Parallel Plates In Relative Motion Research Articles

Friction Force and Radiative Heat Exchange in a System of Two Parallel Plates in Relative Motion: Corollaries of the Levine–Polevoi–Rytov Theory

It has been shown that the fundamental results obtained in the works by Levine–Polevoi–Rytov (1980) and Rytov (1990) adequately describe the rate of radiative heat exchange and frictional force in a system of two thick parallel plates in relative motion, in full agreement with the results obtained by other authors later. A numerically calculated friction force for Drude metals turns out to be higher by a factor of 107 than the early result obtained by Polevoi. In addition, the friction force significantly increases with increasing the conductivity of the plates or increasing the relaxation time of electrons with decreasing temperature.

Monte Carlo simulation of nonlinear gravity driven Poiseuille–Couette flow in a dilute gas

Abstract Through the direct simulation Monte Carlo, the Boltzmann equation is solved numerically for dilute hard spheres gas between two infinite parallel plates in relative motion and at the same time the particles feel the action of a uniform body force along the same direction as the moving plate. The study is conducted on the effect of the external force on the nonlinear properties of the Poiseuille–Couette flow. We have been interested in the bulk properties, to inhibit the influence of finite-size effects, while ignoring linear effects like Knudsen boundary layer to investigate the generalised transport coefficients depending on the shear rate nonlinearly: the two nonlinear thermal conductivity function of normal heat flux and parallel one, the viscosity function, the tangential friction function, and the thermal curvature. The results indicate that the effect of the external force is significant on the nonlinear functions, where the viscosity function and normal thermal conductivity are increasing functions of this field.

Сила трения и радиационный теплообмен в системе двух параллельных пластин при их относительном движении: следствия теории Левина--Полевого--Рытова

AbstractIt has been shown that the fundamental results obtained in the works by Levine–Polevoi–Rytov (1980) and Rytov (1990) adequately describe the rate of radiative heat exchange and frictional force in a system of two thick parallel plates in relative motion, in full agreement with the results obtained by other authors later. A numerically calculated friction force for Drude metals turns out to be higher by a factor of 10^7 than the early result obtained by Polevoi. In addition, the friction force significantly increases with increasing the conductivity of the plates or increasing the relaxation time of electrons with decreasing temperature.

Non-Newtonian Couette-Poiseuille flow of a dilute gas

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.

Director Dynamics Within a Boundary Layer in Contact with a Shearing Solid Surface With Non-Rigid Anchoring

The hydrodynamics of liquid crystals within thin boundary layers in contact with solid surfaces is strongly perturbed by the director anchoring on these surfaces; that manifests by occurrence of strong gradients and backflows. Accordingly, it is legitimate to question the interpretation of rheological measurements based on flow properties in the bulk where, moreover, director and velocity gradients are often assumed to be homogeneous. This remark is enhanced by the fact that rheology probes the fluid in contact with a solid surface. On the other hand, comparison between theoretical predictions and experimental observations close to the solid surface may shed light on the nematic-solid interaction. For these reasons the director dynamics at a solid surface deserves to be analysed theoretically. We have investigated the effect of non-rigid anchoring within the frame-work of Leslie-Ericksen theory combined with Rapini-Papoular model [A. Rapini, M. Papoular, J. Phys., 30C, 4, (1969)] for which the surface energy density is characterised by an anchoring strength and a preferred orientation of the director called easy axis. Calculations have been performed for nematics enclosed between two parallel plates in relative motion. Results for aligning and tumbling low molecular weight liquid crystals are presented. They may be summarised as follows: (i) strong inhomogeneities close to the surfaces, (ii) director precession at the surface for aligning nematics under certain conditions and (iii) relaxation of the stored elastic energy for tumbling nematics.

Linear instability of Poiseuille–Couette–Ekman flows: Local results for flows between differentially rotating disks with throughflow

The instabilities of incompressible flows between two parallel plates in relative motion in a system rotating about an axis perpendicular to the plates are analyzed in the case when a pressure gradient perpendicular to the plate motion is imposed. This system represents the local approximation to flows between differentially rotating disks with imposed throughflow. Relationships of the instabilities to those of the Ekman layer and of the Ekman–Couette layer are discussed.

The stability of the modified plane couette flow in the presence of a transverse magnetic field

The stability against small disturbances of the plane laminar motion of an electrically conducting fluid between parallel plates in relative motion under a transverse magnetic field is investigated. Assuming that the outer regions adjacent to the fluid layer are electrically non-conducting and non-ferromagnetic, the appropriate boundary conditions on the magnetic field perturbations are presented. The Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Reynolds number R c, the critical wavenumber α c and the critical wave speed c c are obtained for wide ranges of the magnetic Prandtl number P m and the Hartmann number M. It is found that there exists a stationary mode of instability in addition to a travelling-wave mode of instability, and that except for the case when P m is sufficiently small, the fluid flow becomes more unstable to the stationary mode as P m increases.

