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In this paper, the steady electrically conducting hybrid nanofluid (CuO-Cu/blood) laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms is considered. Additionally, hybrid nanofluid flow over a horizontal porous stretching sheet along with an induced magnetic field and external magnetic field effectsthat can be used in biomedical fields, such as in drug delivery and the flow dynamics of the microcirculatory system. This investigation can also deliver a perfect view about the mass and heat transfer behavior of blood flow in a circulatory system and various hyperthermia treatments such as the treatment of cancer. The simple partial differential equations (PDEs) are converted into a series of dimensional ordinary differential equations (ODEs), which are determined using appropriate similarities variables (HAM). The influence of the suction or injection parameter, mixed convection, Prandtl number, buoyancy ratio parameter, permeability parameter, magnetic parameter, reciprocal magnetic prandtl number, bioconvection Rayleigh number, coupled stress parameter, thermophoretic parameter, Schmidt number, inertial parameter, heat source parameter, and Brownian motion parameter on the concentration, motile microorganisms, velocity, and temperature is outlined, and we study the physical importance of the present problem graphically.

The present research focuses on the MHD second-grade nanofluid flow with induced magnetic field and viscous dissipation over an exponentially stretching surface. The solutal and thermal energy equations are analyzed in the presence of thermophoretic effect and variable thermal conductivity. The solutal and thermal slip boundary conditions are imposed on the surface of the sheet. In the mathematical modeling, the Brownian motion, and thermophoresis consequences are also discussed. The physical appearance of the induced magnetic field on the second-grade nanofluid is the central aim of this investigation. The mathematical flow model which is in the form of nonlinear PDEs is transformed into the system of couple ODEs by the usage of suitable similarity variables. These couple equations are tackled numerically with the help Bvp4c Matlab approach. The illustration of parameters on the flow model is discussed via graphs and tables. It is noted that the induced magnetic field profile and velocity of fluid intensify for the stronger values of second-grade parameter. Further, the numerical result shows that skin friction rate boosts via greater estimation of second-grade parameter and it reduces for magnetic Prandtl number. [ABSTRACT FROM AUTHOR]

Entropy generation with time periodic thermal boundary conditions have numerous applications in heat exchangers, electronic devices, automatic and thermal control systems. The present research focuses on mixed convective hydromagnetic electrically conducting fluid flow in a vertical annulus using thermodynamic concepts, in the presence of induced magnetic field along with entropy generation and time periodic boundary conditions. The governing equations related to the present model are solved using finite element method. Also to predict heat transport features in the vertical annulus, artificial neural network – backpropogated Levenberg Marquardt algorithm is adopted. The steady and periodic profiles of velocity, skin friction, temperature and induced magnetic field are illustrated graphically for specific range of pertinent parameters to demonstrate significant aspects of the results. It is noted that increase in Hartmann number enhances the entropy generation near the outer cylinder, which illustrates that the fluid friction and magnetic field influence is maximum at the outer cylinder surface. The Bejan number in the annulus reduces with increase in viscous heating parameter. Results indicate that raise in the Prandtl number diminishes the thermal boundary layer thickness. As a result of decrease in the intensity of heating the boundary walls, a raise in Strouhal number lowers the fluid temperature profile. The generalized correlation is expressed to predict heat transport features in the annulus using artificial neural network – backpropogated Levenberg Marquardt algorithm. [ABSTRACT FROM AUTHOR]

The present objective is to numerically analyze the induced magnetic field (IMF) effect of an unsteady MHD flow of Casson fluid through two infinite vertical plates. The effect of radiative heat has been scrutinized. Governing non-dimensional PDEs of the flow are discretized by the finite difference method to some algebraic system of equations, which is then numerically solved concerning the boundary conditions. The effects of the radiations, magnetic Prandtl number, Prandtl number, Hartmann number, and Casson parameter on temperature profile, velocity profile, and induced magnetic field have been depicted through graphs. The radiative effect and Prandtl number have considerable influence on the surface drag force and also on the rate of heat transfer. [ABSTRACT FROM AUTHOR]

This work is focused on Magneto hydrodynamic unsteady flow of Newtonian fluid flow over a perpendicular porous plate along with chemical reaction, heat, and mass transfer. The induced magnetic field and viscous and magnetic dissipation properties are considered throughout the porous plate. Heat source is the added effect in the model to observe the nature of flow in this work. This study finds its applications in understanding the storage of flues, disposal of radioactive waste materials, flow in water purifies, etc. The nonlinear behavior of the governing equation motivates us to use a finite difference approach for solving equations. The major resolution of this research is to work on how the physical elements affect velocity, temperature, concentration, and magnetic field. Fascinating facts are noticed as the unsteady fluid velocity rises with the heat source parameter because as the heat of a material increases, the movement of the fluid particle will be fast. Due to the presence of a magnetic field high thermal radiation is observed at high temperature and concentration. As the magnetic parameter and magnetic field are inversely proportional according to an induced magnetic field, it is noticed that their magnetic field declines for higher values of magnetic Prandtl number & magnetic parameter. This work has dynamic prominence in the field of medicine and engineering, which develops interest among young researchers. [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]

