MHD peristaltic motion of Johnson-Segalman fluid in a channel with compliant walls

A mathematical model for magnetohydrodynamic (MHD) flow of a Johnson-Segalman fluid in a channel with compliant walls is analyzed. The flow is engendered due to sinusoidal waves on the channel walls. A series solution is developed for the case in which the amplitude ratio is small. Our computations show that the mean axial velocity of a Johnson-Segalman fluid is smaller than that of a viscous fluid. The variations of various interesting dimensionless parameters are graphed and discussed.     

Calculations of the parameters of the air plasma produced by an electron beam in the channel of an MHD generator with a nonequilibrium conductivity

Approximate analytic expressions for calculating the electron density in both steady and unsteady plasmas produced by pulsed electron beams are derived and proved to agree well with numerical calculations. It is shown that the algorithm for calculating the parameters of a nonequilibrium plasma in the channel of an MHD plasma generator depends on the type of generator. The effect of the magnetic field strength on the electron density and electric conductivity of the air plasma produced by an electron beam in the channel of a Faraday MHD generator is investigated. The influence of the parameters of the flow and ionizer on the efficiency of an MHD generator with a nonequilibrium conductivity is analyzed.     

Existence of a Hartmann layer in the peristalsis of Sisko fluid

Analytical solutions for the peristaltic flow of a magneto hydrodynamic(MHD) Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field,is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.     

Formation of compression shocks in a nonequilibrium plasma flow in a magnetic field

Plasma flow in a linearly widening, ideally sectioned, short-circuited magnetohydrodynamic (MHD) channel is studied. MHD flows are classified into two types: continuous flows and flows with a compressional MHD shock in plasmas that are stable and unstable against the onset of ionization instability. Specific features in the evolution of a stationary compression MHD shock are investigated, and its position as a function of the Stewart number is determined. It is found that, in a plasma flow in which ionization instability develops, a compression MHD shock arises at lower values of the MHD interaction parameter than in a stable plasma flow. An unidentified type of instability of MHD discontinuities is revealed.     

MHD flow of two immiscible visco-elastic Rivlin-Ericksen fluids through a non-conducting rectangular channel in presence of transient pressure gradient

The aim of this paper is to investigate the problem of MHD flow of two immiscible viscoelastic Rivlin-Ericksen fluids through a non-conducting rectangular channel in presence of transient pressure gradient. Appropriate to the boundary conditions of the problem the solution is derived by variable separation technique. Using this solution the interface velocity, flux, skin friction and mean velocity are derived. In absence of the magnetic field and the elastic behaviour the corresponding classical problem can be derived.     

Completely two-dimensional model for examining the characteristics of a linear cylindrical induction pump

A completely two-dimensional mathematical model for calculating the characteristics of induction magnetichydrodynamic (MHD) machines with a cylindrical channel is proposed. The flow pattern of a liquid metal in an electromagnetic pump under MHD instability is obtained by numeric analysis. This pattern is characterized by the formation of large-scale vortices traveling longitudinally and azimuthally. The calculated basic characteristics of the pump are in good qualitative and in satisfactory quantitative agreement with the experiment.     

大气压下自由燃烧弧的温度场和速度场的数值模拟

采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学(MHD)方程进行数值求解．得到了轴对称情况下，自由燃烧弧的温度场和速度场的分布，并和实验结果进行了比较。分析了不同辐射模型对温度场的影响，发现辐射导致电弧温度降低，但不同的辐射模型对于电弧的温度影响不大。     

Performance Analysis of a Diagonal MHD Accelerator for Space Propulsion

The performance of a diagonal magnetohydrodynamic (MHD) accelerator has been numerically investigated. Studies were carried out using air plasma as a working gas in an equilibrium condition based on the MHD Augmented Propulsion Experiment channel designed by NASA. The MacCormack scheme is employed in order to solve the set of differential equations with MHD approximations. The fundamental performance of a diagonal MHD accelerator considering both flow performance along the channel and propulsion performance has been evaluated under various applied input currents and magnetic fields. The optimum performance is dominated by ${bf j} times {bf B}$ Lorentz body force acceleration, while it is increased with Joule heating and the ${bf u} times {bf B}$ term's contribution, which are detrimental to the propulsion performance. Moreover, friction forces resist the flow performance, particularly near the channel exit.      

