Uniform Transverse Magnetic Field Research Articles

Numerical Analysis of the Unsteady Natural Convection MHD Couette Nanofluid Flow in the Presence of Thermal Radiation Using Single and Two-Phase Nanofluid Models for Cu–Water Nanofluids

The unsteady Couette nanofluid flow with heat transfer is investigated numerically for copper–water nanofluids under the combined effects of thermal radiation and a uniform transverse magnetic field with variable thermo-physical properties, in the case where the flow is established vertically between two parallel plates, so that one of them has an accelerated motion. The homogeneous single-phase model (i.e., Tiwari and Das’s nanofluid model) and the two-phase mixture model (i.e., Buongiorno’s nanofluid model) are utilized in this study together with Corcione’s model to further investigate and clarify the differences between those models and evaluate the validity of the single-phase model for studying the unsteady natural convection MHD Couette nanofluid flow with thermal radiation. In this investigation, we assume that the studied nanofluid is electrically conducting and has a Newtonian rheological behavior. The nonlinear dynamical system of partial differential equations are solved numerically by means of the Gear–Chebyshev–Gauss–Lobatto collocation technique for zero nanoparticles mass flux and no-slip impermeable conditions at the isothermal vertical plates. In a special case, the present numerical solution is also validated analytically and numerically with the earlier available results. For both nanofluid models, the effects of major parameters on the dimensionless velocity, temperature and volumetric fraction of nanoparticles are analysed via representative profiles, whereas the skin friction factor and the heat transfer rate are estimated numerically and discussed through tabular illustrations.

Cattaneo–Christov based study of $${\text {TiO}}_2$$ TiO 2 –CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation

In the present research, a simplified mathematical model is presented to study the heat transfer and entropy generation analysis of thermal system containing hybrid nanofluid. Nanofluid occupies the space over an infinite horizontal surface and the flow is induced by the non-linear stretching of surface. A uniform transverse magnetic field, Cattaneo–Christov heat flux model and thermal radiation effects are also included in the present study. The similarity technique is employed to reduce the governing non-linear partial differential equations to a set of ordinary differential equation. Keller Box numerical scheme is then used to approximate the solutions for the thermal analysis. Results are presented for conventional copper oxide–ethylene glycol (CuO–EG) and hybrid titanium–copper oxide/ethylene glycol ( $${\text {TiO}}_2$$ –CuO/EG) nanofluids. The spherical, hexahedron, tetrahedron, cylindrical, and lamina-shaped nanoparticles are considered in the present analysis. The significant findings of the study is the enhanced heat transfer capability of hybrid nanofluids over the conventional nanofluids, greatest heat transfer rate for the smallest value of the shape factor parameter and the increase in Reynolds number and Brinkman number increases the overall entropy of the system.

Blood flow problem in the presence of magnetic particles through a circular cylinder using Caputo-Fabrizio fractional derivative

In this paper, the flow of blood mixed with magnetic particles subjected to uniform transverse magnetic field and pressure gradient in an axisymmetric circular cylinder is studied by using a new trend of fractional derivative without singular kernel. The governing equations are fractional partial differential equations derived based on the Caputo-Fabrizio time-fractional derivatives NFDt. The current result agrees considerably well with that of the previous Caputo fractional derivatives UFDt.

Orbits of two electrons released from rest in a uniform transverse magnetic field

Two identical charged particles released from rest repel each other radially. A uniform perpendicular magnetic field will then cause their trajectories to curve into a flower petal pattern. The orbit of each particle is approximately circular with a long period for a strong magnetic field, whereas it becomes a figure-eight for a weak magnetic field with each lobe completed in a cyclotron period. For example, such radially bound motions arise for two-dimensional electron gases. The level of treatment is appropriate for an undergraduate calculus-based electromagnetism course.

Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method

In this paper, two-dimensional squeezing flow of nanofluid under the effects of a uniform transverse magnetic field and slip boundary conditions is analyzed using variation of parameter method. The approximate analytical solutions of the variation of parameter method show excellent agreement and accuracy with the solutions of numerical method using shooting method coupled with Runge–Kutta coupled. Therefore, the developed analytical solutions are used to investigate the effects of fluid properties, magnetic field and slip parameters on the squeezing flow of nanofluid. From the results, it is observed that the velocity of the fluid increases with increase in the magnetic field parameter under the influence of slip condition while under no-slip condition, the velocity of the fluid decreases with increase in the magnetic field parameter. Also, the fluid velocity increases as the slip parameter increases but it decreases with increase in the magnetic field parameter and Reynolds number under the no-slip condition. It is hoped that this study will enhance the understanding of squeezing flow process such as found in various biological and industrial applications.

