Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Effects of thermal radiation on the MHD flow past a vertical plate

The effects of thermal radiation on the MHD flow over a vertical and porous plate of an optically thin gray, electrically conducting, viscous and incompressible fluid are studied. The differential equations and their boundary conditions, describing the problemunder consideration, are dimensionalized and the numerical solution is obtained. The numerical results for the velocity and temperature profiles are shown for different dimensionless parameters entering the problem under consideration, such as the radiation parameter S, Grashof number G, Prandtl number P, and the magnetic parameter M.     

Characteristics of plasma Beltrami states

Beltrami states in several models of plasma dynamics – incompressible magnetohydrodynamic (MHD) model, barotropic compressible MHD model, incompressible Hall MHD model, barotropic compressible Hall MHD model, electron MHD model, barotropic compressible Hall MHD with electron inertia model, are considered. Notwithstanding the diversity of the physics underlying the various models, the Beltrami states are shown to exhibit some common features like – certain robustness with respect to the plasma compressibility effects (albeit in the barotropy assumption), the Bernoulli condition. The Beltrami states for these models are deduced by minimizing the appropriate total energy while keeping the appropriate total helicity constant.     

MHD swirling flow and heat transfer in Maxwell fluid driven by two coaxially rotating disks with variable thermal conductivity

We develop a mathematical modeling for an electrically conducting non-Newtonian Maxwell fluid flow occurring between two coaxially parallel stretchable rotating disks at constant distant apart. The pressure and heat transfer analysis is carried out subject to the effects of axial magnetic field and temperature dependent thermal conductivity. The stretching and rotating rates of both disks are assumed different from each other. The two diverse phenomena, such as, when both disks are rotating with different angular velocities in the same as well as in the opposite directions are discussed. The similarity procedure adopted by von Kármán is utilized to reduce the governing momentum and energy equations into nonlinear ordinary differential equations. The solution of the governing problem is obtained numerically using bvp4c scheme in Matlab. The effects of active parameters including stretching rates, Deborah number, magnetic number, Prandtl number, thermal conductivity parameter and Reynolds number are examined for same as well as opposite rotation direction for radial, azimuthal, and axial flows, pressure and temperature fields. The classical flow pattern happening between the disks is significantly altered by the stretching action which is a main physical significances of this study. The azimuthal flow is observed higher for the same direction of disks rotation as compared to opposite disks rotation. The pressure field drops near the lower disk with increasing values of Reynolds number. The role of thermal conductivity parameter is quite useful to enhance the fluid temperature.     

Stability of hydromagnetic Dean flow between two arbitrarily spaced concentric circular cylinders in the presence of a uniform axial magnetic field

The effect of a uniform axial magnetic field on the stability of the flow of an incompressible viscous electrically conducting fluid between two arbitrarily spaced concentric circular cylinders driven by a constant azimuthal pressure gradient is studied. The linearized stability equations for steady axisymmetric disturbances form an eigenvalue problem, which are solved by using a classical Runge–Kutta scheme combined with a shooting method, termed unit disturbance method. It is observed that for fixed gap width, the magnetic field has a stabilizing influence on the flow for both perfectly conducting and nonconducting walls. It is also found that for a given value of magnetic parameter, stabilization is more as the gap width increases. Further the electrically nonconducting walls are found to be more destabilizing than the perfectly conducting walls. The critical value of the radii ratio (0<η<1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of the magnetic parameter.     

Peristaltically induced transport of a MHD biviscosity fluid in a non-uniform tube

We have analyzed an incompressible flow of electrically conducting biviscosity fluid through an axisymmetric non-uniform tube with a sinusoidal wave under the considerations of long wavelength and low Reynolds number. In our analysis we are taking into account the induced magnetic field. The analytic solution has been obtained from which the axial velocity, the axial induced magnetic field and the axial pressure gradient have been derived. The results for the pressure rise ΔP_λ(t), frictional force per wavelength F_λ(t) and the axial induced magnetic field h_z have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the magnetic Prandtl number p_m, the magnetic field parameter M, the Reynolds number Re, the upper limit apparent viscosity coefficient β, and the time averaged mean flow rate θ.     

