Simulation of Natural Convection Flow with Magneto-Hydrodynamics in a Wavy Top Enclosure with a Semi-Circular Heater

Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.

三维Magneto-Hydrodynamics方程关于压强的正则准则

通过Navier-Stokes方程以及利用光滑解的先验估计方法,来探讨三维MHD方程的压强在Besov空间B·r!,!(R3)中的弱解正则准则.证明了当压强π(t)满足:π(t)∈L22+r(0,T;B·r!,!(R3)),-1≤r≤1此条件时,则三维MHD方程的一组弱解(v(x,t),b(x,t))在(0,T]上是正则解.

Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation

We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.

Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics （TMHD）, which explicitly reflects the anisotropy of a high temperature tokamak plasma. The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in tokamaks. Free from the Courant restriction on the time step, this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model. At the same time, TMHD requires the use of magnetic field aligned numerical grids. Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented. For the 3-dimensional case of an ergodic magnetic field, this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.

LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS

This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] （Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365： 806-808） and [18] （Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375：799 802）.

WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES

This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic(GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data(u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FN^1-2α+3/p'+λ/pp,λ,q(R^3) Moreover, stability of global solutions is also discussed.

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.

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD fows

The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional derivative concept,while the model is solved via the full-spectral method(FSM)and the semi-spectral scheme(SSS).The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques.The SSS is developed by discretizing the time variable,and the space domain is collocated by using equal points.A detailed comparative analysis is made through graphs for various parameters and tables with existing literature.The contour graphs are made to show the behaviors of the velocity and magnetic fields.The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows,and the concept may be extended for variable order models arising in MHD flows.

Quasi-static magnetic compression of field-reversed configuration plasma:amended scalings and limits from two-dimensional MHD equilibrium

In this work,several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC)plasma(Spencer et al 1983 Phys.Fluids 261564)are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ.Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall,the empirically stable limits for the compression ratio,the fusion gain,and the neutron yield are evaluated,which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.

Stability impacts from the current and pressure profile modifications within finite sized island

The stability(or instability)of finite sized magnetic island could play a significant role in disruption avoidance or disruption mitigation dynamics.Especially,various current and pressure profile modifications,such as the current drive and heating caused by electron cyclotron wave,or the radiative cooling and current expulsion caused by the shattered pellet injection could be applied within the island to modify its stability,thus changing the ensuing dynamics.In this study,we calculate the mode structure modification caused by such profile changes within the island using the perturbed equilibrium approach,thus obtain the change of stability criterion Δ′ and assess the corresponding quasi-linear island stability.The positive helical current perturbation is found to always stabilize the island,while the negative one is found to do the opposite,in agreement with previous results.The pressure bump or hole within the island has a more complicated stability impact.In the small island regime,its contribution is monotonic,with pressure bump that tends to stabilize the island while pressure hole destabilizes it.This effect is relatively weak,though,due to the cancellation of the pressure term’s odd parity contribution in the second derivatives of the mode structure.In the large island regime,such cancellation is broken due to the island asymmetry,and the pressure contribution to stability is manifested,which is non-monotonic.The stability analysis in this paper helps to more accurately clarify the expected island response in the presence of profile modifications caused by disruption avoidance or mitigation systems.

Superposability in Hydrodynamic and MHD Flow

In this paper, phenomena of superposability and self superposability in hydrodynamics and magneto hydrodynamics have been discussed. One of the most important applications of superposability in hydrodynamics is the construction of exact analytic solution of the basic equation of fluid dynamics. Kapur and Bhatia have given a simple idea that if two velocity vectors have self superposable and mutually superposable motion then sum or difference of these two is self superposable and vice versa and if each of the vector is superposable on the third then their sum and difference are also superposable on the third. For superposability in magneto-hydrodynamics many mathematicians like Ram Moorthy, Ram Ballabh, Mittal, Kapur & Bhatia and Gold & Krazyblocki have defined it in various ways, especially Kapur & Bhatia generalized the well-known work on superposability by Ram Ballabh to the case of viscous incompressible electrically conducting fluids in the presence of magnetic field. We found the relationship of two basic vectors for two important curvilinear coordinate systems for their use in our work. We’ve found the equations of div, curl and grad for a unit vector in parabolic cylinder coordinates and ellipsoidal coordinates for further use.

Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet

In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method （HAM） for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer＇s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.

Project New Orion: Pulsed Nuclear Space Propulsion Using Photofission Activated by Ultra-Intense Laser

Project New Orion entails a pulsed nuclear space propulsion system that utilizes photofission through the implementation of an ultra-intense laser. The historical origins derive from the endeavors of Project Orion, which utilized thermonuclear devices to impart a considerable velocity increment on the respective spacecraft. The shear magnitude of Project Orion significantly detracts from the likelihood of progressive research development testing and evaluation. Project New Orion incorporates a more feasible pathway for the progressive research development testing and evaluation of the pulsed nuclear space propulsion system. Photofission through the application of an ultra-intense laser enables a much more controllable and scalable nuclear yield. The energy source for the ultra-intense laser is derived from a first stage liquid hydrogen and liquid oxygen chemical propulsion system. A portion of the thermal/kinetic energy of the rocket propulsive fluid is converted to electrical energy through a magneto-hydrodynamic generator with cryogenic propellant densification for facilitating the integral superconducting magnets. Fundamental analysis of Project New Orion demonstrates the capacity to impart a meaningful velocity increment through ultra-intense laser derived photofission on a small spacecraft.