MHD Free Convective Boundary Layer Flow through Porous medium Past a Moving Vertical Platewith Heat Source and Chemical Reaction

In this paper, we have considered the unsteady magnetohydrodynamic (MHD) free convection in a boundary layer flow of an electrically conducting fluid through porous medium subject to uniform transverse magnetic field over a moving infinite vertical plate in the presence of heat source and chemical reaction. The equations for governing flow through porous medium based on Brinkman’s model. The non-linear partial differential equations have been transformed into a two point boundary value problem using similarity variables and then solved numerically by Runge-Kutta fourth order method with the help of shooting technique. Computational results are discussed for velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are tabulated for different values of governing parameters controlling the flow system.

HALL EFFECTS ON MHD PERISTALTIC FLOW OF JEFFREY FLUID THROUGH POROUS MEDIUM IN A VERTICAL STRATUM

In this paper, we discuss heat transfer on the peristaltic magnetohydrodynamic flow of a Jeffrey fluid through a porous medium in a vertical echelon under the influence of a uniform transverse magnetic field normal to the channel, taking Hall current into account. This study is motivated towards the physical flow of blood in a microcirculatory system by taking account of the particle size effect. Here we consider the Reynolds number to be small enough and wavelength-to-diameter ratio large enough to neglect inertial effects. The nonlinear governing equations for the Jeffrey fluid are solved making use of the perturbation technique. The exact solutions for the velocity, temperature, and the pressure rise per one wavelength are determined analytically. Its behavior is discussed computationally with reference to different physical parameters. Some parameters are the strongest on the trapping bolus phenomenon and the pumping characteristics. The size of the trapping bolus decreases with increasing Hartmann number or permeability parameter and increases with increasing Hall parameter or Jeffrey number.

Hydro magnetic heat and mass transfer flow in a porous plate with varying temperature

Objectives: To study the unsteady hydro magnetic naturally convicting flow with heat and mass flux in the presence of chemical reaction, fluid past an infinite vertical porous plate with varying temperature and concentration. Statistical Analysis: An analysis is carried out to study the heat transfer in unsteady two dimensional Mass transfer flow of a magneto hydrodynamic over a porous medium. The flow is subjective in the action of uniform transverse magnetic field. With the help of dimensionless variable, the governing flow equation are reduced to a system of nonlinear Partial Differential Equation. This system has been solved analytically using Perturbation Approximation. Findings: The influence of the temperature distribution, concentration distribution, Skin friction coefficient, BrandtNumber, Magnetic Parameter, chemical Reaction Parameter, Gash of number, Modified Gash of Number, Schmidt Number, Heat source Parameter, Radiation Parameter are discussed in Graph. In this paper, suppression of velocity on magnetic Parameter and chemical reaction are discussed. The Gash of Number and Modified Gash of Number increase the velocity, whereas in the literature survey, the analytical or numerical solution obtained by assuming that the temperature at the interface was continuous and well defined. The highlights of the results are helpful to variety the ramped temperature and ramped concentration on the wall of the infinite vertical porous plate. Applications: The combined heat and mass transfer problem along with chemical reaction play a prominent role in chemical and hydrometallurgical industries. It is used by different scientific disciplines for different processes and mechanisms. In many practical situations, mass transfer is accomplished in order to bring chemical reagents together so that a reaction can take place. Thus for example reaction can be used to provide more rapid solution of a gas in to a liquid than physical solution. Keywords: Hydro Magnetic, Heat Transfer, Mass Transfer, Chemical Reaction, Porous Medium

Magnetohydrodynamic stability of pressure-driven flow in an anisotropic porous channel: Accurate solution

The stability of fully developed pressure-driven flow of an electrically conducting fluid through a channel filled with a saturated anisotropic porous medium is studied under the influence of a uniform transverse magnetic field using a modified Brinkman equation. An analogue of Squire's transformation is used to show that two-dimensional motions are more unstable than three-dimensional ones. The modified Orr–Sommerfeld equation for the problem is solved numerically and a more accurate solution is obtained using the Chebyshev collocation method combined with Newton's and golden section search methods. The critical Reynolds number Rc and the corresponding critical wave number αc are computed for a wide range of porous parameter σp, the ratio of effective viscosity to the fluid viscosityΛ, the mechanical anisotropy parameter K1, the porosity ε and the Hartman number M. It is found that the system remains unconditionally stable to small-amplitude disturbances for the Darcy case and the energy stability analysis is also performed to corroborate this fact.

