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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]

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]

This investigation presents an analysis of the transient magnetohydrodynamic flow of Newtonian viscous fluid in a vertical microporous channel with the inclusion of ion slip‐Hall current as well as an induced magnetic field (IMF) effects. Owing to the nature of the flow equations which are difficult to obtain an analytical result, a numerical scheme (PDEPE) based on finite difference approximation is adopted in solving the governing dimensional partial differential equation. The active influence of different flow parameters on velocity and IMF along the main flow and induced flow directions are visualized. Furthermore, variations of shear stress and induced current density are also presented in tabular form for active nondimensional flow quantities and later on analyzed. To establish the validity of the results obtained in this computation, values for velocity and IMF in this analysis were correlated with the steady‐state existing benchmark when the values of nondimensional time are considered large. Significant results from the analysis show that at the transient time and in the simultaneous occurrence of suction/injection at the microchannel walls, higher values of ion slip current have no considerable influence on flow formation along the primary flow direction, whereas an oscillatory phenomenon is observed along the secondary flow direction. It is also significant to note that at a transient time, magnetic induction could be improved or controlled by choosing favorable values of the suction/injection parameter. [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]

Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real‐world applications the model exists in the nonequilibrium state. Also, local thermal non‐equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non‐equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter‐phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case. [ABSTRACT FROM AUTHOR]

In the present study, the influence of the induced magnetic field on the MHD mixed convective electrically conducting fluid flow inside the vertical cylindrical annulus is analyzed numerically. The heat transfer is presumed to be due to a combination of mixed convection and radiation. The stability of the flow is examined when the solid and fluid phases are not in local thermal equilibrium. The governing equations are solved numerically by both finite difference and finite element methods. To control the flow formation rate more accurately the induced magnetic field is also considered in this study. As the magnetic Prandtl number (Pm) and Hartmann number (M) get enhanced, the velocity and induced magnetic fields get retarded in the annulus due to the presence of drag‐like force, namely, the Lorentz force. When there is an increase in the mixed convection parameter the induced magnetic field gets enhanced. An increase in radiation parameter tends to decline the fluid temperature and reverse the behavior of the solid temperature. Increment in Pm decreases the wall shear stress near the conducting cylinder. Increasing values of porous, magnetic, and radiation parameters lead to an unstable system with smaller heat transfer coefficient values but the system gets stabilized for larger values of heat transfer coefficient. The results could be used as first‐hand information for comprehending and developing the thermal flow phenomenon in porous media. The obtained numerical results are in good accordance with the existing results. Using an artificial neural network, heat transfer characteristics are analyzed through mean square error and regression analysis. [ABSTRACT FROM AUTHOR]

The five large moons of Uranus are important targets for future spacecraft missions. To motivate and inform the exploration of these moons, we model their internal evolution, present‐day physical structures, and geochemical and geophysical signatures that may be measured by spacecraft. We predict that if the moons preserved liquid until present, it is likely in the form of residual oceans less than 30 km thick in Ariel, Umbriel, and less than 50 km in Titania, and Oberon. The preservation of liquid strongly depends on material properties and, potentially, on dynamical circumstances that are presently unknown. Miranda is unlikely to host liquid at present unless it experienced tidal heating a few tens of million years ago. We find that since the thin residual layers may be hypersaline, their induced magnetic fields could be detectable by future spacecraft‐based magnetometers. However, if the ocean is maintained primarily by ammonia, and thus well below the water freezing point, then its electrical conductivity may be too small to be detectable by spacecraft. Lastly, our calculated tidal Love number (k2) and dissipation factor (Q) are consistent with the Q/k2 values previously inferred from dynamical evolution models. In particular, we find that the low Q/k2 estimated for Titania supports the hypothesis that Titania currently holds an ocean. Plain Language Summary: The major moons of Uranus, Miranda, Ariel, Umbriel, Titania, and Oberon, are interesting targets for a future space mission because they might host liquid at present. Studying these bodies would help address the extent of habitable environments in the outer solar system. We model their thermal, physical, and chemical evolution. Because their heat budget is limited, with little or no tidal heating at present, we find that most of the moons can preserve only a few tens of kilometers of liquid until present. Furthermore, if the oceans are maintained by antifreeze, such as ammonia and chlorides, then their electrical conductivities may be close to zero. In this case, the detection of a magnetic field induced in these oceans would be challenging. We explore additional geophysical, as well as compositional, observations that would reveal the existence of a deep ocean in these moons. None of the scenarios studied produce residual liquid in Miranda at present. Our simulations are consistent with constraints on the dissipative properties of the moons inferred from dynamical evolution models. Key Points: Most of the major Uranian moons may host a residual ocean a few tens of kilometers thick at present, except for MirandaThermal metamorphism could create a late, second generation ocean in Titania and OberonThese models represent a baseline for the formulation of observations with the Uranus Orbiter and Probe [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 inertial and viscous effects on mixed hydromagnetic convection in a vertical porous channel using a local thermal nonequilibrium model with uniformly distributed internal sources are analyzed. The flow in the porous medium is described by the Brinkman–Forchheimer extension of Darcy's momentum equation. The vertical rigid boundaries are maintained at constant but different temperatures and a uniform magnetic field H0 ${H}_{0}$ is applied across the porous layer. The governing equations are solved numerically by the finite element method and analytically by the perturbation method. The influence of governing parameters on the flow variables and heat transfer is discussed. An extensive study designates that an increase in the Darcy number enhances the velocity distribution due to increased permeability of the medium while the opposite trend is observed with increasing Hartmann number due to the increased retarding nature of Lorentz force. The presence of an external heat source has a notable impact on the temperature gradient of the fluid, which results in an increase in temperature distribution and thermal state of the fluid. A quantitative increase in heat transfer coefficient results in an increase of fluid temperature toward the electrically nonconducting wall, and as the fluid moves toward the electrically conducting wall the fluid temperature decreases. The results indicate that the Nusselt number declines with an increase in the solid internal heat generation parameter. [ABSTRACT FROM AUTHOR]

