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The aim of the present analysis concerns the magnetohydrodynamic flow of fluid which is natural convective and electrically charged through two vertical insulated walls. Influences of radiative heat flux, induced magnetic field, and the Newtonian heating/cooling are taken. We found exact expressions for the temperature field, the velocity field, and the induced magnetic field by solving the set of dimensionless coupled governing equations. Further, we obtained the equations for induced current density, Nusselt number, skin frictions as well as mass flux. The influences of the several constraints like the magnetic, the radiation and the Newtonian heating/cooling on the profiles of the velocity, the temperature field, the induced magnetic field as well as the current density display with graphics. Moreover, the influence of these non-dimensional parameters on the skin frictions, the Nusselt number, and the mass flux is explored in tabular form. The outcome of the radiation raised the velocity, the temperature field, the induced magnetic field and the current density field in view of enhancing the thickness of the boundary layer. Also, the impact of Newtonian heating is to raise the velocity, temperature, induced magnetic field and induced current density, whereas all these fields have opposite behaviors in case of Newtonian cooling.

The principal objective of the present paper is to know the reaction of thermal radiation and the effects of magnetic fields on a viscous dissipative free convection fluid flow past an inclined infinite plate in the presence of an induced magnetic field. The Galerkin finite element technique is applied to solve the nonlinear coupled partial differential equations and effects of thermal radiation and other physical and flow parameters on velocity, induced magnetic field, along with temperature profiles are explained through graphs. It is noticed that as the thermal radiation increases velocity and temperature profiles decrease and the induced magnetic field profiles increases.

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.

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.

The presented communication provides the analysis of entropy generation and heat transport rate in peristalsis of hybrid nanofluid induced by metachronal ciliary beating under magnetic environment for sufficiently large magnetic Reynolds number. Nanoparticles of Cu and Al2O3 are suspended in water. Features of their structures are determined by using long-wavelength approximation with zero Reynolds number. Adams Bashforth method has been applied to compute the results of the flow variables as well as entropy generation number from the formulated differential system which are then interpreted graphically to establish physical significance for different values of physical interest. This investigation reveals that thermal performance of fluid can be boosted by utilizing hybrid nanomaterial about the strength of a wall for stability. Irreversibility analysis ensures that entropy reduced for strong magnetic field while thermal heat generation results in an increase in temperature causing an enhancement in entropy of the system. Error analysis has been performed with reasonably accurate tolerance level. The comparative outcomes of both numerical approaches are presented with plentiful graphical as well as numerical demonstrations which demonstrate the importance in terms of robustness, accuracy and stability.

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.

The article performs a conjugate study of heat transfer for a stretching sheet, whose surface is exposed to a cooling fluid. Through curve fitting, the problem reduces to a set of linear problems, which are solved recursively. The physical processes of heat diffusion and viscous dissipation in both media, as well as Joule heating and magnetic induction in the MHD fluid flow are retained. Examples involving cases of prescribed surface temperature, prescribed surface flux, and a conductive sheet are considered., The article contains 4 tables, 8 figures and 25 references.

The present article communicates mathematical and theoretical study of three dimensional mixed convection flow of an electrical conducting third grade fluid flow near a non-uniform irregular wavy surface. The flow field is incorporated with an applied magnetic field. Heat and mass transfer characteristics are scrutinized with combined impact of enthalpy change along with energy activation and non-linear thermal radiation. The prime structure of differential equations is achieved in momentum, energy, magnetic and concentration forms. We defined some new dimensionless functions which transformed non-linear PDEs into dimensionless ODEs. Lobatto(iiiA) formula based technique Bvp4c is used for graphical and numerical solution of governing equations. Features of different dimensionless parameters are studied for velocity, concentration, magnetic and energy distributions by using graphical approach. Skin friction coefficients, rate of heat and mass fluxes are calculated by changing the values of some dimensionless parameters. Comparative study of Nusselt number with previous published results are demonstrated to investigate the accuracy of current problem. Final outcome justifies that better agreement is achieved with existing published work.

The objective of this investigation is to study the influence of thermal radiation and radiation absorption parameter on a mixed convection flow over a continuously moving porous vertical plate under the action of transverse applied magnetic field taking into account the induced magnetic field with convective boundary. Under certain assumptions, the solutions for the velocity field, temperature distribution and induced magnetic field are obtained. The influences of various parameters on the velocity, temperature fields and on induced magnetic fields are studied graphically. It is also found that the dimensionless Prandtl number, Grashof number, Schmidt number and magnetic parameter have an appreciable influence on the independent variables.

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.