导电突扩管中磁流体管流的数值模拟

采用基于OpenFOAM环境自主开发的低磁雷诺数磁流体求解器,对45°和90°突扩矩形管中液态金属流体在受到垂直流向的外加磁场作用时的速度、感应电流、压力的分布及突扩位置处的MHD三维现象进行数值模拟.结果表明：磁场沿突扩方向时,由于无回流涡,45°比90°突扩管在肩部位置速度分布更优.哈特曼数增大,强射流和突扩结构,在突扩肩部位置引发流动的不稳定性.伴随感应电流的不稳定,流动不稳定发展到突扩位置上游.磁场沿垂直突扩方向时感应电流的三维效应显著.哈特曼数增大,MHD压降显著增大.同方向磁场和相同哈特曼数,不同突扩角度的三维无量纲压力梯度无明显差异.     

Entropy generation minimization and statistical declaration with probable error for skin friction coefficient and Nusselt number

Main emphasis of present work is to analyze the novel feature of entropy generation in MHD nanomaterial flow between two rotating disks. Heat transfer process is explored in the presence of Joule heating and thermal radiation. Tiwari–Das nanofluid model is employed in mathematical modeling. Aluminum oxide and copper water nanoparticles are accounted. Statistical declaration and probable error for problem accuracy are computed. Total entropy generation subject to Bejan number is scrutinized. Suitable variables are utilized to transform nonlinear PDEs to ordinary ones. Convergent series solutions are computed. Zeroth and mth order problems are discussed for stability analysis. The impact of physical flow variables like Reynolds number, magnetic parameter, porosity parameter, stretching parameter, rotational parameter, radiation parameter, Eckert number, suction injection parameter, Brinkman number and temperature ratio parameter on velocities, temperature, total entropy generation and Bejan number are examined and discussed through graphs. Velocity and thermal gradients at the surface of disks are computed.     

Free convection effects and radiative heat transfer in MHD Stokes problem for the flow of dusty conducting fluid through porous medium

The present note deals with the effects of radiative heat transfer and free convection in MHD for a flow of an electrically conducting, incompressible, dusty viscous fluid past an impulsively started vertical non-conducting plate, under the influence of transversely applied magnetic field. The heat due to viscous dissipation and induced magnetic field is assumed to be negligible. The governing linear partial differential equations are solved by finite difference technique. The effects of various parameters (like radiation parameter N, Prandtl number Pr, porosity parameter K) entering into the MHD Stokes problem for flow of dusty conducting fluid have been examined on the temperature field and velocity profile for both the dusty fluid and dust particles.     

带通道插件管道流磁流体动力学效应的数值模拟

采用二维完全发展流模型对聚变反应堆包层带通道插件和压力平衡槽隙的矩形磁流体管流的MHD效应进行数值模拟,分析速度分布,MHD压降随哈德曼数以及通道插件的电导率的变化规律.与无插件磁流体管流相比,带绝缘通道插件管流MHD压降显著降低,MHD压降随哈德曼数的增加而减小,通道插件材料的电导率增加MHD压降系数减小.压力平衡槽隙处的回流与通道插件的电导率有关.在宏观上计算结果与实验结果和简化理论结果一致.     

Effect of Hall current and chemical reaction on MHD flow along a fluctuating porous flat plate with internal heat absorption/generation

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid past a fluctuating porous flat plate with internal heat absorption/generation in the presence of foreign gasses (such as H₂, CO₂, H₂O, NH₃) was investigated. The results are discussed with the effect of the parameters m, the Hall current, Mt, the hydromagnetic parameter, G _r the Grashoff number for heat transfer, G _c , the Grashoff number for mass transfer, S, the internal heat absorption/generation parameter, α, the transpiration parameter, S _c , the Schmidt parameter, and K _c the chemical reaction parameter for Prandtl number P _r = 0.71, which represents air. Further, the present study accounts for the 1st order chemical reaction affecting the flow characteristics. The governing equations are solved in closed form applying Hh _n (x) function. The effects of pertinent parameters characterizing the flow field are discussed with the help of graphs and tables. The important observation of the present study is that heat generation/absorption modifies the flow of current simultaneously to a magnetic force and thermal bouncy force. Heat generation combined with blowing leads to a sharp fall of temperature.     

Effects of Hall current on unsteady MHD flows of a second grade fluid

The aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B ₀ → 0 and for a Newtonian fluid when α ₁ → 0.     