In this study, we investigate the profound impact of the Pöschl–Teller double-ring-shaped Coulomb (PTDRSC) potential to induce persistent currents within the S-states of the hydrogenic atom. The confinement of the system is achieved through an impenetrable spherical boundary. Leveraging first-order perturbation theory, we quantify the charge current across various states induced by the PTDRSC potential with its inherent angular and azimuthal dependence, leading to angular and azimuthal distortion, respectively. Notably, persistent currents are observed within S-states without external excitation mechanisms. The magnitude of the induced current is intricately linked to the strength of the PTDRSC potential parameters. These results underscore the prospect of manipulating persistent currents and their associated induced magnetic fields within S-states by tailoring the potential strength and confining boundary size. This discovery presents a compelling avenue for the controlled generation and experimental verification of induced S-state magnetism, opening new possibilities for innovative applications. [ABSTRACT FROM AUTHOR]

Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations' model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of a / c = 0. 5 , while it depicted the counter behavior for a / c = 1. 5. The skin friction is heightened with improving values of Re because R e boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of M p cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of β. [ABSTRACT FROM AUTHOR]

Purpose: Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis. Design/methodology/approach: Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H2O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach. Findings: There is no fund for the research work. Social implications: This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells. Originality/value: This investigation unfolds the hydrothermal changes of radiative water-based Fe3O4-Ag-MgO-H2O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study. [ABSTRACT FROM AUTHOR]

The current article deals with a novel idea of a suspension of spherical silver Ag , cylindrical aluminium oxide Al 2 O 3 and platelet aluminium Al nanoparticles in water–ethylene glycol as a conducting fluid through a convective stretching surface. The effects of induced magnetic field, heat sink or source, thermal radiation and slip condition aspect are also incorporated during ternary hybrid nanofluid flow. The significance of the current investigation lies in enhancing heat transfer efficiencies, high-temperature processes, electronic devices where heat is generated or cooling systems and metal casting. The numerical solutions of nonlinear ordinary differential are obtained by employing a finite difference approach via the bvp4c solver (MATLAB package). The obtained results pointed out that the spherical silver nanoparticles provide a higher rate of heat transfer followed by cylindrical alumina nanoparticles and platelet aluminium nanoparticles, respectively. Moreover, the velocity profile and induced magnetic profile decrease with increasing volume fraction of spherical Ag nanoparticles, cylindrical Al 2 O 3 alumina nanoparticles, platelet Al nanoparticles and induced magnetic parameter. The ternary hybrid nanofluid's heat transfer rate is greatly increased by larger values of the radiative parameter, Biot number and slip parameter. Additionally, the temperature profile is improved when the heat source parameter grows while the heat sink parameter decreases. [ABSTRACT FROM AUTHOR]

The physiological system loses heat energy through the bloodstream to nearby cells. Such energy loss can lead to a quick death, anemia, severe hypothermia and high or low blood pressure to heart surgery. As a result, biomedical engineers and physicians are increasingly attracted to the study of entropy production to calculate the energy loss of biological systems. Furthermore, the thermodynamic state of entropy production is used to access cancer cells during chemotherapy treatment and heat transfer in tissues. The current model intends to explore the significance of the non-Fourier heat flux model on Eyring–Powell/Maxwell hybrid nanofluid (Fe3O4–CuO/blood) flow in a linear extending sheet with induced magnetic field and entropy generation. Suitable self-similarity variables are performed to convert momentum and thermal equations determined using the homotopy perturbation method into ordinary differential equations. The significance of distinct physical parameters such as thermal relaxation parameter, volume fraction, fluid parameter, magnetic Prandtl number, Biot number, Brinkman number, heat source, Eckert number, radiation and heat source on velocity, temperature, skin friction coefficient, Nusselt number, entropy production, streamlines and isotherm are represented through figures. It is recognized that the fluid friction irreversibility is comparatively higher than thermal irreversibility and highly dominates the total entropy generation. The nanoparticle volume fraction diminishes the velocity and induced magnetic field of both Eyring–Powell and Maxwell hybrid nanofluid. Fluid friction irreversibility is more in Maxwell fluid compared to the Eyring–Powell fluid. [ABSTRACT FROM AUTHOR]

The axisymmetric stagnation point flow of brick and blade-shaped Silver and Copper nanoparticles immersed in an ethylene glycol base fluid under the influence of an induced magnetic field over an unsteady radial stretching surface is investigated in this study. The unsteady phenomenon is considered because most flow issues in practice are unsteady. The fundamental laws of mass, momentum, and energy conservation are used to present the physical model. Heat transmission is also examined under the effects of magnetohydrodynamics, Joule heating, viscous dissipation, and convective boundary conditions to give a realistic physical investigation. Scaling analysis transforms the flow-governing issue into a collection of higher-order nonlinear ODEs. These are, then, solved numerically using the fourth-order Runge–Kutta and shooting techniques. Moreover, the numerical technique is validated by calculating residual error. It is concluded that, compared to the Ag–EG nanofluid, the Cu–EG nanofluid had the highest IMF, lowest temperature, minimum surface drag, and maximum heat flux, making it the ideal choice for creating a radial module. [ABSTRACT FROM AUTHOR]

