格子Boltzmann方法分析加热尺寸和瑞利数对可变形开口腔内自然对流的影响

采用格子Boltzmann方法对可变形腔体内自然对流问题进行数值研究，给出平均努赛尔数的经验关系式.腔体左壁加热长度分为左壁面的整个区域（H）和左壁面的中间区域（0.5H）两种情况，右壁向外界环境开放，上下边界绝热且可以上下移动，以此调节右出口尺寸.主要研究瑞利数（10⁴ ≤ Ra ≤ 10⁶），右出口尺寸（1.0H ≤ L ≤ 2.0H），左壁加热尺寸（L_h=0.5H或L_h=H）对腔体内等温线、流线、局部努塞尔数和平均努赛尔数的影响.结果表明：腔体内换热随着瑞利数的增大越来越强烈，表现为椭圆形准静止区域更加靠近上绝热壁，且热分层厚度逐渐变小，平均努赛尔数增加.而右出口尺寸的增加，对于两种加热尺寸下腔内的换热效果有不同程度影响，其中与加热尺寸为左壁面的全部区域L_h=H相比，加热尺寸为左壁面的中间情况L_h=0.5H时，右侧开口尺寸的增加对换热效果的影响不显著.此外，左壁加热尺寸为0.5H时显示出比加热尺寸为H时更高的平均传热效率.最后，针对不同的加热尺寸，提出加热面平均努赛尔数与Ra数及右壁面开口尺寸L^*之间函数关系的经验预测，拟合效果满足工程实践与设计需要.     

AN EMPIRICAL CORRELATION FOR NATURAL CONVECTION FROM CONFINED ELLIPTIC TUBE

An experimental study was conducted to obtain a correlation for free convection heat transfer from isothermal elliptic tubes of minor to major axis ratios of ∈ = 0.53, 0.67, 0.8, and 1 confined between two adiabatic walls. Local and average Nusselt numbers were determined for several different tube axis ratios, Rayleigh numbers, and wall spacings by means of the Mach-Zehnder Interferometery (MZI) technique. For each tube axis ratio, the Rayleigh number varied from 1,000–2,750 and the wall spacing to tube minor axis ratio from 1.25–∞. For all the tube axis ratios, the periphery and length of the tubes were kept constant. Experimental data are presented with a correlation which gives the average Nusselt number as a function of the tube axis ratio, Rayleigh number, and wall spacing to tube minor axis ratio. As the tube axis ratio decreases the average heat transfer coefficient increases. Also, for a constant Rayleigh number and tube axis ratio there is an optimum wall spacing which maximizes the heat transferred from the tube.     

格子Boltzmann方法模拟填充纳米流体三角形腔内的自然对流

采用格子Boltzmann方法研究填充水-氧化铝纳米流体的等腰直角三角形腔体中的自然对流.讨论瑞利数、颗粒体积分数、热源位置等因素对对流换热的影响,以及不同纳米流体模型对模拟结果的影响.结果表明:在低瑞利数下,随着热源在左壁面向上移动,换热效率逐渐增加.而在高瑞利数(Ra=106)时,观察到相反的现象;采用单相纳米流体...     

不连续冷源布局多孔介质内热流耦合LBM数值模拟

为研究不连续冷源边界对内置发热体多孔介质方腔内传热及流动的影响,采用格子Boltzmann方法对REV尺度下多孔介质方腔内的自然对流进行计算,并研究瑞利数（Ra）、达西数（Da）、孔隙度对多孔介质方腔内传热流动的影响.发现Da对方腔内的流体流型影响很大,Da为10^-4时,多孔介质方腔内只有一个涡流,而Da为10^-2时,方腔内有两个涡流.增大Ra、Da、孔隙度可以提高冷源壁面的平均努赛尔数（Nu）,增强散热效果,孔隙率对平均Nu影响程度和Da的大小有关.当冷源布置在壁面上方,壁面的平均Nu随Ra的增加剧烈变化,方腔处于高Ra条件下时,将冷源布置在边界的上方可以提高散热效果.6种布置方案中Case 6的散热效果最好.     