Nonlinear solutions of modified plane Couette flow in the presence of a transverse magnetic field

A nonlinear analysis is performed numerically for the motion of an electrically conducting fluid between parallel plates in relative motion when a transverse magnetic field is applied. It is found that steady three-dimensional finite-amplitude solutions exist even when the linear analysis predicts an infinite critical Reynolds number.

A Note on Oscillatory Couette Flow in a Rotating System

An alternative solution is proposed for the oscillatory Ekman boundary layer flow bounded by two parallel plates in relative motion (Muzumder, 1991). The solution brings out among other things, the phenomenon of resonance which is of importance in rotating systems.

Effect of Crossflow on Oscillatory Flow in a Porous Medium Between Two Parallel Plates in Relative Motion

This paper deals with the incompressible flow through a porous medium bounded by two parallel permeable plates, one of which is stationary and the other slides and oscillates in its own plane. Also uniform crossflow is superimposed through the plates. Analytical solutions for flow parameters are obtained. The effect of crossflow, permeability, and the frequency of the moving plate on the velocity, skin friction has been investigated. It is shown that skin friction can be reduced considerably by injection at the lower plate.

Heat transfer in unsteady flow through a porous medium between two infinite parallel plates in relative motion

An approximate solution to the heat transfer in a flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented. Expressions for the mean temperature, the amplitude, and phase of the first and second harmonic of the rate of heat transfer and the mean rate of heat transfer are derived. The mean temperature is shown on graphs and the numerical values of the amplitudes and the phase are entered in a table. It is observed that the mean rate of heat transfer decreases with more ease of percolation but increases with increasing the frequency ω.

Closure to “Discussion of ‘Unsteady Flow in a Porous Medium Between Two Infinite Parallel Plates in Relative Motion’” (1986, ASME J. Fluids Eng., 108, p. 489)

Closure to “Discussion of ‘Unsteady Flow in a Porous Medium Between Two Infinite Parallel Plates in Relative Motion’” (1986, ASME J. Fluids Eng., 108, p. 489)

Unsteady Flow in a Porous Medium Between Two Infinite Parallel Plates in Relative Motion

An approximate solution to the unsteady flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented here. Expressions for the transient velocity, the amplitude, the phase angle α and the skin-friction are derived and numerically calculated. It is observed that the amplitude increases with increasing σ, the permeability parameter, and ω, the frequency. Also, there is always a phase lead, and the phase angle α decreases with increasing σ.

Flow of a Nonlinear Heat-Conducting Viscoelastic Fluid

The Koh-Eringen formulation of nonlinear thermoviscoelasticity is used to study the behavior of a heat-conducting Rivlin-Ericksen fluid characterized by a set of constitutive equations involving the coupled dependence of stress and heat flux on temperature gradient and the first two Rivlin-Ericksen tensors. Slow steady-state flow of the fluid under a small temperature gradient is considered. With the use of a perturbation technique, the basic equations and boundary conditions are derived for each increasing order of approximation. The first order equations are precisely those of a Newtonian fluid. Succeeding higher order corrections involve linear equations also although the results of preceding lower order approximations are used. The given boundary conditions are satisfied in the first order analysis. Homogeneous boundary conditions are then applicable for higher order corrections. Two specific problems are considered: (1) pressure flow of the fluid between two parallel plates in relative motion and at different constant temperatures; and (2) Couette-helical flow in the annular region between two coaxial circular cylinders in relative translational velocity parallel to the axis and at two different constant temperatures. Numerical results are plotted for several Eckert numbers and other thermomechanical parameters.

Plane couette flow of an incompressible non-Newtonian fluid with temperature dependent viscosity

It has previously been shown by one of the authors that the variational principle of minimum entropy production with constant fluxes, established by Glansdorff and Prigogine, may be used in presence of convection by defining appropriately the generalized fluxes and forces. In this paper, this principle is applied to the description of the stationary flow of a non-Newtonian viscous incompressible fluid between two parallel plates in relative motion. The fluid is characterized by a viscosity decreasing exponentially with the temperature and by a thermal conductivity independent of the temperature.

The Hydromagnetic Stability of the Modified Plane Couette Flow in the Presence of a Transverse Magnetic Field

The hydromagnetic stability against small disturbances is investigated on the plane laminar motion of an electrically conducting fluid between parallel plates in relative motion in the presence of a transverse magnetic field. Curves of the neutral stability in the (α, R )-plane (α, the wave-number; R , the Reynolds number) are calculated for various values of the Hartmann number M . It is thus found that the critical Reynolds number R c is infinite for M 15). Thus, we may conclude that the flow is always stable for 0≦ M ≦3.91, destabilized by the magnetic field for 3.91 5.4.