In this article, the Caputo Fabrizio fractal fractional order derivatives operator with an exponential kernel was employed to examine the radiative heat and mass transfer characteristics of time dependent flow with variable fluid viscosity, induced magnetic field, Soret and Dufour effects. The local mathematical model for the flow problem is formulated by take into account the impacts of thermal radiation, heat source, and viscous dissipation. The governing equations in-terms of fractal fractional model with an exponential kernel were solved numerically using finite difference method. The influence of flow variables such as induced magnetic field, concentration field, entropy rate, thermal field, and velocity field profiles against the pertinent parameters are discussed through graphs. Increase the values of magnetic Prandtl number results to rises of induced magnetic field. Higher Dufour number significantly grows the thermal field. The fractal fractional parameters enhance the velocity field, thermal field, Bejan number, entropy rate, concentration field and induced magnetic field profiles. The velocity field profiles recede with higher values of fluid variable viscosity parameter whereas the thermal field and induced magnetic field has an opposite effect. Larger Soret number amplifies the concentration field. Increase of Brinkman number, thermal radiation parameter, and magnetic Prandtl number intensifies the entropy generation rate. Increases of Brinkman number, magnetic Prandtl number, Soret number and Dufour number leads to a decrease of Bejan number whereas Bejan number rises with an increase of thermal radiation parameter and heat source. [ABSTRACT FROM AUTHOR]

This paper focuses on the effects of heat radiation and chemical reactions on naturally occurring convective MHD flow that conducts electricity when there is an induced magnetic field present between two vertical walls having a porous medium between them. An analytical method is adopted to investigate the impacts of all pertinent parameters concerning the presented multi-physics problem. With the aid of relevant conversions, the nonlinear PDEs are remodeled into nonlinear ODEs.The effects of radiation parameters, Hartmann number, Hall current, chemical reaction and porosity parameters are scrutinized on velocity components, induced magnetic field, and current density. The results predict that the temperature profile decreases as the radiation factor rises, whereas the induced magnetic field would exhibit the opposite pattern. The profiles of component velocity get more intense for high rates of the porosity parameter. Additionally, profiles of induced magnetic field surges with elevated chemical reaction parameter values have been noted. The presented approach is very promising for multi-physics phenomena like chemical reactors and solar thermal devices. [ABSTRACT FROM AUTHOR]

Magnetic nanoparticles can enhance the electrical and thermal conductivity of polymers, which are widely used in fields such as machinery, biomedicine, and energy storage. When a non-uniform magnetic field is imposed externally, the induced magnetic field cannot be ignored in the case of high Reynolds numbers. To explore the effects of magnetic nanoparticles on the unsteady flow and magnetic diffusion of viscoelastic fluid over the stretching sheet within the laminar boundary layer, the time distributed-order Maxwell constitutive equation was coupled with the momentum equation to establish partial differential equations for the velocity and magnetic diffusion of a 2D incompressible Maxwell magnetic nanofluid. Numerical analysis was performed with the finite difference method, and the velocity and the induced magnetic field distribution of the fluid within the boundary layer were analyzed by control of the magnetic nanoparticle type, the volume fraction and the magnetic parameter magnitude. The results show that, the velocity and induced magnetic field of the fluid are the largest in the case of Fe2O3 nanoparticles added to molten polymers, besides, the velocity and magnetic boundary layer thickness is the largest. With the increase of the Maxwell nanofluid relaxation time parameter, both the velocity and the magnetic diffusion will decrease. In addition, the velocity boundary layer thickness and the magnetic boundary layer thickness of the fluid decrease with the magnetic parameter. The larger the volume fraction of Fe3O4 nanoparticles is, the faster the fluid flow and the smaller the induced magnetic field will be. Therefore, the study of the addition of magnetic nanoparticles to polymers in non-uniform magnetic fields gives referential data for improving material properties. [ABSTRACT FROM AUTHOR]

The paper studies effect of induced magnetic field on laminar convection flow of a viscous electrically conducting incompressible fluid between two parallel porous plates at constant temperature gradient in presence of a uniform inclined magnetic field. An angle (θ) is formed with the vertical line by applying a magnetic field in that direction and field is strong enough to induce another field along the line of flow. Using the proper similarity transformations, the flow equations are converted into ordinary differential equations, which are then numerically solved by using MATLAB's bvp4c solver. Plotting of the graphs allows one to examine the effects of several critical parameters such as Hartmann number, Darcy number, Magnetic Reynolds number, Prandtl number, and Field inclination on velocity field, induced magnetic field, temperature field at the plates. The acquired results demonstrate that the flow system is effectively influenced by the field inclination, the magnetic parameter, and the plate porosity. The rise in field inclination leads to an increase in magnetic drag force. [ABSTRACT FROM AUTHOR]

An analysis is carried out to study the two-dimensional stagnant point flow of titanium dioxide (T i O 2) -titanium alloy (T i 6 A l 4 V) /carboxymethyl cellulose (CMC) water-based hybrid nanoliquid over an expanding surface characterized by the induced magnetic field (IMF). Further, the consideration of thermal buoyancy and the additional nonuniform heat source is involved in the modeling. The intent of this work has significant novelty due to the elastic deformation behavior over a stretching surface. The governing mathematical equations of the problem are reduced to a set of simultaneous ordinary differential equations and are elucidated numerically by employing the Runge-Kutta-Fehlbergs fourth-and-fifth (RKF-45) order process combined with a shooting approach. This article examines the properties of change in parameters on the functions including temperature profiles, induced magnetic field, and velocity profiles of hybrid nanoliquid, shown through graphs. The impact of the Elastic deformation coefficient reduces the temperature where as magnetic field enhance the velocity profile. Magnetic parameter boosts skin friction coefficient with an increase in the buoyancy effect. Momentum profile and induced magnetic field are affected most by the Magnetic Prandtl number [ABSTRACT FROM AUTHOR]