Numerical study of flow and heat transfer from a torus placed in a uniform flow

Forced convection heat transfer characteristics of a torus (maintained at a constant temperature) immersed in a streaming fluid normal to the plane of the torus are studied numerically. The governing equations, namely, continuity, momentum and thermal energy in toroidal coordinate system, are solved using a finite difference method over ranges of parameters (aspect ratio of torus, 1.4 ≤ Ar ≤ 20; Reynolds number, 20 ≤ Re ≤ 40; Prandtl number, 0.7 ≤ Pr ≤ 10). Over the ranges of parameters considered herein, the nature of flow is assumed to be steady. In particular, numerical results elucidating the influence of Reynolds number, Prandtl number and aspect ratio on the isotherm patterns, local and average Nusselt numbers for the constant temperature (on the surface of the torus) boundary condition. As expected, at large aspect ratio the flow pattern and heat transfer are similar to the case of flow and heat transfer over a single circular cylinder.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Numerical simulations of electro-thermo-convection and heat transfer in 2D cavity

In this article the electro-thermo-convective phenomena in a dielectric liquid enclosed in a 2D cavity and subjected to the simultaneous action of an electric field and a thermal gradient is studied. We solved directly the full set of coupled equations of Electro-Hydro-Dynamic (EHD) and energy equation using a finite volume method. In order to characterize the influence of the electric field on heat transfer the liquid is first heated (from a lateral wall) till the thermal steady state is obtained and then the electric potential and injection of electric charge is applied. Two cases of injection are considered: from the lower electrode and from a lateral wall (left or right). The flow pattern and Nusselt number strongly depend on the non-dimensional characteristic parameters: electrical parameter, Rayleigh number, Prandtl number and mobility parameter M. The convective motion passing from a purely thermal convection to a purely electrical convection and the number of electro-thermo-convective rolls patterns are investigated.As a consequence of the analysis of the combined effect of electric and thermal fields on the flow structure and on Nusselt number, we have also evaluated the heat transfer enhancement due to electroconvection. It is shown that the injection of electric charge increases the heat transfer and Nusselt number is independent of Rayleigh number for high enough values of T.     

Experimental Study of Natural Convection from Electrically Heated Vertical Cylinders Immersed in Air

Abstract

An experimental study of laminar steady-state natural convection heat transfer from electrically heated vertical cylinders immersed in air has been undertaken. Three stainless steel (316 SS) test sections of different slenderness ratios were employed. Surface temperature profiles along the vertical cylinders were obtained using miniature thermocouples when the cylinders were heated with different power levels resulting in different total wall heat fluxes. After the mandatory corrections for the radiation heat fluxes were made, three correlation equations relating the local Nusselt number Nu_y with the local modified Rayleigh number Ra^* _y and the position-to-cylinder diameter y/d were developed. The correlation equations are valid for Ra^* _y ≤ 2 × 10¹².     

Lattice Boltzmann simulation of double diffusive natural convection in heterogeneously porous media of a fluid with temperature-dependent viscosity

Double diffusive natural convection inside a porous cavity with non-uniform porosity has been numerically studied. The cavity was filled with two parallel porous layers with different porosity. Considering the effects of temperature-dependent viscosity, simulations have been done via the Lattice Boltzmann method (LBM) at representative elementary volume (REV) scale. In this study, the effect of porosity, buoyancy ratio, the viscosity-variation number and thermal Rayleigh number on heat and mass transfer rates was investigated. The streamlines, isotherms, isoconcentrations, average Nusselt number and average Sherwood number curves of different parameters were discussed in detail. It was observed that the governing parameters has significant impact on the fluid flow, temperature and concentration distributions. In addition, the average Nusselt and Sherwood numbers are increase with an reduce in the viscosity-variation number. Further, as the absolute value of buoyancy ratio and thermal Rayleigh number increases, the effect of porosity and viscosity changes on the heat and mass transfer enhancement was augmented.     

