Creeping axisymmetric MHD flow about a sphere translating parallel with a uniform ambient magnetic field

2017 ◽  
Vol 53 (1) ◽  
pp. 5-14
Author(s):  
A. Sellier ◽  
S. H. Aydin
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tarek N. Abdelhameed

AbstractThis article examines the entropy generation in the magnetohydrodynamics (MHD) flow of Newtonian fluid (water) under the effect of applied magnetic in the absence of an induced magnetic field. More precisely, the flow of water is considered past an accelerated plate such that the fluid is receiving constant heating from the initial plate. The fluid disturbance away from the plate is negligible, therefore, the domain of flow is considered as semi-infinite. The flow and heat transfer problem is considered in terms of differential equations with physical conditions and then the corresponding equations for entropy generation and Bejan number are developed. The problem is solved for exact solutions using the Laplace transform and finite difference methods. Results are displayed in graphs and tables and discussed for embedded flow parameters. Results showed that the magnetic field has a strong influence on water flow, entropy generation, and Bejan number.


2021 ◽  
Vol 33 (7) ◽  
pp. 076602
Author(s):  
Guo-Liang Peng ◽  
Jun-Jie Zhang ◽  
Jian-Nan Chen ◽  
Tai-Jiao Du ◽  
Hai-Yan Xie

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.


2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.


1987 ◽  
Vol 5 (2) ◽  
pp. 233-255 ◽  
Author(s):  
Nagendra Singh ◽  
H. Thiemann ◽  
R. W. Schunk

Various mechanisms for driving double layers in plasmas are briefly described, including applied potential drops, currents, contact potentials, and plasma expansions. Some dynamic features of the double layers are discussed. These features, as seen in simulations, laboratory experiments and theory, indicate that double layers and the currents through them undergo slow oscillations, which are determined by the ion transit time across an effective length of the system in which the double layers form. It is shown that a localized potential dip forms at the low potential end of a double layer, which interrupts the electron current through it according to the Langmuir criterion, whenever the ion flux into the double is disrupted. The generation of electric fields perpendicular to the ambient magnetic field by contact potentials is also discussed. Two different situations have been considered; in one, a low-density hot plasma is sandwiched between high-density cold plasmas, while in the other a high-density current sheet permeates a low-density background plasma. Perpendicular electric fields develop near the contact surfaces. In the case of the current sheet, the creation of parallel electric fields and the formation of double layers are also discussed when the current sheet thickness is varied. Finally, the generation of electric fields (parallel to an ambient magnetic field) and double layers in an expanding plasma are discussed.


Author(s):  
D. R. V. Prasada Rao ◽  
D. V. Krishna ◽  
Lokenath Debnath

This paper gives a steady linear theory of the combined effect of the free and forced convection in rotating hydromagnetic viscous fluid flows in a porous channel under the action of a uniform magnetic field. The flow is governed by the Grashof numberG, the Hartmann numberH, the Ekman numberE, and the suction Reynolds numberS. The solutions for the velocity field, temperature distribution, magnetic field, mass rate of flow and the shear stresses on the channel boundaries are obtained using a perturbation method with the small parameterS. The nature of the associated boundary layers is investigated for various values of the governing flow parameters. The velocity, the temperature, and the shear stresses are discussed numerically by drawing profiles with reference to the variations in the flow parameters.


Sign in / Sign up

Export Citation Format

Share Document