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.     

Natural convection produced by unsteady heating of a viscoplastic liquid in a plane vertical layer

A study is made of the unsteady heating of a viscoplastic liquid in the space between two infinite vertical plates when one is thermally insulated and a constant, uniformly distributed heat flux is supplied to the other after a certain initial time. It is assumed that at the initial time the liquid is uniformly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–150, July–August, 1982.     

Natural convection of a viscoplastic fluid in vertical circular channels

In contrast to a Newtonian fluid, a viscoplastic fluid can be in a state of mechanical equilibrium when heat is supplied from the side. Therefore, natural convection in a viscoplastic fluid heated from the side occurs only when the determining parameters exceed certain threshold values. The threshold conditions for the onset of convection for a flat vertical layer have been investigated several times [1–4]. The present paper is an investigation of the conditions of occurrence of plane-parallel natural convection of a viscoplastic fluid in regions with cylindrical symmetry: in a vertical annular layer and in a vertical circular tube.     

On the stopping of thermal convection in viscoplastic liquid

The thermal convection in a square cavity filled in with a viscoplastic liquid is considered as a model example to illustrate the mechanism of convection termination. It is shown that at low Rayleigh numbers, the stopping of convection corresponds to a limit point in the parameter space. Using this observation, we propose a heuristic numerical approach to calculate the critical Rayleigh numbers.     

Steady-state convection of a non-Newtonian fluid in a vertical layer

Steady-state thermal convection is investigated for a non-Newtonian fluid with a power-law rheological characteristic in a plane vertical channel bounded by parallel planes x=±h maintained at different temperatures.perm'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–139, July–August, 1972.     

Thermocapillary convection in a horizontal layer of liquid

An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.     

Stationary solution of the equations of microconvection in a vertical layer

The stationary problem of convection in liquids is considered using the model of microconvection developed by V. V. Pukhnachev. Velocity profiles for boundary conditions of different classes are constructed. The solutions of the problem under study and the classical problem based on the Oberbeck—Boussinesq model are compared.     

Numerical modeling of the turbulent convection mode in a vertical layer

An approach to the numerical modeling of turbulent natural convection modes on the basis of two-dimensional nonstationary Navier-Stokes equations without the use of additional empirical information is elucidated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostii Gaza, No. 5, pp. 8–15, September–October, 1977.The authors are grateful to A. G. Kirdyashkin for consultations on the method and results of the experiments to G. S. Glushko for useful remarks, and to K. G. Dubovik for aid in performing the computations.     

Thermocapillary convection in a liquid layer with local heating

The motion induced in a liquid by a heat pulse is mathematically described. The velocity and temperature distributions on the surface and in the body of the liquid are determined numerically. The theoretical results obtained are compared with the experimental data of [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–156, September–October, 1987.The authors are very grateful to V. A. Al'vares-Suares for discussing their results.     

Study of convection in a liquid layer with vibrating forces

We consider convection in a gravity force field in a liquid enclosed in a vessel which is vibrating along the vertical axis according to the lawa/ sin t ( ).Time-averaged convection equations describing the basic motion in first approximation are derived in [1]. In addition, criteria are introduced in [1] which determine the initiation of convection in this case, and a model problem is considered: the case of spatially periodic disturbances. It is found that in this case high frequency vibrations stabilize the state of relative rest.In the present paper we consider convection in a liquid layer between two horizontal planes whose equations are z=±l/2.The temperatures T₁ and T₂ are specified on the upper and lower surfaces, respectively. It is shown (§1) that for small values of the vibrational criterion the principle of stability variation is satisfied. In this case there is a variational principle (§2) from which it follows that high frequency vibrations prevent the occurrence of convection in the horizontal liquid layer. With the aid of the variational principle a calculation is made of the dependence of the values of Rayleigh criterion on the vibrational criterion.The author wishes to thank I. B. Sinomenko and V. I. Yudovich for their continued interest in this study.     

Finite-amplitude regimes of mixed convection in a vertical layer with undulating boundaries

The method of finite differences is used to construct convective motions in a vertical layer with sinusoidally curved boundaries, fluid being pumped through longitudinally. Apart from steady and oscillation regimes, found earlier by analytical means for small amplitudes of undulation and slow pumping through [1, 2], new, essentially nonlinear, types of motion are discovered in the form of two-stroke cycles, and also of complex multi-revolution cycles which are two-dimensional resonance tori. The regions are determined in which regimes of various types exist.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–20, January–February, 1987.The author is grateful to E. M. Zhukhovitskii for constant interest in the study, and also to V. S. Anishchenko and A. A. Nepomnyashchii for useful discussions.     

Convective stability of a vertical layer of a non-newtonian liquid

We consider the convective stability of a non-Newtonian (nonlinearly viscous) liquid in a two-dimensional vertical channel. We solve a nonlinear boundary value problem concerning plane-parallel stationary convection for the case of piecewise-linear and power-law type rheological characteristics. We discuss the problem concerning the stability of equilibrium and of stationary motions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 88–95, September–October, 1973.The authors thank D. V. Lyubimov for his help in carrying out the calculations.     

Stability of a plane conducting fluid layer under convection in a vertical magnetic field

The nonlinear convective instability of a plane horizontal conducting fluid layer placed in a uniform vertical magnetic field is studied [1]. A similar problem was previously considered in [2] but with allowance only for so-called weakly nonlinear third-order effects. In the present paper attention is concentrated on the study of the finite-amplitude instability mechanisms associated with the "hard" excitation of vibrations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–28, January–February, 1998.     

Thermocapillary convection in a plane liquid layer with concentration heat sources

Thermocapillary instability of a plane liquid binary-mixture layer with time-dependent surface tension is studied under weightlessness conditions. The liquid is heated (or cooled) due to heat release by an active admixture. The heat release rate is proportional to the active-component concentration. The admixture is transported by convection and diffusion. The active component “burns up” with time. The neutral curves for monotonous and oscillating disturbances are found for different values of the nondimensional parameters. Some nonlinear convection regimes are studied numerically by a finite-difference method. The dependence of the convective flow intensity on the Marangoni number is determined. The phase portraits of unsteady regimes are found.