Magnetic Field Boundary Conditions Research Articles

Combined Free and Forced Convection Couette-Hartmann Flow in a Rotating Channel with Arbitrary Conducting Walls and Hall Effects

AbstractCombined free and forced convection Couette-Hartmann flow of a viscous, incompressible and electrically conducting fluid in rotating channel with arbitrary conducting walls in the presence of Hall current is investigated. Boundary conditions for magnetic field and expressions for shear stresses at the walls and mass flow rate are derived. Asymptotic analysis of solution for large values of rotation and magnetic parameters is performed to highlight nature of modified Ekmann and Hartmann boundary layers. Numerical solution of non-linear energy equation and rate of heat transfer at the walls are computed with the help of MATHEMATICA. It is found that velocity depends on wall conductance ratio of moving wall and on the sum of wall conductance ratios of both the walls of channel. There arises reverse flow in the secondary flow direction near central region of the channel due to thermal buoyancy force. Thermal buoyancy force, rotation, Hall current and wall conductance ratios resist primary fluid velocity whereas thermal buoyancy force and Hall current favor secondary fluid velocity in the region near lower wall of the channel. Magnetic field favors both the primary and secondary fluid velocities in the region near lower wall of the channel.

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

The present study examines the effect of induced magnetic field and convective boundary condition on magnetohydrodynamic (MHD) stagnation point flow and heat transfer due to upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles. Boundary layer theory is used to simplify the equation of motion, induced magnetic field, energy and concentration which results in four coupled non-linear ordinary differential equations. The study takes into account the effect of Brownian motion and thermophoresis parameters. The governing equations and their associated boundary conditions are initially cast into dimensionless form by similarity variables. The resulting system of equations is then solved numerically using fourth order Runge-Kutta-Fehlberg method along with shooting technique. The solution for the governing equations depends on parameters such as, magnetic, velocity ratio parameter B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, reciprocal of magnetic Prandtl number A, the thermophoresis parameter Nt, and Maxwell parameter β.The numerical results are obtained for velocity, temperature, induced magnetic field and concentration profiles as well as skin friction coefficient, the local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient, the local Nusselt number and Sherwood number decrease with an increase in B and M parameters. Moreover, local Sherwood number -ϕ′(0) decreases with an increase in convective parameter Bi, but the local Nusselt number -θ′(0) increases with an increase in Bi. The results are displayed both in graphical and tabular form to illustrate the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

Analysis and experiment of stair‐shaped waveguide‐fed dielectric resonator antenna

Theoretical analysis of a stair-shaped waveguide-fed hemispherical dielectric resonator antenna (DRA) using method of moments (MoM) is presented in this study. Waveguide steps are used to enhance the coupling of direct coupled waveguide-fed DRA. Theoretical analysis is performed by solving coupled integral equations obtained by imposing magnetic field boundary conditions at various apertures using MoM. DRA and the steps are analysed using Green's function. For waveguide, modal analysis is performed. In order to determine the effects of various design parameters, parametric analysis has been carried out using the code developed. Experimental results confirm the validity of the proposed theory. The antenna has a maximum gain of 5.7 dBi at 9.09 GHz with a 3 dB gain bandwidth of 11.08%. Reasonable agreement is observed between the measured and simulated radiation patterns. The proposed coupling enhancement technique guarantees more than 98% coupling.

Electromagnetothermoelastic behavior of a rotating imperfect hybrid functionally graded hollow cylinder

The electro-magneto- thermo-elastic behavior of a rotating functionally graded long hollow cylinder with functionally graded piezoelectric (FGPM) layers is analytically analyzed. The layers are imperfectly bonded to its inner and outer surfaces. The hybrid cylinder is placed in a constant magnetic field subjected to a thermo-electro-mechanical loading and could be rested on a Winkler-type elastic foundation. The material properties of the FGM cylinder and radially polarized FGPM layers are assumed to be graded in the radial direction according to the power law. The hybrid cylinder is rotating about its axis at a constant angular velocity. The governing equations are solved analytically and then stresses, displacement and electric potential distribution are calculated. Numerical examples are given to illustrate the effects of material in-homogeneity, magnetic field, elastic foundation, applied voltage, imperfect interface and thermo-mechanical boundary condition on the static behavior of a FG smart cylinder.

Incompressible limit of the non-isentropic magnetohydrodynamic equations in bounded domains

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condition for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

Sakiadis flow of Maxwell fluid considering magnetic field and convective boundary conditions

In this paper we address the flow of Maxwell fluid due to constantly moving flat radiative surface with convective condition. The flow is under the influence of non-uniform transverse magnetic field. The velocity and temperature distributions have been evaluated numerically by shooting approach. The solution depends on various interesting parameters including local Deborah number De, magnetic field parameter M, Prandtl number Pr and Biot number Bi. We found that variation in velocity with an increase in local Deborah number De is non-monotonic. However temperature is a decreasing function of local Deborah number De.

