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.

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.

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.

Analysis of Magnetohydrodynamic Flow in Annular Duct

2004 ◽  
Author(s):  
Geun Jong Yoo ◽  
Hoon Ki Choi ◽  
Jae Jeong Eun
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Lorentz Force ◽  
Stokes Equations ◽  
Scalar Potential ◽  
Mhd Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Potential Methods ◽  
Volume Method

Numerical analysis is performed for magnetic and magnetohydrodynamic (MHD) flow fields in electromagnetic (EM) pump. A finite volume method is applied to solve governing equations of magnetic field and the Navier-Stokes equations. Vector and scalar potential methods are adopted to obtain the electric and magnetic fields and the resulting Lorentz force in solving Maxwell equations. The magnetic field and velocity distributions are found to be affected by the phase of applied electric current and the magnitude of the Reynolds number. Computational results indicate that the magnetic flux distribution with changing phase of input electric current is characterized by pairs of counter-rotating closed loops. The axial velocity distributions are represented with S-type profiles for the case of the r-direction of Lorentz force dominated flows.

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.

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

2021 ◽  
Vol 17 ◽  
Author(s):  
B. Kanimozhi ◽  
M. Muthtamilselvan ◽  
Qasem M. Al-Mdallal ◽  
Bahaaeldin Abdalla
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Radial Magnetic Field ◽  
Navier Stokes Equations ◽  
Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions

2018 ◽  
Vol 28 (9) ◽  
pp. 2189-2207 ◽  
Author(s):  
Erman Ulker ◽  
Sıla Ovgu Korkut ◽  
Mehmet Sorgun
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Non Linear ◽  
Fully Developed Turbulent Flow ◽  
Effects Of Temperature ◽  
Eccentric Annuli ◽  
Pipe Rotation

Purpose The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals MHD convection ow in a constricted channel

2018 ◽  
Vol 26 (2) ◽  
pp. 267-283
Author(s):  
M. Tezer-Sezgin ◽  
Merve Gürbüz
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particular Solution ◽  
Laminar Convection ◽  
Long Channel ◽  
Velocity Pressure

Abstract We consider the steady, laminar, convection ow in a long channel of 2D rectangular constricted cross-section under the inuence of an applied magnetic field. The Navier-Stokes equations including Lorentz and buoyancy forces are coupled with the temperature equation and are solved by using linear radial basis function (RBF) approximations in terms of the velocity, pressure and the temperature of the fluid. RBFs are used in the approximation of the particular solution which becomes also the approximate solution of the problem. Results are obtained for several values of Grashof number (Gr), Hartmann number (M) and the constriction ratios (CR) to see the effects on the ow and isotherms for fixed values of Reynolds number and Prandtl number. As M increases, the ow is flattened. An increase in Gr increases the magnitude of the ow in the channel. Isolines undergo an inversion at the center of the channel indicating convection dominance due to the strong buoyancy force, but this inversion is retarded with the increase in the strength of the applied magnetic field. When both Hartmann number and constriction ratio are increased, ow is divided into more loops symmetrically with respect to the axes.

scholarly journals Experimental validation of wind energy estimation

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3795-3806
Author(s):  
Predrag Zivkovic ◽  
Mladen Tomic ◽  
Vukman Bakic
Keyword(s):  
Wind Speed ◽  
Linear Model ◽  
Linear Models ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Electricity Production ◽  
Navier Stokes ◽  
Energy Estimation ◽  
Navier Stokes Equations ◽  
Non Linear

Wind power assessment in complex terrain is a very demanding task. Modeling wind conditions with standard linear models does not sufficiently reproduce wind conditions in complex terrains, especially on leeward sides of terrain slopes, primarily due to the vorticity. A more complex non-linear model, based on Reynolds averaged Navier-Stokes equations has been used. Turbulence was modeled by modified two-equations k-? model for neutral atmospheric boundary-layer conditions, written in general curvelinear non-orthogonal co-ordinate system. The full set of mass and momentum conservation equations as well as turbulence model equations are numerically solved, using the as CFD technique. A comparison of the application of linear model and non-linear model is presented. Considerable discrepancies of estimated wind speed have been obtained using linear and non-linear models. Statistics of annual electricity production vary up to 30% of the model site. Even anemometer measurements directly at a wind turbine?s site do not necessarily deliver the results needed for prediction calculations, as extrapolations of wind speed to hub height is tricky. The results of the simulation are compared by means of the turbine type, quality and quantity of the wind data and capacity factor. Finally, the comparison of the estimated results with the measured data at 10, 30, and 50 m is shown.

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