low-velocity fluid in the boundary layer can be accelerated, and the Lorentz force directed along the stream can reduce the size of the separation bubble. [ABSTRACT FROM AUTHOR]

This study intends to assess the heat transmission of a steady two-dimensional MHD Casson nanofluid flow across a non-linearly stretching sheet concerning viscous dissipation, heat generation, thermal radiation, and chemical radiate parameters. Mathematically, the flow is outlined as PDE systems, converted to ODE systems by a well-posed transformation, which are afterwards solved numerically in Matlab employing the fourth-order precision program (Bvp4c). The comparison indicates adequate agreement, demonstrating the correctness of the numerical strategy. It is observed that in the existence of a chemical reaction, the temperature is elevated, while the concentration profile is markedly reduced, in contrast to a scenario where no chemical reaction is taking place. In consideration of viscosity, heat radiation, thermophoresis impact, and suction or injection parameter, the Nusselt number reveals a growing tendency. In contrast, it exhibits opposing behavior with regard to the other addressed factors. The findings of this study have applications in the engineering, biomedical and industrial sectors, including food processing, polymer making, glass and fiber production, material processing, and enhanced oil recovery. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for non-Newtonian fluids together with the Maxwell correction for the Ampère law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables. [ABSTRACT FROM AUTHOR]

The study of convective magnetohydrodynamic (MHD) biofluid transport through a non-uniform duct is of interest due to its applications to biomedical devices and equipment. Because of this, a comparative study of free convective peristaltic flow of non-Newtonian (Casson and Jeffrey) fluids in a tapered porous symmetric duct with Hall current and viscous dissipation effects is carried out. The proposed dimensional governing equations are converted into a system of non-dimensional partial differential equations by invoking adequate non-dimensional parameters. Furthermore, a long-wavelength approximation is used to reduce the complexity of the system. Then the reduced system of partial differential equations is solved analytically using the regular perturbation method. The fascinating features of the influential parameters on the flow characteristics are demonstrated and analyzed in depth through graphs and tables. The results demonstrate that the velocity and temperature in the Jeffrey fluid flow are larger compared to those in the Casson fluid flow. The thermal Grashof number and the Hall current parameter enhanced the pressure rise profile. This research has significant implications in biomedical devices (MRI, vitamins A and D injections, heart-lung machines, etc.) and pharmaceutical fluid preparation in biomedical sciences. [ABSTRACT FROM AUTHOR]

In this study, we have analyzed magnetohydrodynamic (MHD) consequences on the heat and mass transmission within unsteady dissipated liquid film flow. Flow is generated due to stretchable surface accompanied with effects of ohmic heating, chemical reaction and heat absorption. Moreover, the flow governing partial differential equations (PDEs) are further modified into equivalent ordinary differential equations (ODEs) by applying regular perturbation method to get its analytical solution after that we have applied sixth-order Runge–Kutta technique to get its numerical solution. These two solutions are validating each other in the simulations. Figures are plotted to study the changes in physical quantities like skin friction coefficient, concentration, velocity, temperature, Sherwood and Nusselt number with the variations of Prandtl numbers Pr, parameters of chemical reaction β , Eckert numbers Ec, magnetic parameter Ha (also known as Hartman number) Schmidt number and coefficient of heat absorption Δ. [ABSTRACT FROM AUTHOR]

AbstractPresent communication investigates the magnetohydrodynamics (MHD) bioconvection Williamson nanofluid with mass and thermal characteristics caused by the swimming of gyrotactic microorganisms subjected to a radially magnetic field and thermal radiation through a curved stretching surface. To emphasize the significance of thermal engineering processes, this novel mathematical model is designed to simulate the transportation of energy through the boundary layer flow of non-Newtonian nanofluid, taking into account the influences of thermophoresis, the density of motile microbes, and Brownian motion. Based on these assumptions, the fundamental governing equations are initially modeled in terms of partial differential equations (P DEs) through boundary layer theory and then formulated into a system of ordinary differential equations (ODEs) by utilizing similarity transformations. The numerical solution for the given nonlinear system, along with their respective boundary conditions, is computed using the BVP4c package in MAT LAB. To comprehensively evaluate the influence of various emerging parameters, results are discussed through graphs and tables for nanofluid’s temperature, concentration profile, local Sherwood number, skin fraction, axial velocity, heat transfer, and distribution of motile microorganisms. The nanofluid’s velocity experiences a decrease with the simultaneous increase of both curvature and magnetic parameters. As a primary finding, the motile microorganism profile exhibits a substantial increase concerning the curvature parameter. Similarly, the nanofluid parameters, including thermophoresis and Brownian motion, along with the radiation parameter, enhance the temperature of the nanofluid. [ABSTRACT FROM AUTHOR]

