Development of electroconvection in liquid dielectrics

The development of electroconvection in liquid dielectrics is analyzed theoretically from the standpoint of the dissociation-injection model of conductivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 34–42, January–February, 1989.The author wishes to thank the participants in the G. A. Lyubimov seminar for discussing his work and making useful suggestions.     

Stability of nonisothermal couette flow

A study is made of the loss of stability of the stationary flow of a viscous fluid between two heated rotating cylinders. The linearized stability problem is studied in the Boussinesq approximation. The perturbations are assumed to be periodic in the time, and also in the axial and azimuthal directions. The neutral curves are calculated numerically. The ranges of variation of the parameters of the problem are found, and in them the most dangerous perturbations (in the class of spatially periodic perturbations) are those without rotational symmetry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 167–170, January–February, 1980.I thank V. I. Yudovich for constant interest in the work.     

Certain nonisothermal flows of fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 83–92, May–June, 1990.     

Numerical modeling of two-dimensional nonisothermal filtration

A numerical method will be offered for the calculation of nonisothermal filtration. The model permits consideration of capillary and gravitational forces, as well as heat loss to the surrounding rock. The process of tongue formation in nonisothermal filtration will be considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–179, November–December, 1978.In conclusion the author thanks A. A. Bekserman, R. M. Kats, and M. I. Shvidler for their valuable remarks.     

Investigation of electroconvection and electroconvective heat transfer in liquid dielectrics with unipolar injection conductivity

The characteristics of electroconvection and electroconvective heat transfer in liquid dielectrics possessing unipolar injection conductivity [1, 2] are investigated and certain types of EHD pumps are calculated. These investigations are necessary because so far there is no theoretical explanation for the slowing of heat transfer with increase in voltage in strong fields [3, 4]. Moreover, there is no satisfactory theory of EHD pumps that would make it possible not only to establish the basic operating principles of existing (grid [5], knife-edge [6] and other [7, 8]) equipment but also to predict the performance of high-pressure EHD pumps.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 14–20, March–April, 1988.     

On the formulation of problems of nonisothermal water and vapor flow through a high-permeability formation

The formulation of self-similar problems of single- and two-phase water and vapor flow through high-permeability rocks is considered in the case when heat conduction is unimportant. The properties of the corresponding system of conservation laws, which affect the relative position of the integral curves of the Riemann waves and the discontinuity adiabatic curves, are investigated. The problem of breakdown of an arbitrary discontinuity in a geothermal formation with supercritical water parameters is solved.     

Equilibrium of a free nonisothermal liquid film

The equilibrium of a free weightless liquid film fixed over a planar contour and acted upon by thermocapillary forces is studied. Trends in the behavior of free liquid films are important for understanding the processes occurring in foams. The equilibrium equations for a nonisothermal weightless free film are derived for the two limiting cases: the temperature of the film is considered a known function of the coordinates; the free surface of the film is thermally insulated. For the plane and axisymmetric cases, the existence conditions for the solutions of the resulting nonlinear boundary-value problems are found and their properties are studied. For the general case, an approximate solution of the equilibrium problem is obtained provided that the analogue of the Marangoni number is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 16–29, May–June, 2007.     

Plane nonisothermal poiseuille flow for four molecular models

The method of three-dimensional moments in the third approximation is used to solve the problem of plane nonisothermal Poiseuille flow. Flows due to temperature and pressure gradients, as well as the rate of thermal slip, are obtained for four molecular models. A comparison is made with the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 182–183, July–August, 1973.     

Quasiequilibrium Knudsen boundary layer on a nonisothermal porous body

The state of a gas near a permeable nonisothermal body with ultrathin pores, that is, pores in which the motion of molecules is not accompanied by intermolecular collisions, is studied. A boundary layer of a new type, namely, the quasiequilibrium Knudsen boundary layer on the porous body surface, is investigated. It is formed on condition that within the body there is a heat flux, even when the body is in an equilibrium gas. The statistical methods for solving the Boltzmann equation are used to determine the temperature and pressure jumps across the Knudsen layer near thin perforated and porous membranes.     

Derivation of the equations of slow nonisothermal gas flows

In recent years, some new phenomena have been predicted theoretically on the basis of the Burnett approximation. These include thermal-stress and concentration-stress convection [1–3], and also effects due to the influence of a magnetic field in a multiatomic gas (viscomagnetic heat flux, etc., [4]). It has been shown theoretically (see [5]) that under certain conditions various terms of the Burnett approximation must be taken into account in the expression for barodiffusion. The conclusions relating to a viscomagnetic heat flux have recently been confirmed experimentally [4]. The predicted phenomena follow rigorously from the Burnett equations. However, many hydrodynamicists adopt a sceptical attitude to these equations, which is due partly perhaps to attachment to the classical Navier-Stokes equations, which have served theoreticians without fail for a century and a half. In this connection, we discuss the evolution of ideas relating to the validity of the Burnett approximation. We discuss the minimal assumptions which must be made in order to derive the equations of slow [Reynolds number R = 0(1)], essentially nonisothermal [ ln T = 0(1)] flows of a gas as a continuous medium (Knudsen number K O) in the case when the derivatives of the thermal Burnett stresses in the momentum equation have the same order of magnitude as the Euler and Navier-Stokes terms of this equation [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 77–84, November–December, 1979.We thank G. I. Petrov and L. I. Sedov for discussions that stimulated the above analysis.     

Numerical analysis of the stability of nonisothermal couette flow

The stability of convective motion of a liquid between two rotating heated cylinders is investigated in the absence of external forces. The mathematical model for describing the convection is obtained from the general equations [1, 2] on the assumption that the density of the liquid, the thermal conductivity, the specific heat and the viscosity coefficients depend only on temperature, and that the work done by the pressure forces and the viscous dissipation are negligibly small. The thermal expansion coefficient of the liquid is not assumed to be small, which distinguishes the models in question from the classical Oberbeck-Boussinesq model [1, 3, 4]. Rostov-on-Don. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–76, September–October, 1988.