The effects of induced magnetic field, thermal and concentration convection on the peristaltic flow of Prandtl nanofluids are explored in this study in an inclined asymmetric channel. A detailed mathematical explanation is given for Prandtl nanofluids with double-diffusivity convection and induced magnetic field. To simplify non-linear partial differential equations, the long wavelength and low approximation of the Reynolds number are used. Using numerical technique, the non-linear differential equations are solved. Exact solutions of thermal and concentration are calculated. The impact of the various physical parameters of flow quantities is shown in graphical results. [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 current examination employs a numerical analysis to ascertain the effect of the Eckert number along with the Prandtl number on a magnetohydrodynamic natural convection flow of an incompressible viscous fluid in which it is electrically conducting, passing through a perpendicular microchannel. Conduction along with non‐conducting immeasurable perpendicular walls within the existence of temperature and velocity slip at the microchannel is analyzed. The induced magnetic field (IMF) generated by the motion of an electrically conducting fluid in the presence of a transverse magnetic field is considered. The momentum and induction equations are coupled in the presence of an induced magnetic field. A set of similar variables are used to convert the governing set of equations to nonlinear‐coupled ordinary differential equations. With the aid of MATLAB in built solver is carried out to get the numerical solutions. The influences of Hartman number, Prandtl number, and Eckert number along with some physical parameters are explained through graphs. The results indicate that increasing the Hartmann and magnetic Prandtl numbers results in a significant decrease in volume flow rate. [ABSTRACT FROM AUTHOR]

It is of great practical interest to study the fluid flow phenomena using buoyancy‐induced flow in a microchannel. The present problem is concerned with the natural convection in a vertical microchannel within electrically nonconducting surfaces with asymmetric wall temperature and concentration distributions. The interplay of velocity slip, temperature, and concentration jump at the walls contribute to salient features of the analysis. The governing equations of the fully developed flow are solved analytically as well as numerically. The results of both methods are in good agreement, providing the consistency and reliability of the applied numerical method. The striking outcome of the present study is that temperature, as well as concentration jump conditions at the walls, lead to flow reversal and non‐laminarity distributions of the induced current intensity and magnetic field. The higher rarefaction parameter, which ascribes the microchannel flow characteristics, prevents the growth of negative current intensity, whereas it favors the growth of velocity with induced magnetization. [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 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]

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 this paper, the steady magnetohydrodynamic mixed convection flow of a viscoelastic fluid over a magnetized vertical surface embedded in a uniform porous material with rotation is considered. The Hall and induced magnetic field effects are also considered in this investigation. The regular perturbation technique is used to find the solutions of flow governing equations. To analyze the consequences of flow'influencing parameters to the flow variables, numerical computation has been performed and the results are illustrated in graphical and tabular forms. It is interesting to note that magnetic diffusion leads to the increase of the fluid flow. It brings a decrement in the induced magnetic field in the vicinity of the magnetized vertical surface. [ABSTRACT FROM AUTHOR]

