Unsteady Couette Research Articles

The Boltzmann equation for plane Couette flow in a finite channel

The dynamics of a rarefied gas in a finite channel with the same temperatures and opposite velocities is a fundamental problem in kinetic theory. The relative motion of the planar boundaries can induce a non-equilibrium state which is referred to as the Couette flow. In this paper, we demonstrate that the unsteady Couette flow for the Boltzmann equation in 3D finite channel time asymptotically converges to the 1D steady state constructed in Duan et al. (2022), we also prove the exponential time decay rate as a byproduct. The validity of the analysis is established for all hard potentials.

A Numerical Investigation of Hydro-Magnetic Mixed Convection Flow of Viscous Dissipative Fluid in a Channel Filled with Porous Material

The purpose of this paper is to inspect the unsteady MHD mixed convective Couette flow of viscous dissipative fluid in a vertical channel filled with porous material. The steady state analytical solutions of temperature, velocity, frictional force and heat transfer rate are obtained using the Homotopy perturbation method (HPM). The implicit finite difference technique is used to solve the transient leading equations numerically. Plots and tables with the dynamic flow parameters and dimensionless variables are displayed. During this computation, it was found that raising the Darcy parameter (Da) and the mixed convection (Gre) parameters both push the fluid flow upwards, but increasing the magnetic field's values had the opposite effect (M). HIGHLIGHTS Effect of viscous Dissipation on unsteady MHD Mixed Convection Flow with Porous Material is investigated Increasing Darcy number improves the flow pattern Rate of heat transfer could be enhance by considering high values of Brinkman number GRAPHICAL ABSTRACT

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.

Method of Lines Analysis of Soret and Dufour Effects on an Unsteady Heat and Mass Transfer MHD Natural Convection Couette Flow

This study examines the numerical solutions of an unsteady natural convection Couette flow of a viscous, incompressible and electrically conducting fluid between the two vertical parallel plates in the presence of thermal radiation, Soret and Dufour. The fundamental dimensionless governing partial differential equations for the impulsive movement of the plate are solved by method of lines (MOL). The numerical simulations for the effects of Soret and Dufour on the velocity profile, the temperature profile and the concentration profile of the flow are shown graphically. The analysis indicates that the fluid velocity is an increasing function of Soret and Dufour numbers. Also, the concentration profile and the temperature profile increase with increase in the Soret number and Dufour number respectively.

EXISTENCE OF SOLUTIONS OF THE TEN VELOCITY SPATIAL DISCRETE MODEL OF GAS

We use the fractional step approximation method to prove the existence and the uniqueness of solutions of an initial boundary value problem for a spatial ten velocity discrete model in the study unsteady Couette flow.

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

A multiple-scale perturbation analysis is presented to analyse the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid flowing between two parallel plates filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation in its own plane moving with a constant velocity, and the periodic pressure gradient. Mei’s homogenization technique is used to find the concentration distribution up to third order, complemented with the dispersion coefficients for four different situations, namely, steady, pulsatile, oscillatory and the combined effect of all these. We observe that when the flow is under the combined effect of wall oscillation and pressure pulsation, then the respective frequency (Womersley number) and amplitude parameters oppose each other while influencing the dispersion coefficient. Our analysis reveals that for a fixed amplitude of oscillation and pulsation, the frequency of pressure pulsation has a stronger effect on the dispersion coefficient compared with the wall oscillation. On the other hand, when the Womersley number is kept fixed, amplitude of the wall oscillation dominates the pressure pulsation. This behaviour is more prominent for higher values of the Darcy number. The transverse concentration distribution and its dependency on porous medium parameters are also discussed in detail.

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.

Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement

A general unified solution of the plane Couette–Poiseuille–Stokes–Womersley incompressible linear fluid flow in a slit in the presence of oscillatory pressure gradients with periodic synchronous vibrating boundaries is presented. Oscillatory flow remains stable and laminar with no-slip boundary conditions applied. Eigenfunction expansion method is used to obtain the exact analytical solution of the general linear inhomogeneous boundary value problem. Fourier expansion of arbitrary harmonic pressure gradient and non-harmonic wall oscillations was used to calculate arbitrary driving of the fluid. In-house developed optimized computational fluid dynamics marching-in-time finite-volume method was used to test and verify all analytical results. A number of particular transients, steady-state and combined flows were obtained from the general analytical result. Generalized Stokes and Womersley flows were solved using the analytical computations and numerical experiments. The combined effects of periodic non-harmonic wall movements with oscillatory pressure gradients offers rich and interesting flow patterns even for a linear Newtonian fluid and may be particularly interesting for pumping-assist microfluidic devices. The main motivation for developing a unified solution of the unsteady laminar planar Couette–Stokes–Poiseuille–Womersley flow originates in a need for, but is not limited to, in-depth exploration of flow patterns in hemodynamic and microfluidic pumping applications.

