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.     

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.     

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.     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Mixed convection in a vertical channel with discrete heat sources at the wall

The mixed convection in a vertical plane-parallel channel with two heat sources of finite dimensions located at the wall is analyzed on the basis of a two-dimensional numerical simulation. The effect of the distance between the heat sources on the flow pattern and the temperature field is studied. Calculations are performed on the Grashof and Reynolds number ranges from 0–10⁵ and 0–10, respectively, at a Prandtl number of 0.7. The mathematical model is based on the time-dependent Navier-Stokes equations in the Boussinesq approximation. The problem is solved by the finite element method.     

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.     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.     

Calculation of unsteady natural concentration convection in binary mixtures of gases with arbitrary ratio of their densities

The approximate system of equations formulated by Nikulin, Potekhin, and Strelets [1] can, in contrast to the system in the Boussinesq approximation [2], be used to describe natural concentration convection in the presence of significant changes in the composition in gas mixtures with arbitrary ratio of the molecular weights of the components. In the present paper the possibilities opened up by the use of this system of equations are illustrated by the example of a numerical investigation of unsteady free convection of an isothermal binary gas mixture in a closed rectangular region in a wide range of variation of the Archimedes number and the ratio of the molecular weights of the components of the mixture.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 27–31, July–August, 1982.     

Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convection

Experiments have been conducted for natural convection heat transfer from protruding discrete heat sources, mounted at different positions on a substrate, to determine the optimal configuration, and to study the effect of surface radiation on them, which reduces their temperature upto 12 %. The optimal configuration has been determined by a non-dimensional geometric distance parameter (λ). An empirical correlation has been proposed between the non-dimensional steady state temperature (θ) and λ, by taking into account the effect of surface radiation heat transfer.     

Approximate system of equations for describing nonstationary natural concentration convection in binary gas mixtures

Analysis of the Navier-Stokes equations at small values of the hydrostatic compressibility parameter leads to the formulation of an approximate system of equations for describing nonstationary natural convection in isothermal binary mixtures of gases with arbitrary ratio of the densities. A system of equations for nonstationary concentration convection is also obtained in the Boussinesq approximation, and it is shown that its use in the solution of the considered class of problems may lead to not only quantitative errors but also to a qualitative distortion of the results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 57–61, September–October, 1980.     

Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources

The problem of combined conduction-mixed convection-surface radiation from a vertical electronic board provided with three identical flush-mounted discrete heat sources is solved numerically. The cooling medium is air that is considered to be radiatively transparent. The governing equations for fluid flow and heat transfer are converted from primitive variable form to stream function-vorticity formulation. The equations, thus obtained, are normalised and then are converted into algebraic form using a finite volume based finite difference method. The resulting algebraic equations are then solved using Gauss–Seidel iterative method. An optimum grid system comprising 151 grids along the board and 111 grids across the board is chosen. The effects of various parameters, such as modified Richardson number, surface emissivity and thermal conductivity on temperature distribution along the board, maximum board temperature and relative contributions of mixed convection and radiation to heat dissipation are studied in detail. Further, the contributions of free and forced convection components of mixed convection to board temperature distribution and peak board temperature are brought out. The exclusive roles played by surface radiation and buoyancy in the present problem are clearly elucidated.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Combined heat and mass transfer by laminar natural convection from a vertical plate with uniform heat flux and concentration

This paper studies combined heat and mass transfer by laminar natural convection from a vertical plate maintained with uniform surface heat flux and species concentration. Very accurate finite-difference solutions of a set of nonsimilarity equations have been obtained for most practical gaseous solutions (Pr?=?0.7, 0.21 ≤ Sc ≤ 2.1) and aqueous solutions (Pr?=?7, 140 ≤ Sc ≤ 1400). Variations of heat and mass transfer rates with buoyancy ratio and Lewis number are presented. Precise correlations have been developed for predicting heat and mass transfer rates of natural convection arising from single (solutal or thermal) buoyancy force and dual buoyancy forces.     

Calculation of neutral monotonic instability curves in the problem of concentration convection in a mixture with an infinite number of components

The Oberbeck-Boussinesq approximation for concentration convection in a mixture with an infinite number of components is constructed. The features of the formulation of the problem are described in detail. The large-parameter asymptotics are constructed for the linear problem of hydrodynamic stability. The problem is substantially simplified and equations not previously encountered in hydrodynamic stability theory are obtained. In the case of the non self-adjoint problem the asymptotics of the eigenvalues and eigenfunctions are obtained. Numerical results which, in particular, show that the spectrum of the boundary value problem is not connected are presented. The critical values obtained make it possible to solve the important practical problem of improving the process of mixture separation by the isoelectric focusing method.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 11–20, September–October, 1995.