Shape optimization of unsteady natural convection fields

This paper presents a numerical method for two shape optimization problems, namely, prescribing the temperature history distribution on sub-boundaries and maximizing the discharged heat on sub-boundaries of unsteady natural convection fields. The square error integral between the actual temperature distribution and the target temperature distribution on the sub-boundaries during a specified period of time was used as the objective functional for the prescribed temperature history distribution. The shape gradients of these shape determination problems were derived theoretically using the Lagrange multiplier method, adjoint variable method, and the material derivative formulae. Reshaping was performed by the traction method, which was proposed as an approach for solving shape optimization problems. Numerical programs for the shape determination problems are developed based on FreeFem++ in order to verify the proposed method.     

Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a horizontal shallow porous cavity filled with an electrically conducting fluid. The magnetic field is assumed to be induced by two long wires, carrying current, parallel to the horizontal boundaries of the system. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. The governing parameters of the problem under study are the thermal Rayleigh number, Ra, Hartmann number, Ha, position of the electrical wires, d, current intensity ratio, r, and aspect ratio of cavity, A. An analytical solution, valid for a shallow layer (A ? 1), is derived on the basis of the parallel flow approximation. The critical Rayleigh number, Ra _c , for the onset of motion is derived in closed form in terms of the parameters of the problem. For finite-amplitude convection the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.     

Effect of partitions on flow structure with natural convection in a closed volume. II. Two vertical partitions

The authors consider natural-convective flow of gas under the action of a heat source in a two-dimensional closed rectangular cavity with two vertical partitions. The effect of the relative position and dimensions of the partitions on the flow pattern is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 3, pp. 339–342, September, 1992.     

Transient natural convection in a liquid during cooling

An experimental study was made for an analysis of cooling of a liquid under conditions of natural convection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 1, pp. 5–12, July, 1979.     

基于微腔自然对流的PCR芯片的热设计

对薄圆盘腔体内自然对流实现PCR过程进行了热分析,在此基础上对薄圆盘腔体的边界条件、几何尺寸和内部结构进行了优化设计.结果表明,在所研究的范围内,周壁绝热,上下壁温分别为反应允许退火-延伸温度的下限和反应允许变性温度的上限,同时腔体的高径比为0.275左右时,腔体内能够满足PCR反应要求的流体的体积最大.保持腔体高径比不变和流体体积不变,在腔体内加入一个固体的圆环结构,且将下表面保持高温的区域由全表面缩小到1/2圆盘半径范围,流体在变性区停留时间与退火延伸区停留时间之比大大减小,且满足PCR反应要求的流体的体积改变不大,能进一步提高PCR的效率.     

The effect of the structure of mixing chamber on the operation of a water-air nozzle with a large fraction of liquid

A theoretical-and-experimental procedure is suggested for obtaining a maximal-velocity flow of droplets in a preassigned nozzle, and an example of application of this procedure is given. It is demonstrated that the structure of the mixing chamber may affect significantly the phase distribution in the nozzle flow even in the case of a large mass fraction of liquid and a significant length of the nozzle.     

Effect of discrete flow distribution on heat transfer at a vertical surface in natural convection

The influence of a discrete distribution of injection and suction of air on heat transfer at a vertical flat surface under free convection has been investigated experimentally. The results are presented together with empirical formulas for the heat transfer coefficients.     

Investigation of the occurrence of convection in horizontal liquid layers

The occurrence of convection in horizontal layers of ethanol, distilled water, and ethylene glycol heated from below was investigated by the interferometric method. The limits of roller-type convection and its effect on the magnitude of heat flux through the layer were determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 3, pp. 427–433, March, 1971.     

Some problems of the hydrodynamics of a horizontal cylinder with natural convection

The article examines the special features of vortex flow in the vicinity of the upper critical point, and approximating dependences are obtained for the point of detachment from the data of numerical solution and experiments.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 6, pp. 905–909, December, 1982.     