In the present analysis, we have discussed the mixed convective of flow over an exponential sheet in presence of induced magnetic field and surface roughness. The effects of hall current and chemical reaction on flow are also considered. The non-Newtonian model behavior is characterized by Casson nanofluid. The similarity transformations are employed for the transformation of partial differential equations into non-dimensional form and obtained equations are solved by employing the Differential transformation method (DTM). Further, the importance of various parameters on various profiles and gradients are explored graphically with some suitable discussion. At the wall, the small (α ) and frequency (n ) parameters influence on gradients are illustrated. [ABSTRACT FROM AUTHOR]

In this study, we investigated the influence of the induced magnetic field on the Jeffrey fluid under peristalsis through the curved channel. The governing equations, such as the continuity equation, momentum equation, and magnetic force functions, are formulated. The lengthy equations are shortened by considering the approximations of the tiny Reynolds number and the long wavelength. From the resulting reduced equations, the exact solution is determined. Graphs are used to explain the graphical results of the impact of important parameters of velocity, magnetic force function, current density, induced magnetic field, pressure rise, and stream functions. [ABSTRACT FROM AUTHOR]

This article presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic six-constant Jeffrey nanofluids. Various configurations of the outer boundaries are considered, namely, square wave, trapezoidal wave, multisinusoidal wave, and triangular wave. An induced magnetic field together with nanoparticles and mass concentration are considered. Influences of the Dufour and Soret numbers are examined, and the cases of long wavelength and low Reynolds number are applied. All the computations are obtained numerically via MATHEMATICA symbolical software (built-in command ND-Solve), and the obtained results are presented in terms of the axial velocity u , current density J z , the function of magnetic force Φ , axially induced magnetic field h x , nanoparticle fraction profile Ω , concentration profile γ , temperature profile θ , extra stress tensor S x y , pressure gradient d p d x , pressure rise Δ p λ , and stream function ψ. The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multisinusoidal wave gives periodic behaviors of d p d x. Also, higher axial-induced magnetic fields are given at the higher values of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

This study investigates the influence of an induced magnetic field on the flow behavior of a hybrid nanofluid comprising AA7072 and AA7075 alloys dispersed in water within a vertical channel with a suction velocity. The research considers the effects of both the induced magnetic field and suction velocity, taking into account the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. This unique mixture offers potential applications in various engineering fields, making it an important subject for investigation. The suitable similarity rules are adopted for the transformation of the designed problem into a set of ordinary differential equations, which were solved using the DTM (Differential Transform Method). The study examined the influence of various non-dimensional parameters on the various flow profiles. The characteristics of these profiles, as well as the skin friction coefficient, heat transfer rate were extensively analyzed through the use of plots and tables. In important outcomes, it is observed that the enhanced magnetization augments the induced magnetic profile within the entire domain, whereas the particle concentrations have significant role in controlling the same profiles. [ABSTRACT FROM AUTHOR]

Stagnation point flow defines the fluid motion near the stagnation point of a solid surface and has utilization in the process of polymer extrusion, electronic gadgets cooling, nuclear reactor, etc. Furthermore, the main theme of this work is to analyze the heat transfer characteristics of stagnation point flow of Casson nanofluid over stretching sheet using induced magnetic field and Cattaneo-Christov model. The Casson fluid is a non-Newtonian fluid model; and in the current work the working fluid consists of nanoparticles of Au (Gold) and blood (Casson fluid). In the existing model, temperature of the surface depends on the distance from the stagnation point. Therefore, Darcy-Forchheimer porous model is incorporated. The solution of coupled nonlinear PDEs is obtained by bvp4c. The heat transfer and flow characteristics of Au-blood based Casson nanofluid are discussed graphically. The dual behavior is observed in the profiles of induced magnetic field with increase in the value of reciprocal magnetic Prandtl number, however the velocity outlines of Au-blood nanofluid declined. A comparison is presented with previous article and is found to be in good agreement. [ABSTRACT FROM AUTHOR]

• A new model of elastic wave propagation incorporating the microstructure effects and the Lorentz force is proposed. • The microstructure effects are modelled by the dipolar gradient elasticity and the influences on wave propagation are discussed. • The Lorentz force due to the external magnetic field is derived and the influences on wave propagation are discussed. • The reflection and transmission for incident P wave, SV wave and SH wave are provided. • The influences of the direction of external magnetic field deviating from the incident direction are discussed. The elastic wave propagation and the reflection and transmission at interface with consideration of the microstructure effects and the Lorentz force simultaneously are investigated in the present work. The microstructure effects are modelled by the dipolar gradient elasticity and the Lorentz force due to the external magnetic field is derived by the electromagnetic induction law and Maxwell equation. The numerical results are provided for incident P wave, incident SV wave and incident SH wave, respectively. It is found that the microstructure effects induce the dispersive feature of elastic waves but the external magnetic field do not contribute to the dispersion with only influence on the amplitude of speed. The surface waves are more sensitive to the external magnetic field and the microstructure effects compared with the bulk waves. [ABSTRACT FROM AUTHOR]