The influence of microrotational velocity on a fully developed laminar, natural convection flow in vertical concentric annuli in the presence of radial magnetic field between two nonconducting vertical concentric annuli is investigated in the present study. The induced magnetic field is generated due to the motion of an electrically conducting fluid in the annulus; the polar fluid has been considered in the present analysis. Transport equations such as momentum, energy, polar fluid, and induced magnetic field are solved analytically for the isothermal case. The effects of the different pertinent parameters of the present model are obtained and analyzed after verification of present methodology. The effects of the Hartmann number, the gap between two cylinders, and vertex viscosity parameters on velocity profiles, induced magnetic field, induced current density, and microrotational velocity profiles are studied. It is observed that the velocity profile and induced magnetic field decrease due to the vertex viscosity parameter; the Hartmann number accelerates the velocity of the microrotation; the induced current density profile decreases for both the Hartmann number and vertex viscosity parameter. The Hartmann number reduces the magnitude of mass flux and skin frictions at the inner and outer cylinder. [ABSTRACT FROM AUTHOR]

The Nucleus Independent Chemical Shift (NICS) method was invented in 1996 by the late Paul v. R. Schleyer as a computational tool for the assessment of aromaticity. In the intervening years, NICS has developed considerably. This Minireview describes the NICS‐based methods that are currently available and concludes with recommendations for choosing the appropriate NICS‐based methods to study a given problem. [ABSTRACT FROM AUTHOR]

The steady fully developed hydromagnetic flow of a viscous incompressible and electrically conducting fluid in a vertical microchannel has been studied taking into account the influence of Hall current, ion‐slip effects and an induced magnetic field. Exact solutions for the governing equations responsible for the flow formation are obtained by the method of the undetermined coefficient and presented graphically. It is found that in the presence of the ion‐slip effect, both primary and secondary components of fluid velocity increase with the Hall parameter for symmetric as well as asymmetric heating of the microchannel surfaces. Also, the magnetic field supports flow along the secondary flow direction while the reverse impact is observed along the primary flow direction. [ABSTRACT FROM AUTHOR]

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the peristaltic transport of a micropolar fluid in a tapered asymmetric channel with heat transfer and induced magnetic field effect. The flow is analyzed by long wavelength and low Reynolds number approximations. The reduced equations have been solved by using Adomian decomposition method and the expressions for velocity, stream function, microrotation component, magnetic‐force function, pressure gradient, axial induced magnetic field, and current density distribution across the channel have been computed. Expressions for shear stresses are also obtained. The effect of pertinent parameters is illustrated graphically. [ABSTRACT FROM AUTHOR]

We use Mars Atmosphere and Volatile EvolutioN observations of the upstream solar wind, and Mars Express observations of ionospheric electron densities and magnetic fields, to study how the topside ionosphere (>320 km) of Mars is affected by variations in solar wind dynamic pressure. We find that high solar wind dynamic pressures result in the topside ionosphere being depleted of plasma at all solar zenith angles, coincident with increased induced magnetic field strengths. The depletion of topside plasma in response to high solar wind dynamic pressures is observed in both weak and strong crustal magnetic field regions. Taken together, our results suggest that high solar wind dynamic pressures lead to ionospheric compression, increased ion escape, and reduced day‐to‐night plasma transport in the high‐altitude nightside ionosphere. Plain Language Summary: Mars lacks a global dipole magnetic field to hold off the solar wind. As a consequence, the solar wind can significantly affect the structure of the topside ionosphere. Previous studies detailing these effects, however, have primarily focused on impulsive space weather events. In this work, we use observations from two spacecraft (MAVEN and Mars Express) to statistically study how the solar wind dynamic pressure affects the topside ionosphere. We find that, during times of high solar wind dynamic pressure, the ionosphere is globally depleted of plasma, which suggests that the ionosphere is compressed and plasma escape is enhanced. Key Points: The topside ionosphere is globally depleted of plasma during times of high solar wind dynamic pressureThe topside ionosphere responds to changes in solar wind dynamic pressure in regions of both weak and strong crustal magnetic fieldsDay‐to‐night plasma transport in the high‐altitude nightside ionosphere is reduced during times of high solar wind dynamic pressure [ABSTRACT FROM AUTHOR]

This study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non‐aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring‐shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring‐shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring‐shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e. in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity. Interpreting aromaticity: Here, we introduced the bifurcation analysis of the induced magnetic field to interpret the aromatic or antiaromatic character of a representative set of monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring‐shaped domain adequately classifies the studied molecules according to their aromatic character, providing a useful tool to assess aromaticity according to the magnetic criteria. [ABSTRACT FROM AUTHOR]