A study of natural convection in horizontal cylindrical gaps

A study was made of natural convection in horizontal cylindrical gaps. For hot tubes of small diameters, the convection factor has been related not only to the Rayleigh number but also to the geometrical dimensions (diameter of the hot tube and relative gap width). The construction of experimental tubes is also described.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 4, pp. 676–680, October, 1973.     

Nonlinear instability of mixed convection flow over a horizontal cylinder

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy—with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation—that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer.     

Scale of the convection cell structure in a horizontal layer of liquid with unsymmetrical boundary conditions for heat transfer

An interpretation is given of some experimental results on the effects of initial conditions on the cellular structure of convective motion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 4, pp. 602–605, April, 1974.     

Concentration-dependent convection in a horizontal porous bed containing a chemically active liquid

The limits to convective stability of a mixture in a horizontal porous bed have been derived for several types of boundary conditions subject to the occurrence of a homogeneous isothermal reaction.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 1, pp. 133–138, January, 1979.     

Analysis of early-stage frost formation in natural convection over a horizontal cylinder

Frost growth process on a cold surface consists of two stages: The early-stage or one-dimensional growth of ice columns and multidimensional growth in the form of a porous structure. The transition time which marking these two stages is important for any numerical modeling of frost formation. This paper proposes a mathematical model to predict the transition time and frost properties in natural convection of frost formation over a cooled horizontal cylinder in the first stage of growth period. Comparison is performed among the results of this model and experimental observations reported in the literatures. It is observed that the presented model can be used more efficiently to determine transition time and frost properties in the early-stage of frost formation. Based on the obtained results a new correlation is developed for the duration time of early-stage of frost formation process (transition time) in natural convection.     

Burn-out of a liquid under conditions of natural convection

A relation for the critical heat flux density in liquid boiling under conditions of natural convection is derived by means of a previously obtained approximate analytical solution of the problem of the hydrodynamics of an evaporating meniscus.     

Mixed convection around a horizontal circular cylinder immersed in a Darcy flow

The forced and free mixed convection problem around a horizontal circular cylinder in a fluid-saturated porous medium is investigated at small Peclet number with Gr/Re = O(1). The Darcy flow model is used for the velocity field. The method of matched asymptotic expansions is used to obtain asymptotic solutions for small Peclet number. It is shown that, up to the present order of approximation, natural convection has no effects on the temperature field, and the effects of the parameter Gr/Re on the velocity field are examined in detail.     

Periodic and chaotic regimes of liquid dielectric convection in a horizontal capacitor

Electroconvective oscillations in nonuniformly heated dielectric liquid occurring in an alternating electric field between plates of a horizontal plane capacitor have been studied within the framework of a low-mode model. The general case of arbitrary frequencies and amplitudes of the electric field is considered and nonlinear dynamics of the convective structures arising as a result of the parametric instability is determined. Two classes of synchronous electroconvective oscillations in the system are found, and the competition and hysteresis of these regimes are analyzed. The average heat flux via the plane capacitor in one of these regimes is greater by a factor of 2.5 than the heat flux in the other regime. The transition to chaotic oscillations proceeds either via a quasi-periodic regime or directly from equilibrium. The boundaries of domains corresponding to various types of behavior of the dielectric liquid are determined in the space of parameters.     

The effect of an alternating electric field on the liquid dielectric convection in a horizontal capacitor

The electroconvective instability in a low conducting nonuniformly heated liquid occurring in an alternating electric field between plates of a horizontal plane capacitor was studied in terms of the equations of electrohydrodynamics for arbitrary field modulation frequencies and various shapes (harmonic and triangular). In the gravitational field, the instability is determined by the interplay of dielectrophoretic and thermogravitational mechanisms. The layer heated from above can feature the parametric instability. In the low-frequency range, a numerical solution to the problem obtained by the Floquet method well agrees with the asymptotic results.     

Problem of describing the flow field in an injector mixing chamber

The use of a three-component flow model is proposed. The results of numerical calculations are presented and compared with the experimental results.