AbstractThe stretching surface flow phenomenon plays novel significance in the differential industrial sectors like manufacturing processes, food processing, polymers, petroleum engineering, glass fiber production, metal spinning, and many others. This research focuses on investigating the flow of electroosmotic-driven transport of magnetic Casson fluid over an exponential stretching sheet. The study employs mathematical modeling based on partial differential equations which are further truncated into ordinary system under the implementation of dimensionless variables. The quartic B-spline method is applied for obtaining solutions. Key findings indicate that electroosmotic and Helmholtz–Smoluchowski effects enhance fluid velocity, while magnetic forces reduce velocity. Additionally, an increase in the Hartmann parameter leads to a decrease in the skin friction coefficient. [ABSTRACT FROM AUTHOR]

A neural network is employed to address a non-binary classification problem of plasma instabilities in astrophysical jets, calculated with the Legolas code. The trained models exhibit reliable performance in the identification of the two instability types supported by these jets. We also discuss the generation of artificial data and refinement of predictions in general eigenfunction classification problems. [ABSTRACT FROM AUTHOR]

This work objective focuses on studying the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. Additionally, thermophoresis and Brownian motion impacts are taken into account. The phenomena of heat transfer are analyzed considering several factors such as thermal radiation, Joule heating and nonlinear heat source. On the other hand, mass transfer is explored under the effect of chemical reaction. Tangent hyperbolic fluid is an important branch of non-Newtonian fluids known for its ability to describe shear thinning effects. Understanding fluid flow on exponentially stretched surfaces is of great significance due to its applications in various industrial processes. These applications include fluid film condensing methods, plastic production for making plastic covers, fiber manufacturing (where it is used to spin fibers), glass blowing, metallurgical procedures, and the paper industry. The concept of magnetohydrodynamics (MHD) is significant due to its various engineering applications, such as MHD generators, flow meters, heat reservoirs, small components in different devices, and cooling systems for nuclear reactors. To analyze the system, using similarity transformations, the governing equations of continuity, velocity, and concentration are transformed into non-dimensional differential equations. The numerical solution is obtained using the shooting technique. The study presents the physical significance of all the fluid parameters involved, focusing on the velocity, temperature, and concentration profiles. These profiles are presented graphically and discussed in detail. The results show that the fluid velocity profile increases with enhancing values of the We and the magnetic number M. The thermal profile increases with higher Nt and Rd The concentration profile decreases with higher values of Q t and Nb. [ABSTRACT FROM AUTHOR]

In this paper, we investigate time-dependent viscous fluid flow along a stretching horizontal plate with a magnetic field, viscous dissipation and chemical reaction are taken into account. A system of partial differential equations (PDEs) governs the flow problem. Using dimensionless variables, system of governing PDEs is transformed to dimensionless form. Finite difference method is the numerical method adopted for solving the system of PDEs with initial and boundary conditions. The impact of potential variables is examined and displayed graphically. The results suggest that greater Hartmann number reduces velocity and temperature, whereas raising chemical reaction parameter decreases concentration profile. Moreover, skin friction increases with Hartmann number values and Nusselt number, showing increase for growing Eckert and Prandtl numbers. [ABSTRACT FROM AUTHOR]

This paper establishes the global well‐posedness of strong solutions for the 3D compressible magnetohydrodynamics (MHD) with non‐flat doping profile and Coulomb force, which is of hyperbolic–parabolic–elliptic mixed type. It is essentially shown that for the initial value problem with initial density allowed to contain vacuum states, the strong solution exists globally under small energy but possible large oscillations. [ABSTRACT FROM AUTHOR]

The purpose of the present research is to examine the effect of porosity in the presence of radiation and viscous dissipation on two-dimensional unsteady MHD mixed convection heat and mass transport at the stagnation point. The governing time-dependent nonlinear PDEs are converted into nonlinear ODEs by utilizing similarity transformations. The mathematical formulation is produced as ordinary differential equations. The achieved coupled system has been analyzed using the Keller–Box technique. Newton's system dictates that the coefficients must be accurate and refined. To assess the influence of flow-controlling factors on relevant profiles, quantitative, and qualitative analysis are conducted. With the use of graphs and tables, beneficial talks were conducted. Under the restricting conditions, prior findings were compared and determined to be satisfactory. The conclusions of this study are widely accepted by the scientific community. [ABSTRACT FROM AUTHOR]

In this research article, the effect of rotating and second-grade fluid on an MHD Jeffery–Hamel flow (J–HF) has been investigated. Here, the MHD second-grade fluid theory has been used. The PDEs that represent this flow are transformed into ODEs, which are then solved using two separate methods: the 4th–5th-order Runge–Kutta Fehlberg technique with shooting methodology and the DTM technique. The impact of diverse physical factors, like rotational factor, Deborah, and Hartmann numbers, on the dimensionless rapidity F of the second-grade fluid and the wall frictional force factor is analyzed. Backflow is not detected in the lower part of the channel, according to the study. Additionally, the results show that the reverse flow disappears completely as the Hartmann number increases. Also, it is found that the Deborah quantity has less impact on the dimensionless velocity F of second-grade fluid nearby the down surface of the rotative diverging channel, but a significant increase in the thickener of the momentum boundary layer at the upper half of the channel is noticed with the rise in the magnitude of the Deborah number, hence signaling the beginning of the backflowing behavior. The current findings are contrasted to those of prior investigations and the HAM-built Mathematica package BVPh 2. The newly used analytical method shows high reliability, usefulness, and precision, as evidenced by the excellent agreement between DTM, HAM-BMP BVPh 2, and computational RKF45. [ABSTRACT FROM AUTHOR]

We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a known recent result on the stability of Yudovich's solutions to the incompressible Euler equations in |$L^{\infty }([0,T];H^{1})$| by providing a new approach to its proof based on the idea of compactness extrapolation and by extending it to the whole plane. This new method of proof is robust and, when applied to viscous models, leads to a remarkable logarithmic improvement on the rate of convergence in the vanishing viscosity limit of two-dimensional fluids. Loosely speaking, this logarithmic gain is the result of the fact that, in appropriate high-regularity settings, the smoothness of solutions to the Euler equations at times |$t\in [0,T)$| is strictly higher than their regularity at time |$t=T$|⁠. This "memory effect" seems to be a general principle that is not exclusive to fluid mechanics. It is therefore likely to be observed in other setting and deserves further investigation. Finally, we also apply the stability results on Euler systems to the study of two-dimensional ideal plasmas and establish their convergence, in strong topologies, to solutions of magnetohydrodynamic systems, when the speed of light tends to infinity. The crux of this asymptotic analysis relies on a fine understanding of Maxwell's system. [ABSTRACT FROM AUTHOR]

Nanofluidic peristaltic transport is an emerging field of research with potential biomechanical, industrial, and biotechnological applications. Motivated by these utilizations, the present investigation addresses the mixed convective magneto peristaltic flow of radiative Ree-Eyring nanofluid through an inclined divergent channel under the consequences of energy generation, activation energy, viscous and Ohmic dissipation effects. In order to mimic the problem, we employ Cartesian coordinates along with the lubrication approach. The computational software MATLAB is implemented to actualize the numerical shooting process. The impact of major factors on velocity, skin friction coefficient, temperature, heat transfer rate, concentration, and Sherwood number is explored extensively with graphical and tabular representations. The findings discovered that both thermal and solute Grashof numbers cause an upsurge in the distribution of velocity. The Brownian movement parameter decreases the mass transfer rate and increases the heat transfer rate at the channel walls. Temperature distribution of the Ree-Eyring liquid enhances for Eckert number and energy generation parameter. Further, it is found that the concentration field of Ree-Eyring nanofluid is an enhancing function of activation energy. [ABSTRACT FROM AUTHOR]