The Effect of Induced Magnetic Field and Convective Boundary Condition on MHD Stagnation Point Flow and Heat Transfer of Nanofluid Past a Stretching Sheet

This study examines the effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer due to nanofluid over a stretching sheet. It takes into account the effect of Brownian motion and thermophoresis parameters. The nonlinear governing equations and their associated boundary conditions are reduced into dimensionless form by similarity variables. The resulting systems of equations are then solved numerically using fourth-order Runge-Kutta method along with shooting technique. The solution for the problem depends on parameters: magnetic M, velocity ratio B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, thermophoresis Nt, and reciprocal of magnetic Prandtl number A. Numerical results of the study are obtained for velocity, temperature, induced magnetic field, and concentration profiles as well as skin friction coefficient, the local Nusselt number, and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number, and Sherwood number decrease with an increase in B and M parameters. However, the local Nusselt number -θ'(0) increases with an increase in Bi, and local Sherwood number -φ'(0) decreases with an increase in convective parameter Bi. The study indicated that the flow velocity and the skin friction coefficient on stretching sheet are strongly influenced by velocity ratio (B <; 1) and magnetic parameters. It is also observed that the skin friction coefficient -f"(0) is an increasing function of magnetic parameter and a decreasing function of velocity ratio parameter B. The study also shows that the local heat transfer rate -θ'(0) is an increasing function of the convective parameter Bi, but it is a decreasing function of magnetic parameter M, velocity ratio parameter B, and thermophoresis parameter Nt. The obtained results are displayed both in graphical and tabular form to show the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

Entropy generation in MHD porous channel with hydrodynamic slip and convective boundary conditions

Combined effects of hydrodynamic slip, magnetic field, suction/injection and convective boundary conditions on the global entropy generation in steady flow of an incompressible electrically conducting fluid through a channel with permeable plates are studied. Analytical solutions of the governing equations are obtained in closed form. Particularly, using thermal boundary conditions of the third kind, the temperature field is derived analytically. Also, the influences of the governing parameters on global entropy generation are discussed in detail and depicted graphically. The analysis of our results indicates that entropy generation minimization can be achieved by appropriate combination of the geometrical and physical parameters of the system. It is possible to determine optimum values of Hartmann number, Biot number and Prandtl numbers which lead to a minimum global entropy generation rate. The effects of slip flow on the optimum values of some other parameters are also explored.

A Plane Magnetothermoelastic Waves Reflection and Refraction Between Two Solid Media with External Heat Sources and Initial Stress

In this article, an estimation to illustrate the reflection and transmission of thermoelastic waves at the interface of two different thermoelastic solid half-spaces under initial stress, magnetic field, and external heat sources is made. The governing equations are considered for an isotropic and homogeneous generalized thermoelastic model under initial stress, heat sources, magnetic field, and perfect boundary condition. The reflected and transmitted waves amplitudes are obtained for the incidence of SV-waves. Approximate expressions are obtained as a special case from the present problem. The results obtained are computed numerically for the amplitude ratios under initial stresses and are displayed graphically. It appears that the effects of initial stress, magnetic field, and external heat sources are very pronounced on the propagation phenomena. If the magnetic field and heat sources are neglected, the results obtained then lead to the same results obtained by relevant authors.

Low Mach number limit of non-isentropic magnetohydrodynamic equations in a bounded domain

This paper verifies the low Mach number limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient in a two dimensional bounded domain with Navier’s slip boundary condition for velocity and perfectly conducting boundary condition for magnetic field.

Influence of Magnetohydrodynamic and Thermal Radiation Boundary Layer Flow of a Nanofluid Past a Stretching Sheet

The problem of laminar fluid flow which results from a permeable stretching of a flat surface in a nanofluid with the effects of heat radiation, magnetic field, velocity slip and convective boundary conditions have been investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. thermal radiation parameter R, magnetic parameter M, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, velocity slip parameter A convection and Biot numbe Bi. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved using fourth order Runge-Kutta method along with shooting technique. An analysis has been carried out to elucidate the effects of governing parameters corresponding to various physical conditions. Numerical results are obtained for distributions of velocity, temperature and concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. Keywords: Nanofluid, Boundary layer flow; Stretching sheet; Thermal radiation; MHD; Velocity slip; Convective boundary. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i2.17233 J. Sci. Res. 6 (2), 257-272 (2014)

Peristaltic Flow with Inclined Magnetic Field and Convective Boundary Conditions

Peristaltic flow of viscous fluid in an asymmetric inclined channel with heat transfer and inclined magnetic field is examined. The convective boundary conditions have been handled. Complexity of emerging equations is simplified by utilizing long wavelength and low Reynolds number approximation. Variation of emerging parameters embedded in flow system are discussed. It is observed that an increase in Brikman number increases the temperature profile. Further, it is seen that temperature distribution is an increasing function of Biot number at lower wall.