We present new evidence that supports the aromatic character of the clusters of formula: [M3(µ‐X)3X6]0/2– (M = Re and Tc, X = Cl, Br, I). Our computations clearly show that these clusters present a special response to an applied external magnetic field, which is characteristic of aromatic systems. Both analyzed response properties, the magnetically induced current density and the induced magnetic field, agree that the magnetic perturbation induces two concentric diatropic ring currents: the inner one inside the M3 core and the outer one around the M3(µ‐X)3 triangle. The flow strength of these two ring currents is significant, confirming the high diatropicity of these clusters. In the dianionic species, aromaticity is increased, mainly by an increment of the diatropicity of the inner ring current. These findings support a chemical bonding pattern with delocalized M–M bonds in these species. [ABSTRACT FROM AUTHOR]

Abstract: We present model results of the interaction of proton and hydrogen atom precipitation with the Martian atmosphere. We use a kinetic Monte Carlo model developed earlier for the analysis of the Analyzer of Space Plasmas and Energetic Atoms (ASPERA‐3) Mars Express data. With the availability of Mars Atmosphere and Volatile Evolution Mission in situ measurements, not only the flux of protons incident on the atmosphere but also their degradation along the orbit may now be described. The comparison of the simulations with data collected with the Solar Wind Ion Analyzer shows that the Monte Carlo model reproduces some of the measured features. The results of comparison between simulations and measurements of the proton fluxes at low altitudes make it possible to infer the efficiency of charge exchange between solar wind and the extended hydrogen corona if the value of the magnetic field is measured simultaneously. We also find that the induced magnetic field plays a very important role in the formation of the backscattered flux and strongly controls its magnitude. At the same time, discrepancies between the modeled and the measured energy spectra of the backscattered protons are pointed out. We suggest that some of the physical processes controlling the upward flux are not fully understood or that the data processing of the measured backscattered proton flux should be improved. [ABSTRACT FROM AUTHOR]

The induced magnetic field (IMF) of naphthalene, biphenyl, biphenylene, benzocyclobutadiene, and pentalene is dissected to contributions from the total π system, canonical π-molecular orbitals (CMO), and HOMO→ π* excitations, to evaluate and interpret relative global and local diatropicity and paratropicity. Maps of the IMF of the total π system reveal its relative strength and topology that corresponds to global and local diatropic and paratropic ring currents. The total π magnetic response is determined by this of canonical HOMOs and particularly by paratropic contributions of rotational excitations from HOMOs to unoccupied π* orbitals. Low energy excitations and similar nodal structure of HOMO and π* induce strong paratropic fields that dominate on antiaromatic rings. High energy excitations and different nodal structures lead to weak paratropic contributions of canonical HOMOs, which are overwhelmed by diatropic response of lower energy canonical orbitals in aromatic rings. CMO-IMF analysis is found in agreement with ring current analysis. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Analysis has been made for the curvature effects on the MHD peristaltic flow of an incompressible Carreau fluid in a channel. The flow problem is first reduced in the wave frame of reference and then solved after employing the long wavelength and low Reynolds number approximations. Expressions of stream function, pressure gradient, magnetic force function, induced magnetic field and current density are derived and then examined for various parameters of interest. [ABSTRACT FROM AUTHOR]

Of concern in this paper is an investigation of peristaltic transport of a physiological fluid in an asymmetric channel under long wave length and low-Reynolds number assumptions. The flow is assumed to be incompressible, viscous, electrically conducting micropolar fluid and the effect of induced magnetic field is taken into account. Exact analytical solutions obtained for the axial velocity, microrotation component, stream line pattern, magnetic force function, axial-induced magnetic field as well as the current density distribution across the channel. The flow phenomena for the pumping characteristics, trapping and reflux are also investigated. The results presented reveal that the velocity decreases with the increase of magnetic field as well as the coupling parameter. Moreover, the trapping fluid can be eliminated by the application of an external magnetic field. Thus, the study bears the promise of important applications in physiological systems. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Various isomers of the trigonal dianion metal clusters, X32-, X = Be, Mg, Ca, and their mono- and disodium complexes are optimized at the B3LYP/6-311+G(d) level. Different conceptual density functional theory based reactivity descriptors as well as the induced magnetic field values are calculated to understand the stability and aromaticity of these systems. Possibility of bond stretch isomerism is explored. Genetic algorithm results lend additional insights into the structures of these isomers. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [ABSTRACT FROM AUTHOR]

