Onset of Rayleigh-Bénard convection in gases - classical and extended thermodynamics

This paper deals with the determination of the critical parameters that induce instability in the Rayleigh-Bénard arrangement, viz. a gas confined between two rigid plates and heated from below. In order to compute the critical values of the parameters, classical thermodynamics with the Navier-Stokes and Fourier constitutive relations and extended thermodynamics with thirteen moments are used. Linear stability analysis is performed. The results of both theories are illustrated and compared.Received: 26 August 2003, Accepted: 1 September 2003, Published online: 5 December 2003     

Solution of problems involving the stress state of composite materials with curved layers in the geometrically nonlinear statement

Mechanics Institute, Academy of Sciences of the Ukraine, Kiev. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaijan Republic, Baku. Translated from Prikladnaya Mekhanika, Vol. 28, No. 6, pp. 3–8, June, 1992.     

Effect of plastic properties of fluids on phase permeabilities

The linearity of Darcy's law is known to be disturbed at both high and low flow velocities [1–3]. In the first case, this is associated with the increase in the inertial component of the hydraulic losses in the presence of large pressure gradients. The effect was theoretically investigated, for example, in [4]. In the second case, the nonlinearity is associated with the interphase interaction of the fluids and the skeleton of the porous material on the contact surface [5]. Here, within the context of the percolation approach [6, 7], the behavior of the phase permeabilities is analyzed for low flow velocities, when on the microlevel (flow in an individual pore channel) the fluids display plasticity properties [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 110–115, March–April, 1991.     

Turbulent flow of non-Newtonian substances

Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ _m and a factor _m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension.The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm. Nomenclature C volume fraction solid in suspension - D tube diameter - f Darcy-Weisbach friction factor - g gravitational acceleration - K _s proportionality constant defined by eq. [10] - L length of tube - P pressure - Re Reynolds number - t exponent defined by eq. [1] - V mean velocity - V ^* volume of particles in pipe lengthL - W settling velocity of particles - _m factor defined by eq. [1] - shear rate - turbulent pseudo shear rate defined by eqs. [8] and [9] - _w wall shear stress - ( _w) _s increment in wall shear stress due to presence of settling particles - µ _m limiting viscosity at high rate of shear - ₁ density of carrier liquid - _m density of mixture - _s density of solid Professor of Chemical Engineering, University of Toronto and scientific advisor to Worthington (Canada) Ltd.With 8 figures     

The experimental determination of velocity distribution in annular flow

In the study of the flow of a fluid through an annular gap, the outer surface of which is stationary while the inner surface may be rotated, it is necessary to be able to accurately determine the velocity profiles obtaining in the axial, tangential, and radial directions of flow.

A method is described for this purpose employing hot-wire anemometry techniques and typical profiles are presented for each of the above flow directions. In the case of pure axial flow, a comparison is made between experimental and theoretical results, showing a close correspondence.     

The theory of dispersion of chemically active solutes in a rectilinear flow field

We report a procedure for the construction of the dispersion coefficients which define the dispersion approximation to the transverse average of the solution of the scalar convective diffusion equation; the procedure enjoys a generalization to the vector convective diffusion equation. We exhibit the full time dependence of the dispersion coefficients in any transverse average and identify a mathematically preferred transverse average for the dispersion of chemically active solute.     

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–190, January–February, 1977.     

Evaluation of three-dimensional stresses in shrink-fit problems by scattered-light photoelasticity

Stresses caused by shrink fits are commonly evaluated by using Lame's solution or by other analytical methods in which it is assumed that the radial stresses on the surface of contact are distributed uniformly, or in some stepwise manner, and that friction forces between the bodies are zero. These assumptions were not necessary in the experimental problem solved. Heretofore, no experimental techniques have been available to check the existing theories on a three-dimensional basis. The stresses which result when a short, hollow, thick-walled cylinder is shrunk over a shaft which is a solid shaft or a thick-walled, hollow shaft were determined. Equipment and techniques using scattered-light three-dimensional photoelasticity with a laser light source were developed and applied.     

Experimental and theoretical determination of frequencies of elastic toroids

Experiments are described which determine natural frequencies of five toroidal models whose major diameters are of 10 in. and whose minor diameters vary from 0.25 to 2 in. The experimentally determined frequencies are compared with the theoretical frequencies derived using the elementary theories for the in-plane and out-of-plane vibrations of circular rings of R. Hoppe and J. H. Michell, as well as the method of internal constraints. The comparative results for the frequencies are presented in tabular form.