Convection in mixtures with nonuniform heat release proportional to the density of an active component

A study is made of the stability of a horizontal layer of a two-component mixture with concentration gradient of the active (heat releasing) component directed upward. The nature of the instability depends strongly on the direction of the gradient. In the investigated case, the stability may be either monotonic or oscillatory in nature. The problem is also distinguished by the existence of two independent neutral curves associated with the thermal and concentration instability mechanisms. The regions in which monotonic and oscillatory convection occur are found by stepwise integration. Graphs of the amplitudes of the critical perturbations of the velocity, temperature, and concentration are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 21–27, November–December, 1980.We thank E. M. Zhukhovitskii for discussing the results.     

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.     

Effect of Longitudinal Forced Motion on the Stability of Convection in a Plane Vertical Layer with Internal Heat Sources

The effect of longitudinal forced fluid motion on the mechanisms of instability of a convection flow developing in a plane vertical layer in the presence of internal heat sources is considered. It is found that forced motion which intensifies the central stream of the convection flow can lead to moderate stabilization of the hydrodynamic and thermal crisis mechanisms. In the presence of counterstream forced motion the flow stability increases sharply.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 14–17.Original Russian Text Copyright © 2005 by Lobov.     

A physical mechanism of large-scale structure generation in turbulent convection

The generation of large-scale structures during turbulent convection in a rotating layer of incompressible fluid heated by internal heat sources is considered. The results of a theoretical and experimental investigation of a physical mechanism of large-scale structure formation which operates under conditions of high-intensity small-scale turbulent convection and low boundary heat transfer are discussed. The theoretical investigation is based on a system of evolutionary equations obtained for the transverse space moments of the physical fields, which describes the motion in thin layers of rotating fluid. The stability of the solution of the mathematical model is studied using the small perturbation method. As a result, a condition of existence of longwave instability of the system and a criterion determining the threshold of its onset are obtained. The theoretical conclusions are confirmed by a series of experiments carried out on a laboratory model. The design of the laboratory apparatus and the experimental technique are described.Moscow, Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–29, September–October, 1996.     

Finite-amplitude convection in mixtures with heat sources proportional to the concentration of one of the components

A numerical investigation has been made into the equilibrium stability with respect to finite perturbations of a mixture with heat sources proportional to the concentration of an active component. The convective motions that develop after the loss of stability were also studied. The equations of thermoconcentration convection were solved by the grid method for a planar region of rectangular shape simulating a convective cell in the horizontal layer. Neutral curves for finite-amplitude perturbations are constructed, the regions of existence of subcritical motions are found, and a comparison with the results of linear theory is made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–16, November–December, 1982.We thank E. M. Zhukovitskii for discussing the results of the paper.     

Convection in a low prandtl number fluid with internal heating

This paper studies the problem of non-linear thermal convection in a horizontal layer of a low Prandtl number fluid with nearly insulating boundaries and in the presence of horizontally uniform internal heat sources. Two-dimensional rolls and hexagonal cells are found to be the only possible stable convection cells. Subcritical instability associated with the hexagons can occur for a range of the amplitude of convection. It is found that non-uniform internal heating can affect various flow features and the stability of the convective motion. A new subcritical instability which exists even in a symmetric layer with arbitrary Prandtl number is also found for the case where the variations of the internal heating with respect to the vertical variable is sufficiently high.     

Calculation of the boundary layer of a transparent gas on a radiating surface

Heat transfer in the laminar boundary layer of a transparent gas flowing aroud a plane radiating surface is studied. Radiative heat-transfer processes in gases may be divided into two main groups. The first involves heat transfer in absorbing and radiating media. In this case, the effect of radiation lies in the introduction of new terms into the energy equation, representing internal heat sources and sinks. The second group embraces heat-transfer processes in a transparent gas when the effect of radiation on convection expresses itself solely by way of the boundary conditions. Here we study a case of practical importance belonging to the second group: heat transfer in the laminary boundary layer of a transparent gas flowing around a flat plate with the thermal flux q_w specified on its surface.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–110, January–February, 1972.     

Thermoconvective instability of longitudinal flow in a vertical layer

An experimental study has been made of convection in a vertical slit cavity heated from below and with longitudinal horizontal forced flow. It was shown that the convective stability of such flow increases appreciably when the velocity of the forced flow is raised. In the case of slow pumping, an increase in the pressure difference leads to superposition on the rectilinear flow of first monotonic convection and then auto-oscillatory convection. At high flow velocities, the instability is immediately of an oscillatory nature. A diagram of the flow regimes is constructed, and the evolution of the supercritical structures described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhikosti i Gaza, No. 2, pp. 28–33, March–April, 1984.     

Non-linear convection in a porous medium with internal heat sources

The paper studies non-linear thermal convection in a horizontal porous layer of fluid with nearly insulating boundaries and in the presence of internal heat sources. Square and hexagonal cells are found to be the only possible stable convection cells. Finite amplitude instability could exist for some particular forms of an internal heat source Q. For a uniform Q, the preferred flow pattern is that of hexagons for amplitude ε smaller than some critical value ε_c, while both squares and hexagonal cells are stable for ε ? ε_c. The convective motion is downward at the hexagonal cell's centers. For a non-uniform Q, the qualitative features of thermal convection depend on the actual form Q. In particular, a non-uniform Q can increase or decrease the cell's size and the critical Rayleigh number at the onset of convection, and stabilize or destabilize the convective motion in the form of hexagonal cells with either upward or downward motion at the cell's centers.     

The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Stability of convective motion caused by inhomogeneously distributed internal heat sources

The stability of steady convective plane-parallel flow in a vertical layer of viscous incompressible liquid of thickness h is investigated. The motion is caused by heat sources distributed in the liquid with volume density Q = Q₀exp (^–x) (the x axis is taken perpendicular to the boundary layer). The region of instability is determined for various values of the Prandtl number and the parameter N = h characterizing the inhomogeneity of the internal sources. It is shown that with increase in N there is qualitative rearrangement of the stability limit for perturbations of hydrodynamic type and incremental thermal waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–144, May–June, 1977.     

Convection and heat transfer in a spherical vessel,partly filled with liquid,under low-gravity conditions

In [1] the problem of natural and thermocapillary convection in a spherical vessel containing a bubble under low-gravity conditions, i.e., at low Bond numbers (Bo 1), was examined in one of the limiting cases — where the bubble is located in the center of the vessel. The results of [1] and experimental data, however, indicate that when heat is supplied from outside over a long period, the most probable location of the bubble under low-gravity conditions is at the vessel wall. In this paper, which is a continuation of [1], convection and heat transfer in the latter case are investigated. Possible locations of the bubble at the top and bottom of the vessel relative to the resultant of the weak mass forces are discussed. It is shown that natural and thermocapillary convection contribute to the increase in the mean free-surface temperature, which determines the increase in pressure in the closed vessel for a prescribed heat flux. The rates of increase of this temperature are compared in the cases considered here and in [1–4], where there is a fuller bibliography relating to convective heat and mass transfer under low-gravity conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–159, March–April, 1976.     

Parametric excitation of Rayleigh convection in the presence of a variable heat flux on the free surface

The onset of Rayleigh convection in a semi-infinite fluid layer is investigated for a heat flux harmonically modulated along the normal to the surface of the fluid. The problem of the evolution of the velocity and temperature perturbations is solved numerically by means of a finite-difference method. The stability limits and the characteristics of the critical perturbations are determined as functions of the Prandtl numbers. The behavior of the critical Rayleigh number is studied for finite layer depths.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 40–44, November–December, 1996.     

Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium

Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.     

Double-diffusive convection induced by selective absorption of radiation in a fluid overlying a porous layer

A linear instability analysis for the inception of double-diffusive convection with a concentration based internal heat source is presented. The system encompasses a layer of fluid which lies above a porous layer saturated with the same fluid. Detailed stability characteristics results are presented for key physical parameters including the solute Rayleigh number, depth ratio of the fluid to porous layer and strength of radiative heating.     

Effect of rotation on the vibroconvective stability of a fluid layer with internal heat release

The equilibrium stability of a horizontal fluid layer with homogeneous internal heat release is investigated theoretically for the case in which the layer simultaneously undergoes high-frequency circular vibration in a horizontal plane and rotates about a vertical axis. The rotation frequency is assumed to be small as compared with the vibration frequency. It is found that the rotation has a stabilizing effect on the vibrational-gravitational convection. At the high-frequency limit the dependence of the critical values of the controlling parameters (gravitational and vibrational Rayleigh numbers) and the wave number on the rotation frequency is obtained.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 53–61. Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Kolesnikov.     

Secondary convective motions in a plane inclined layer

A linear theory of stability of a plane-parallel convective flow between infinite isothermal planes heated to different temperature was developed in [1–6]. At moderate Pr values the instability is monotonic and leads to the development of steady secondary motions. These motions for the case of a vertical layer have been investigated by the net [7, 8] and small-parameter [9] methods. In this paper steady secondary motions in an inclined layer are investigated. The small-parameter and net methods are used. The hard nature of excitation of secondary motions in a defined range of tilt angles is established. There are two types of secondary motions, whose regions of existence overlap — vortices at the boundary of countercurrent streams and convection rolls; the hard instability is due to the development of convection rolls. The analog of the Squire transformation obtained in [4] for infinitely small disturbances of a plane-parallel convective flow is extended to secondary motions of finite amplitude.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1977.I thank G. Z. Gershumi, E. M. Zhukhovitskii, and E. L. Tarunin for interest in the work and valuable discussion.     

Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

In the present study, double-diffusive convection in an anisotropic porous layer with an internal heat source, heated and salted from below, has been investigated. The generalized Darcy model is employed for the momentum equation. The fluid and solid phases are considered to be in equilibrium. Linear and nonlinear stability analyses have been performed. For linear theory normal mode technique has been used, while nonlinear analysis is based on a minimal representation of truncated Fourier series. Heat and mass transfers across the porous layer have been obtained in terms of Nusselt number Nu and Sherwood number Sh, respectively. The effects of internal Rayleigh number, anisotropy parameters, concentration Rayleigh number, and Vadasz number on stationary, oscillatory, and weak nonlinear convection are shown graphically. The transient behaviors of Nusselt number and Sherwood number have been investigated by solving the finite amplitude equations using a numerical method. Streamlines, isotherms, and isohalines are drawn for both steady and unsteady (time-dependent) cases. The results obtained, during the above analyses, have been presented graphically, and the effects of various parameters on heat and mass transfers have been discussed.     

Stability of the equilibrium of a flat layer in a microconvection model

The stability of the equilibrium state of a flat layer bounded by rigid walls is studied using a microconvection model. The behavior of the complex decrement for longwave perturbations has an asymptotic character. Calculations of the full spectral problem were performed for melted silicon. Unlike in the classical Oberbeck–Boussinesq model, the perturbations in the microconvection model are not monotonic. It is shown that for small Boussinesq parameters, the spectrum of this problem approximates the spectra of the corresponding problems for a heatconducting viscous fluid or thermal gravitational convection when the Rayleigh number is finite.