Influence of anisotropy of the permeability on the convection and heat transfer in a porous annular layer

Investigations into the convective transport of heat in porous materials are of interest for many applications in connection with the problem of increasing the efficiency of thermal insulation. In [1–5], convection in Isotropic porous media was considered. However, in many cases porous materials have an essential anisotropy of their permeability. Convective heat transfer has been inadequately studied for this case. In [6], the linearized equations were used to study the convection between infinite horizontal planes with a filling of an anisotropic material; the value of the critical Rayleigh number was found, and this agreed satisfactorily with experimental data. In the present paper, we investigate numerically convection between two infinite coaxial cylinders with an anisotropic porous filling, using the equations of convection in the Darcy—Boussinesq approximation [1–3]. The permeability tensor in the annular region is constructed from its principal values, which can be found experimentally. A method of calculation is developed and a parametric study made of the structure of the flow and of the local and averaged characteristics of the heat transfer, which are of interest for the design of thermal insulation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–64, January–February, 1980.     

Investigation into the influence of periodic pulsations of the pressure on the natural convection at a heated surface

A theoretical investigation is made into the influence of periodic pulsations of the pressure on natural convection. A detailed analysis is made of the natural convection near the lower front point of a horizontal cylinder. The cases when the direction of the pulsations coincides with the direction of natural convection and when the two directions are at right angles are considered. The results correspond well to the experimental data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 203–208, September–October, 1979.     

Flow and heat exchange in the neighborhood of a subterranean pipeline

The present study considers flow and heat exchange in the neighborhood of a subterranean pipeline on irrigated sector of a route. The flow is caused by thermal convection of the liquid in the field of gravitational forces, this convection being connected with the cooling or heating of the liquid near the surface of the pipeline.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1987.     

Control of the convective equilibrium stability of a fluid heated from below

Potentially unstable equilibrium is stabilized by means of a method of control based on the single-channel feedback principle using the characteristics of the solution of the complete nonlinear thermal convection equations. The convection equations are solved by a finite-difference method.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 6–11, July–August, 1990.     

Convection in a two-layer system due to the combined action of the Rayleigh and thermocapillary instability mechanisms

In a two-layer system loss of stability may be monotonic or oscillatory in character. Increasing oscillatory perturbations have been detected in the case of both Rayleigh [1, 2] and thermocapillary convection [3–5]; however, for many systems the minimum of the neutral curve corresponds to monotonic perturbations. In [5] an example was given of a system for which oscillatory instability is most dangerous when the thermogravitational and thermocapillary instability mechanisms are simultaneously operative. In this paper the occurrence of convection in a two-layer system due to the combined action of the Rayleigh (volume) and thermocapillary (surface) instability mechanisms is systematically investigated. It is shown that when the Rayleigh mechanism operates primarily in the upper layer of fluid, in the presence of a thermocapillary effect oscillatory instability may be the more dangerous. If thermogravitational convection is excited in the lower layer of fluid, the instability will be monotonic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1987.     

Investigation of hydrodynamic and heat and mass transfer processes for crystal growing by the Czochralski method

A mathematical model and numerical method are developed and used to investigate nonstationary flow and heat and mass transfer regimes in a melt appropriate to the conditions of Czochralski crystal growth. A study is made of the separate and combined influence of rotation and thermal, concentration, and thermocapillary convection on the distribution of the temperature and the dopant in the range of regime parameters corresponding to large charging masses of the melt with small value of the kinematic viscosity. Large-scale fluctuations are found to occur when rotation and thermal convection interact. Thermocapillary convection is shown to have an important influence on the resulting motion when it interacts with the thermal and concentration forms of convection. A comparison is made with the results of experimental and theoretical investigations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 55–65, January–February, 1981.     

Chaotic and periodic solutions of the problem of fluid convection in a closed channel

Exact periodic solutions of the nonlinear dissipative system describing the convection of a viscous heat-conducting fluid in a closed channel are shown to exist and are investigated. The question of the compatible existence of stationary, chaotic and periodic solutions is examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 36–42, November–December, 1992.     

Friction and heat transfer with simultaneous convection on a permeable surface

The velocity and heat transfer fields near a vertical permeable surface with simultaneous convection are investigated. A solution is found for the boundary layer equations with known laws of surface temperature and flow velocity change. The transformed boundary layer equations contain the parameter G/R², which determines the effect of free convection on friction and heat transfer for constrained motion. Calculations of friction and heat transfer as functions of draft (suction) with simultaneous convection are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 96–100, March–April, 1973.     

The degeneration of nucleate boiling conditions under conditions of free convection

An experimental investigation was made of the effect of the degeneration of nucleate boiling conditions under conditions of natural convection for alkali metals (potassium, cesium) in working sections with diameters of 14 and 11 mm in a pressure range of 0.04–1.7 bar, and for nonmetallic liquids (ethanol, benzene, and carbon tetrachloride) in working sections with diameters from 0.1 to 10 mm in a pressure range of 0.05–2.5 bar. The regions were determined for thermal flows, with which the appearance of a vapor phase after single-phase natural convection leads to the formation of a stable vapor film. The results of high-speed movingpicture photography of this phenomenon are also given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 69–73, January–February, 1972.     