Three-dimensional numerical analysis of a liquid metal MHD generator has been carried out. The three-dimensional structures of the electromagnetic field and fluid flow in the MHD generator have been clarified, and the effect of the electrode width on the performance has also been examined, taking account of the current flow in the electrode. Structures of the electromagnetic field and fluid flow are complicated owing to the three-dimensional current flow, induced magnetic field, and Lorentz force. The highest performance is found to be obtained when the width of the electrode is equal to that of the generator. The performance predicted from three-dimensional analysis is somewhat lower than that from two-dimensional analysis because of the larger input power. The increase in the input power is attributed to the increase in Lorentz force caused by less reduced magnetic flux density and to the additional friction loss on the insulator walls (x-y plane). © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(3): 19–26, 2007; Published online in Wiley InterScience (www. interscience.wiley.com). DOI 10.1002/eej.20282 [ABSTRACT FROM AUTHOR]

The authors discuss the role of the σ and π contributions to the induced magnetic field for simple hydrocarbons containing a double or a triple bond, as well as for benzene and cyclobutadiene. While the magnetic field induced by the σ electrons is short-ranged, the π system is responsible for the formation of long-range cones. These cones influence the chemical shift of atoms by additional shielding (for aromatic) or deshielding (for antiaromatic molecules) contributions. While the hydrogen atoms of benzene are found to lie within the deshielded region of the magnetic field induced by the π electrons, they are shielded by the total induced magnetic field. The induced magnetic field of the π electrons support Pople's model on the basis of first-principles calculations. © 2006 Wiley Periodicals, Inc. J Comput Chem 2007 [ABSTRACT FROM AUTHOR]

The performance of a liquid metal MHD generator is investigated with a two-dimensional numerical simulation. The effects of the electrode length, the position of current lead connection, and the insertion of an insulator on the performance are examined taking account of the current flow in the electrode. There exists an optimal electrode length for a given distribution of applied magnetic flux density. For a short electrode, the efficiency decreases because the power output becomes small. For a long electrode, on the other hand, the efficiency also decreases owing to the leakage current from the upstream and downstream edges of the electrode. An optimal current lead position was revealed. This fact is ascribed to the distributions of induced magnetic field and the current flow in the electrode. It was found that insertion of the insulator is effective for improving the performance, by which the eddy current can be reduced. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 156(1): 25–32, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ eej.20165 [ABSTRACT FROM AUTHOR]

The main purpose of this research is to explore a comparative study of viscous and Jeffrey nanofluid flows through a parallel channel embedded in a porous medium under the influence of an induced magnetic field, Brownian motion, and thermophoresis. The convective boundary conditions are employed to study the heat and mass transfer at the lower plate. The system of transport constituent relations is reduced into coupled nondimensional ordinary differential equations through similar variables with appropriate boundary conditions. The resulting equations are analyzed for flow characteristics, heat and mass transfers, and magnetic diffusivities throughout the channel with various physical nondimensional parameters via shooting technique along with Runge‐Kutta fourth‐order scheme. It is observed that the temperature and concentration decrease with increasing Brownian motion parameters for both the viscous and Jeffrey fluid. The velocities decrease with increasing of the inverse Darcy parameter for Jeffrey fluid whereas velocities increase for a viscous fluid. The profiles of temperature and concentration for both fluids decrease with increasing of the Brownian motion parameter. The velocity profiles rise with suction/injection parameter for the both fluids. Finally, the numerical results of the present method are compared with a work available in the literature for the Newtonian case. An excellent agreement is found between the present and published numerical results. [ABSTRACT FROM AUTHOR]

The problem of a two-dimensional free convective mass transfer flow of an incompressible, viscous, and electrically conducting fluid past a continuously moving semi-infinite vertical porous plate with large suction in the presence of a magnetic field applied normal to the plate is studied. The non-linear partial differential equations governing the flow have been transformed by a set of similarity transformations into a system of non-linear ordinary differential equations. The resulting system of the similarity equations are solved analytically adopting the perturbation technique. The expressions for the velocity field, temperature field, concentration field, induced magnetic field, drag coefficient, and the coefficient of the rate of heat and mass transfer at the plate are obtained. The results are discussed in details through graphs and tables to observe the effect of various physical parameters involved in the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (). DOI 10.1002/htj.21097 [ABSTRACT FROM AUTHOR]