Effect of vibrating electrode on temperature profiles,fluid flow,and pool shape in ESR system based on a comprehensive coupled model

The vibrating electrode method was proposed in the electro-slag remelting(ESR) process in this paper,and the effect of vibrating electrode on the solidification structure of ingot was studied.A transient threedimensional(3D) coupled mathematical model was established to simulate the electromagnetic phenomenon,fluid flow as well as pool shape in the ESR process with the vibrating electrode.The finite element volume method is developed to solve the electromagnetic field using ANSYS mechanical APDL software.Moreover,the electromagnetic force and Joule heating are interpolated as the source term of the momentum and energy equations.The multi-physical fields have been investigated and compared between the traditional electrode and the vibrating electrode in the ESR process.The results show that the drop process of metal droplets with the traditional electrode is scattered randomly.However,the drop process of metal droplets with the vibrating electrode is periodic.The highest temperature of slag layer with the vibrating electrode is higher than that with the traditional electrode,which can increase the melting rate due to the enhanced heat transfer in the vicinity of the electrode tip.The results also show that when the amplitude and frequency of the vibrating electrode increase,the cycle of drop process of metal droplets decreases significantly.

Effects of background pressure on the arc characteristics of gas spark gap

Gas spark gap is widely used in any pulsed power system as the key element which directly determines its repetitive performance and output characteristics. Among many factors of threeelectrode gas spark gap, background pressure is of much importance in determining the gap performance parameters such as the delay and jitter, and relevant studies have been rarely performed. A magneto-hydrodynamic model of the arc in gas spark gap is built and the effects of background pressure on the arc characteristics are discussed in this paper. It is demonstrated that a higher background pressure may result in radial compression of the arc column, a higher arc voltage, and a lower declination rate of arc resistance in the first quarter cycle. Relevant simulation data would be helpful for the optimization of the design of gas spark gap.

Theoretical Investigation of Two-Dimensional Nonlinear Radiative Thermionics in Nano-MHD for Solar Insolation:A Semi-Empirical Approach

In this contemporary study,theoritical investigation of nanofluidic model is thought-out.Two-dimensional nanomaterials based mixed flow is considered here.Convective solar radiative heat transport properties have been investigated over a nonlinearly stretched wall in the presence of magneto-hydrodynamic(MHD),by innovative application of semi analytical“optimal homotopy asymptotic method(OHAM)”.OHAM does not require any discretization,linearization and small parameter assumption.OHAM describes extremely precise 1^(st)/2^(nd) order solutions without the need of computing further higher order terms,therefore,fast convergence is observed.Nanofluidic governing model is transformed into system of ordinary differential equations(ODEs)by exploitation of similarity transformation.To study the significance of radiation parameter alongwith thermophoresis parameter,a semi analytical solver is applied to the transformed system.In this work,Brownianmotion,influence ofmagnetic field,Lewis number,Prandtl number,Eckert number and Biot number have investigated on velocity,temperature and nanoparticle concentration profiles.The study provides sufficient number of graphical representations to demonstrate the inspiration of mentioned parameters.

Impact of Magnetic Field on a Peristaltic Flow with Heat Transfer of a Fractional Maxwell Fluid in a Tube

Magnetic field and the fractional Maxwell fluids’impacts on peristaltic flows within a circular cylinder tube with heat transfer was evaluated while assuming that they are preset with a low-Reynolds number and a long wavelength.Utilizing,the fractional calculus method,the problem was solved analytically.It was deduced for temperature,axial velocity,tangential stress,and heat transfer coefficient.Many emerging parameters and their effects on the aspects of the flow were illustrated,and the outcomes were expressed via graphs.A special focus was dedicated to some criteria,such as the wave amplitude’s effect,Hartman and Grashof numbers,radius and relaxation–retardation ratios,and heat source,which were under discussions on the axial velocity,tangential stress,heat transfer,and temperature coefficients across one wavelength.Multiple graphs of physical interest were provided.The outcomes state that the effect of the criteria mentioned beforehand(the Hartman and Grashof numbers,wave amplitude,radius ratio,heat source,and relaxation–retardation ratio)were quite evident.

Non-Newtonian Power-Law Fluid Flow and Heat Transfer over a Non-Linearly Stretching Surface

The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

Viscous and Joules Dissipation on MHD Flow past a Stretching Porous Surface Embedded in a Porous Medium

This paper investigates the influence of both viscous and joules dissipation on the problem of magneto-hydrodynamic flow past a stretching porous surface embedded in a porous medium for rotating case. Using similarity approach the system of partial differential equations is transformed into ordinary differential equations which strongly depend on the magnetic parameter, stretching parameter, rotation parameter, permeability parameter and Prandtl number. The coupled differential equations are numerically simulated using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration schemes. The velocity and temperature profiles are discussed and presented graphically. The comparisons for dimensionless skin friction coefficient and local Nusselt number are also taken into account and discussed and presented graphically.

Approximate Methods for the Calculation of Plasma Internal Inductance for Circular Cross Section Tokamak

Calculation of Plasma internal inductance (li) is essential in Tokamak plasma research. Much more plasma parameters such as the plasma current density profile, magnetohydrodynamics instability, and plasma energy confinement time can be determined by using this parameter. Discrete poloidal magnetic probes along with the diamagnetic loop can be utilized in measurement of the Plasma internal inductance (li). In this paper Plasma internal inductance (li) is studied by theoretical and experimental approach for HT-7 Tokamak plasmas. The results of two methods are in good agreement with each other.