Numerical analysis of natural convection in a thin-walled cylindrical vessel with hemispherical end-plates completely filled with liquid

The results are given of calculations of convection in a thin-walled cylindrical vessel with hemispherical end-plates over the range of Rayleigh and Fourier numbers that correspond to the main regimes of unsteady laminar convection in the presence of a given heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 204–203, September–October, 1984.     

Free convection in inclined layers of liquid and with a jumpwise change in the temperature of the heat-transfer surfaces

This paper gives the results of investigations of hydrodynamics and heat transfer with the laminar flow of a liquid in inclined layers, closed at the ends, as well as in layers of liquid with a jumpwise change in the temperature of the heat-transfer surface, under conditions of free convection.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–121, November–December, 1971.     

Experimental study of the effect of vertical vibrations on convection in a horizontal cylindrical layer

An experimental study is made of the effect of vertical vibrations on convection in a cylindrical layer formed by two horizontal coaxial cylinders of circular cross section at different temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 180–183, November–December, 1985.     

The effect of vertical vibrations on the onset of convection in a planar rotating layer

The effect of vertical vibrations on the convection in a rotating planar fluid layer heated from below was studied. In this case a modulation parameter, the acceleration due to gravity, appears in the problem. The modulation of the parameter may have a significant effect on the onset of convective instability. Parameter modulation in nonrotating layers has been investigated in earlier work [1–3]. The presence of rotation significantly increases the complexity of the mathematical problem, introducing an additional dependence of the solution on the Taylor number Ta and the Prandtl number Pr. Furthermore, an oscillatory convection regime can occur at the stability limit in rotating fluids with Pr < 1. Parameter modulation in the rotating fluid may not only lead to a change in the stability limit and critical wavelength but also to a change in the eigenfrequency of the oscillatory convection. Rauscher and Kelly [4] examined the effect of parameter modulation on the convective stability of a rotating fluid only for the particular case of a sinusoidal variation in the temperature gradient with a small amplitude for Pr = 1, i.e., the effect of modulation was studied on only a steady convection regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–22, July–August, 1984.     

Thermocapillary convection in two-layer systems in the presence of a surface active agent at the interface

Convective instability in a layered system due to the thermocapillary effect was investigated in [1–5]. In these studies it was shown that the perturbations responsible for equilibrium crisis may build up either monotonically or in an oscillatory fashion. In [6] the stabilizing effect of a surface active agent (SAA) on thermocapillary instability was established for a layer with a free surface. For layers of infinite thickness the effect of SAA on thermocapillary convection was studied in [7–9]. The present investigation is concerned with thermocapillary convection in a system of two layers of finite thickness in the presence of an SAA. Convection due to the lift force is not considered. It is established that the principal result of the action of the SAA is not the stabilizing effect on the monotonic mode but the appearance of a new type of oscillatory instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2 pp. 3–8, March–April, 1986.In conclusion the authors wish to thank E. M. Zhukhovitskii for discussind the results.     

Thermal convection in a cylindrical enclosure with intense internal heat generation in the presence of a longitudinal magnetic field

Steady convection in a gaseous medium with intense heat generation is considered without making use of the Boussinesq approximation. The effect on convection of the thermal boundary conditions at the walls of the enclosure is investigated, together with the influence of a longitudinal magnetic field which is effective when the medium is strongly heated and becomes electrically conducting.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 11–18, May–June, 1992.The authors are grateful to the participants in the G. A. Lyubimov seminar for discussing their work.     

Numerical modeling of thermocapillary convection in a liquid layer with a nonlinear dependence of the surface tension on temperature

The principal characteristics of thermocapillary convection in a rectangular channel with one of the boundaries heated to a temperature higher and the other to a temperature lower than T₀ are investigated numerically on the basis of the Navier-Stokes equations. Certain convection characteristics corresponding to normal and anomalous thermocapillary effects are qualitatively compared. The conditions under which self-similar solutions of the type obtained in [10] can be used to describe the flow in a bounded region are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 138–143, January–February, 1991.     

Capillary and gravitational convection in a droplet immersed in a nonuniformly heated liquid

Under the conditions of the Plato technique, the problem of convection in a droplet immersed in a nonuniformly heated liquid is solved analytically. The influence of gravitational convection on the thermocapillary flow is studied. In the linear approximation with respect to the Marangoni and Grashof numbers and their product, the shape of the droplet and the displacement of its center of the mass are obtained.Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–51, July–August, 1996.     

Penetrative convection in the isothermally incompressible fluid approximation

The onset of penetrative convection in an infinite horizontal fluid layer bounded by isothermal rigid or free nondeformable surfaces is numerically examined. It is assumed that the specific volume of the fluid depends quadratically on temperature and reaches a minimum inside the layer. The isothermally incompressible fluid convection model in which, as distinct from the Oberbeck-Boussinesq approximation, the thermal expansion is not assumed to be small is considered. Both the neutral stability curves of the conductive regime and the amplitudes of two-dimensional periodic and three-dimensional doubly-periodic convective flow are calculated. The results are compared with those previously obtained for the equations of penetrative convection in the Boussinesq approximation.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 40–52, March–April, 1996.     

Combined convection of a viscoplastic liquid in a plane vertical layer

The combined (free and induced) convection of a viscoplastic Shvedov-Bingham liquid in a plane vertical layer is considered. The influence of the temperature dependence of the yield shear stress on the conditions of occurrence of the flow and the stationary convection regime in the case of heating from the side is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–113, November–December, 1979.