The stability of stratified conducting shear flow in an aligned magnetic field

The stability of a horizontally stratified, electrically conducting fluid permeated by a uniform magnetic field aligned with the motion is investigated. The resulting linear stability problem for the special case of constant density gradient and linear shear in an unbounded fluid is reduced to the study of a third order differential equation in time. In the absence of dissipation, the linear shear eventually causes hybrid Alfvén-gravity waves to decay algebraically. The effect of the shear is to shorten the vertical length scale. So with the addition of even small diffusivity, dissipation is strongly stabilising and all modes eventually collapse exponentially, generally at a fast rate. The evolution from wave motion to exponential decay is examined for particular limiting cases. When the fluid is bounded by horizontal planes a nonlinear stability criterion is derived using the energy method

Numerical Investigation of Combined Buoyancy and Surface Tension Driven Convection in an Axi-Symmetric Cylindrical Annulus

A numerical study is conducted to understand the effect of surface tension on buoyancy driven convection in a vertical cylindrical annular cavity filled with a low Prandtl number fluid. The inner and outer cylinders are maintained at different uniform temperatures and the horizontal top and bottom walls are thermally insulated. The upper free surface is assumed to remain flat and non-deformable. A finite difference scheme consisting of the Alternating Direction Implicit method and the Successive Line Over Relaxation method is used to solve the vorticity stream function formulation of the problem. Detailed numerical results of heat transfer rate, temperature and velocity fields have been presented for a wide range of physical parameters of the problem. The flow pattern and temperature distribution in the annular cavity are presented by means of contour plots of streamlines and isotherms. The rate of heat transfer is estimated by evaluating the average Nusselt number. Further, the present numerical results are compared with the existing results and are found to be in good agreement

Propagation of internal gravity waves in perfectly conducting fluids with shear flow, rotation and transverse magnetic field

The propagation of internal Alfven-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolisforce is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency ad = 0, rt: SZ,, or & Q rf: ( SZ2 + a:)*, where QA is the Alfvhn frequency and SZ is the Coriolis frequency,and the angular momentum is transferred to the mean flow there by Alfvhn-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydromagnetic flows

Study of propagation of linear and non-linear Alfvén-gravity waves in rotating medium

Travelling waves in an incompressible, infinitely conducting, inviscid fluid of variable density are investigated under the influence of a horizontal magnetic field and Coriolis force. Periodic solutions are found in the limit of infinite vertical wave length. Phase diagrams are drawn to show the solution. © 2011 Elsevier Ltd

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms. Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number. (c) 2010 Elsevier Inc. All rights reserved

Combined surface tension and buoyancy-driven convection in a rectangular open cavity in the presence of a magnetic field

A numerical study is conducted to understand the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054). The two side walls are maintained at uniform but different temperatures θh and θc (θh > θc), while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of the ADI (Alternating Direction Implicit) method, which incorporates upwind differencing for non-linear convective terms and the SLOR (Successive Line Over Relaxation) method are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Grashof number Gr ranging from 2 à 104 to 2 à 106, Marangoni number Ma from 0 to 105 and Hartmann number Ha from 0 to 100. The detailed flow structure and the associated heat transfer characteristics inside the cavity are presented. At large Ma, two counter-rotating cells are formed at the upper half and lower half of the enclosure. As Ha increases, the temperature field resembles that of a conduction type and the streamlines are elongated in nature in the horizontal direction. The upper cell is crowded and stretched along the free surface. The average Nusselt number increases with Ma but decreases with Ha. © 1995

An Analysis of Internal Gravity Wave Tunnelling in a Stratified Region Along with Rotation

The internal gravity wave tunnelling in presence of earths rotation is studied for different density barriers. An exponential approximation used reveals the existence of evanescence in the barrier region which signifies the trapping of wave energy in the tunnelling region. The Transmission coefficients are computed for different density barriers and the comparative study shows that across the locally mixed region the transmission is enhanced. The asymptotic analysis of the transmission co-efficient using the rotational parameter reveals the convergence and the graphs shows that the transmission decreases continuously and leads to the non-rotating case. The results are compared with the non-rotations case and we observe that the evanescence caused by the rotation makes the waves travel more along the horizontal direction than in the vertical direction

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameter N and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid for N < 1 and several features of the effect of large values of N are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow