A two-dimensional nonlinear incompressible magneto-hydrodynamics (MHD) code is presented to solve steady state or transient charged or neutral convection problems. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by a relaxation scheme as pseudo-iterations between the real time levels. The numerical method takes the advantage of a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta algorithm. It is shown that the code developed here can be accurately used for the solutions of incompressible Navier Stokes or MHD equations.

In this article, a laminar MAGNETOHYDRODYNAMICS (MHD) developing flow of an incompressible electrically conducting fluid subjected to an external magnetic field is considered. The aim of the study is to propose a correlation for computing the development length of the laminar MHD developing flow in a pipe. A numerical approach is considered to solve the problem. In the first step, the numerical Finite Volume Method (FVM) is conducted to analyze the problem. Hereafter, the artificial neural network (ANN) is used to develop the datasets and in the last step, the curve fitting is applied to find a correlation for the prediction of the development length as a function of the Reynolds and Hartmann numbers. In addition, the effect of the problem parameters on the development length is studied. It is found that the development length declines with the increase of the Hartmann number and grows with the rising of the Reynolds number.

We have developed a mathematical model for capillary rise of magnetohydrodynamic fluids. The liquid starts to imbibe because of capillary suction in an undeformed and initially dry sponge-like porous material. The driving force in our model is a pressure gradient across the evolving porous material that induces a stress gradient which in turn causes deformation that is characterized by a variable solid fraction. The problem is formulated as a non-linear moving boundary problem which we solve using the method of lines approach after transforming to a fixed computational domain. The summary of our finding includes a notable reduction in capillary rise and a decrease in solid deformation due to magnetic effects.

The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra), melting parameter (M) and Hartmann number (Ha) are graphically illustrated. As melting parameter and Rayleigh number increase, the rate of fluid flow and temperature gradients also increase. And in the presence of magnetic field, the temperature gradient reduces and hence, the conduction mechanism is dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameter in the both cases of heating of bottom wall.

A harmonically-driven, incompressible, electrically conducting, and viscous liquid metal magnetohydrodynamic flow through a thin walled duct of rectangular cross section interacting with a uniform magnetic field traverse to its motion direction is numerically investigated. Chebyshev spectral collocation method is used to solve the Navier-Stokes equation under the inductionless approximation for the magnetic field in the gradient formulation for the electric field. Flow is considered fully developed in the direction perpendicular to the applied magnetic field and laminar in regime. Validation of numerical calculations respect to analytical calculations is established. Flow structure and key magnetohydrodynamic features regarding eventual alternating power generation application in a rectangular channel liquid metal magnetohydrodynamic generator setup are numerically inquired. Influence of pertinent parameters such as Hartmann number, oscillatory interaction parameter and wall conductance ratio on magnetohydrodynamic flow characteristics is illustrated. Particularly, it is found that in the side layer and its vicinity the emerging flow structures/patterns depend mainly on the Hartmann number and oscillatory interaction parameter ratio, while the situation for the Hartmann layer and its vicinity is less eventful. A similar feature has been discussed in the literature for the steady liquid metal flow case and served as rationale for developing the composite core-side-layer approximation to study the MAGNETOHYDRODYNAMICS of liquid metal flows usable in direct power generation. In this study that approximation is not considered and the analysis is performed on liquid metal oscillatory (i., e., unsteady) flows usable in alternating power generation. Conversely, in terms of prospective practical applicability the formulation developed and tested with these calculations admits the implementation of a load resistance and walls conductivity optimization. That means that besides representing a numerical study on the MAGNETOHYDRODYNAMICS of the oscillatory flow under consideration, absent in the literature for the parametric ranges reported, the formulation presently implemented can also be applicable to study the performance of an alternating liquid metal magnetohydrodynamic generator in the rectangular channel configuration.

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.

This paper focuses on using the numerical finite volume method (FVM) and artificial neural network (ANN) in order to propose a correlation for computing the entrance length of laminar MAGNETOHYDRODYNAMICS (MHD) channels flow. In the first step, for different values of the Reynolds (Re) and Hartmann (Ha) numbers (600

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into other sets of variables in a way that infinite boundary condition becomes a finite boundary condition. The effects of physical parameters affecting the velocity and temperature are shown. The results show that with increasing the magnetic and suction parameters, the normal velocity component of fluid increases over the sheet whereas the tangential velocity component of fluid decreases. Moreover, when the suction parameter, the Prandtl and Eckert numbers increase, the rate of the heat transfer increases. However, when the magnetic parameter increases, the rate of heat transfer reduces. Finally, the solution shows that the results of the analytical method using a special technique have an excellent agreement with numerical solutions.

This article attempts to evaluate the impact of MAGNETOHYDRODYNAMICS and ferrohydrodynamics on the free convection of a magnetic nanofluid in a square porous cavity. The published literature shows that the magnetic nanofluid convection problems have been mostly simulated by the single-phase model. In the present work, a two-phase model is used to consider the effects of Brownian diffusion, thermophoresis, and magnetophoresis of particles. The Darcy-Brinkman formulation is employed to treat mass, momentum, and energy transport phenomena in the porous medium. The governing equations are solved numerically by the finite volume technique. Numerical computations are performed for various Rayleigh numbers ( and ), Hartmann numbers ( ), magnetic numbers ( ), and porosity ratio of  and 0.9. The current results are validated via comparison with existing experimental or numerical results in the literature. Impacts of MAGNETOHYDRODYNAMICS, ferrohydrodynamics, and ferrohydrodynamics/MAGNETOHYDRODYNAMICS on the flow field and heat transfer rate are discussed separately in detail by contour plots of streamlines, isotherms, and distribution profiles of nanoparticles. Numerical results indicate that at  heat is mainly transferred by conduction and its rate is unaffected by porosity, magnetic, or Hartmann numbers. However, at  and  the average Nusselt number decreases by increasing magnetic and Hartmann numbers.