Heat transfer in MHD flow in a rotating channel

An exact solution of the temperature profile in the MHD flow in a rotating straight channel is derived. It is found that the rate of heat transfer decreases with increasing the Hartmann numberM whenK is small, but at large values ofK it increases with increasingM.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

Slip effects on the peristaltic transport of MHD fluid with variable viscosity

This Letter concerns with the peristaltic analysis of MHD viscous fluid in a two-dimensional channel with variable viscosity under the effect of slip condition. A long wavelength and low Reynolds number assumption is used in the problem formulation. An exact solution is presented for the case of hydrodynamic fluid while for magnetohydrodynamic fluid a series solution is obtained in the small power of viscosity parameter. The salient features of pumping and trapping phenomena are discussed in detail through the numerical integration. It is noted that an increase in the slip parameter decreases the peristaltic pumping region. Moreover, the size of trapped bolus decreases by increasing the slip parameter.     

Design of Closed-Cycle MHD Generator with Nonequilibrium Ionization and System

A closed-cycle MHD generator topping a steam bottoming plant is analyzed. The combined power plant involves three working fluids in three loops. The MHD loop is investigated more thoroughly since it is the least conventional of the three. Equations are developed to determine the geometric and thermodynamic variables throughout the MHD channel for inlet conditions of mass flow, temperature, pressure, and velocity. Limiting design parameters are output power, channel length, channel aspect ratio, Hall parameter, and interaction parameter. The basic closed-cycle MHD loop working fluid can consist of either argon or helium seeded with cesium. Both non-equilibrium ionization produced by the elevation of the electron temperature from joule heating of the plasma and thermal ionization are considered. Equations used to calculate the electrical conductivity and the elevation of electron temperatures are derived. These equations are coupled with the one-dimentional differential equations applicable to an MHD generator. The chief interest is in determining those MHD channel conditions which result in the most thermodynamically efficient MHD-steam plantcombination. Thus an overall heat balance forthe system is required. Equations are developed to calculate the gas properties at the various stations of the closed loop and to determine the overall efficiency of the cycle. A rather flexible computer program written in Fortran is used to solve the MHD generator equations and to make the overall heat balance. Some typical results presented demonstrate the feasibility and adaptability of the analysis for optimizing the thermal efficiency and the sensitivity of thermal efficiency to various parameters.     

Numerical modelling of magnetogasdynamic processes in the pulsed setup duct

A computational model for processes in the duct of an experimental setup consisting of a shock tube and an MHD duct is presented. The one-dimensional model is used for determining the flow characteristics in the entire setup duct, and the three-dimensional model is used for studying the current layer dynamics in the MHD channel. Computations have enabled the elucidation of flow structure and of the peculiarities of current layer formation.     

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.     

Hall effects on steady hydromagnetic flow in a rotating channel in the presence of an inclined magnetic field

Effects of Hall current on a steady hydromagnetic (MHD) fully developed flow in a rotating environment within a parallel plate channel in the presence of an inclined magnetic field is studied. From an extension of literature [13] subject to a forced oscillation it is observed that the present paper is methodically more correct to work first in the steady state where forced oscillation becomes insignificant and then new results are expected for an unsteady MHD flow under the influence of a pulse-oscillator. Exact solutions of the governing equations are obtained in a closed form. The graphical representation for the velocity and the induced magnetic field are depicted graphically and the heat transfer at both the plates are presented in tables.     

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.     

Approximate solution of the flow over a nonlinear magneto-hydrodynamic stretching sheet

The approximate solution of the magneto-hydrodynamic(MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method.The approximate solution is tabulated,plotted for the values of various parameters and compared with the known solutions.It is found that the approximate solution agrees very well with the known numerical solutions,showing the reliability and validity of the present work.     

On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium

The effect of elasticity of the flexible walls on the MHD peristaltic flow of a Newtonian fluid in a two-dimensional porous channel with heat transfer has been studied under the assumptions of long-wavelength and low-Reynolds number. The analytical solution has been obtained for the stream function, temperature and heat transfer coefficient. The effect of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The numerical results show that the trapped bolus increases in size and more trapped bolus appears with increasing permeability parameter, elastic tension and mass characterizing parameters but decreases for large values of Hartmann number.     

Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet

The approximate solution of the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.