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. These equations were subsequently solved using the Runge–Kutta–Fehlberg (RKF) method. Through graphical representations like graphs and tables, the study demonstrates how various dynamic factors influence the fluid's transport characteristics. Additionally, the artificial neural network (ANN) approach is considered an alternative method to handle fluid flow issues, significantly reducing processing time. In this study, a novel intelligent numerical computing approach was adopted, implementing a Levenberg–Marquardt algorithm-based MLP feed-forward back-propagation ANN. Data collection was conducted to evaluate, validate, and guide the artificial neural network model. Throughout all the investigated geometries, both velocity and induced magnetic profiles exhibit a declining trend for higher values of the magnetic parameter. An increase in the Dufour number corresponds to a rise in the nanofluid temperature. The concentration of nanofluid increases with higher values of the Soret number. Similarly, the nanofluid velocity increases with higher velocity slip parameter values, while the fluid temperature exhibits opposite behavior, decreasing with increasing velocity slip parameter values. [ABSTRACT FROM AUTHOR]

The current study analyzes the implications of an Arrhenius‐controlled heat transfer fluid on free convection in a micro‐channel confined by two immeasurable vertical parallel plates that are electrically non‐conductive due to an induced magnetic field (IMF) effect. The governing coupled nonlinear equations are ordinary differential equations, and the dimensionless steady‐state solutions were determined using the homotopy perturbation method (HPM). The derived results were discussed and represented graphically with the help of illustrative line graphs for momentum, IMF, temperature, and volume flow rate for the major controlling parameters, namely arrhenius kinetics, rarefaction, wall ambient temperature difference ratios, and Prandtl magnetic number. Thermo‐physical properties that are of engineering interest, like sheer stress and Nusselt number, are also computed and displayed. It is pertinent to report that the velocity of the fluid increases as a result of chemical reactions and rarefaction factors, whereas strengthening the Prandtl magnetic number decreases the volume flow rate. Also, numerical data was obtained and presented in tabular form to compare this research outcome to those of Jha and Aina, and great consistency was found. Microelectronics and microfluidics are some areas where this study can find relevance. [ABSTRACT FROM AUTHOR]

Consequence of thermal and concentration convection on peristaltic pumping of hyperbolic tangent nanofluid in a non‐uniform channel and induced magnetic field is discussed in this article. The brief mathematical modeling, along with induced magnetic field, of hyperbolic tangent nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Exact solutions are calculated for temperature, nanoparticle volume fraction, and concentration. Numerical technique is manipulated to solve the highly non‐linear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial induced magnetic field, magnetic force function, stream functions, pressure rise, and pressure gradient. [ABSTRACT FROM AUTHOR]

In this analysis, Sutterby nanofluid flow with an induced magnetic field at a nonlinear stretching cylinder is deliberated. The effects of variable thermal conductivity, Darcy resistance, and viscous dissipation are discussed. Thermal radiation and chemical reaction are considered to analyze the impact on the nonlinear stretching cylinder. The governing model of the flow problem is developed under the boundary layer approximation in terms of partial differential equations. Partial differential equations are transformed into ordinary differential equations by performing the suitable transformations. A numerical structure is applied to explain ordinary differential equations. The impact of each governing physical parameters on the temperature, concentration, skin friction, Sherwood, and Nusselt number is presented in graphs and tabular form. Increment in Prandtl number, which declined the curves of the temperature function. Temperature declined because the Prandtl number declined the thermal thickness as well as reduce the temperature of the fluid. Temperature curves showed improvement as Eckert number values increased because the Eckert number is a ratio of kinetic energy to the specific enthalpy difference between the wall and the fluid. As a result, increasing the Eckert number causes the transformation of kinetic energy into internal energy via work done against viscous fluid stresses. [ABSTRACT FROM AUTHOR]

Continuous two-dimensional boundary layer heat transfer in an electroconductive Newtonian fluid from a stretching surface that is biased by a magnetic field aligned with thermal radiation is the subject of this study. The effects of magnetic induction are induced because the Reynolds number is not small. The sheet is traveling with a temperature and velocity that are inversely related to how far away from the steady edge it is from the plane in which it is traveling. We also imposed external velocity u = u e x = D x p in the boundary. The necessary major equations are made dimensionless by the local non-similarity transformation and become a system of non-linear ordinary differential equations after being transformed from non-linear partial differential equations. The subsequent numerical solution of the arisen non-dimensional boundary value problem utilizes a sixth-order Runge–Kutta integration scheme and Nachtsheim–Swigert shooting iterative technique. A good correlation is seen when the solutions are compared to previously published results from the literature. Through the use of graphical representation, the physical impacts of the fluid parameters on speed, induced magnetic field, and temperature distribution are carried out. Furthermore, the distributions for skin friction coefficient and local Nusselt number are also studied for different scenarios. The skin friction coefficient and local Nusselt number are observed to increase with greater values of the temperature exponent parameter and velocity exponent parameter. However, as heat radiation increases, the local Nusselt number decreases even though temperatures are noticeably higher. The study finds applications in magnetic polymer fabrication systems. [ABSTRACT FROM AUTHOR]

