scholarly journals Hydrodynamic behaviour of velocity of applied magnetic field on unsteady MHD Couette flow of dusty fluid in an annulus

2021 ◽  
Vol 137 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Magnetic Field ◽  
Phase Velocity ◽  
Skin Friction ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Fluid Phase ◽  
Dusty Fluid ◽  
Riemann Sum ◽  
Hydrodynamic Behaviour ◽  
Laplace Transform Technique

AbstractThis research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field. For large time, it is anticipated that higher profiles for velocity and skin friction are seen with fluid phase and an accelerated moving wall.

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.

The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

1971 ◽  
Vol 69 (2) ◽  
pp. 337-351 ◽  
Author(s):  
D. J. Temperley ◽  
L. Todd
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Classical Model ◽  
Critical Discussion ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Wall Conductivity ◽  
Expansion Procedure

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

scholarly journals Mathematical modeling of slip and magnetohydrodynamics effects in blade coating

2018 ◽  
Vol 35 (1) ◽  
pp. 9-21 ◽  
Author(s):  
M Sajid ◽  
H Shahzad ◽  
M Mughees ◽  
N Ali
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Shooting Method ◽  
Hartmann Number ◽  
Volumetric Flow Rate ◽  
Maximum Pressure ◽  
Slip Parameter ◽  
Slip Effects ◽  
Blade Coating ◽  
The Web

A mathematical analysis for magnetohydrodynamics and slip effects is presented for blade coating onto a moving sheet of viscous fluid. An applied magnetic field is imposed normal to the flow and slip is considered at the web surface. The shooting method is applied to obtain the numerical solution of governing differential equations. Both numerical and exact solutions are utilized to describe the velocity profile, volumetric flow rate, pressure gradient, pressure and maximum pressure. How slip parameter and the Hartmann number influences properties is discussed through the graphical results. It is calculated that the presence of slip and applied magnetic field controls the sheet velocity in the blade coating process.

Unsteady Hydromagnetic Radiative Flow of a Dusty Fluid Past a Porous Plate With Ramped Wall Temperature

2013 ◽  
Author(s):  
R. Nandkeolyar ◽  
P. Sibanda ◽  
Md. S. Ansari
Keyword(s):  
Magnetic Field ◽  
Laplace Transform ◽  
Porous Plate ◽  
Inverse Laplace Transform ◽  
Combined Effects ◽  
Dusty Fluid ◽  
Electrically Conducting ◽  
Flow Parameters ◽  
Energy Transfers ◽  
Laplace Transform Technique

The combined effects of applied magnetic field, thermal radiation and suction on the flow and free convective heat transfer of a viscous, incompressible, electrically conducting dusty fluid past a flat plate with ramped temperature are studied. The governing partial differential equations for momentum and energy transfers, for both the fluid and particle phases, are solved using Laplace transform technique. The inverse Laplace transform is obtained numerically using Matlab. A comparison of Numerical solution and analytical solution for energy transfer is made which shows an excellent agreement. The effects of pertinent flow parameters are analyzed with the help of graphs and tables.

scholarly journals Effect of the Direction of Uniform Horizontal Magnetic Field on the Linear Stability of Natural Convection in a Long Vertical Rectangular Enclosure

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1689
Author(s):  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Linear Stability ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Horizontal Magnetic Field ◽  
Direction Parallel ◽  
Vertical Side ◽  
Rectangular Enclosure

The effect of the direction of external horizontal magnetic fields on the linear stability of natural convection of liquid metal in an infinitely long vertical rectangular enclosure is numerically studied. A vertical side wall is heated and the opposing vertical wall is cooled both isothermally, whereas the other two vertical walls are adiabatic. A uniform horizontal magnetic field is applied either in the direction parallel or perpendicular to the temperature gradient. In this study, the height of the enclosure is so long as to neglect the top and bottom effects where returning flow takes place, and thus the basic flow is assumed to be a parallel flow and the temperature field is in heat conduction state. The Prandtl number is limited to the value of 0.025 and horizontal cross-section is square. The natural convection is monotonously stabilized as increase in the Hartmann number when the applied magnetic field is parallel to the temperature gradient. However, when the applied magnetic field is perpendicular to the temperature gradient, it is once destabilized at a certain low Hartmann number, but it is stabilized at high Hartmann numbers.

