侧加热腔内的自然对流

开展侧加热腔内自然对流的研究具有重大的环境及工业应用背景. 总结侧加热腔内水平温差驱动的自然对流的最新研究进展, 并概述相应的流动性质、动力机制和传热特性以及对不同无量纲控制参数的依赖也有重要的科学价值. 已取得的研究结果显示突然侧加热的腔内自然对流的发展可包括初始阶段、过渡阶段和定常或准定常阶段. 不同发展阶段的流动依赖于瑞利数、普朗特数及腔体的高宽比, 且定常或准定常阶段的流态可以是定常层流流动、非定常周期性流动或者湍流流动. 此外, 回顾了对流流动失稳机制的研究成果以及湍流自然对流方面的新进展. 最后, 展望了侧加热腔内的自然对流研究的前景.      

Natural convection in an inclined quadrantal cavity heated and cooled on adjacent walls

Natural convective flow and heat transfer in an inclined quadrantal cavity is studied experimentally and numerically. The particle tracing method is used to visualize the fluid motion in the enclosure. Numerical solutions are obtained via a commercial CFD package, Fluent. The working fluid is distilled water. The effects of the inclination angle, ? and the Rayleigh number, Ra on fluid flow and heat transfer are investigated for the range of angle of inclination between 0° ? ? ? 360°, and Ra from 10⁵ to 10⁷. It is disclosed that heat transfer changes dramatically according to the inclination angle which affects convection currents inside, i.e. flow physics inside. A fairly good agreement is observed between the experimental and numerical results.     

An efficient Legendre-Galerkin spectral method for the natural convection in two-dimensional cavities

An efficient numerical method is developed for solving the natural convection in two-dimensional cavities. The numerical scheme is proposed by using second-order projection scheme in time direction and Legendre-spectral in spatial variable of the incompressible flow. Finally, a series of numerical examples are presented to demonstrate the efficiency of our algorithm. The numerical strategies developed in this article could be readily applied to study other incompressible fluid problems.     

Natural convection in an infinite square under low-gravity conditions

In order to study natural convection effects on fluid flows under low-gravity in space, we have expanded variables into a power series of Grashof number by using perturbation theory to reduce the Navier-Stokes equations to the Poisson equation for temperature T and biharmonic equation for stream function φ. Suppose that a square infinite closed cylinder horizontally imposes a specified temperature of linear distribution on the boundaries, we investigate the two dimensional steady flows in detail. The results for stream function φ, velocity u and temperature T are gained. The analysis of the influences of some parameters such as Grashof number G_r and Prandtl number P_r on the fluid motion lead to several interesting conclusions. At last, we make a comparison between two results, one from approximate equations, the other from the original version. It shows that the approximate theory correctly simplifies the physical problem, so that we can expect the theory will be applied to unsteady or three-dimensi     

Natural convection in an inclined enclosure containing internal energy sources and cooled from below

Natural convection in an inclined enclosure from below and containing internally heated fluid has been investigated using a finite difference calculation procedure. Results have been obtained for Rayleigh number values up to 10⁶ and for inclination angles of 30 and 60°. For internal Rayleigh numbers that are much larger than the external Rayleigh number, the flow rises in the interior and moves down both the hot and cold walls. On the other hand, if the external Rayleigh number has a larger magnitude, the flow moves upwards along the hot surface and downwards along the cold surface. For the latter situation, the inner core is multicellular in nature at large external Rayleigh numbers. The average heat flux ratio along the cold surface (convective heat flux/corresponding conduction heat flux) increases with increasing external Rayleigh number and decreasing internal ratio is non-monotonic in nature. The heat flux ratio along both surfaces is observed to be strongly dependent on the inclination angle at high external Rayleigh numbers. A maximum in the local heat flux along the cold surface is obtained in the vicinity of x/L = 1 where hot fluid, either from the interior or directly from the opposite hot wall, meets the surface. Along the hot wall, a maximum in the heat flux ra flo     

Stability properties of the vertical boundary layers in differentially heated cavities

In the present study, the two-dimensional (2-D) stability properties of the vertical boundary layers in a cavity that is differentially heated over two opposing vertical walls is considered. The study is performed by introducing artificial, controlled perturbations at the base of the vertical boundary layer along the hot cavity wall and by following the evolution of these disturbances. For small initial perturbations, the evolution is governed by linear effects. This method accurately predicts the frequency of the bifurcation, which occurs for (much) larger Rayleigh numbers. Convective instability sets in for Rayleigh numbers much smaller than those at which the absolute instability (i.e., the bifurcation) occurs, and these Rayleigh numbers are in reasonable agreement with those for the boundary layer along a plate. The absolute instability does not result from the first wave which becomes unstable. For small Prandtl numbers (≤ 2), the unstable waves which lead to the absolute instability are shear-driven, and a single frequency is introduced in the flow after the bifurcation. For larger Prandtl numbers, the unstable waves are buoyancy driven and no single-frequency unsteady flow is observed after the bifurcation.     

Natural convection of a viscoelastic fluid

The influence of elasticity and shear thinning viscosity on the temperature distribution and heat transfer in natural thermal convection is discussed. The numerical investigations are based on a four-parameter Oldroyd constitutive equation, which represents the typical fluid response of dilute solutions and melts. It was found that especially the second normal-stress difference affects the heat transfer mechanism.     

Transient conduction in a plate cooled by free convection

An approximate analytical solution of the one-dimensional conduction equation with a natural convection boundary condition is presented. The solution is based on the heat balance integral technique and possesses considerable utility. The accuracy of the solution is tested by comparison with an exact solution for a range of linear forced convection problems and with a Crank-Nicolson solution for a range of nonlinear free convection problems. It is demonstrated that significant differences can occur between the temperature responses of a solid cooled by either free of forced convective flow at similar Biot numbers.     

