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The analysis of squeeze‐film performances between curved annular plates with an electrically conducting fluid in the presence of a transverse magnetic field is presented in this study. The magneto‐hydrodynamic (MHD) Reynolds‐type equation for squeezing‐film curved annular disks is derived using the continuity equation and the MHD motion equations. A closed‐form solution for the squeezing film pressure is obtained, and applied to predict the MHD squeeze‐film characteristics. According to the results obtained, the presence of applied magnetic fields signifies an increase in the MHD squeeze‐film pressure. Compared with the classical non‐conducting‐lubricant case, the magnetic‐field effect characterized by the Hartmann number provides an enhancement to the MHD load‐carrying capacity and the response time, especially for larger values of the curved shape parameter or smaller values of inner‐outer radius ratio of the curved annular disks.

The purpose of this article is to analyse the effects of surface roughness on the magneto-hydrodynamic (MHD) squeeze-film characteristics between a sphere and a porous plane surface, which have not been studied so far.

The analytical model takes into account the effect of porosity by assuming that the flow in the porous matrix obeys modified Darcy's law. The stochastic MHD Reynold's type equation is derived by using the Christensen's stochastic method developed for hydrodynamic lubrication of rough surfaces. Two types of one-dimensional surface roughness (radial and azimuthal) patterns are considered.

The expressions for the mean MHD squeeze-film pressure and mean load-carrying capacity are obtained numerically. The results are shown graphically for selected representative parametric values. It is found that the response time increases significantly for the MHD case as compared to the corresponding non-conducting lubricants. The effect of roughness parameter is to increase/decrease the load-carrying capacity and the response time for azimuthal/radial roughness patterns as compared to the smooth case. Also, the effect of porous parameter is to decrease the load-carrying capacity and response time as compared to the solid case.

In this paper, an attempt has been made to analyse the combined effects of surface roughness and permeability on the MHD squeeze-film characteristics between a sphere and a plane surface.

The purpose of this paper is to consider magnetohydrodynamic (MHD) squeeze film characteristics between finite porous parallel rectangular plates with surface roughness.

Based upon the MHD theory, this paper analyzes the surface roughness effect squeeze film characteristics between finite porous parallel rectangular plates lubricated with an electrically conducting fluid in the presence of a transverse magnetic field.

It is found that the magnetic field effects characterized by the Hartmann number produce an increased value of the load carrying capacity and the response time as compared to the classical Newtonian lubricant case. The modified averaged stochastic Reynolds equation governing the squeeze film pressure is derived.

The present study has considered both Newtonian fluids and non-Newtonian liquids.

The work represents a very useful source of information for researchers on the subject of MHD squeeze film with finite porous parallel rectangular plates lubricated with an electrically conducting fluid.

This paper is relatively original and illustrates the squeeze film characteristics between finite porous parallel rectangular plates with MHD effects.

Magneto hydrodynamic (MHD) flows in fluids is known to have an important effect on heat transfer and fluid flow in various substances while the quality of the substances and the considered shapes can influence the amount of changes. Thus, MHD flows in a different form and widespread alterations in the kind of the material and the power of MHD flow were carried out by lattice Boltzmann method (LBM) in this investigation. The aim of this paper is to identify the ability of LBM for solving MHD flows as the effect of different substances in the presence of the magnetic field changes.

This method was utilized for solving MHD natural convection in an open cavity while Hartmann number varies from 0 to 150 and Rayleigh number is considered at values of Ra=10³, 10⁴ and 10⁵, with the Prandtl number altering in a wide range of Pr=0.025, 0.71 and 6.2. An appropriate validation with previous numerical investigations demonstrated that this attitude is a suitable method for MHD problems.

Results show the alterations of Prandtl numbers influence the isotherms and the streamlines widely at different Rayleigh and Hartmann numbers simultaneously. Moreover, heat transfer declines with the increment of Hartmann number, while this reduction is marginal for Ra=10³ by comparison with other Rayleigh numbers. The effect of the magnetic field on the average Nusselt number at Liquid Gallium (Pr=0.025) is the least among considered materials.

In this method, just the force term at LBM changes in the presence of MHD flow as the added term rises from the classic equations of fluids mechanic. Moreover, all parameters of the added term and the method of their computing are exhibited.

This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.

The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.

The method is computationally very attractive and gives very accurate results.

Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field.

The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials.

The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems.

In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally.

Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions.

This work was supported by the NSF of China (No. 11971152).

This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD) equations. The Euler semi-implicit scheme is used for time discretization and (P _1b , P ₁, P ₁) finite element for velocity, pressure and magnet is used for the spatial discretization.

Several numerical experiments are provided to show this scheme is unconditional stability and unconditional L2−H2 convergence with the L2−H2 optimal error rates for solving the non-stationary MHD flows.

In this paper, the authors mainly focus on the numerical investigation of the Euler semi-implicit scheme for MHD flows. First, the unconditional stability and the L2−H2 unconditional convergence with optimal L2−H2 error rates of this scheme are validated through our numerical tests. Some interesting phenomenons are presented.

The Euler semi-implicit scheme is used to simulate a practical physics model problem to investigate the interaction of fluid and induced magnetic field. Some interesting phenomenons are presented.

The effect of a transverse magnetic field on the squeeze film behaviors between two parallel annular disks lubricated within an electrically conducting fluid is studied. The modified Reynolds equation governing the squeeze film pressure is derived by using the continuity equation and the magneto‐hydrodynamic (MHD) motion equations. According to the results obtained, the influence of magnetic fields signifies an enhancement in the squeeze film pressure. On the whole, the magnetic field effect characterized by the Hartmann number provides an increase in value of the load‐carrying capacity and the response time as compared to the classical non‐conducting lubricant case. It improves the MHD squeeze film characteristics of the system.

The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.

The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface.

The present results are original and new for the MHD flow near the stagnation‐point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.