English

An analysis is carried out to examine the effects of the steady flow of an electrically conducting viscous incompressible nanofluid in the existence of a uniform transverse magnetic field with chemical reaction over a stretching sheet considering suction or injection. The present model is demonstrated experimentally to reveal the effects of Thermophoresis and Brownian motion. Similarity solutions are investigated for the governing equations and solved numerically by using a shooting technique with fourth-order Runge-Kutta integration scheme. The impact of associated parameters on velocity profile, concentration profile and temperature profile is plotted graphically. Also the impact of local skin friction coefficient, the reduced Nusselt number and the reduced Sherwood number are discussed. The experimental setup revealed good agreement of the results with the literature.

Singular perturbation and differential transform methods to two-dimensional flow of nanofluid in a porous channel with expanding/contracting walls subjected to a uniform transverse magnetic field

This paper presents a comparative study of two approximate analytical methods for the analysis of two-dimensional unsteady flow of nanofluid in a porous channel through expanding/contracting walls with large injection or suction under the influence of a uniform transverse magnetic field. Similarity transformations are used to reduce the systems of the governing partial differential equations to a nonlinear fourth-order ordinary differential equation which is solved using method of matched asymptotic expansion and differential transform method. From the verification of the approximate analytical solutions, it is established that the results obtained using differential transformation method demonstrate remarkable accuracy and better agreements with the results of numerical method than the results obtained using method of matched asymptotic expansion. Therefore, the differential transform method gives more accurate results than method of matched asymptotic expansion. Also, due to the higher accuracy of the differential transformation method than the method of matched asymptotic expansion, the approximate analytical solutions through the differential transformation method are used to investigate the effects of permeation Reynolds number, wall expansion ratio and magnetic parameter on the flow behavior of the fluid. From the results, it is established that increase in the Reynolds number decreases the axial velocity at the center of the channel during the expansion while the axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. Also, as the wall expansion ratio increases, the velocity at the center decreases and increases near the wall. For every level of injection or suction, in the case of expanding wall, increasing the wall dilation rate leads to increase in axial velocity near the center and decrease in the axial velocity near the wall. The results present in this work can serve as references for the other methods of analysis of the problem.

Hall Effects on Unsteady MHD Reactive Flow Through a Porous Channel with Convective Heating at the Arrhenius Reaction Rate

This paper deals with the study of an unsteady magnetohydrodynamic (MHD) flow and heat transfer of a reactive, viscous, incompressible, electrically conducting fluid between two infinitely long parallel porous plates where one of the plates is set into impulsive/uniformly accelerated motion in the presence of a uniform transverse magnetic field at the Arrhenius reaction rate, with the Hall currents taken into account. The transient momentum equations are solved analytically with the use of the Laplace transform technique, and the velocity field and shear stresses are obtained in a unified closed form. The energy equation is tackled numerically using Matlab. The effects of the pertinent parameters on the fluid velocity, temperature, shear stresses, and the heat transfer rate at the plates are investigated. The results reveal that the combined effects of magnetic field, suction/injection, exothermic reaction, and variable thermal conductivity have a significant impact on the hydromagnetic flow and heat transfer.

MHD Stagnation Point Flow over Exponentially Stretching Sheet with Exponentially Moving Free-Stream, Viscous Dissipation, Thermal Radiation and Non-Uniform Heat Source/Sink

An investigation is carried out for the steady, two dimensional stagnation point flow of a viscous, incompressible, electrically conducting, optically thick heat radiating fluid taking viscous dissipation into account over an exponentially stretching non-isothermal sheet with exponentially moving free-stream in the presence of uniform transverse magnetic field and non-uniform heat source/sink. The governing boundary layer equations are transformed into highly nonlinear ordinary differential equations using suitable similarity transform. Resulting boundary value problem is solved numerically with the help of 4th-order Runge-Kutta Gill method along with shooting technique. Effects of various pertinent flow parameters on the velocity, temperature field, skin friction and Nusselt number are described through figures and tables. Also, the present numerical results are compared with the earlier published results for some reduced case and a good agreement has been found among those results.

Heat and Mass Transfer on MHD Free convective flow of Second grade fluid through Porous medium over an infinite vertical plate

In this paper, we have considered the unsteady free convective two dimensional flow of a viscous incompressible electrically conducting second grade fluid over an infinite vertical porous plate under the influence of uniform transverse magnetic field with time dependent permeability, oscillatory suction. The governing equations of the flow field are solved by a regular perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the boundary, the heat flux in terms of the Nusselt number and rate of mass transfer in terms of Sherwood number are also obtained and their behavior computationally discussed.