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

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

The aim of this work is to relate the Soret and Dufour parameters of peristaltic flow in magneto Oldroyd 4-constant nanofluids in non-uniform channel. The discussion explores the numerical modelling of Oldroyd 4-constant nanofluids with convective double diffusion under induced magnetic flux. The use of a low finite Reynolds number and a long wavelength simplify non-linear partial differential equations. Numerical method is applied to solve reduced differential equation. Furthermore, the exact solutions of nanoparticle, temperature and concentration are computed. The graphical and numerical presentation show the significance of different physical parameters. The results reveal the fact that the greater value of Soret number and Brownian motion parameter decreases the concentration nanosolid particle. In addition, molecular kinetic energy transforms into thermal energy by random collision in the process of micro-mixing of nanoliquid resultantly raise the temperature of the liquid. Moreover, the magnetic force function increases due to enhancing electric field and magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

We have investigated the influence of the induced non-uniformity on thermomagnetic convection when the inner cylinder of an annular gap has high magnetic permeability and a special wave-like shape. The outer uniform magnetic field induces a non-uniformity, which causes thermomagnetic convection. The problem is analyzed numerically. The in-house code uses the finite volume method with exponential interpolation functions for vorticity and temperature and linear functions for the stream function and magnetic field potential. It was found that increasing the periodicity and amplitude of the wave-like structure enhances heat transfer by 30–50 % compared to a circular annular gap filled with magnetic fluid, and 3–5 times compared to an annular gap filled with ordinary fluid. Such a way of creating induced non-uniformity of magnetic field and convection enhancement is especially effective for microfluidics, as the gravitational Rayleigh number is low in this case, and it is a hard technical problem to create a non-uniform magnetic field in small channels by directly using permanent magnets. [ABSTRACT FROM AUTHOR]

This study aims to scrutinize the hydrodynamic and heat transmission of MHD water (H2O)-based nanoliquid flow across a permeable stretched curved surface affected by an induced magnetic field. The thermal equation incorporates the Cattaneo–Christov (C-C) heat flux's influence. The partial differential equations (PDEs) that constitute the mathematical description of the flow phenomenon are developed using a curvilinear coordinate system. Koo–Kleinstreuer–Li (KKL) correlations for dynamic viscosity and thermal conductivity are used to investigate the Brownian motion and static behavior of nanoparticles in the working liquid. A MATLAB bvp4c approach is employed to compute the momentum- and energy-based ordinary differential equations, which are obtained through similarity transformation. Graphs are used to establish the impression of relevant nondimensional parameters. Further, the impact of engineering quantities is illustrated through tables. The results indicate that when enhancing the curvature parameter the induced magnetic field profile escalates. It is also inferred that when the Brownian motion is taken into account rather than just taking into account the static feature of particles, the surface drag coefficient is observed to be higher. Furthermore, when the Brownian motion of nanoparticles is evaluated rather than static motion, the heat transfer rate achieved is found to be greater. [ABSTRACT FROM AUTHOR]

The focus of this paper is to examine the heat and mass transport behavior of transient magnetohydrodynamics second‐grade fluid (elastico‐viscous fluid) flow within a vertical channel bounding the porous regime with the Hall phenomenon and induced magnetic field (IMF). The flow system consists of a strong transverse magnetic field that gives rise to the Hall phenomenon and IMF. The right vertical surface of the channel is conducting and oscillations in its plane in the vertical direction while the left vertical surface of the channel is nonconducting and stationary. The suitable dimensionless setup transforms the flow model into a simplified comparable model which is solved analytically with the assistance of the method of separation of variables. Numerical computation is performed with the aid of MATHEMATICA software to explore the results from the analytical solutions. The results of the investigation are helpful in analyzing the nature of the elastic‐viscous fluids. A noteworthy result noted from the investigation is that there appears a reverse flow in the direction of normal flow when the magnetic interaction parameter is large. For the small magnetic interaction parameter, such a flow is not seen. Hall current reduces the strength of the principal IMF and induces the strength of the secondary generated magnetic field. Furthermore, it is explored that the elastico‐viscous nature of the second‐grade fluid has a tendency of enhancing the principal flow and principal‐produced magnetic field. [ABSTRACT FROM AUTHOR]

The current work focuses on magnetohydrodynamic free convective flow mixed with radiation between vertical walls under the consequences of hall current as well as the induced magnetic field and is concerned with panel cooling for the aluminum smelting plant. It has been proposed that the fluid channel has a porous medium. The isothermal transport equations, which primarily concern mass, momentum, energy, and induced magnetic field, are solved analytically. After comparing the model findings with those from the literature, the effect of the different relevant parameters of the current model is gathered and presented. Hartmann number, Hall current on velocity components, current density, induced magnetic field, porosity, and Soret effect are all investigated for their effects. Due to the applied radiation field on plates, the influence of the radiation parameter has also been included. Under the effect of the Hall parameter, the velocity's primary component is observed to increase; nevertheless, the secondary component has been shown to decrease. The Hall effect is observed to be reducing the generated magnetic field, and the Lorentz force Hartmann number decreases the flow. The magnitude of the velocity and current density is decreased because of the radiation parameter. Such methodology should be employed to get first-cut results and to analyze the system in a better way before the prototype development and demonstration. [ABSTRACT FROM AUTHOR]