Weyl semimetals (WSM) are a new class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking, as well as a chiral magnetic effect due to inversion symmetry breaking. These unusual electromagnetic responses can be characterized by an axion term $\theta \textbf{E} \cdot \textbf{B}$ with space and time dependent axion angle $\theta (\textbf{r} ,t)$. In this paper we compute the electromagnetic fields produced by an electric charge near to a topological Weyl semimetal with two Weyl nodes in the bulk Brillouin zone. We find that, as in ordinary metals and dielectrics, outside the WSM the electric field is mainly determined by the optical properties of the material. The magnetic field is, on the contrary, of topological origin in nature due to the magnetoelectric effect of topological phases. We show that the magnetic field exhibits a particularly interesting behavior above the WSM: the field lines begin at the surface and then end at the surface (but not at the same point). This behavior is quite different from that produced by an electric charge near the surface of a topological insulator, where the magnetic field above the surface is generated by an image magnetic monopole beneath the surface, in which case, the magnetic field lines are straight rays. The unconventional behavior of the magnetic field is an experimentally observable signature of the anomalous Hall effect in the bulk of the WSM. We discuss a simple candidate material for testing our predictions, as well as two experimental setups which must be sensitive to the effects of the induced magnetic field., Comment: Accepted for publication in Physical Review B

The present work consists of theoretical investigation of MHD natural convection flow in vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates. The influence of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expressions for the induced current density and skin friction have also been obtained. The effects of various non-dimensional parameters such as rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number on the velocity, the induced magnetic field, the induced current density, and skin friction have been presented in graphical form. It is found that the effect of Hartmann number and magnetic Prandtl number on the induced current density is found to have a decreasing nature at the central region of the microchannel.

In this article, a numerical analysis has been performed to study the effect of radial magnetic field on natural convection of a viscous incompressible and electrically conducting fluid within the concentric vertical annuli containing a ramped type temperature profile at the surface of inner cylinder taking into account the induced magnetic field. Two cases are considered which are case 1, when inner cylinder is perfectly conducting and outer cylinder is non-conducting and case 2, has opposite configuration. The governing partial differential equations have been solved by using Matlab software. The influence of Hartmann number and magnetic Prandtl number on different profiles has been presented graphically. It is found that the effect of Hartmann number and magnetic Prandtl number is to decrease the velocity profile in both the cases. This study suggest that the heat transfer can be controlled by using ramped temperature and conductivity of the cylinder.

International audience; We report the indirect detection of an induced magnetic field in the ionosphere of Mars and its effects on the electron density behaviour. The observations were made by the Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) aboard Mars Express, in its Active Ionospheric Sounding mode. During several orbits on June 2006, the ionosphere showed an unusual behaviour, characterised by a compression of the plasma above the main ionospheric peak as observed by the topside total electron content, the plasma scale height, and the local plasma in the Mars Express surroundings. The compression was most likely due to an induced magnetic field originating from the solar wind and measured by the MARSIS antennas, which was able to penetrate into the ionosphere. In particular, for several profiles, the density distribution can be clearly defined by two different plasma scale heights, which indicates a transition region between both of them. From the balance of magnetic and thermal plasma pressures and from a comparison with a numerical model of the Martian ionosphere, the hypothesis of a penetrating induced magnetic field down to a transition altitude around 150 km is confirmed. This compressed ionosphere has also been compared with data from other orbits in the same location and at the same time period, i.e. 18.5 days of difference between first and last orbits, where there is no measured induced magnetic field, and the orbits show a clearly different behaviour.

The ferrofluid are useful nanofluid and can be prepared by mixing magnetic types of nanoparticles in base fluid. The mathematical modelling of ferrofluid under induced magnetic field through a vertical stretching surface is formulated in the current theoretical study. The study is performed for ferrofluid by considering magnetite Fe 3 O 4 magnetic nanoparticles in base fluid. In ferrofluid, the appropriate mixture of magnetic nanoparticles can lead to desire heat transfer phenomena. This theoretical study indicates that both Nusselt number and skin friction coefficient for Fe 3 O 4 -water ferrofluid increase by improving the effects of magnetic parameter β . Velocity and magnetic boundary layer thicknesses increase/decrease for assisting/opposing flow by strengthening magnetic effects and in the presence of magnetic type Fe 3 O 4 nanoparticle boundary layer thickness further enhances for pure water as compared to Fe 3 O 4 type of ferrofluid. Temperature profile and thermal boundary layer thickness increase for both assisting/opposing flow with enhancing the concentration of Fe 3 O 4 magnetic nanoparticle, however, thermal distribution reduces/upsurges in case of assisting/opposing flow with the increase of magnetic strength and thermal boundary layer thickness is greater for Fe 3 O 4 - water based ferrofluid as compared to regular fluid. The bvp4c built-in code in MATLAB software is employed for solution purposes. Results are displayed for the selection of effective parameters in data and graphical forms for both assisting and opposing flows.

Study the significance of double-diffusive convection and induced magnetic field on peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel with different four wave forms have been investigated. Formulation and governing equations of this problem were deduced representing by highly partial differential equations. Hence, exact and analytical solutions of the resulting equations were deduced. Therefore, effects of pressure rise, pressure gradient, temperature, concentration, nanoparticle volume fraction, magnetic force function and stream functions were graphical represented and discussed. It was found that, on rising in the tapered asymmetric channel parameter, the pumping rate increases (decreases) in copumping region (in the retrograde pumping and free pumping regions). Further, the temperature distributions increase with growing in Brownian motion, Soret, Dufour and thermophoresis parameters while the concentration profile decreases with these parameters.