On Two-Dimensional Laminar Hydromagnetic Fluid-Particle Flow Over a Surface in the Presence of a Gravity Field

2000 ◽  
Vol 123 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Fluid Phase ◽  
Skin Friction Coefficient ◽  
Two Dimensional ◽  
Particle Phase ◽  
Phase Stresses ◽  
The Magnetic Field

A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

Magneto-hydrodynamics of a solid-liquid two-phase fluid in rotating channel due to peristaltic wavy movement

2019 ◽  
Vol 30 (5) ◽  
pp. 2501-2516 ◽  
Author(s):  
Sajjad Haider ◽  
Nouman Ijaz ◽  
A. Zeeshan ◽  
Yun-Zhang Li
Keyword(s):  
Magnetic Field ◽  
Phase Velocity ◽  
Fluid Phase ◽  
Peristaltic Flow ◽  
Particulate Phase ◽  
Two Phase ◽  
Content Type ◽  
Solid Liquid ◽  
Phase Fluid ◽  
Rotating Channel

Purpose Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied. Design/methodology/approach The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail. Findings It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior. Practical implications The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement. Originality/value The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

On the slow rotation of axisymmetric solids in magnetohydrodynamics

1967 ◽  
Vol 63 (4) ◽  
pp. 1331-1339 ◽  
Author(s):  
R. Shail
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Alternative Treatment ◽  
Hartmann Number ◽  
Axisymmetric Body ◽  
Subsequent Paper ◽  
Slow Rotation ◽  
Stokes Approximation ◽  
Equation Formulation ◽  
The Subject

The motion of a solid in a viscous conducting fluid permeated by a magnetic field has been the subject of a number of papers. Using the Stokes approximation Chester (3) first derived an expansion in powers of the Hartmann number for the drag on a sphere translating uniformly through a fluid, parallel to the applied magnetic field. In a subsequent paper (4) the same author treated the high Hartmann number limit. Later, Chang (2) considered, in the low Hartmann number regime, the motion of an axisymmetric body translating slowly along the axis of a fluid filled tube, and was able to calculate a drag formula which includes the lowest order wall effect term. An alternative treatment of this class of problems has recently been given by Williams (13), using an intergral equation formulation.

scholarly journals Impact of Electrification and Particle Loading on Velocity Profile of Dusty Fluid Flow Over a Stretching Sheet

2020 ◽  
Vol 9 (3) ◽  
pp. 3140-3143
Keyword(s):  
Fluid Flow ◽  
Velocity Profile ◽  
Phase Velocity ◽  
Particle Density ◽  
Vertical Direction ◽  
Fluid Phase ◽  
Particle Phase ◽  
Particle Loading ◽  
Carrier Fluid ◽  
Dusty Fluid

The performance of incompressible, laminar, boundary- layer flows over a semi-infinite horizontal stretchable plate is considered. The dusty fluid flow problems are modelled and solved in agreement with two-way coupling model. The particle phase momentum equation in the vertical direction is considered where as that for fluid phase is neglected. Here the electrification term added in not from the supply from outside rather it is the generation due to collision of particles So the effects of particle loading and electrification on velocity profile have been studied. From the result analysis it is concluded that electrification and particle density have significant effect on particle phase velocity, whereas carrier fluid phase has negligible effect. The particle phase velocity increases with increasing of electrification parameter and decreases with increase of loading ratio.

Magnetohydrodynamic Free Convective Couette Flow With Suction and Injection

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Basant K. Jha ◽  
Clement A. Apere
Keyword(s):  
Skin Friction ◽  
Couette Flow ◽  
Porous Plate ◽  
Moving Plate ◽  
Electrically Conducting ◽  
Flow Parameters ◽  
Riemann Sum ◽  
Injection Parameter ◽  
Laplace Transform Technique ◽  
The Time Domain

This paper considers the unsteady MHD free convective Couette flow of a viscous incompressible electrically conducting fluid between two parallel vertical porous plates. Both cases of the applied magnetic field being fixed either to the fluid or to the moving porous plate are considered. The solution of the governing equations has been obtained by using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The unified solution obtained for the velocity have been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as Prandtl number, Grashof number, and the suction/injection parameter are discussed with the aid of line graphs. The skin friction have been seen to decrease with both suction and injection on the surface of the moving plate when the channel is being cooled, while on the stationary plate, the magnitude of the skin friction increases with injection.

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