Unsteady Couette Research Articles

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.

Effects of ion slip and Hall current on unsteady Couette flow of a dusty fluid through porous media with heat transfer

In this study, the unsteady Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid through a porous medium is studied with the consideration of both Hall current and ion slip. The parallel plates are porous and subjected to a uniform suction from above and injection from below while an external uniform magnetic field is applied perpendicular to the plates. A numerical solution for the governing momentum and energy equations are obtained using the finite difference method. The influence of magnetic field parameters, the porosity of the medium, suction or injection velocity, and ion slip parameter on velocity and temperature fields of both fluid and dust particles is demonstrated.

Modelling the Effect of Variable Viscosity on Unsteady Couette Flow of Nanofluids with Convective Cooling

This paper investigates numerically the effects of variable viscosity on unsteady generalized Couette flow of a water base nanofluid with convective cooling at the moving surface. The Buongiorno model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The nonlinear governing equations of continuity, momentum, energy and nanoparticles concentration are tackled numerically using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme. Numerical results for velocity, temperature, and nanoparticles concentration profiles together with skin friction and Nusselt number are obtained graphically and discussed quantitatively.

Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation

This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.

Effect of chemical reaction and radiation absorption on the unsteady MHD free convection Couette flow in a vertical channel filled with porous materials

This paper deals with effect of chemical reaction and radiation absorption on the unsteady MHD natural convection flow in a vertical channel filled with porous materials. One of the plate moves with a constant velocity in the direction of fluid flow while the other plate is stationary. A uniform magnetic field acts perpendicular to the porous plate, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this problem are solved analytically using two-term harmonic and non-harmonic perturbation series method. The results of the analytical solutions for velocity, temperature and concentration profiles of both phases are graphically presented and discussed. It is noteworthy to mention that growing permeability and channel width parameter lead to increase in the fluid velocity profile. Results in the present work have been compared with other works in literature and an excellent agreement is found.

Irreversibility analysis of unsteady couette flow with variable viscosity

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.

Thermal decomposition of unsteady non-Newtonian MHD Couette flow with variable properties

Purpose – The purpose of this paper is to investigate the unsteady magnetohydrodynamic (MHD) Couette flow of an electrically conducting incompressible non-Newtonian third grade reactive fluid with temperature-dependent variable viscosity and thermal conductivity properties under isothermal surface conditions. Design/methodology/approach – The coupled non-linear partial differential equations for momentum and energy balance governing the transient problem are obtained and tackled numerically using a semi-discretization finite difference technique. Findings – The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal stability conditions are presented graphically and discussed quantitatively. Practical implications – The approach is applicable to modelling the complex physical phenomenon in MHD lubrications that occurs in numerous areas of engineering and industrial processes. Originality/value – This paper may be of industrial and engineering interest especially in understanding the combined effects of unsteadiness, variable thermophysical properties and magnetic field on the thermal stability condition for a reactive non-Newtonian third grade fluid under Couette flow scenario.

FINITE ELEMENT ANALYSIS OF UNSTEADY RADIATIVE MHD NATURAL CONVECTION COUETTE FLOW BETWEEN PERMEABLE PLATES WITH VISCOUS ND JOULE DISSIPATION

This paper discusses the unsteady magnetohydrodynamic free convection Couette flow of an incompressible viscous fluid between two infinite vertical permeable plates in the presence of thermal radiation with an exponentially decaying pressure gradient. A uniform magnetic field that is perpendicular to the plates, and uniform suction and injection through the plates are applied. The magnetic field lines are assumed to be fixed relative to the moving plate. The momentum equation takes buoyancy forces into consideration, while the energy equation considers thermal radiation effects and viscous and Joule dissipations. The fluid is considered to be a gray absorbing-emitting but nonscattering medium in the optically thick limit. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The coupled pair of non-linear partial differential equations is discretized using the Galerkin finite element method. This yields a system of non-linear algebraic equations which is solved using an iterative method to obtain the velocity and temperature distributions. The effects of suction parameter S, radiation parameter Rd, Received: May 15, 2014 c © 2015 Academic Publications, Ltd. url: www.acadpubl.eu Correspondence author 124 V.M. Job, S.R. Gunakala Grashof number Gr, magnetic parameter H, Prandtl number Pr and Eckert number Ec on the velocity and temperature distributions are investigated. AMS Subject Classification: 76R10, 76W05

Ion slip effect on unsteady Couette flow of a dusty fluid in the presence of uniform suction and injection with heat transfer

The combined effects of Hall current, ion slip, viscous dissipation, and Joule heating on unsteady magnetohydrodynamic Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid are studied under a constant pressure gradient. The fluid is subjected to an external uniform magnetic field and a uniform suction and injection perpendicular to the plates (y-direction). Numerical solutions for the constitutive equations are obtained using the method of finite differences. The effects of the magnetic field, Hall parameter, and ion slip parameter on the velocity and temperature distributions for both the fluid and particle phases are investigated in details and shown graphically. It is found that, the Hall current and ion slip parameters have a great effect on the fluid and dust velocities and temperature.

Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current

The aim of the present paper is to study the unsteady magneto-hydrodynamic viscous Couette flow with heat transfer in a Darcy porous medium between two infinite parallel porous plates considering Hall effect, and temperature dependent physical properties under constant pressure gradient. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is flowing through a porous medium that is assumed to obey Darcy’s law. A numerical solution for the governing nonlinear partial differential equations coupled with set of momentum equations and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions are investigated. It is found that the porosity number M has a marked effect on decreasing the velocity distribution (owing to a simultaneous increase in Darcy porous drag). Also the temperature T is decreased considerably with increasing porosity number. With increasing Hall current parameter m, the velocity component u (x-direction) is considerably increased, whereas velocity component w (z-direction) is reduced. Temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing m.

A parallel Runge–Kutta discontinuous Galerkin solver for rarefied gas flows based on 2D Boltzmann kinetic equations

The high-order Runge–Kutta Discontinuous Galerkin (RKDG) method is applied to solve the 2D Boltzmann kinetic equations. A conservative DG type discretization of the non-linear collision relaxation term is formulated for both the Bhatnagar–Gross–Krook and the ellipsoidal statistical kinetic models. Verification is carried out for a steady and an unsteady oscillatory 1D Couette flows, a 2D conduction problem as well as for a 2D long microchannel flow by comparison with the DSMC and analytical solutions. The computational performance of the RKDG method is compared with a widely used second-order finite volume method. The RKDG method has up to 3rd-order spatial accuracy and up to 4th-order time accuracy and is more efficient than the finite volume approach. The parallelization by domain decomposition in physical space is implemented and parallel performance is evaluated. It is shown that 2nd order RKDG is over 15 times faster than the 2nd-order FVM method for the Couette flow test case. The high-order RKDG method is especially attractive for solution of low-speed and unsteady rarefied flows.

Unsteady Couette Flow in a Composite Channel Partially Filled with Porous Material: A Semi-analytical Approach

This study is devoted to investigate the unsteady fully developed time-dependent Couette flow in a composite channel partially filled with porous material. The Brinkman-extended Darcy model is used to simulate momentum transfer in the porous medium. The fluid and porous regions are interlinked by equating the velocity and by considering shear stress jump conditions in the interface. The solutions of the governing equations are obtained using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert from Laplace domain to time domain. The solution obtained is validated by presenting comparisons with closed form solution obtained for steady flow which has been derived separately and also by implicit finite difference method. During the course of numerical comparison, an excellent agreement was found between steady-state solution obtained exactly and unsteady solution obtained by implicit finite difference method or Riemann-sum approximation method at large values of time. The effect of various flow parameters entering into the problem is discussed with the aid of line graphs. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated time-dependent Couette flow in composite channel.

Unsteady Couette Flow of a Thermally Conducting Viscoelastic Fluid under Constant Pressure Gradient in a Porous Medium

Unsteady Couette flow through a porous medium of an incompressible non-Newtonian viscoelastic fluid between two parallel horizontal porous plates is studied. A constant pressure gradient in the axial direction and a uniform suction and injection normal to the surface of the plates are applied. The two plates are kept at different but constant temperatures, heat transfer through the conducting fluid is considered, and viscous dissipation is not neglected. Numerical solutions for the governing momentum and energy equations are obtained using the finite difference method. The results show that the porosity of the medium and the departure from the Newtonian characteristics of the fluid to viscoelasticity result in a drop in the velocity of flow and a drop in temperature and change the transient duration. The suction and injection reduce both the velocity and temperature at the middle plane.

A fractional step local boundary integral element method for unsteady two-dimensional incompressible flow

A meshless local boundary integral method is used to analyse incompressible fluid flow in two-dimensional domains. The method solves the incompressible Navier–Stokes equations in terms of the primitive variables using the characteristic-based split scheme. The basic equations are derived via interpolation using radial basis functions. Three test cases are presented here: unsteady Couette flow and the problems of a lid-driven cavity and a backward-facing step. The procedure produces stable solutions with results comparable to those of other conventional methods.

On MHD unsteady reactive Couette flow with heat transfer and variable properties

Abstract This study is devoted to investigate the effect of magnetic field on a reactive unsteady generalized Couette flow with temperature dependent viscosity and thermal conductivity. It is assumed that conducting incompressible fluid is subjected to an exothermic reaction under Arrhenius kinetics, neglecting the consumption of the material. The model nonlinear differential equations governing the transient momentum and energy balance are obtained and tackled numerically using a semi-discretization finite difference technique coupled with Runge-Kutta Fehlberg integration scheme. Important properties of the velocity and temperature fields including thermal stability conditions are presented graphically and discussed quantitatively.

Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates

In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar–Gross–Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the implementation of the high-order compact finite-difference Lattice Boltzmann method (CFDLBM) in the generalized curvilinear coordinates is robust, efficient and accurate for solving steady and unsteady incompressible flows over practical geometries.

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.

Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls

The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.

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.

Three-dimensional oscillating flow between two parallel plates through a porous medium

An unsteady Couette flow between two parallel plates when upper plates oscillates in its own plane and is subjected to a constant suction and the lower plate to a injection velocity distribution through the porous medium has been analyzed. The approximate solution has been obtained using perturbation technique. It is seen that the primary velocity increases whereas the secondary velocity decreases with an increase in permeability parameter. It is also found that the primary velocity increases with an increase in the Reynolds number as well as the suction parameter. The magnitude of the secondary velocity increases near the stationary plate but decreases near the oscillating plate with an increase in the Reynolds number. Whereas, it increases with an increase in the suction parameter.