Mutual Composite Fermion and Composite Boson approaches to balanced and imbalanced bi-layer quantum Hall system: An electronic analogy of the Helium 4 system

We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and imbalanced Bi-layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid (ESF) state. The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin-charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances d_c1 < d_c2 and three phases as the distance increases. When 0 < d < d_c1, the system is in the ESF state which breaks the internal U(1) symmetry, when d_c1 < d < d_c2, the system is in an pseudo-spin density wave (PSDW) state which breaks the translational symmetry, there is a first-order transition at d_c1 driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When d_c2 < d < ∞, the system becomes two weakly coupled ν = 1/2 Composite Fermion Fermi Liquid (FL) state. There is also a first-order transition at d = d_c2. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature. We also suggest that the correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag consistent with the experimental data. Then we study the effects of imbalance on both ESF and PSDW. In the ESF side, the system supports continuously changing fractional charges as the imbalance changes. In the PSDW side, there are two quantum phase transitions from the commensurate excitonic solid to an incommensurate excitonic solid and then to the excitonic superfluid state. We also comment on the effects of disorders and compare our results with the previous work. The very rich and interesting phases and phase transitions in the pseudo-spin channel in the BLQH is quite similar to those in ⁴He system with the distance playing the role of the pressure. A BLQH system in a periodic potential is also discussed. The Quantum Hall state to Wigner crystal transition in single layer Quantum Hall system is studied.     

Heat transfer enhancement of laminar nanofluids flow in a triangular duct using vortex generator

In this work, two dimensional laminar flow of different nanofluids flow inside a triangular duct with the existence of vortex generator is numerically investigated. The governing equations of mass, momentum and energy were solved using the finite volume method (FVM). The effects of type of the nanoparticles, particle concentrations, and Reynolds number on the heat transfer coefficient and pressure drop of nanofluids are examined. Reynolds number is ranged from 100 to 800. A constant surface temperature is assumed to be the thermal condition for the upper and lower heated walls. In the present work, three nanofluids are examined which are Al₂O₃, CuO and SiO₂ suspended in the base fluid of ethylene glycol with nanoparticles concentrations ranged from 1 to 6%. The results show that for the case of SiO₂–EG, at ? = 6% and Re = 800, it is found that the average Nusselt number is about 50.0% higher than the case of Re = 100.     

Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer

An analysis of the MHD Couette flow on taking into account the Hall and the ion-slip effects has been carried out for fully developed flow. Exact solutions to the velocity components, magnetic field components, axial and transverse components of the skin-friction, temperature and the rate of heat transfer have been derived. The numerical values of the transverse induced pressure gradient, the skin friction and the rate of heat transfer are entered in tables and the others have been shown on graphs. It has been observed that the flow may become unstable when M is small and ?e (Hall parameter) and ?i (ion-slip parameter) are large or at large value of M.     

Analysis of the sequence of insulator-metal phase transitions at high pressure in systems with spin crossovers

Possible variants of the Mott-Hubbard phase transitions at high pressure in systems with spin crossovers are considered. Owing to the universal character of the dependence of the effective Hubbard parameter U _eff(d ⁿ ) on the average number of d electrons, which is determined by the presence of spin crossovers, cascades of insulator-metal-insulator phase transitions in systems with d ³, d ⁶, and d ⁸ configurations become possible. Moreover, the systems with d ⁶ configuration can exhibit transitions from a metal in the absence of external pressure to an insulator at high pressure.     

Zener tunneling between the landau levels in quasi-two-dimensional electronic Corbino disks at large filling factors

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E _dc. It is shown that the observed oscillations are related to the Zener tunneling induced by E _dc. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field.     

A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part III: On a staggered mesh

The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh.     

Pressure dependence of F-center hyperfine interactions

We report a study of the effects of intense hydrostatic stress (10 Kbar) on the ENDOR spectra of F-centers in several alkali halides. In LiF, KCl, and KBr, the first shell contact hyperfine interaction constant, a_I, increases with compression, while the second shell term, a_II, decreases. In LiCl, however, da_II/dP and da_I/dP are both less than zero. We explain our experimental results, including the anomaly cf LiCl, with a model involving (1) ionic motion in a non-constant spin-density gradient and (2) ion-motion-induced perturbation of the F-center envelope function.