MHD power law fluid flow and heat transfer analysis through Darcy Brinkman porous media in annular sector

We have investigated the influence of uniform transverse magnetic field on the forced convective power law fluid flow through the annular sector duct, filled with Darcy Brinkman porous media. A system of equations are obtained from the law of conservation of momentum and energy are transformed into dimensionless form with the help of dimensionless parameter and discretized on the base of control volume method. Algebraic equations are solved with the help of strongly implicit procedure (SIP) or successive over relaxation (SOR) method, depending on the value of flow behaviour index. Characteristics of power law fluid flow and heat transfer rate are studied numerically and graphically against different parameters such as Hartman number, porosity factor, sector angle and ratio of radii of concentric pipes. Limiting case results are obtained for the Newtonian fluid and compared with the literature.

Magnetohydrodynamic flows in u-shaped ducts under a uniform transverse magnetic field

In this study, the three-dimensional liquid metal (LM) magnetohydrodynamic (MHD) flows in a u-shaped duct under a uniform magnetic field applied perpendicular to the flow plane are numerically analyzed with the use of commercial software CFX. The u-shaped duct system is made up of an inflow channal, an outflow channal and a connecting channel located between the inflow channel and outflow channel. In the current study, the effects of the length of the connecting channel and the conductance ratio on the flow characteristics are investigated. Higher velocities are observed in the side layers of the inflow, outflow and connecting channels, forming “M-shaped” velocity profiles. In addition, the velocity recirculations are created in the inner regions of the two right-angle segments just after turning due to the inertial force therein, yielding complicated distributions of the current and electric potential, and found are the diverging and converging of the velocity component parallel to the magnetic field when fluids are turning. The results show that the pressure drop is in close relationship with the conductance ratio and the length of the connecting channel. The characteristics of the fluid velocity, current, electric potential and pressure gradient of LM MHD flows in a u-shaped duct are examined in detail.

Analysis of hydromagnetic natural convection radiative flow of a viscoelastic nanofluid over a stretching sheet with Soret and Dufour effects

PurposeThe purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.Design/methodology/approachThe governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.FindingsNumerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.Originality/valueStudy of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

Analytical formulation for the dielectric tensor and field equations of the inhomogeneous drift plasma cylinder in rotating magnetic field

In this procedure, the fundamental electromagnetic equations and fluid equations in a cylindrical coordinate system for a new drift plasma configuration have been analyzed. The system is a long nonhomogeneous drift plasma column, which is imbedded in a uniform transverse magnetic field rotating about the symmetric axis of the system. The elements of the dielectric permittivity tensor are obtained for a pattern propagating in an arbitrary direction, and coupling equations of fields will be derived. It will be observed that the time variable dielectric tensor can be written as non-operational Hermitian and pure spatial operational parts which satisfy the limiting special cases.

Instability of a Magnetic Fluid Jet in a Transverse Magnetic Field

The instability behavior of moving magnetic fluid jet in the presence of a constant uniform transverse magnetic field is investigated theoretically within the framework of linear stability analysis. The corresponding dispersion relation between the wave growth rate of instability and the magnitude of its wavenumber is obtained. The dependence of the wave growth rate on the polar angle in the presence of magnetic field is found. The influence of the magnetic field on the length of undisturbed jet section and the instability wavelength is studied. The correlation with the experimental results is demonstrated.

General planar transverse domain walls realized by optimized transverse magnetic field pulses in magnetic biaxial nanowires

The statics and field-driven dynamics of transverse domain walls (TDWs) in magnetic nanowires (NWs) have attracted continuous interests because of their theoretical significance and application potential in future magnetic logic and memory devices. Recent results demonstrate that uniform transverse magnetic fields (TMFs) can greatly enhance the wall velocity, meantime leave a twisting in the TDW azimuthal distribution. For application in high-density NW devices, it is preferable to erase the twisting so as to minimize magnetization frustrations. Here we report the realization of a completely planar TDW with arbitrary tilting attitude in a magnetic biaxial NW under a TMF pulse with fixed strength and well-designed orientation profile. We smooth any twisting in the TDW azimuthal plane thus completely decouple the polar and azimuthal degrees of freedom. The analytical differential equation describing the polar angle distribution is derived and the resulting solution is not the Walker-ansatz form. With this TMF pulse comoving, the field-driven dynamics of the planar TDW is investigated with the help of the asymptotic expansion method. It turns out the comoving TMF pulse increases the wall velocity under the same axial driving field. These results will help to design a series of modern magnetic devices based on planar TDWs.