Natural convection to water from arrays of short wall-attached cylinders

Experiments of natural convection from arrays of one, two, and three horizontal cylinders attached vertically one above the other to a heated, vertical flat plate in water have shown that the lowest cylinder is essentially unaffected by cylinders above it and has a heat transfer rate less than that of an infinitely long cylinder. The effect on the heat transfer from cylinders in the wake of the lowest cylinder is primarily a function of the spacing between the cylinders, with the increase being larger for greater spacing. For these wake cylinders, increases are sufficient to cause the heat transfer to equal that of an infinite cylinder.     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998     

Natural convection in cavities containing internal sources

 Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working fluid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar flow, and one well above it. In those latter cases, the long-term behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces. Received on 17 January 2000     

Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects

The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour coefficients around the density maximum is studied numerically. The right vertical wall has constant temperature θ_c, while left vertical wall is partially heated θ_h, with θ_h > θ_c. The concentration in right wall is maintained higher than left wall (C_c < C_h) for case I, and concentration is lower in right wall than left wall (C_h > C_c) for case II. The remaining left vertical wall and the two horizontal walls are considered adiabatic. Water is considered as the working fluid. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. The effect of the various parameters (thermal Rayleigh number, center of the heating location, density inversion parameter, Buoyancy ratio number, Schmidt number, and Soret and Dufour coefficients) on the flow pattern and heat and mass transfer has been depicted. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.     

Natural convection in inclined two dimensional rectangular cavities

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated. The channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. The field equations for a Newtonian Boussinesq fluid are solved numerically for three cavity height based Rayleigh numbers, Ra = 10⁴, 10⁵ and 10⁶, and several aspect ratios. The calculations are in excellent agreement with previously published benchmark results. The effect of the inclination of the cavity to the horizontal with the angle varying from 0° to 180° and the effect of the startup conditions on the flow pattern, temperature distribution and the heat transfer rates have been investigated. Flow admits different configurations at different angles as the angle of inclination is increased depending on the initial conditions. Regardless of the initial conditions Nusselt number Nu exhibits discontinuities triggered by gradual transition from multiple cell to a single cell configuration. The critical angle of inclination at which the discontinuity occurs is strongly influenced by the assumed startup field. The hysteresis effect previously reported is not always present when the calculations are reversed from 90° to 0°. A comprehensive study of the flow structure, the Nu variation with varying angle of inclination, the effect of the initial conditions and the hysteresis effect are presented.     

Natural convection heat transfer in the annular region between porous confocal ellipses

The Darcy–Boussinesq equations are solved in two dimensions and in elliptical cylindrical co‐ordinates using a second‐order‐accurate finite difference code and a very fine grid. For the limiting case of a circular geometry, the results show that a hysteresis loop is possible for some values of the radius ratio, in agreement both with previous calculations using cylindrical co‐ordinates and with the available experimental data. For the general case of an annulus of elliptical cross‐section, two configurations, blunt or slender, are considered. When the major axes are horizontal (blunt case) a hysteresis loop appears for a certain range of Raleigh numbers. For the slender configuration, when the major axes are vertical, a transition from a steady to a periodic regime (Hopf bifurcation) has been evidenced. In all cases, the heat transfer rate from the slender geometry is greater than that obtained in the blunt case. Copyright © 1999 John Wiley & Sons, Ltd.     

Natural convection in partially heated vertical channels

A numerical analysis has been performed on laminar natural convection of air in open vertical channels partially heated at uniform wall temperature (UWT) or at uniform heat flux (UHF). The governing equations have been solved by means of a finite difference technique. Results showing axial velocity and temperature developments as well as heat transfer performances and correlations between non-dimensional groups, are presented.

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Natürliche Konvektion in teilweise erwärmten vertikalen Kanälen

Zusammenfassung Eine numerische Analyse wurde über die natürliche Luftkonvektion in vertikalen, mit gleichmäßiger Wandtemperatur (UWT) oder mit gleichmäßigem Wärmestrom (UHF) teilweise erwärmten Kanälen durchgeführt. Die analytischen Gleichungen des Problems wurden mit der Finit-Differenzen-Technik gelöst, und es werden Ergebnisse hinsichtlich der Geschwindigkeits- und Temperaturverteilungen im Inneren des Kanals sowie der thermischen Leistung des Systems aufgeführt.

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Nomenclature a thermal diffusivity of the fluid - c _p specific heat (at constant pressure) of the fluid - g acceleration due to gravity - Gr =[·g·S ³ ·(T₁-T₀)]/v²,Grashof number (UWT case) - Gr =[-g-S ⁴ -q ₁]/(v ²·k), Grashof number (UHF case) - Gr ^* =(S/H) Gr, modified Grashof number - H overall channel height - I, J X andY coordinate indexes - k thermal conductivity of the fluid - Nu mean Nusselt number of the channel - p difference between pressure inside the channel and pressureoutside, at the same heightx - P dimensionless difference pressure - Pr Prandtl number - q specific heat flux - q ₁ specific heat flux from heated plates (UHF case) - Q heat flux (per unit length in thez-direction) from walls - S channel width - T temperature - T _w reference wall temperature - T _o fluid temperature at the inlet section - T ₁ heated plates temperature (UWT case) - u, axial and transverse velocity of the fluid - u _o axial velocity of the fluid at the inlet section - U, V dimensionless axial and transverse velocity - U _o dimensionless axial velocity at the inlet section - x, y axial and transverse coordinate - X, Y dimensionless axial and transverse coordinate - X =H/(S·Gr), dimensionless overall channel height - thermal expansion coefficient of the fluid - dimensionless temperature - v kinematic viscosity of the fluid - density of the fluid