Étude numérique du modèle de Boussinesq de convection naturelle laminaire axisymétrique permanente dans un espace annulaire compris entre deux sphères

Authors study numerically the axisymetric steady natural convection in the annular space between two vertically eccentric spheres applying the Boussinesq approximation and an integro-interpolation finite volumes method. In the case of two isothermal concentric spheres their results agree with those of the literature. Also, they obtain correlations between the average Nusselt number and the Rayleigh number quasi identical to those publish by Chiu and Scanlan. When the internal sphere is heated by the application of a constant heat flux and eccentric as compared to the supposed external sphere isothermal, they propose correlations between the average Nusselt number and the Rayleigh number that depend on the eccentricity and on the Prandtl number. According to initialising conditions of calculation, the external sphere being isothermal, authors show that there exists a critical Rayleigh number beyond which the flow can be found unicellular or bicellular. This critical Rayleigh number depends on others parameters of the system as the eccentricity and the aspect ratio when the internal sphere is isothermal as well as subjected to a uniform constant heat flux density.     

高Rayleigh数条件下竖圆环夹层内自然对流换热的实验研究

对内壁维持恒热流和外壁向环境冷却的大高宽比竖圆环夹层内自然对流换热进行了实验研究。实验装置高宽比分别为２３５和６６６７，半径比分别为２．０３和３．９２。实验数据整理考虑了热辐射影响以获得对流规律。由于已有工作均未考虑高Ｒａ数区域，首次得到Ｒａ数高达１０￣９的区域内平均Ｎｕ数的换热准则式。在低Ｒａ数区域，亦取得了与前人工作一致的结论。本文结果改进了高Ｒａ数区域换热规律的预测能力。     

Natural Convection from a Corrugated Heated Surface at the Bottom of Vented Rectangular Enclosure

Natural convection heat transfer characteristics enclosures from a tilted rectangular enclosure heated at the corrugated bottom wall and vented by uniform slots opening at the top wall are experimentally investigated. The experiments were carried out to study the effects of the angle of opening of the corrugated surface, opening ratio, enclosure's tilt angle, and Rayleigh number on the passive cooling of the enclosure. The experiments were carried out at Rayleigh numbers ranging from 2 × 10⁸ to 1.52 × 10⁹ for enclosure tilt angles ranging from 0° to 90° and angle of opening of corrugated surface ranging from 0° to 25°. The top venting arrangement was studied at different opening ratios of 1, 0.75, 0.5, and 0.25. The results gave an optimum angle of opening of the corrugated surface at which Nusselt number is maximum.     

Mesoscopic analysis of heatline and massline during double-diffusive MHD natural convection in an inclined cavity

Double-diffusive natural convection in an inclined cavity with the presence of magnetic field is studied numerically via heatline and massline approach. The governing equations are discretized using the Lattice Boltzmann Method (LBM). In this investigation, the controlling parameters involved are Rayleigh number (10³ ≤ Ra ≤ 10⁵), buoyancy ratio (−5 ≤ N ≤ 5), cavity inclination angle (0° ≤ Ø ≤ 180°), Lewis number (2 ≤ Le ≤ 10), Prandtl number (Pr = 5.0) and Hartmann number (0 ≤ Ha ≤ 50). The numerical results obtained by the effect of parameters mentioned above are reported as contours of streamlines, isotherms, isoconcentrations, heatlines, and masslines. The obtained results are compared with the existing literature to validate the coding. The heat and mass transfer rate decrease with increasing the magnetic field and increase with an increase in Rayleigh number. The impact of Ø is maximum for higher Ra and negligible for lower Ra (10³). Increasing Le influences the mass transfer rate to increase and heat transfer to reduce for both opposing and aiding flow.     

