Numerical Solution of the Navier-Stokes Equations for Unsteady Magnetohydrodynamic Flow Between Two Parallel Porous Plates

2007 ◽  
Author(s):  
S. Ganesh ◽  
S. Krishnambal
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Transverse Magnetic ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Electrically Conducting

The Unsteady Laminar flow of an electrically conducting viscous, incompressible fluid between two parallel porous plates of a channel in the presence of a transverse magnetic field when the fluid is being withdrawn through both the walls of the channel at the same rate is discussed. Numerical solution is obtained for different values of R (Suction Reynolds number) using R-K Gill’s method and the graphs of dimensionless functions f′ and f have been drawn.

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

2016 ◽  
Vol 9 (2) ◽  
pp. 239-261 ◽  
Author(s):  
X. He ◽  
C. Vuik
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Flat Plate ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Driven Cavity

AbstractIn this paper we explore the performance of the SIMPLER, augmented Lagrangian, ‘grad-div’ preconditioners and their new variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem the Reynolds number varies from a low to the limiting number for a laminar flow.

scholarly journals The Effect of Varying Magnetic Number, Reynolds Number and Pressure Gradient on Velocity Profiles in an MHD Flow

2020 ◽  
Vol 5 (7) ◽  
pp. 387-394
Author(s):  
LIHAVI ANNET ◽  
Dr. Virginia Kitetu ◽  
Dr. Mary wainaina
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Electrically Conducting

Magnetohydrodynamic ow of a hot viscous electrically conducting incompressible uid through parallel plates is studied. In the study, the e ect of Hartmann number (M), pressure gradient and Reynolds number (Re) on the velocity eld is investigated. The Navier-stokes equations were coupled with Ohms law and then solved using nite di erence method (FDM). The velocity eld was computed for various values of the physical parameters and shown graphically. It was found that as the Hartmann number M increases, the velocity pro les decreased due to increased Lorents force while an increase in Reynolds number causes an increase in the velocity of the uid. All these analysis was done using MATLAB program and the results were presented in tables and graphs.

On Oseen's approximation

1962 ◽  
Vol 13 (4) ◽  
pp. 557-569 ◽  
Author(s):  
W. Chester
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Stokes Equations ◽  
Absolute Magnitude ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Order ◽  
Hydrodynamic Effects

An investigation is made into the validity of the Oseen equations, for incom-pressible, viscous flow past a body, as an approximation to the Navier-Stokes equations. It is shown that, when the body is such that a reversal of the uniform flow at infinity merely reverses any component of the force on the body without changing its absolute magnitude, that component can be determined correctly to the first order in the Reynolds number, though the detailed velocity field is not correct to this order. Moreover, this force can be deduced simply from a knowledge of the force on the body according to Stokes's approximation.The analysis is also generalized to include the magneto-hydrodynamic effects when the fluid is conducting and the flow takes place in the presence of a magnetic field.

Coupled magneto-buoyant convection and radiation in an inclined enclosure

2013 ◽  
Vol 24 (1) ◽  
pp. 237-264 ◽  
Author(s):  
Sofen K. Jena ◽  
Swarup K. Mahapatra ◽  
Amitava Sarkar
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Participating Media ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Electrically Conducting ◽  
Inclined Enclosure ◽  
Realistic Problem

Purpose – The current study aims to address the interaction between participating media radiation with thermo-gravitational convection of an electrically conducting fluid enclosed within a tilted enclosure under an externally imposed time-independent uniform magnetic field. Design/methodology/approach – The differentially heated boundaries of the tilted enclosure are considered to be diffuse, gray and the enclosed fluid is assumed to be absorbing, emitting and isotropically scattering. The Navier-Stokes equations, meant for magneto convection are solved using modified MAC method. Gradient dependent consistent hybrid upwind scheme of second order is used for discretization of the convective terms. Discrete ordinate method, with S8 approximation, is used to model radiative transport equation in the presence of radiatively active medium. Findings – Effect of uniform magnetic field with different magnitudes and orientations of cavity has been numerically simulated. The effect of participating media radiation has been investigated for different optical thicknesses, emissivities, scattering albedos and Planks number. The results are provided in both graphical and tabular forms. The flow lines, isotherms bring clarity in the understanding of flow behaviour and heat transfer characteristics. Originality/value – Despite the idealized nature, the present study is quite essential to understand the cumbersome physics of realistic problem.

scholarly journals MHD Flow of an Incompressible Viscous Fluid through Convergent or Divergent Channels in Presence of a High Magnetic Field

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Reza Hosseini ◽  
Sadegh Poozesh ◽  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Homogeneous Magnetic Field ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Electrically Conducting ◽  
Non Linear

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM). The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme). The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.

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