The narrower a conductor the more significant is its induced magnetic field, or the Ørsted magnetic field. The calculation of the Ørsted magnetic field in current-carrying wires is a standard textbook exercise that generally assumes that the wire has a circular cross-section, and where a simplified form of the Biot–Savart equation is applied. While such formalism can be suitable for macroscopic wire structures, it will not be ideal for nano-sized wire structures because of the presence of structural features that might impact detailed structure of the Ørsted magnetic field. This work introduces a microscopic approach for the prediction of the Ørsted magnetic field in nanowires. The approach combines the current magnetization hypothesis (Tawfik, 2022) with molecular dynamics that applies the electron force field. The formalism can be utilized for predicting the Ørsted magnetic field of more complex nano-conductors. • The work introduces a microscopic approach to predict the Ørsted magnetic field. • Combines the current magnetization hypothesis with MD within the electron force field. • The theory is demonstrated for a lithium nanowire. [ABSTRACT FROM AUTHOR]

The core part of current model is to analyze the entropy generation and 2-dimensional unsteady stagnation flow with suction/injection constraint present in the boundary. Further, the induced magnetic field has applied with this flow model, which is formed by the motion of fluid that conducts electrically. The time-dependent partial differential equations (PDE) of the recent model are first converted to non-linear ordinary differential equations (ODE) using suitable similarity variables. We obtain solutions numerically using inbuilt shooting technic. We demonstrate the results using the graphs, tables and discussed them in detail. It is found that as the injection parameter is responsible for the thinning of the boundary layer, induced magnetic boundary layer; Suction, and unsteady constraints decelerate Bejan number; and the unsteady parameter (M) decelerates the f ′ , g ′ profiles and the temperature distributions accelerate by the M. [ABSTRACT FROM AUTHOR]

This paper investigates the mobility of cilia in a non-uniform tapered channel in the presence of an induced magnetic field and heat transfer. Thermal radiation effects are included in the heat transfer analysis. The Jeffrey model is a simpler linear model that uses time derivatives rather than convected derivatives as the Oldroyd-B model does; it depicts rheology other than Newtonian. The Jeffrey fluid model is used to investigate the rheology of a fluid with cilia motion. The proposed model examines the behavior of physiological fluids passing through non-uniform channels, which is responsible for symmetrical wave propagation and is commonly perceived between the contraction and expansion of concentric muscles. To formulate the mathematical modeling, the lubrication approach is used for momentum, energy, and magnetic field equations. The formulated linear but coupled differential equations have been solved analytically. Graphs for velocity profile, magnetic force function, induced magnetic field, current density, pressure rise, and heat profile are presented to describe the physical mechanisms of significant parameters. It is found that the eccentricity parameter of the cilia equations opposes the velocity and the magnetic force functions. The thermal radiation decreases the temperature profile while it increases for Prandtl and Eckert numbers. A promising impact of the magnetic Reynolds number and electric field on the current density profile is also observed. [ABSTRACT FROM AUTHOR]

The major motive of the current investigation is to analyze an exact solution for an unsteady magnetohydrodynamics natural convective flow of a viscous incompressible electrically conducting non‐gray optically thick fluid past an impulsively started infinite vertical plate with ramped wall temperature and concentration in the presence of radiation, diffusion‐thermo effect, and induced magnetic field. Laplace transform method is used to acquire the specific solutions of the dimensionless domain equations. The impact of various physical parameters on fluid velocities, temperature, concentration, and moreover on the rate of heat transfer, mass transfer, and skin friction at the wall are shown graphically. It is also found that the Dufour effect causes an increase in fluid velocity as well as temperature. The ramped condition influences the rise in Nusselt number. [ABSTRACT FROM AUTHOR]

The effect of the induced magnetic field on the motion of Eyring-Powell nanofluid Al2O3, containing gyrotactic microorganisms through the boundary-layer is investigated. The viscoelastic dissipation is taken into consideration. The system is stressed by an external magnetic field. The continuity, momentum, induced magnetic field, temperature, concentration, and microorganisms equations that describe our problem are written in the form of 2-D non-linear differential equations. The system of non-linear PDE is transformed into ODE using appropriate similarity transformations with suitable boundary conditions and solved numerically by applying the NDSolve command in the MATHEMATICA program. The obtained numerical results for velocity, induced magnetic field, temperature, the nanoparticles concentration, and microorganisms are discussed and presented graphically through some figures. The physical parameters of the problem play an important role in the control of the obtained solutions. Moreover, it is obvious that as Grashof numbe increases, both the velocity, f ', and the induced magnetic field, h', increase, while, the reciprocal magnetic Prandtl number, A, works on decreasing both f' and h'. As Eckert number increases the temperature increases, while it decreases as the velocity ratio B increases. [ABSTRACT FROM AUTHOR]

It is possible for dust particles to naturally exist in fluids. In the study of fluid mechanics, these problems related to flow characteristics of temperature. How the magnetic field of suspended particulate matter affects the temperature axially symmetrical jet mixing of incompressible dusty fluid. we assume that the velocity and temperature in the jet deviate from the surrounding stream. To linearize the equation that was solved using Laplace Transformation, a perturbation method was used. The solution of temperature of the particle phase which is depends on fluid phase temperature with in the weak induced Magnetic field. [ABSTRACT FROM AUTHOR]

