Steady Couette Flow Research Articles

Nonlinear-response theory for steady planar Couette flow

We present a simplified derivation of the Yamada-Kawasaki formula for the nonlinear adiabatic response of the stress tensor to planar Couette flow. This formally exact expression is then used to prove the validity of two nonequilibrium molecular-dynamics algorithms that have been used to study fluids undergoing planar Couette flow, very far from equilibrium.

Steady Couette flow in a strong external field

Plane steady Couette flow at low Mach number is studied in the presence of an external force field. Force strengths may be so great that the gas is highly rarefied in one region of the flow but a continuum nearby. An approximate solution to the Boltzmann equation, of modified Liu–Lees type, is found to yield simple analytic expressions for flow velocity and shear stress. These predictions give correct results in both the continuum and rarefied limits, and show reasonable agreement with other more exact predictions in the limited regimes for which such predictions have been obtained. It is also shown that the predicted relation between flow and shear stress may be described by a simple generalized viscosity coefficient of the Cha–McCoy type which applies over the complete range of force strength and rarefaction.

Analytical solutions of the discrete Boltzmann equation for the steady couette flow for bynary gas mixtures

Analytical solutions of the discrete Boltzmann equation for the steady couette flow for bynary gas mixtures

Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow

Nonequilibrium computer simulations reveal that the equation of state of fluids undergoing shear flow, varies with strain rate. This observation prompted the development of a nonlinear generalization of irreversible thermodynamics to describe steady planar Couette flow, very far from equilibrium. In this paper we use computer simulation to perform a quantitative test of a prediction of this thermodynamics. The prediction tested is: fluids which exhibit positive shear dilatancy for isothermal shear flow should also cool as the strain rate is increased while keeping the internal energy constant. To perform calculations of this effect a new nonequilibrium molecular dynamics algorithm was developed to simulate Couette flow at constant internal energy.

Hall effect on Couette flow

The effect of Hall currents on a steady hydromagnetic Couette flow was studied using porous and non-conducting plates. Closed-form solutions were obtained for the velocity field and the shearing stresses at the plates. The effects of various parameters on the velocity field and shearing stress are shown by graphs and tables.

Nonlinear shear viscosity of a gas

This article contains a derivation of the shear rate dependence of the viscosity of a gas in steady Couette flow. The viscosity is found from a solution of the Bhatnagar-Gross-Krook model kinetic equation, taking into account the viscous heating of the gas. The results are in reasonably good agreement with computer molecular dynamic experiments by Naitoh and Ono.

Kinetic theory boundary conditions for discrete velocity gases

Boundary conditions are investigated for a model gas composed of identical particles with velocities restricted to a given finite set of vectors. A possible model of the gas surface interaction is given and an H theorem for a gas in a vessel is obtained. Then, the steady Couette flow between two parallel plates is studied. The model with four coplanar velocities is used and the velocity set has arbitrary orientation. The exact kinetic solution is compared with the solutions of the associated Navier–Stokes problems.

Temperature distribution in Couette flow past a permeable bed

The temperature distribution in a steady plane Couette flow having one permeable bounding wall is investigated in the presence of buoyancy forceN 0 whenN 0>0, it is shown that heat is transported both by convection and diffusion. The effect of convection is to increase the magnitude of the temperature distribution both in the free and Darcy flows. In particular, it is shown that the wall shear has no significant effect on the temperature distribution. The rate of heat transfer between the fluid and the surface is also calculated and it is shown that, it increases with the porous parameterσ. Although the viscous dissipation has very little effect on the temperature distribution yet its effect is significant on heat transfer.

Steady Couette flow of a simple fluid between porous plates

Steady Couette flow ofNoll's simple fluid between two porous plates has been considered. It is seen that such flow, though not strictly lineal, is viscometric and unique solution for the main flow exists, in general, under Lipschitz's condition on the shearing function. Special cases have been discussed.

Hall effects on hydromagnetic Couette flow of Class-II in a rotating system in the presence of an inclined magnetic field with asymmetric heating/cooling of the walls

Hall effects on steady hydromagnetic Couette flow of class-II of a viscous, incompressible and electrically conducting fluid with non-conducting walls in a rotating system in the presence of an inclined magnetic field is investigated. Exact solution of the governing equations is obtained in closed form. Expressions for the shear stress at the moving plate due to primary and secondary flows and mass flow rates in the primary and secondary flow directions are also derived. Asymptotic behavior of the solution for velocity and induced magnetic field is analyzed, for small and large values of rotation parameter K2 and magnetic parameter M2 to gain some physical insight into the flow pattern. Heat transfer characteristics of the fluid are considered taking viscous and Joule dissipations into account when walls of the channel are asymmetrically heated or cooled. Numerical solution of energy equation and numerical values of rate of heat transfer at the stationary and moving plates are computed with the help of MATLAB software. The numerical values of velocity, induced magnetic field and fluid temperature are displayed graphically versus channel width variable η for various values of Hall current parameter m and angle of inclination of magnetic field θ whereas numerical values of shear stress at the moving plate due to primary and secondary flows, mass flow rates in the primary and secondary flow directions and rate of heat transfer at the stationary and moving plates are presented in tabular form for various values of m and θ.

Laminar heat transfer to a steady couette flow between parallel plates

An exact analytical solution of the energy equation is given for the laminar, steady state Couette flow of an incompressible viscous fluid between parallel plates. Thermophysical properties of the fluid are assumed to be temperature independent. Four cases of boundary conditions are considered. These include unit temperature steps at one or both plates or a unit temperature step at one plate, the other plate being completely insulated. The spacial development of the temperature profiles is set forth graphically. Variation of the local Nusselt number with longitudinal distance and limiting values for the region of full thermal stabilization are reported.

Unsteady couette flow of a conducting fluid between two parallel plates under a transverse magnetic field—II

The effect of a sudden change in magnetic field and pressure gradient on a steady Couette flow of a viscous incompressible fluid between two parallel plates in the presence of a transverse magnetic field is considered. Expressions for the velocity of the fluid in the disturbed flow, the intensities of the electrical and magnetic fields are obtained in two cases when the plates are non-conducting and when they are perfectly conducting.

Perturbation of steady viscoelastic flows with application to the couette viscometer

Equations are developed to describe infinitesimal time-dependent perturbations of slow steady viscoelastic flows of any order. The theory is specialized to viscometric flows of order four or less, and the particular case of Couette flow is considered in detail. It is shown that the material constants appearing in the third-order theory can be determined using a Couette viscometer. In the experiments which are required the torque applied to the viscometer has a constant component producing a steady Couette flow, and a sinusoidally time-dependent component producing an infinitesimal time-dependent perturbation. A possible experimental set-up for making the necessary measurements is described.

Heat transfer to a steady Couette flow with pressure gradient

The steady temperature distribution in an incompressible fluid flowing under a specified pressure gradient between a semi-infinite flat plate and a parallel moving belt, both of which are maintained at a temperature different from that of the entering fluid, is obtained. After separation of variables, the lower eigenvalues and eigenfunctions of the resulting Sturm-Liouville problem are found by numerical integration, and the asymptotic values by the Langer method for one transition point. Numerical results are presented for the dimensionless temperature field and heat fluxes.