In a previous study, Huang et al. used the Alfvén Wave Solar atmosphere Model, one of the widely used solar wind models in the community, driven by ADAPT-GONG magnetograms to simulate the solar wind in the last solar cycle and found that the optimal Poynting flux parameter can be estimated from either the open field area or the average unsigned radial component of the magnetic field in the open field regions. It was also found that the average energy deposition rate (Poynting flux) in the open field regions is approximately constant. In the current study, we expand the previous work by using GONG magnetograms to simulate the solar wind for the same Carrington rotations and determine if the results are similar to the ones obtained with ADAPT-GONG magnetograms. Our results indicate that similar correlations can be obtained from the GONG maps. Moreover, we report that ADAPT-GONG magnetograms can consistently provide better comparisons with 1 au solar wind observations than GONG magnetograms, based on the best simulations selected by the minimum of the average curve distance for the solar wind speed and density. [ABSTRACT FROM AUTHOR]

This computational study was designed to examine the effect of alumina and copper on the flow of a nanofluid based on engine oil through a Darcy–Forchheimer porous media. The flow model incorporates the generalized radiative heat and mass transport rules. The Darcy–Forchheimer terms in the momentum equation and radiation term in the energy equation are integral parts of the governing nonlinear Navier–Stokes equations, which are two-dimensional partial differential equations. Under the constraint of the convective boundary, the stated PDEs are transformed into highly nonlinear versions of the ordinary differential equations. In order to solve the final ODEs, the numerical RK-45 approach is combined with the shooting methodology. Important aspects of the governing model include porosity, magnetohydrodynamics (MHD), a convective boundary, thermal radiation, and viscous dissipation. The final findings show that when the Forchheimer number increases, the velocity decreases because of the inertial effect included in the flow model. In addition, the velocity profile is improved due to the increased volume percentage of both kinds of nanoparticles. The temperature varies greatly depending on the volume fraction. A higher Biot number and the resulting convective border cause a greater heat flow than a non-convective barrier. For two particular examples, with and without MHD influence, interesting streamlines and contour graphs are produced. [ABSTRACT FROM AUTHOR]

AbstractThis work enlightens the magnetohydrodynamics (MHD) natural convective hydrothermal scenario and entropy generation analysis in a corrugated enclosure filled with MoS2–SiO2–water hybrid nanofluid. Three discrete uniform heaters are kept fixed to the enclosure bottom wall. The enclosure top wall and the remaining parts of its bottom wall are isothermally cooled. The enclosure has adiabatic vertical walls. A higher-order compact (HOC) finite difference technique is used to determine the solutions to the dimensionless governing equations. To demonstrate the accuracy of the mathematical model, experimental and numerical verifications are accomplished. The numerical investigation is accomplished for Rayleigh number (Ra=104−106), aspect ratios of heater length (AR=0.2,0.4,0.6,0.8), nanoparticle volume percentage (ϕ=0−4%), and Hartmann number (Ha=0−120). The numerical outcomes are presented and studied by means of isotherms, streamlines, and the average Nusselt number. Furthermore, local entropy generation resulting from heat transmission, fluidic friction, and magnetic field, along with overall entropy formation and Bejan number are analyzed. This study reveals that the aspect ratio AR=0.2 enhances the convective flow process at Ra=106, even when a magnetic field is present. The heat transfer rate increases as a function of the Rayleigh number, while it exhibits a decreasing trend with the aspect ratio of heater length and Hartmann number. Total entropy generation reduces as the Hartmann number and aspect ratio of heater length increase. Bejan number graphs show a reverse pattern as compared to total entropy generation. It has been noted that an increase in the Hartmann number from 0 to 120 decreases the average Nusselt number and total entropy generation by 19.77 and 46.63%, respectively, for AR=0.2, Ra=106, and ϕ=4%. [ABSTRACT FROM AUTHOR]

In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grunwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a nonporous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow. [ABSTRACT FROM AUTHOR]

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material's low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle's volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids. [ABSTRACT FROM AUTHOR]

The linear stability of a pressure-driven channel flow of an electrically conducting Navier–Stokes–Voigt type of the viscoelastic fluid subject to a transverse magnetic field is investigated. The validity of Squire's theorem is proved, and the generalized eigenvalue problem for two-dimensional modes is obtained by adopting the Galerkin method, which is subsequently solved using the QZ-algorithm. Although the base flow retains its Newtonian fluid characteristics, the noticeable influence of the Kelvin–Voigt parameter in conjunction with the Hartmann number on the stability of fluid flow is perceived. Instability is exclusively identified within a specific range of the Kelvin–Voigt parameter, markedly affected by the Hartmann number. Furthermore, closed neutral stability curves arise, indicating the requirement of two values of the Reynolds number to completely assess the linear stability criteria, in contrast to the typical single value observed in the case of Newtonian fluids. [ABSTRACT FROM AUTHOR]

