Unsteady Couette Research Articles

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 Couette flow in a rotating system

The unsteady Couette flow between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system under the boundary layer approximations is investigated. An exact solution of the governing equations has been obtained by using Laplace transform technique. It is shown that when the oscillating plate situated at an infinite distance from stationary plate then the problem reduces to the unsteady boundary layer problem in a rotating system with non-torsional oscillations of the free-stream velocity.

Dispersion in Oscillatory Couette Flow with Absorbing Boundaries

This paper presents the longitudinal dispersion of passive contaminant released in an incompressible viscous fluid flowing between two infinite parallel plates, where the contaminant undergoes irreversible heterogeneous reaction with the boundary walls. The flow is driven by the oscillation of the upper plate in its own plane with a constant velocity as well as by an imposed constant pressure gradient. This type of flow may be termed unsteady generalized Couette flow. A finite difference implicit scheme has been adopted to solve the unsteady convection-diffusion equation for all time periods based on the Aris method of moments. The influence of applied constant pressure gradient, oscillation of the upper plate, and the absorption parameter at both walls on dispersion is discussed. The dispersion coefficients are obtained for three different flow situations: plane and generalized Couette flow, unsteady generalized Couette flow, and for comparison, the combined effect of steady and unsteady Couette flows, separately. The most striking result is that unlike the case of parallel flow under periodic pressure gradient, the double-frequency period in the dispersion phenomena does not vanish, even for the high frequency of upper-plate oscillation for the case of unsteady generalized Couette flow. The axial distributions of mean concentration are determined from the first four central moments using Hermite polynomial representation for the periodic flow with or without nonzero mean flow.

Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus

This paper deals with the unsteady axial Couette flow of fractional second grade fluid (FSGF) and fractional Maxwell fluid (FMF) between two infinitely long concentric circular cylinders. With the help of integral transforms (Laplace transform and Weber transform), generalized Mittag–Leffler function and H-Fox function, we get the analytical solutions of the models. Then we discuss the exact solutions and find some results which have been known as special cases of our solutions. Finally, we analyze the effects of the fractional derivative on the models by using the numerical results and find that the oscillation exists in the velocity field of FMF.

A note on a Discrete Boltzmann Equation with multiple collisions

We compute a non-trivial explicit solution for the one-dimensional plane 6-velocity discrete Boltzmann model with multiple collisions introduced in [E. Longo, R. Monaco, On the discrete kinetic theory with multiple collisions: Plane six-velocity and unsteady Couette flow, in: Muntz, et al. (Eds.), The Proceedings of Rarefied Gas Dynamics, in: AIAA Publ., vol. 118, 1989, pp. 118–130] which asymptotically connects two particular equilibrium states. We prove that such a solution exists provided that a suitable condition on the differential elastic cross sections holds.

Unsteady Couette flows in a second grade fluid with variable material properties

Fluid solid mixtures are generally considered as second grade fluids and are modeled as fluids with variable physical parameters. Thus, an analysis is performed for a second grade fluid with space dependent viscosity, elasticity and density. Two types of time-dependent flows are investigated. An eigen function expansion method is used to find the velocity distribution. The obtained solutions satisfy the boundary and initial conditions and the governing equation. Remarkably some exact analytic solutions are possible for flows involving second grade fluid with variable material properties in terms of trigonometric and Chebyshev functions.

Unsteady free covection oscillatory couette flow through a porous medium with periodic wall temperature

This communication investigates the effect of free convection on the heat transfer and the flow through a highly porous medium bounded by two vertical parallel porous plates. It is assume that free stream velocity oscillates
 in times about a constant mean. Assuming periodic temperature at the moving plate, the approximate solutions for velocity field, emperature field, skin-friction and the rate of heat transfer are obtained and discussed with the help of graphs and tables.

The effect of variable properties on the unsteady Couette flow with heat transfer considering the Hall effect

The influence of temperature dependent viscosity and thermal conductivity on the transient Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the Hall effect is taken into consideration. The fluid is acted upon by a constant pressure gradient. The two plates are kept at two constant but different temperatures and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing non-linear equations of motion and the energy equation is obtained. The effect of the Hall term and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is examined.

On the Effectiveness of Porosity on Unsteady Flow and Heat Transfer between Parallel Porous Plates with Exponential Decaying Pressure Gradient

The unsteady Couette flow through a porous medium of a viscous, incompressible fluid bounded by two parallel porous plates is studied with heat transfer. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the viscous dissipation is included in the energy equation. The effect of the porosity and the uniform suction and injection on both the velocity and temperature distributions is examined.

Effect of Hall current on transient hydromagnetic Couette–Poiseuille flow of a viscoelastic fluid with heat transfer

The unsteady Couette–Poiseuille flow of an electrically conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer considering the Hall effect. A sudden uniform and constant pressure gradient, an external uniform magnetic field that is perpendicular to the plates and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained using finite difference approximations. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is examined.