Peristaltic Flow with Inclined Magnetic Field and Convective Boundary Conditions

Peristaltic flow of viscous fluid in an asymmetric inclined channel with heat transfer and inclined magnetic field is examined. The convective boundary conditions have been handled. Complexity of emerging equations is simplified by utilizing long wavelength and low Reynolds number approximation. Variation of emerging parameters embedded in flow system are discussed. It is observed that an increase in Brikman number increases the temperature profile. Further, it is seen that temperature distribution is an increasing function of Biot number at lower wall.

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth di to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification ItorIinj and formation time τf demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates ItorIinj and exhibits much a longer τf. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.

Time-Domain Electric Current Formulation for the Analysis of Arbitrarily Shaped Dielectric Bodies

In this paper, we present a novel stable time-domain procedure to analyze the transient electromagnetic response from 3-D dielectric bodies. The principal method is based on the application of electric- and magnetic-field boundary conditions on the surfaces of homogeneous structures while considering the electric currents as unknowns. Triangular patches as well as quadrangular patches model the surface of the composite body. The method of moments is implemented to solve the resultant integral equations. The scattered electromagnetic fields that are dependent only on the electric surface currents are computed with less effort compared with other methods, which use both equivalent electric and magnetic surface currents. Comparing these methods, also our innovative method reduces the number of the submatrix elements by considering them as zero, when dealing with more than one homogeneous body, or combined PEC and body structures.

Comparison of self‐consistent simulations with observed magnetic field and ion plasma parameters in the ring current during the 10 August 2000 magnetic storm

We assess whether magnetically and electrically self‐consistent ring current simulations can account simultaneously for in situ magnetic field and ion flux measurements in the inner magnetosphere during the large 10 August 2000 storm (min Dst = −107 nT). We use the Rice Convection Model–Equilibrium (RCM‐E) and drive it with time‐dependent magnetic field, electric field, and plasma boundary conditions that are guided by empirical and assimilative models. Comparisons of the simulated and observed magnetic field from Geostationary Operational Environmental Satellites (GOES) and observed proton differential flux spectra from Los Alamos National Laboratory (LANL) satellites are made at geosynchronous orbit (GEO). Similarly, simulated and observed magnetic field and proton density and temperature are compared along the orbit of Polar (r ∼ 1.8–9 RE) for the event. The simulated and observed magnetic field components agree reasonably well at GEO and along the orbit of Polar. However, since the effects of substorm dipolarizations are not explicitly modeled, the simulation fails to reproduce observed sawtooth fluctuations in the magnetic field. Over energies from 1 to 150 keV, the RCM‐E reproduced well the ion dispersion features in the LANL 1994‐084 ion differential flux spectra over energies at GEO and proton densities and temperatures calculated from Polar proton flux measurements. Thus, the RCM‐E simulations can account simultaneously for in situ magnetic field and ion flux measurements for the 10 August 2000 storm. This demonstrates that a self‐consistent model can produce realistic features of the storm time inner magnetosphere.

Storm-time ring current: model-dependent results

Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.

The thermo-electromagnetoelastic behavior of a rotating functionally graded piezoelectriccylinder

In this paper, the dynamic response of a rotating radially polarized functionally gradedpiezoelectric hollow cylinder is investigated. The cylinder is placed in a constant magneticfield and subjected to a thermo-electro-mechanical loading. All material propertiesare taken to follow a power law along the radial direction of the cylinder. Thetemperature distribution through the thickness of the cylinder is obtained by solving theheat conduction equation. The two coupled differential equations in terms of thedisplacement and electric potential accounting for the effects of the thermal andmagnetic fields are solved directly. Numerical examples of the analytical results aregiven to illustrate the effects of non-homogeneity parameter, angular velocity,temperature gradient, magnetic field, and different boundary conditions on thethermo-electromagnetoelastic behavior of the hollow cylinder. The results in the absence ofthe thermo-magnetic loading are verified with those reported in the literature.

Three-dimensional solutions of the magnetohydrostatic equations: rigidly rotating magnetized coronae in cylindrical geometry

Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.

Transient source current formulation for the analysis of arbitrarily shaped dielectric/conducting composite structures

In this paper, a novel time-domain integral equation (TDIE) approach is presented to analyze the transient electromagnetic response from three-dimensional dielectric/conducting composite structures. The composite bodies with different materials and conductor structures are considered as autonomous scattering objects. The scattered electromagnetic field is derived by superposition of the individual scatterers. The principal method is based on the application of electric and magnetic field boundary conditions on the surfaces of dielectric and conducting objects while considering the electric currents as unknowns. Triangular patches as well as quadrangular patches model the surfaces of the combined structure. The scattered electromagnetic fields inside and outside the combined structure depend only on the electric surface currents. This improves the post-processing time and complexity as compared with other methods using both equivalent electric and magnetic surface currents. To solve the resultant integral equations, the implicit method of moments is used. In our approach, the internal fields are independent of external currents and vice-versa, reducing the number of the matrix elements by considering them as zero.