Present communication explores a novel application of the computational intelligence technique, namely, the Levenberg–Marquardt scheme under a Backpropagated Neural Network (LM-BNN) to solve the mathematical model for the magnetohydrodynamic peristaltic transport of Reiner–Philippoff (R–Ph) pseudoplastic fluid considering the influences of Ohmic heating, mixed convection, and viscous dissipation through a symmetric channel. The R–Ph fluid model is used in this investigation to elucidate the non-Newtonian behavior of the fluid under consideration. The Reiner–Philippoff fluid model delineates the intricate relationship between stress and deformation rate within the fluid. There are a few studies available on the peristaltic transport of the Reiner–Philippoff fluid that do not incorporate Joule heating, mixed convection, and magnetic field effects. Therefore, a novel mathematical model is developed to employ an artificial neural network technique with a different approach that has not been examined before. The governing equations of the problem are simplified using long wavelength and low Reynolds number approximations, and the resulting system is numerically solved using the BVP4c scheme in MATLAB based on the shooting algorithm. Furthermore, a dataset is constructed through the BVP4c technique for the proposed LM-BNN, considering eight scenarios of peristaltic motion of the Reiner–Philippoff fluid model by varying the Bingham number, the Brinkman number, the Grashof number, the R–Ph fluid parameter, and the Hartmann number. The numerical dataset is divided into 15 % for testing, 15 % for training, and 70 % for validation, which are utilized in LM-BNN to analyze the numerical solutions and Levenberg–Marquardt neural networks (LM-NNs) predicted results. The consistency and effectiveness of LM-BNN are validated through regression analysis, stresses at the wall, error histogram, correlation index, heat transfer, and mean squared error based fitness curves, which vary from 10 − 3 → 10 − 11 . Variations in several flow parameters affecting temperature and velocity profiles are explained physically through graphs. Additionally, an analysis of heat transfer and stresses at the wall, including absolute errors, is provided through tables. The outcomes reveal that the improving Grashof number and the Hartmann number tend to increase the temperature profile. Tabular results indicate that rates of heat transfer improve when assigning higher values to the Hartmann number, the Brinkman number, and the Grashof number, whereas stresses at the wall decrease for the Reiner–Philippoff fluid parameter and the Bingham number. The error analysis of numerical simulations is a valuable step in determining whether the data obtained are reliable and accurate. In terms of absolute error, the disagreement between numerical solutions and those predicted by LM-NNs is approximately 10 − 5 → 10 − 11 . It is clear from this error analysis that LM-NNs predicted results are consistent and reliable. [ABSTRACT FROM AUTHOR]

Outflows play a pivotal role in star formation as one of its most visible markers and a means of transporting mass, momentum, and angular momentum from the infalling gas into the surrounding molecular cloud. Their wide reach (at least thousands of astrnomical units) is a contrast to typical disk sizes (∼10–100 au). We employ high-resolution three-dimensional nested-grid nonideal magnetohydrodynamic (MHD) simulations to study outflow properties in the Class 0 phase. We find that no disk wind is driven from the extended centrifugal disk that has weak magnetic coupling. The low-velocity winds emerge instead from the infalling magnetic pseudodisk. Much of the disk actually experiences an infall of matter rather than outflowing gas. Some of the pseudodisk wind (PD-wind) moves inward to regions above the disk and either falls onto the disk or proceeds upward. The upward flow gives the impression of a disk wind above a certain height even if the gas is originally emerging from the pseudodisk. The PD-wind has the strongest flow coming from a disk interaction zone that lies just outside the disk and is an interface between the inwardly advected magnetic field of the pseudodisk and the outwardly diffusing magnetic field of the disk. The low-velocity wind exhibits the features of a flow driven by the magnetic pressure gradient force in some regions and those of a magnetocentrifugal wind in other regions. We interpret the structure and dynamics of the outflow zone in terms of the basic physics of gravity, angular momentum, magnetic fields, and nonideal MHD. [ABSTRACT FROM AUTHOR]