Unsteady MHD Couette Flow Research Articles

TIME DEPENDENT PRESSURE GRADIENT EFFECTS ON UNSTEADY MHD COUETTE FLOW THROUGH A PARALLEL POROUS PLATE

In this paper, the unsteady MHD Couette flow through a porous medium of a viscous incompressible fluid bounded by two parallel porous plates under the influence of thermal radiation and chemical reaction is investigated. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to time dependent pressure gradient. The transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using perturbation and Eigenfunction expansion techniques. The effects of some non-dimensional parameters are graphically represented and interpreted. It is observed that primary velocity is maximum when pressure gradient is time dependent as compared to when it is independent on time. Also, increase in temperature dependent pressure gradient leads to oscillation in primary velocity along distance y.

Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature

Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature

Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature

Unsteady MHD Couette flows in a vertical porous channel with effect of thermal radiation and variable temperature have been studied. The governing equations at first were transformed by usual transformation non-dimensional form. The numerical solutions for time dependent velocity, temperature and special concentration are obtained by the implicit finite difference method. The computed values of fluid velocity, temperature and concentrations are analyzed for different flow parameters such as thermal Grashof number Gr, modify Grashof number Gm, Prandtl number Pr, thermal radiation parameter R and Schmidt number Sc. The effect of these parameters depicting physical situation of the flow profile is expressed with the aid of line graphs. Significant results from this study showed that the velocity, temperature and concentration increases with increase in thermal radiation, magnetic field parameters and time, and decreases with the effect of Prandtl number, Schmidt number at increasing values.

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

This 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.

Radiative Effects on Unsteady MHD Couette Flow through a Parallel Plate with Constant Pressure Gradient

In this paper, the unsteady MHD Couette flow through a porous medium of a viscous incompressible fluid bounded by two parallel porous plates under the influence of thermal radiation and chemical reaction is investigated. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to the constant pressure gradient. The transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using the Eigenfunction expansion technique. The influence of some emerging non-dimensional parameters namely, pressure gradient, suction parameter, radiation parameter, and Hartman number are examined in detail. It is observed that the primary velocity is increased with increasing pressure gradient while the increase in radiation parameter leads to adecrease in the thermal profile of the flow.

Numerical Solution of Unsteady MHD Couette Flow in the Presence of Uniform Suction and Injection with Hall Effects

In this paper, unsteady magnetohydrodynamic Couette flow is studied numerically for a viscous, incompressible and electrically conducting fluid between two infinitely long parallel porous plates, taking Hall current into account. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and fluid motion is subjected to a uniform suction and injection at upper and lower plates. Magnetic lines of force are assumed to be fixed relative to the fluid. Numerical solutions for primary and secondary velocities are obtained from the governing momentum equation by employing explicit finite difference method. Numerical solutions of the primary and secondary velocities are displayed graphically versus non-dimensional channel width variable $$y$$ for various values of Hall current parameter $$m$$ , magnetic parameter $$M$$ , suction/injection parameter $$S$$ and time $$t$$ whereas the numerical values of co-efficient of skin-frictions at the moving plate due to primary and secondary flows are presented in tabular form for different values of $$m$$ , $$M$$ , $$S$$ and $$t$$ .

Role of Sudden Application or Withdrawal of Magnetic Field on MHD Couette Flow

This article investigates the impact of a sudden application or sudden withdrawal of a magnetic field on an unsteady MHD Couette flow formation in a parallel plate channel. The governing momentum equation is derived and solved exactly in Laplace domain using the Laplace transform technique with the necessary initial and boundary conditions to capture the present physical situation for the cases; sudden application or sudden withdrawal of a magnetic field. Due to the complexity of the solution obtained, the Riemann-sum approximation technique is used to transform the Laplace domain to time domain. During the course of graphical and tabular representations, results show that the Hartmann number, time and nature of application of a magnetic field play an important role in the transition from hydrodynamic to magnetohydrodynamic flow and vice-versa. Also, fluid velocity steady-state solution is independent on whether the magnetic field is fixed relative to the moving plate or to the fluid for sudden withdrawal of magnetic field. In addition, the application of a sudden magnetic field leads to a delay in the attainment of steady-state solution.

Novel Numerical Analysis of Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Models for Simulating Unsteady Mhd Couette Flow of a Generalized Oldroyd-B Fluid

Abstract In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H 1 norm and prove that their accuracy is of O(τ + h 2) and O(τ min{3–γs ,2–αq ,2–β}+h 2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

Finite Element Method for Two-Dimensional Unsteady MHD Couette Flow of a Generalized Oldroyd-B Fluid

In recent years, non-Newtonian fluids have been widely applied in engineering and industry. Due to the complexity of these fluids, there are several constitutive equations of non- Newtonian fluids. One particular subclass of non-Newtonian fluids is the class of a generalized Oldroyd-B fluids with fractional derivative constitutive equations, which has been found to approximate the response of many dilute polymeric liquids. Although the analytic solution of these equations can be derived, it contains a multi-level sum of an infinite series and Fox H-functions, which is extremely complex and difficult to evaluate. Therefore, seeking the numerical solution of the equation is of great importance. Different from the general time fractional diffusion equation, the constitutive equation is a novel multi-term time fractional diffusion equation and has a special time fractional operator on the spatial derivative, which is challenging to approximate. In this paper, we will consider the finite element method for the two-dimensional multi-term time fractional diffusion equation. Firstly, we utilise the L1 and L2 schemes to approximate the two different time fractional derivatives, respectively. Secondly, we apply the finite element method to the equation and establish the fully variational formulation. Then we adopt linear polynomials on triangular elements to derive the matrix form of the numerical scheme. Furthermore, we present the stability and convergence of the scheme. Finally, two numerical examples are investigated to show the effectiveness of our method, in which a two-dimensional unsteady MHD Couette flow of a generalized Oldroyd-B fluid is considered.