The communication pertains to transient magnetohydrodynamics radiative free convection flow with induced magnetic field in a porous medium channel of width L. The setup is subjected to a uniform magnetic field H* o normal to the channel walls and H*x stands for the induced magnetic field. A Cartesian coordinate system is chosen where x*-axis is taken along the left channel wall and y*-axis is normal to it. At the time t* = 0, both the walls and the fluid bear a fixed temperature T*m. At the time t* > 0, that is, the onset of the convection, the temperatures of the walls at y* = 0 and at y* = L are just changed to T* o and T*L, respectively, where T*m

The aromaticity of [n]starphenes (n = 1, 4, 7, 10, 13, 16), as well as starphene-based [19]dendriphene, is addressed by calculating the magnetically induced current density and the induced magnetic field, using the pseudo-π model. When an external magnetic field is applied, these systems create diatropic currents that split into a global peripheral current surrounding the starphene skeleton and several local currents in the acene-based arms, resulting in large shielding cones above the arms. In particular, the arm currents are smaller than their linear analogs, and in general, the strengths of the ring currents tend to weaken as the starphene get larger. [ABSTRACT FROM AUTHOR]

The bioconvective stagnation point flow involving carbon nanotubes along a lengthening sheet subject to induced magnetic field and multiple stratification effects has been considered for investigation. Relevant similarity formulas are effectuated in converting the modelled equations into a first‐order system of ODEs and are further treated in MATLAB using ODE45 and Newton Raphson method. Illustrations on the consequence of effectual parameters on the physical quantities and the flow profiles are achieved with the aid of graphs. It is observed that the nanofluid temperature profile ascends with augmenting volume fraction and Eckert number. The numerical veracity of the present study is displayed through a restrictive study with prior published works and a commendable agreement is noted. Nusselt number is found to elevate with volume fraction and lower with thermal stratification parameter. Moreover, the findings of the present numerical exploration have applications in biomedical imaging, hyperthermia, targeted drug delivery, and cancer therapy. [ABSTRACT FROM AUTHOR]

Due to the uncertain behavior of real‐life problems, fuzzification is one of the most suitable ways to find the interval at which the problems show their accurate results. Various imprecise parameters and conditions make the fluid flow problems more uncertain. Here, we try to solve a boundary value problem of fluid mechanics numerically using fuzzy conditions. The fuzzified governing partial differential equations along with the fuzzified boundary conditions are solved by finite difference method using Python (an object-oriented programming language). The values of the parameters and the boundary conditions are taken as triangular fuzzy numbers. α‐cut technique is used to find the results and they are presented graphically for various values of α and the involved parameters. [ABSTRACT FROM AUTHOR]

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase. [ABSTRACT FROM AUTHOR]

In this study, a mathematical analysis is presented for the hydromagnetic convective flow of an incompressible, chemically reacting, and electrically and thermally conducting viscoelastic fluid through a vertical channel bounded by the porous regime under the action of an applied magnetic field with Hall current and induced magnetic field effects. The left wall of the channel is considered to be nonmagnetic, whereas the right wall of the channel is periodically magnetized. The flow within the channel is induced due to the nonuniform wall temperature and concentration, periodic pressure gradient, and periodic movement of the right wall. The method of separation of variable is used to convert the flow governing coupled partial differential equations into the ordinary differential equations that are solved analytically, and the solution for fluid velocity, induced magnetic field, temperature, and concentration is presented in a closed form. Numerical computation has been performed to demonstrate the impact of various system parameters on the fluid flow behavior. It is observed that oscillations increase the primary flow and primary induced magnetic field. Buoyancy forces have a tendency to lessen the secondary induced magnetic field. Furthermore, it is examined that magnetic diffusivity increases the primary flow, whereas it decreases the secondary flow and primary induced magnetic field. [ABSTRACT FROM AUTHOR]

The investigation explores the influence of the induced magnetic field and variable mass diffusivity on an unsteady incompressible mixed convective double stratified and chemically reactive flow of Jeffrey fluid through a porous medium with heat, and mass flux boundary conditions. The system of flow field nonlinear partial differential equations is reduced into coupled nondimensional ordinary differential equations using appropriate similar variables, then worked out a numerical solution via shooting technique along with Rung-Kutta fourth-order scheme. The results are analyzed for various physical flows, heat and mass transfers, induced magnetic field, and skin friction against disparate prominent parameters via graphs and tables. It is recognized that the temperate of the fluid is enhanced with thermal stratification; however, the concentration of the fluid is decreased with magnetic Reynold's number. The comparison of numerical values of skin friction with the existing literature for limiting sense. [ABSTRACT FROM AUTHOR]

In the present article, importance of double-diffusivity convection in nanofluids on peristaltic pumping of Carreau fluid in tapered channel with induced magnetic field and different waveforms has been theoretically discussed. Mathematical modeling of the two-dimensional and two-directional flow of a Carreau fluid are described in detail. A well-known assumption (long wave length and low Reynolds numbers) are employed in order to find the exact and analytical solution of the proposed problem. Exact solutions of temperature, concentration, and nanoparticle volume fraction are computed. Perturbation technique is used to calculate the solutions of highly nonlinear partial differential equations. With the help of Mathematica software and MATLAB, graphical results are displaced to see the behavior of temperature, concentration, nanoparticle volume fraction, pressure rise, pressure gradient, magnetic force function, and stream functions. It is observed that temperature and concentration profile increases with an increase in Nb, Nt, NCT, and NTC. [ABSTRACT FROM AUTHOR]