Present theoretical investigation is a mathematical illustration of an application to endoscopy by incorporating hybrid nanoparticles and an induced magnetic field with a rheological fluid model for more realistic results. Rheological fluid behavior is characterized by the Ostwald-de-Waele power-law model. A hybrid nanofluid mechanism is considered comprising platelet-shaped nanoparticles since nanoparticles are potential drug transportation tools in biomedical applications. Moreover, ciliary activity is encountered regarding their extensive applications in performing complex functions along with buoyancy effects. An endoscope is inserted inside a ciliated tube and peristalsis occurred due to ciliary activity in the gap between tube and endoscope. A non-Newtonian model is developed by mathematical formulation which is tackled analytically using homotopy analysis. The outcomes are interpreted graphically along with the pressure rise and streamlining configuration for the case of negligible inertial forces and long wavelength. A three-dimensional graphical interpretation of axial velocity is studied as well. Moreover, tables are prepared and displayed for a more physical insight.

This paper is aimed to investigate the effect of induced magnetic field and Newtonian heating/cooling on fully developed laminar natural convective flow of a viscous incompressible and electrically conducting fluid in the presence of radial magnetic field. The governing equations of the model are transformed into non-dimensional simultaneously ordinary differential equations and solved analytically. We have analyzed the influence of the Hartmann number and Biot number on the fluid velocity, induced magnetic field and induced current density by the graphs while the values of skin-friction and mass flux are given in the tabular form. We observed that the values of the velocity, induced magnetic field and induced current density have decreasing tendency with increasing the values of Hartmann number. Also, the results show that on increasing the value of Biot number leads to increase the velocity, induced magnetic field, induced current density and skin-friction in case of the Newtonian heating and decrease the velocity, induced magnetic field, induced current density and skin-friction in case of the Newtonian cooling.

This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B . The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.

In the present paper, an analysis has been performed to study the influence of induced magnetic field on the transient free convective flow of an electrically conducting and viscous incompressible fluid over a vertical cone. The coupled nonlinear partial differential equations governing the transient flow have been solved numerically by using the implicit finite difference method of Crank–Nicolson type. The influence of magnetic parameter, magnetic Prandtl number and semi-vertical angle of the cone on the velocity and induced magnetic field profiles has been illustrated graphically. Also, the local as well as average skin-friction and Nusselt number has been presented graphically. For result validation, we have done a comparative study and the present results are found to be in very good agreement with available results.

In the present analysis, we have investigated the effects of induced magnetic field and heat source/sink on fully developed laminar natural convective flow of a viscous incompressible and electrically conducting fluid in the presence of radial magnetic field by considering induced magnetic field into account. The governing equations of the considered model are transformed into simultaneously ordinary differential equations and solved analytically. We have analyzed the effect of Hartmann number, heat source/sink parameter and ratio of outer radius to inner radius on the fluid velocity, induced magnetic field, induced current density and temperature field by the graphs while the values of skin-friction, Nusselt number, mass flux and induced current flux are given in the tabular form. We observed that the values of the velocity, induced magnetic field and induced current density have decreasing tendency with increasing the values of the Hartmann number. The results show that an increasing value of the heat source/sink parameter leads to increase the velocity, induced magnetic field, induced current density and temperature in case of heat source and viceversa in case of heat sink.

In this paper, the steady two-dimensional hydromagnetic free convective flow of an incompressible viscous and electrically conducting fluid between two parallel vertical porous plates has been considered. The effect of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into account. The governing equations of the motion are a set of simultaneous ordinary differential equations and their analytical solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expression for the induced current density has been also obtained. The effects of various non-dimensional parameters on the velocity profile, the induced magnetic field profile, the temperature profile and the induced current density profile have been shown in the graphs. It is found that the effect of suction parameter is to decrease the velocity field and induced current density while it has increasing effect on the induced magnetic field.

Supersonic magnetohydrodynamic field analysis is carried out for energy conversion using a weakly ionized plasma. The magnetic field induced by a generated electric current is taken into account. A three-dimensional simulation shows that the Lorentz force induces a shock wave and boundary-layer separation in the plasma duct flow.

The working principle of Lorentz force velocimetry (LFV) is based on a linear dependence between measured force and velocity. We consider a case when a violation of that linear law takes place in order to take this effect into account for LFV. The response of the Lorentz force to a time-dependent velocity of solid conducting rods is experimentally studied. Solid conductors were chosen due to the fact that at a limited length of imposed magnetic field the end effects of secondary field generation are identical both in liquid and solid conductors. Thus one can simulate clearly a distortion of the imposed magnetic field in the case of non-stationary fluid flows. The magnetic Reynolds number based on advection time was of the order of unity. It is demonstrated that magnetic field advection effects lead to a Lorentz force difference in low- and finite- cases. The induced magnetic field measurements and experimental estimation of the eddy current density are reported.