scholarly journals The Effects of Electrical Conductivity on Fluid Flow between Two Parallel Plates in a Porous Medioum

2021 ◽  
pp. 4953-4963
Author(s):  
Alaa Hammodat ◽  
Ghanim Algwauish ◽  
Iman Al-Obaidi
Keyword(s):  
Reynolds Number ◽  
Hartmann Number ◽  
Method Of Lines ◽  
Magnetic Reynolds Number ◽  
Temperature Profiles ◽  
Parallel Plates ◽  
Brinkman Number ◽  
The Method Of Lines ◽  
Energy Equations ◽  
Physical Quantities

This paper deals with a mathematical model of a fluid flowing between two parallel plates in a porous medium under the influence of electromagnetic forces (EMF). The continuity, momentum, and energy equations were utilized to describe the flow. These equations were stated in their nondimensional forms and then processed numerically using the method of lines. Dimensionless velocity and temperature profiles were also investigated due to the impacts of assumed parameters in the relevant problem. Moreover, we investigated the effects of Reynolds number , Hartmann number M, magnetic Reynolds number , Prandtl number , Brinkman number , and Bouger number , beside those of new physical quantities (N , ). We solved this system by creating a computer program using MATLAB.                                                                               

Second Law Analysis of Magneto-Micropolar Fluid Flow Between Parallel Porous Plates

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Abbas Kosarineia ◽  
Sajad Sharhani
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Second Law ◽  
Brinkman Number ◽  
Viscosity Parameter ◽  
Micropolar Fluid Flow ◽  
Second Law Analysis

In this study, the influence of the applied magnetic field is investigated for magneto-micropolar fluid flow through an inclined channel of parallel porous plates with constant pressure gradient. The lower plate is maintained at constant temperature and the upper plate at a constant heat flux. The governing motion and energy equations are coupled while the effect of the applied magnetic field is taken into account, adding complexity to the already highly correlated set of differential equations. The governing equations are solved numerically by explicit Runge–Kutta. The velocity, microrotation, and temperature results are used to evaluate second law analysis. The effects of characteristic and dominate parameters such as Brinkman number, Hartmann Number, Reynolds number, and micropolar viscosity parameter are discussed on velocity, temperature, microrotation, entropy generation, and Bejan number in different diagrams. The results depicted that the entropy generation number rises with the increase in Brinkman number and decays with the increase in Hartmann Number, Reynolds number, and micropolar viscosity parameter. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the presence of magnetic field tends to increase the contribution of fluid friction entropy generation to the overall entropy generation; in other words, the irreversibilities caused by heat transfer reduced. Therefore, to minimize entropy, Brinkman number and Hartmann Number need to be controlled.

A magneto-hydrodynamic Stokes flow

1961 ◽  
Vol 260 (1300) ◽  
pp. 79-90 ◽  
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Hartmann Number ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Slow Flow ◽  
Magnetic Pole ◽  
Total Drag ◽  
Conducting Sphere ◽  
Stokes Drag

This paper considers the slow flow of a viscous, conducting fluid past a non-conducting sphere at whose centre is a magnetic pole. The magnetic Reynolds number is assumed to be small, and the modifications to the classical Stokes flow and the free magnetic pole field are obtained for an arbitrary Hartmann number. The total drag D on the sphere has been calculated, and the ratio D / D s determined as a function of the Hartmann number M , where D s is the Stokes drag. In particular ( D — D s )/ D s = 37/210 M 2 + O ( M 4 ) for small M and ( D — D s )/ Ds ~ 0·7205 M - 1 as M → ∞.

scholarly journals Steady Magnetohydrondynamic Natural Convection Coutte Flow With Variable Electrical Conductivity

2020 ◽  
Author(s):  
Terhemen Tuleun
Keyword(s):  
Electrical Conductivity ◽  
Natural Convection ◽  
Skin Friction ◽  
Hartmann Number ◽  
Line Graphs ◽  
Parallel Plates ◽  
Grashof Number ◽  
Electrically Conducting ◽  
Undetermined Coefficient ◽  
Energy Equations

The steady MAGNETOHYDRODYNAMIC natural convection coutte flow of viscous incompressible and electrically conducting fluid having variable electrical conductivity between two parallel plates when one of the plate is set into motion is studied. The dimensionless differential equations as well as energy equations are solved analytically using the method of undetermined coefficient. The analytical solution are presented numerically inform of line graphs given interms of velocity and skin friction. The result reveal that the effect of the Hartmann number and grashof number are to reduce and increase the velocity respectively. Similarly the skin friction on the moving and stationary plates increase with Grashof number and decreases with increase in Hartmann, a comparetive study review that the effect of Hartmann number and grashof number on velocity and skin friction are same.

MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field

1980 ◽  
Vol 96 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Richard J. Holroyd
Keyword(s):  
Magnetic Field ◽  
Experimental Study ◽  
Reynolds Number ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Rectangular Duct ◽  
Mean Velocity ◽  
Side Walls

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann numberMand interaction parameterNhave very large values and the magnetic Reynolds number is extremely small.The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.

Solver Development for Three-Dimensional Magnetohydrodynamic Flow on a Collocated Structured Grid System Based on SIMPLE Method

2014 ◽  
Vol 525 ◽  
pp. 247-250
Author(s):  
Jie Mao ◽  
Ke Liu ◽  
Hua Chen Pan
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Velocity Vector ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Grid System ◽  
Simple Method ◽  
Conservative Scheme ◽  
Structured Grid

A steady state magnetohydrodynamic laminar solver with low magnetic Reynolds number has been developed in OpenFOAM platform. SIMPLE method has been used to solve the velocity vector and pressure. The induced electric potential and induced electric current has been solved according to a consistent and conservative scheme on a collocated structure grid. The solver has been validated by simulating Shercliff's case with medium Hartmann number. The results show that the numerical solution results match the analytical solutions well.

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.

Transient Analysis of Natural Convection in a Horizontal Open Ended Cavity

2002 ◽  
Author(s):  
Assunta Andreozi ◽  
Oronzio Manca ◽  
Yogesh Jaluria
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Chemical Vapor ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Penetration Length ◽  
Energy Equations

The configuration of two horizontal parallel walls can be found in many applications, such as the cooling of electronic components, solar energy systems and chemical vapor deposition systems (CVD). In the present investigation a transient numerical analysis for laminar natural convection in air between two horizontal parallel plates, with the upper plate heated at uniform heat flux and the lower one unheated, is carried out by means of the finite volume method. The model was assumed to be two-dimensional. The full two-dimensional Navier-Stokes equations together with the continuity and energy equations are solved by a numerical scheme derived from a SIMPLE-like algorithm in an H-shaped domain. Results are presented in terms of velocity and temperature profiles, wall temperature profiles and the temporal behavior of several significant variables, such as the penetration length, is reported for different Rayleigh numbers and aspect ratio values.

scholarly journals Azimuthal magnetorotational instability with super-rotation

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
G. Rüdiger ◽  
M. Schultz ◽  
M. Gellert ◽  
F. Stefani
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Outer Cylinder ◽  
Magnetic Reynolds Number ◽  
Neutral Stability ◽  
Magnetorotational Instability ◽  
Magnetic Prandtl Number ◽  
The Stability

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

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