DTM-FDM hybrid approach to unsteady MHD Couette flow and heat transfer of dusty fluid with variable properties

The present paper studies the unsteady MHD Couette flow and heat transfer of dusty fluid between two parallel plates and the effects of the temperature dependent properties on it. The viscosity and thermal conductivity are considered as exponential and linear functions of the temperature, respectively. An external uniform magnetic field and a constant pressure gradient are considered in directions of the main flow and perpendicular of the plates, respectively. A hybrid technique based on differential transform method (DTM) and finite difference method (FDM) is used to solve the governing coupled flow and heat transfer equations. The effects of the magnetic field (Hartman number) and temperature dependent of the thermal conductivity and viscosity are discussed by considering the velocity and temperature profiles of the clean fluid and dust particle. Applying a magnetic field in the present problem decreases the value of the Nusselt number and skin friction coefficient.

Unsteady MHD Couette flow between two Parallel Plates with Uniform Suction

Unsteady MHD Couette flow between two Parallel Plates with Uniform Suction

Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling

Purpose– The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel.Design/methodology/approach– The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme.Findings– Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods.Practical implications– This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems.Originality/value– Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

Effect of Hall Current on Unsteady MHD Couette Flow and Heat Transfer of Nanofluids in a Rotating System

The Hall effect on MHD Couette flow and heat transfer between two parallel plates in a rotating channel is investigated. A uniform magnetic field is applied normal to the plates and the flow is induced by the effects of Coriolis force, moving upper plate and the constant pressure gradients. Cu-water, Al2O3-water and TiO2-water nanofluids are compared for heat transfer performance. The Galerkin approximation and method of lines are employed to tackle the governing non-linear PDEs. The results show that Hall current significantly affects the flow system. The skin friction and Nusselt number profiles are presented graphically and discussed quantitatively.

Effects of Hall Current on Unsteady MHD Couette Flow of Class-II in a Rotating System

Effects of Hall Current on Unsteady MHD Couette Flow of Class-II in a Rotating System

Unsteady MHD two-phase Couette flow of fluid–particle suspension

The problem of two-phase unsteady MHD Couette flow between two parallel infinite plates has been studied taking the viscosity effect of the two phases into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving plate. The novelty of this study is that we have obtained the solution of the unsteady flow using the Laplace transform technique, D’Alemberts method and the Riemann-sum approximation method. The solution obtained is validated by assenting comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical result for the velocity of both phases based on the semi-analytical solutions are presented and discussed. A parametric study of some of the physical parameters involved in the problem is conducted. The skin friction for both the fluid and the particle phases decreases with time on both plates until a steady state is reached, it is also observed to decrease with increase in the particle viscosity on the moving plate while an opposite behaviour has been noticed on the stationary plate.

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 Hall Current and Ion-Slip on Unsteady MHD Couette Flow

The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter.

Hall and Ion-Slip Effects on Unsteady MHD Couette Flow in a Rotating System with Suction and Injection

This study deals analytically with the motion of a viscous, incompressible and electrically conducting fluid filling the gap between two infinite porous plates where both the plates and the fluid rotates in unison with uniform angular velocity. A unified closed form analytical expressions is derived for the two cases of the magnetic field being fixed relative to either the fluid or to the moving porous plate. The governing equations obtained are solved using the Laplace transform technique and an exact solution obtained for the velocity and the skin friction. The transient state solution at large time was observed to be in harmony with the steady state solution which has been derived separately. The effects of rotation, suction/injection parameter and Hall and ion-slip parameters on both the primary and secondary velocities and the resultant skin friction are presented graphically. The presence of Hall and ion-slip currents and suction/injection results into the longer time it took both the primary and th...

Time‐dependent MHD Couette flow in a rotating system with suction/injection

AbstractThe unsteady MHD Couette flow of a viscous incompressible electrically conducting fluid between two parallel porous plates in a rotating system when one of the plate is set into uniform accelerated motion is studied. A unified closed form analytical expressions for the velocity and the skin friction for the magnetic lines of force being fixed relative to either the fluid or the moving porous plate are derived using the Laplace transform technique. The effects of suction/injection parameter in the presence of magnetic field and rotation on both the primary and secondary velocities and the resultant skin friction are presented graphically. The analysis of the result shows that the primary velocity increases with increase in the suction/injection parameter while the secondary velocity increases in magnitude near the moving plate and decreases in magnitude near the fixed plate for the two cases. It is interesting to note that the Ekman number has an increasing effect on the primary velocity when the magnetic lines of force are fixed relative to the moving plate. On the other hand, the resultant skin friction decreases with increase in the suction/injection parameter at the porous plate where injection takes place and increases at the porous plate where the fluid is been sucked for the two cases considered.

Unsteady MHD Couette Flows in an Annuli: The Riemann-Sum Approximation Approach

The unsteady MHD Couette flow of a viscous incompressible electrically conducting fluid between two concentric horizontal cylinders of infinite length have been analysed when the outer cylinder has been set into uniform accelerated motion. A unified closed form expressions are derived corresponding to the cases of the magnetic field fixed relative to the fluid or to the accelerated outer cylinder. The well known Laplace transform technique is applied to solve the time-dependent governing equations, while the method of Riemann-sum approximation is employed to invert the Laplace domain to the time domain in order to obtain the velocity and the skin friction. The variations of the velocity and the skin friction with respect to the Hartmann number and time have been discussed.