The development of a Cartesian cut cell method for incompressible viscous flows

AbstractThis paper describes the extension of the Cartesian cut cell method to applications involving unsteady incompressible viscous fluid flow. The underlying scheme is based on the solution of the full Navier–Stokes equations for a variable density fluid system using the artificial compressibility technique together with a Jameson‐type dual time iteration. The computational domain encompasses two fluid regions and the interface between them is treated as a contact discontinuity in the density field, thereby eliminating the need for special free surface tracking procedures. The Cartesian cut cell technique is used for fitting the complex geometry of solid boundaries across a stationary background Cartesian grid which is located inside the computational domain. A time accurate solution is achieved by using an implicit dual‐time iteration technique based on a slope‐limited, high‐order, Godunov‐type scheme for the inviscid fluxes, while the viscous fluxes are estimated using central differencing. Validation of the new technique is by modelling the unsteady Couette flow and the Rayleigh–Taylor instability problems. Finally, a test case for wave run‐up and overtopping over an impermeable sea dike is performed. Copyright © 2006 John Wiley & Sons, Ltd.

WITHDRAWN: The effect of variable properties with the hall effect on unsteady couette flow and heat transfer under exponential decaying pressure gradient

WITHDRAWN: The effect of variable properties with the hall effect on unsteady couette flow and heat transfer under exponential decaying pressure gradient

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.

Unsteady Couette flow in a rotating system

We have studied the unsteady Couette flow of a viscous incompressible fluid confined between parallel plates, rotating with an uniform angular velocity about an axis normal to the plates. The flow is induced by the motion of the upper plate and the fluid and plates rotate in unison with the same constant angular velocity. An exact solution of the governing equations have been obtained for small and large time τ by applying Laplace transform technique. It is found that the primary velocity decreases with increase in rotation parameter for small as well as large time. It is interesting to note that a back flow occurs in the region 0.0 ⩽ η ⩽ 0.7 for large time with increase in K when K = 4 and 5. The secondary velocity increases in magnitude for small time with increase in rotation parameter. It is observed that the secondary velocity increases in magnitude for small values of rotation parameter. On the other hand, for large values of rotation parameter K 2 , it decreases near the stationary plate and increases near the moving plate. The shear stress due to primary flow decreases with increase in rotation parameter K 2 . On the other hand, it increases due to secondary flow with increase in rotation parameter for small time. It is noticed that for large time there exists separation in the primary and secondary flows due to high rotation.

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.

Exact solution on unsteady Couette flow of generalized Maxwell fluid with fractional derivative

In this paper the unsteady Couette flow of a generalized Maxwell fluid with fractional derivative (GMF) is studied. The exact solution is obtained with the help of integral transforms (Laplace transform and Weber transform) and generalized Mittag-Leffler function. It was shown that the distribution and establishment of the velocity is governed by two non-dimensional parameters η, b and fractional derivative α of the model. The result of classical (Newtonian fluid and standard Maxwell fluid) Couette flow can be obtained as a special case of the result given by this paper, and the decaying of the unsteady part of GMF displays power law behavior, which has scale invariance.

Hall effect on couette flow with heat transfer of a dusty conducting fluid between parallel porous plates under exponential decaying pressure gradient

In the present study, the unsteady Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponential decaying pressure gradient is studied without neglecting the Hall effect. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field is applied perpendicular to the plates. The governing equations are solved numerically using finite differences to yield the velocity and temperature distributions for both the fluid and dust particles.

A General Lumped Model for Unsteady Heat Conduction of an Asymmetric Cylinder and Unsteady Couette Flow

A General Lumped Model for Unsteady Heat Conduction of an Asymmetric Cylinder and Unsteady Couette Flow

Three‐dimensional fluctuating Couette flow through the porous plates with heat transfer

Unsteady Couette flow of a viscous incompressible fluid between two horizontal porous flat plates is considered. The stationary plate is subjected to a periodic suction and the plate in uniform motion is subjected to uniform injection. Approximate solutions have been obtained for the velocity and the temperature fields, skin friction by using perturbation technique. The heat transfer characteristic has also been studied on taking viscous dissipation into account. It is found that the main flow velocity decreases with increase in frequency parameter. On the other hand, the magnitude of the cross‐flow velocity increases with increase in frequency parameter. It is seen that the amplitude of the shear stress due to main flow decreases while that due to cross‐flow increases with increase in frequency parameter. It is also seen that the tangent of phase shifts both due to the main and cross‐flows decrease with increase in frequency parameter. It is observed that the temperature increases with increase in frequency parameter.

Unsteady MHD couette flow and heat transfer of dusty fluid with variable physical properties

This paper studies the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with variable viscosity and electric conductivity. The fluid is driven by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates. The governing non-linear partial differential equations are solved numerically using finite differences. The effect of the variation in the viscosity and electric conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.