UNSTEADY CONVECTIVE COUETTE FLOW WITH HEAT SINK AND RADIATION EFFECTS

In this research, the effects of heat sink and radiation on unsteady hydromagnetic convective Couette flow of a viscous, electrically conducting and incompressible fluid is studied. The governing equations that describe the flow formation, heat and mass transfer are modeled as Partial Differential Equations (PDEs) and solved numerically using Finite Element Method (FEM). The effect of physical parameters embedded on the velocity, temperature and concentration were studied graphically. It is noticed that, the momentum boundary layer increases as the value of radiation parameter is increased while the velocity of the fluid falls for higher values of the heat sink parameter

Influence of Exponential Space Based Heat Source on Unsteady Couette Nanoliquid Flow

Present article addresses unsteady Couette flow of nanofluid constricted Couette channel under the impression of exponential space based heat source (ESHS) and temperature based heat source (THS). The novelty of the study is to combine the effects of heat sources of type ESHS and THS to the Couette flow. The governed flow equations are solved employing FEM. The influence of dimensionless quantities such as ESHS, Biot number, variable viscosity and stretching parameter are exposed graphically. From the attained outcomes, it is observed that the profile of temperature rather than the velocity, in the Couette channel is boosted with ESHS and THS parameters.

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.

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 Convective Couette Flow with Heat Source

The effect of heat source on unsteady hydromagnetic convective Couette flow of a viscous, electrically conducting and incompressible fluid is investigated. The governing equations that explain the flow formation are modeled as Partial Differential Equations (PDEs) and solved numerically by Finite Element Method (FEM). The influence of physical parameters on the fluid velocity, temperature and concentration were presented graphically and discussed. It is seen that, the momentum and temperature boundary layers are significantly influenced as the value of heat source parameter is increased while an opposite trend is observed on the velocity as Hatman number is increased.

Kinetic and thermodynamic examinations for the unsteady couette flow problem of a plasma using the BGK cylindrical model

We aim to investigate the kinetic and irreversible thermodynamic treatment of the Couette flow of gaseous plasma (GP) confined between two coaxial rotating circular rigid cylinders. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation (BKE) is solved by applying the perturbation method coupled with the moments' approach with a two-stream Maxwellian distribution function (MDF). Nonlinear partial differential equations are precisely solved. As an actual application, we are considering the laboratory Argon GP. An interesting comparison between the non-equilibrium electron velocity distribution function (EVDF) and the equilibrium EVDF is made carefully with 3-Dimensional graphics in various time values. We found that the system goes to an equilibrium state (ES) with time compatible with Le Chatelier's principles. Moreover, we determined with very high precision the value of the system equilibrium time, which is tequ.≅2.4. That great advantage cannot be reached by solving other macroscopic magnetohydrodynamic models. The relations between the various macroscopic variables of the GP are studied. The irreversible non-equilibrium thermodynamics (NT) properties of the system are presented. We present the extended Gibbs equation (EGE) for the internal energy variation (IEV) in cylindrical geometry for GP for the first time, to the best of our knowledge. We have shown that our model is compatible with the H-theorem of Boltzmann and the Onsager-Casimir relations. The various participations in IEV are introduced. The significance of this search is due to its vast implementations in various fields, such as in GP physics, electrical engineering, medicine, biological systems, and numerous commercial and industrial deployments.

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.

Physics of unsteady Couette flow in an anisotropic porous medium

Physics of unsteady Couette flow in an anisotropic porous medium

Unsteady Couette Flow Past between Two Horizontal Riga Plates with Hall and Ion Slip Effects

Riga plate is the span wise array of electrodes and permanent magnets that creates a plane surface and produced the electromagnetic hydrodynamic fluid behavior and mostly used in industrial processes with fluid flow affairs. In cases where an external application of a magnetic or electric field is required, better flow is obtained by the involvement of the Riga plate. Riga plate acts as an agent to reduce the skin friction and enhance the heat transfer phenomena. It also diminishes the turbulent effects, so that it is possible to get an efficient flow control and it increases the performance of the machine. So the numerical investigation of the unsteady Couette flow with Hall and ion-slip current effects past between two Riga plates has been studied and the numerical solutions are acquired by using explicit finite difference method and estimated results have been gained for several values of the dimensionless parameter such as pressure gradient parameter, Hall and Ion-slip parameters, modified Hartmann number, Prandtl number, and Eckert number. In this article, the importance of the modified Hartmann number on the flow profiles is immense owing to the Riga plate. The expression of skin friction and Nusselt number has been computed and the outcomes of the relevant parameters on various distributions have been sketched and presented as well as graphically.

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.

Unsteady MHD Couette viscous fluid flow through silver metallic parallel plates with an inclined magnetic field and angular velocity subjected to constant suction at lower plate

Abstract In this paper, we discussed unsteady magneto hydrodynamic incompressible viscous couette flow along the silver metallic parallel plates in which constant periodic suction takes place at the bottom porous silver metallic shield subjected to the magnetic field with inclination along with the rotation of system. By means of appropriate choice of stream function we obtained exact solution analytically. Axial Velocity component and radial Velocity component are obtained from the analytical solution. Velocity profiles like axial and transverse are examined for different parameters α , K r , M a n d ω t . The effects of Magnetic parameter, Suction Reynolds number and Rotation parameter on the plates are discussed and illustrated graphically.