Unsteady Couette Flow Research Articles

Unsteady Incompressible Couette Flow Problem for the Eyring-Powell Model with Porous Walls

This work is concerned with the influence of uniform suction or injection on unsteady incompressible Couette flow for the Eyring-Powell model. The resulting unsteady problem for horizontal velocity field is solved by means of homotopy analysis method (HAM). The characteristics of the horizontal velocity field and wall shear stress are analyzed and discussed. Pade approximants and Taylor polynomials are also found for velocity profile and are used to make the maximum error as small as possible. The graphs of the error for the Pade approximation and Taylor approximation are drawn and discussed. Convergence of the series solution is also discussed with the help of h-curve and interval of convergence is also found.

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.

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.

Effective of hall current on unsteady Couette flow with heat transfer in the presence of a heat source and uniform suction and injection

Effective of hall current on unsteady Couette flow with heat transfer in the presence of a heat source and uniform suction and injection

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.

Unsteady MHD dusty viscoelastic fluid Couette flow in an irregular channel with varying mass diffusion

The present investigation deals with the study of unsteady, MHD, heat absorbing and chemically reacting dusty viscoelastic (Walter’s liquid model-B) fluid Couette flow between vertical long wavy wall and a parallel flat wall saturated with porous medium subject to convective cooling and varying mass diffusion. The perturbation method is employed to analyze the coupled equations involving nonlinear problem and solution for the velocity, temperature and concentration distributions are obtained analytically. The graphical results are presented and the physical aspects are discussed in detail to interpret the effect of various significant parameters of the problem. The effect of the skin-friction, rate of heat and mass transfer coefficients at the channel walls are tabulated.

Unsteady Couette flow of viscous fluid under a non-uniform magnetic field

The aim of this letter is to construct the analytic solution for unsteady Couette flow in the presence of an arbitrary non-uniform applied magnetic field. The flow is induced by a generalized velocity given to the lower plate. The perturbed eigenfunction expansion method is employed to develop a series solution for small magnetic field.

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel (formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.

High accuracy numerical solutions of the Boltzmann Bhatnagar-Gross-Krook equation for steady and oscillatory Couette flows

Modeling gas flows generated by micro- and nano-devices often requires the use of kinetic theory. To facilitate implementation, various approximate formulations have been proposed based on the Bhatnagar-Gross-Krook (BGK) kinetic model, including most recently, the lattice Boltzmann (LB) method. While there exists a comprehensive numerical data set for the hard sphere linearized Boltzmann equation for steady Couette flow, no such set of data is available for the Boltzmann-BGK equation. The purpose of this article is to present a high accuracy data set for the linearized Boltzmann-BGK equation over the full range of Knudsen numbers and normalized oscillation frequencies – this encompasses both steady and unsteady Couette flows. This data set is expected to be of particular value in the benchmarking and validation of computational methods such as the LB method and other approaches based on the Boltzmann-BGK equation.

Effects of Radiation on Unsteady Couette Flow Between Two Vertical Parallel Plates with Ramped Wall Temperature

The effect of radiation on unsteady Couette flow between two vertical parallel plates with ramped wall temperature have been studied. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. An analytical solution of the governing equations has been obtained by employing Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field, temperature field, skin friction and rate of heat transfer is discussed with the help of graphs and tables. It is found that an increase in radiation parameter leads to decrease the fluid velocity and temperature. It is also found that both the velocity as well as the temperature of the fluid decrease with an increase in Prandtl number. Further it is observed that the velocity increases with an increase in Grashof number and an increase in time leads to increase the fluid velocity and temperature.

Flow of a binary mixture of fluids in a semicircular duct

The purpose of this work is to examine the flow of a binary mixture including chemically inert incompressible Newtonian fluids in a duct of semicircular cross-section. Such a flow model has great significance not only of its own theoretical interest, but also for application to various engineering processes. The governing equations have been solved analytically using the finite Fourier sine and Hankel transforms for the following four problems: (1) steady Couette flow in a semicircular duct, (2) unsteady Couette flow in a semicircular duct, (3) steady Poiseuille flow in a semicircular duct, (4) unsteady Poiseuille flow in a semicircular duct. The previous solutions corresponding to pure Newtonian fluid appear as the special cases of the present analysis. Key words: Binary mixture, Newtonian fluid, Couette flow, Poiseuille flow, Fourier sine transform, Hankel transform.

Generalized Coordinate Transformation for Lattice Boltzmann Equation Using TTM Structured Grid Generation

The standard lattice Boltzmann method has only been applied to the uniform structured grid so far. This limitation can be removed by discretization of the position as well as the velocity space separately. In the present study the generalized coordinate is introduced to transform the lattice Boltzmann Equation (LBE) from physical domain to computational domain. This method uses the finite difference method to discrete the local derivatives in computational space. The central scheme uses to estimate the convection term. The generalized coordinate transformation method introduced in this study has been validated against a sample case study. For this purpose, an unsteady Couette flow between two cylinders has been examined. Good agreement between most of the results of this study and the available data in the literature is reached. The source of some discrepancies between the current results and available data seems to be due to discretization method used in present work to calculate the Jacobian and metrics of transformation matrix.

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.

Unsteady Couette Flow through a Porous Medium in a Rotating System

An investigation has been made on an unsteady Couette flow of a viscous incompressible fluid through a porous me- dium in a rotating system. The solution of the governing equations has been obtained by the use of Laplace transform technique. It is found that the primary velocity decreases and the magnitude of the secondary velocity increases with an increase in rotation parameter. The fluid velocity components are decelerated by an increase of Reynolds number. An increase in porosity parameter leads to increase the primary velocity and the magnitude of the secondary velocity. It is also found that the solution for small time converges more rapidly than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of rotation parameter and Reynolds number. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the boundary layer increases with an increase in porosity 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...

Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus

The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase 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 outer cylinder. The problem is solved using a combination of the Laplace transform technique, D’Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases.

Magnetohydrodynamic Free Convective Couette Flow With Suction and Injection

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.

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.

Exact solutions for unsteady axial Couette flow of a fractional Maxwell fluid due to an accelerated shear

The velocity field and the adequate shear stress corresponding to the flow of a fractional Maxwell fluid (FMF) between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at time t = 0+ applies a shear stress fta (a ≥ 0) to the fluid. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as special cases of general solutions. The unsteady solutions corresponding to a = 1, 2, 3, ... can be written as simple or multiple integrals of similar solutions for a = 0 and we extend this for any positive real number a expressing in fractional integration. Furthermore, for a = 0, 1 and 2, the solutions corresponding to Maxwell fluid compared graphically with the solutions obtained in [1–3], earlier by a different technique. For a = 0 and 1 the unsteady motion of a Maxwell fluid, as well as that of a Newtonian fluid ultimately becomes steady and the required time to reach the steady-state is graphically established. Finally a comparison between the motions of FMF and Maxwell fluid is underlined by graphical illustrations.

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.