A Diffuse Interface Model and Semi-Implicit Energy Stable Finite Element Method for Two-Phase Magnetohydrodynamic Flows

A theoretical attempt is made to investigate the effect of Hall current on temperature distribution in MHD two-fluid flow of ionized gases (plasma) through horizontal channel bounded by two parallel plates under the action of an applied transverse magnetic field. It is assumed that the magnetic Reynolds number is small. The fluids in the two regions are considered to be incompressible, immiscible and electrically conducting with different viscosities, electrical and thermal conductivities. The transport properties of the two fluids are taken as constant. The governing momentum and energy equations for two-fluids that flow in two regions are detailed when the temperature of the two plates are prescribed to be the same. The solution is carried out in two cases, that is, (1) when the plates are made of the non-conducting and (2) conducting materials. The profiles for temperature distribution and rate of heat transfer coefficients are plotted for different set of values of the governing parameters. The effect of parameters on the temperature distribution and rate of heat transfer coefficient is discussed. It is observed in the case of non-conducting plates that the temperature distribution is independent of the ratio of electron pressure to the total pressure which relies on this parameter for conducting plates. It is seen in the case of conducting plates that an increase in Hall parameter diminishes the temperature distribution in the two regions for fixed values of the remaining parameters (i.e., Hartmann number, viscosity ratio, height ratio, electrical conductivity ratio and the ratio of thermal conductivities). It is expected that this theoretical study may have some practical application to numerous diversified areas like geophysical flows, aerospace science, in particular, aerodynamic heating and in engineering applications such as MHD generators, Hall accelerators, in thermo-nuclear power reactors and so forth.

MHD heat transfer two-ionized fluids flow between parallel plates with Hall currents

The unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel is considered. In addition to the classical no-slip and hyper-stick conditions at the boundary, it is assumed that the fluid velocities and shear stresses are continuous across the fluid-fluid interface. Three cases for the applied pressure gradient are considered to study the problem: one with constant pressure gradient and the other two cases with time-dependent pressure gradients, viz. periodic and decaying pressure gradient. The Crank-Nicolson approach has been used to obtain numerical solutions for fluid velocity and microrotation for diverse sets of fluid parameters. The nature of fluid velocities and microrotation with various values of pressure gradient, Reynolds number, ratio of viscosities, micropolarity parameter and time is illustrated through graphs. It has been observed that micropolarity parameter and ratio of viscosities reduce the fluid velocities.

A study on the unsteady flow of two immiscible micropolar and Newtonian fluids through a horizontal channel: A numerical approach

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Theoretical analyses of immiscible MHD pipe flow

The magnetohydrodynamic (MHD) flow of two immiscible and electrically conducting fluids between isothermal, insulated moving plates in the presence of an applied electric and inclined magnetic field has been investigated in the paper. The partial differential equations governing the flow and heat transfer are solved analytically with appropriate boundary conditions for each fluid and these solutions have been matched at the interface. The numerical results for various values of the Hartmann number, the angle of magnetic field inclination, load parameter and the ratio of electrical and thermal conductivities have been presented graphically. It was found that decrease of magnetic field inclination angle flattens out the velocity and temperature profiles. With the increase of the Hartmann number velocity gradients near the plate’s increases, temperature in the middle of the channel decreases and near the plate’s increases. Induced magnetic field is evidently suppressed with an increase of the Hartman number. The effect of changes of the load factor is to aid or oppose the flow as compared to the short-circuited case.

Stamenković M. Živojin

Papers

Mhd flow and heat transfer of two immiscible fluids between moving plates