UNSTEADY MHD COUETTE FLOW BETWEEN TWO PARALLEL HORIZONTAL POROUS PLATES IN AN INCLINED MAGNETIC FIELD

In this paper, the study of unsteady Magnetohydrodynamic (MHD) couette flow between two parallel horizontal porous plates in an inclined magnetic field was carried out. The momentum and energy equations are written in a dimensionless form using the  imensionless parameters. Variable separable technique was employed to solve the velocity profile and temperature distribution. However, out of many results, we conclude that, at high Hartmann number Ha, the velocity u of the fluid decreases. When the magnetic field is high, it reduces the energy loss through the plates

Hall Current and Radiation Effects on Unsteady Natural Convection MHD flow with Inclined Magnetic field

In the present paper, Hall current and radiation effects on unsteady natural convection MHD flow with inclined magnetic field is studied. The viscous, incompressible and an electrically conducting fluid is considered. This model contains equations of motion, equation of energy and diffusion equation. The system of partial differential equations is transformed to dimensionless equations by using dimensionless variables. Exact solution of governing equations is obtained by Laplace Transform Technique. For analysing the solution of the model, desirable sets of the values of the parameters have been considered. The obtained results of velocity, concentration and temperature have been analysed with the help of graphs drawn for different parameters. The numerical values of Nusselt number have been tabulated. The results of the study may find applications in the field related to the solar physics dealing with the solar cycle, Magnetohydrodynamics sensors, rotating MHD induction machine energy generator, the sunspot development, the structure of rotating magnetic stars etc

Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field the hydrodynamically stable flow can demonstrate non - axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, $\rm Pm=1$. At a fixed $\rm Pm\ne 1$ the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity-time (PT) symmetric.Comment: 34 pages, 8 figures, typos corrected, refs adde

Effect of chemical reaction in a third grade fluid in porous medium analyzed by unsteady magnetohydrodynamic couette

An analysis was carried out on unsteady magnetohydrodynamic (MHD) Couette third grade fluid in a porous medium in the presence of chemical reaction parameter. The Darcy’s law and Fick’s law of diffusion were introduced to stimulate the porosity and chemical reaction in the problem. The resulting flow problem was investigated and model of the problem in form of partial differential equations were obtained. He-Laplace method was used to obtain the solution of the equations and expressions for the velocity field, temperature and concentration distribution were given for each case. Graphical results for various interesting parameters were analyzed and presented.Keywords: Plane Couette; Magnetohydrodynamic; Porous Medium; Chemical Reaction Paramete

Effect of Radiation Absorption and Chemical Reaction on Transient Hydromagnetic Convective Heat and Mass Transfer Flow in a Rotating Porous Medium with Heat Sources

In this paper, we discussed the effect of radiation absorption and chemical reaction on transient hydromagnetic convective heat and mass transfer flow in a rotating porous medium with heat sources, when the temperature of the surface varies with time about a non-zero constant mean and the temperature at the free stream is constant. The non-linear coupled equations have been solved by perturbation technique. The velocity, temperature, concentration, skin friction, rate of heat and mass transfer have been discussed for different variations of the governing parameters G, R, γ, Q1, α and Pr. Keywords: Radiation Absorption, Chemical Reaction, Rotating Porous Medium, Heat Sources

Radiation Absorption and Chemical Reaction Effects on Unsteady Magneto hydrodynamic Convective Heat and Mass Transfer Flow in a Rotating System With Hall Effects

The objective of the present paper is to analyze the effects of permeability variation, mass transfer and chemical reaction on flow of a viscous incompressible fluid past an infinite vertical porous surface in a rotating system, when the temperature of the surface varies with time about a non-zero constant mean and the temperature at the free stream is constant . Keywords: Chemical   Reaction, Radiation  Absorption, Heat and mass transfer, Hall effect

(R1501) Rotational and Hall Current Effects on a Free Convection MHD Flow with Radiation and Inclined Magnetic Field

Rotational and Hall current effects on a free convection MHD flow with Radiation and inclined magnetic field are studied here. Electrically conducting, viscous, and incompressible fluid is taken. The flow is modelled with the help of partial differential equations. The analytical solutions for the velocity, concentration, and temperature are solved by the Laplace integral transform method. The outcomes acquired have been examined with the help of graphs drawn for different parameters like Hartmann number, Hall current parameter, inclination of magnetic field, angular velocity and radiation parameter, etc. The variation of the Nusselt number has been shown graphically. It is observed that Hall current parameter and inclination of magnetic field reduces the resistive effect of the applied external magnetic field. Such a study assumes importance because both rotation and Hall current induce secondary flow in the flow-field. The conclusion of the study may be useful in the field of solar physics, rotating magnetic stars, rotating MHD induction machine energy generator and many industrial applications

Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow

In this paper we present axisymmetric nonlinear simulations of magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momemtum profile and with a magnetic Reynolds number below the threshold of magnetorotational instability. The magnetic field is found to inhibit the Ekman suction. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly-rotating region forms near the outer cylinder. A strong magnetic field leads to a steady Stewartson layer emanating from the junction between differentially rotating rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds number and penetrates deeper into the bulk flow with stronger magnetic field and larger Reynolds number. However, at Reynolds number larger than a critical value $\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilities occur and result in a less prominent Stewartson layer that extends less far from the boundary.Comment: 24 pages, 12 figures, accepted by PRE, revision according to referee

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings