Unsteady Hydromagnetic Couette Flow Research Articles

Unsteady hydromagnetic Couette flow of fluid-particle suspension in a porous channel

Semi-analytic solution representing the time-dependent Couette flow of conducting fluid-particle in a permeable channel is presented in the existence of a magnetic field. The magnetic field is anticipated to be positioned either with the conducting fluid-particle or positioned with the moving wall. Solution to the coupled flow equations is found and given in the Laplace domain. Expressions for fluid-particle velocity and their corresponding skin friction are also found. Influence of a number of flow parameters on flow formation in the permeable channel is demonstrated. Results indicate that, increase in Hartmann number dampens both fluid velocity and particle fluid velocity when the magnetic field is positioned relative to the conducting fluid, while it augments the flow when the magnetic field is positioned relative to the moving plate. In conclusion, it is realized that growing the injection velocity augments the momentum boundary layer yielding an increase in fluid-particle velocity.

Computational analysis on unsteady hydromagnetic Couette flow of fluid—Particle suspension in an accelerated porous channel

In this analysis, Semi-analytical solution representing the time dependent Couette flow of conducting fluid–particle suspension in a permeable channel is offered in the existence of a magnetic field. The magnetic field is anticipated to be positioned either with the conducting suspension or the velocity of the magnetic field is same with the moving wall. Solution to the dimensionless coupled equations are provided by adopting the well known Laplace transform technique and D’Alermbert Method for both flow cases. The obtained solutions are later inverted to the time domain with the help of the Riemann sum approximation. Numerical values for fluid–particle suspension was validated with existing benchmark. Expressions for fluid–particle velocity and their corresponding skin fiction are also found in both cases. Influence of a number of flow parameters on flow formation are demonstrated via graphs. Results indicate that, irrespective of the magnetic field positioned either with the conducting suspension or with the moving wall, injection velocity strengthens the momentum boundary layer yielding an increase in fluid phase velocity and particle phase velocity, whereas the contrast is true with suction.

Magnetohydrodynamics Buoyancy-Driven Unsteady Couette Flow with Fluctuating Viscosity

Magnetohydrodynamics plays a significant role in new development and future perspectives of clean energy power generation systems and flow control technology in the aeronautics, astronautics, plasma, and electrical conducting flow in the electric machinery. This paper examines the inherent irreversibility in an unsteady hydromagnetic Couette flow of a conducting variable viscosity fluid between two vertical parallel plates with thermal buoyancy and heat transfer characteristics. Necessary regulating model equations are obtained and then converted using dimensionless variables to form a set of nonlinear initial boundary valued problem. Employing a semi-discretization finite difference method known as the method of lines, the model is addressed numerically. The velocity and the temperature results obtained are used further to compute the entropy generation rate, the Bejan number, skin friction and Nusselt number. Some effects of the embedded parameters on the above-mentioned results are investigated and displayed by graphs. Our results revealed that entropy generation rate is enhanced with an upsurge in thermal buoyancy but a rise in magnetic field lessened it.

Numerical Solution of Unsteady Hydromagnetic Couette Flow in a Rotating System Bounded by Porous Plates with Hall Effects

Numerical Solution of Unsteady Hydromagnetic Couette Flow in a Rotating System Bounded by Porous Plates with Hall Effects

Non-Newtonian Effects on Hydromagnetic Dusty Stratified Fluid Flow Through a Porous Medium with Volume Fraction

An unsteady hydro-magnetic Couette flow of dusty non-Newtonian stratified fluid through a porous medium bounded by two parallel plates has been investigated in presence of volume fraction. Lower plate is kept fixed and the upper plate is moving with some velocity. The non-Newtonian fluid flow is characterized by Walters liquid (Model $$ B^{\prime } $$ ). Effects of exponentially varying density, viscosity, visco-elasticity, electrical conductivity and dust particle density have been considered in the problem. A magnetic field of strength B 0 is applied along the transverse direction to the plate. Governing equations of motion are solved analytically for various values of flow parameters involved in the solution. Effects of visco-elasticity on velocity profile, skin friction have been studied graphically. Also, effects of stratification parameter and volume fraction in both Newtonian and non-Newtonian fluid flows have been analysed.

Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate

This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.

Thermal radiation effect on an unsteady MHD natural convection Couette flow with Heat and mass transfer

The numerical solution of natural convection in unsteady hydromagneticCouette flow of a viscous incompressible electrically conducting fluid between two vertical parallel plates in the presence of thermal radiation is obtained here. The fluid is considered to be a gray, absorbing – emitting but non – scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing coupled, non – linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank – Nicolson method. Computations are performed for a wide range of the governing flow parameters, viz., the thermal Grashof number, SolutalGrashof number, Magnetic field parameter (Hartmann number), Prandtl number, Thermal radiation parameter and Schmidt number. The effects of these flow parameters on the velocity and temperatureare shown graphically. Finally, the effects of various parameters on the on the skin – friction coefficient and Rate of heat and mass transferat the wall are prepared with various values of the parameters.These findings are in quantitative agreement with earlier reported studies.

Unsteady hydromagnetic couette flow due to ramped motion of one of the porous plates

An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in ramped motion. It is assumed that the porous plates are uniformly permeable and the fluid is entering the flow region through one of the porous plates at same rate as it is leaving through the other porous plate. The resulting boundary value problem has been solved exactly under the assumption of a negligible induced magnetic field, external electric field and pressure gradient. Unified closed form expressions for the velocity field and skin-friction corresponding to the case of a magnetic field fixed relative to the fluid or to the moving porous plate have been presented. In order to highlight the impact of the ramp motion of the porous plate on the fluid flow, it has also been compared with Couette flow between porous plates when one of the porous plates has been set into an impulsive motion.

Hydromagnetic flows of a mixture of two Newtonian fluids between two parallel plates

The paper aims to study the flow of a binary mixture of electrically conducting, incompressible and viscous fluids between two parallel plates in the presence of a transverse uniform magnetic field. The solution of such a flow model has many applications in magnetohydrodynamic (MHD) power generators, MHD pumps, MHD accelerators, and MHD flowmeters. Exact solutions have been obtained for the following four problems: (1) steady hydromagnetic Couette flow, (2) unsteady hydromagnetic Couette flow, (3) steady hydromagnetic Poiseuille flow, (4) unsteady hydromagnetic Poiseuille flow. The mean velocity of the mixture is drawn for different values of magnetic parameters and results are interpreted with the aid of graphs. The previous solutions involving single Newtonian fluid appear as the special cases of the present analysis.

EFFECTS OF HALL CURRENT AND ROTATION ON UNSTEADY HYDROMAGNETIC COUETTE FLOW WITHIN A POROUS CHANNEL

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two parallel porous plates taking Hall current into account in a rotating system is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and is permeated by a uniform transverse magnetic field which is fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of primary and secondary velocities and that of shear stress at the moving plate due to primary and secondary flows are displayed graphically for various values of Hall current parameter m, rotation parameter K2, magnetic parameter M2, suction/injection parameter S and time t.

Effects of Hall Current and Rotation on Unsteady MHD Couette Flow in the Presence of an Inclined Magnetic Field

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of an inclined magnetic field taking Hall current into account is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also derived. Asymptotic behavior of the solution is analyzed for small and large values of time t to highlight (i) the transient approach to the final steady state flow and (ii) the effects of Hall current, magnetic field, rotation and angle of inclination of magnetic field on the flow-field. It is found that Hall current and rotation tend to accelerate fluid velocity in both the primary and secondary flow directions. Magnetic field has retarding influence on the fluid velocity in both the primary and secondary flow directions. Angle of inclination of magnetic field has accelerating influence on the fluid velocity in both the primary and secondary flow directions.

Effects of Rotation and Magnetic Field on Unsteady Couette Flow in a Porous Channel

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of a uniform transverse magnetic field is studied. The plates of the channel are considered porous and fluid flow within the channel is induced due to the impulsive movement of the upper plate of the channel. General solution of the governing equations is obtained which is valid for every value of time t. For small values of time t, the solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the stationary plate due to the primary and secondary flows is obtained in both the cases. It is found that the solution obtained by Laplace transform technique converges more rapidly than the general solution when time t is very small. Magnetic field retards the fluid flow in both the primary and secondary flow directions. Rotation retards primary flow whereas it accelerates secondary flow. There exists incipient flow reversal near the stationary plate on increasing rotation parameter K 2 . Suction accelerates primary flow whereas it retards secondary flow. Injection retards both the primary and secondary flows.

Unsteady hydromagnetic Couette flow through a porous medium in a rotating system

This paper investigates the unsteady hydromagnetic Couette fluid flow through a porous medium between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system using boundary layer approximation. The fluid is assumed to be Newtonian and incompressible. Laplace transform technique is adopted to obtain a unified solution of the velocity fields. Such a flow model is of great interest, not only for its theoretical significance, but also for its wide applications to geophysics and engineering. Analytical expressions for the steady state velocity and shear stress on the plates are obtained, and the case of single oscillating plate is also discussed. The influence of pertinent parameters on the flow is delineated, and appropriate conclusions are drawn.

Unsteady Hydromagnetic Couette Flow within Porous plates in a Rotating System

Unsteady Hydromagnetic Couette Flow within Porous plates in a Rotating System

Unsteady MHD Couette flow in a rotating system

The unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system has been considered. An exact solution of the governing equations has been obtained by using a Laplace transform. Solutions for the velocity distributions as well as shear stresses have been obtained for small times as well as for large times. It is found that for large times the primary velocity decreases with increase in the rotation parameter K 2 while it increases with increase in the magnetic parameter M 2 . It is also found that with increase in K 2 , the secondary velocity v 1 decreases near the stationary plate while it increases near the moving plate. On the other hand, the secondary velocity decreases with increase in the magnetic parameter.

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties and uniform suction and injection

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with Hall effect and temperature dependent properties. The fluid is acted upon by an exponential decaying pressure gradient and an external uniform magnetic field. Uniform suction and injection are applied perpendicularly to the parallel plates. Numerical solutions for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is examined.

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field are applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity under exponential decaying pressure gradient

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. The fluid is acted upon by an exponential decaying pressure gradient and an external uniform magnetic field is applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field as well as uniform suction and injection applied perpendicular to the parallel plates. A numerical solution for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature-dependent viscosity and thermal conductivity on both velocity and temperature distributions is examined.

Unsteady hydromagnetic couette flow in a rotating system

Unsteady hydromagnetic flow of an electrically conducting viscous incompressible fluid in a rotating system under the influence of a uniform transverse magnetic field is investigated when one of the plates is set into motion with the time dependent velocity U(t) in its own plane. Two cases of interest, namely, impulsive start as well as accelerated start of the moving plate are discussed. The asymptotic behaviour of the solution is also analysed for both small and large time to highlight the transient approach to the final steady state and effects of rotation parameter as well as Hartmann number. The shear stresses at the moving plate due to the primary and secondary flows are derived in both cases. It is found that the shear stress components due to the primary flow decrease, whereas that due to the secondary flow increase with the increase in rotation parameter.