热质双扩散与流固共轭传热及吸附的LBM模拟

采用格子Boltzmann方法,基于孔隙尺度,对填有均匀介质的复合方腔顶盖驱动双扩散混合对流及流固共轭传热、吸附进行数值模拟.在孔隙率ε=0.79,普朗特数Pr=0.7,格拉晓夫数Gr=10⁴和路易斯数Le=1.0时,就不同浮升力比（-100≤Br≤100）和吸附率常数（0.001≤k₁≤0.005）对方腔内部热质传输的影响进行比较.给出流线、等温线、等浓度线、平均努赛尔数Nu_av、舍伍德数Sh_av和吸附量等.结果表明Br通过改变介质所处流场的浓度分布影响吸附,而k₁的增加显著地提高吸附效率和吸附能力.     

Buoyancy induced flow in a nanofluid filled enclosure partially exposed to forced convection

A numerical study was performed on natural convection for water–CuO nanofluid filled enclosure where the top surface was partially exposed to convection. The cavity has a square cross-section and differentially heated. Except exposed convection part on the top, all sides are adiabatic on horizontal walls. Effects of Rayleigh number (10³ ? Ra ? 10⁵), Biot number (0 ? Bi ? ∞), length of partial convection (0.0 ? L ? 1.0) and volume fraction of nanoparticles (0.0 ? φ ? 0.1) on heat and fluid flow were investigated. The results showed that for the case of high Biot number that heat transfer along the heated was enhanced by increasing the Rayleigh number mainly at the upper portion of the heated wall. When the top wall was totally exposed to convection, the results prevail that the heat transfer was more effective at high Biot number especially at the upper portion of the heated wall. For the case of high Biot number, the results prevailed that the heat transfer at the upper portion of the heated wall increases considerably at high exposed length to convection (L); however, for L ? 0.75 the effect of L was less pronounced. Contour maps for percentage of heat transfer enhancement were presented and it was shown that the location of maximum enhancement in heat transfer was sensitive to Ra, φ and L.     

基于LBM的部分热活跃边界下多孔腔体内自然对流换热

采用Boltzmann方法模拟部分热活跃边界下的多孔腔体内自然对流,探讨不同热边界布置方案、孔隙度、Da数及Ra数对其流动传热的影响.数值计算表明：Da=10^-4时,腔体内中央出现一个循环流模式,只在Ra数很大时孔隙度才对传热有影响; Da=10^-2时,腔体内出现两个循环流,在Ra数很小时孔隙度对传热产生强烈的的影响.热活跃边界位置影响腔体内流体对流传热的强度,加热边界布置在底部、而冷却边界布置在顶部（Bottom-Top布置方式）,对多孔腔体内对流传热最有利,优于全热边界布置方式的传热效果.     

Rotating turbulent Rayleigh–Bénard convection subject to harmonically forced flow reversals

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = 10⁹ and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/Ro^* = 1 while various modulation frequencies 0.1 ≤ Ro_ω ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.     

Experimental studies on natural convection of water in a closed-loop vertical annulus

Experimental studies on heat transfer and fluid flow of water in a vertical annulus, circulating through a cold leg forming a closed loop thermo-siphon, have been carried out in this article. The annulus has a radius ratio (outer radius to inner radius) of 1.184 and aspect ratio (length to annular gap) equal to 352. The experiments were conducted for constant heat fluxes of 1, 2.5, 5, 7.5, 10, 12.5, and 15 kW/m². Transient behavior during the heat-up period of the system until the steady-state condition is attained and discussed. Variation in the heat transfer coefficient and Nusselt number along the annulus height represent the developing boundary layer at the entrance and fully developed flow in the remaining length. A large drop in the differential pressure is experienced when the liquid is circulated through the flow meters, which restrict the flow due to their very small passages. Flow restriction causes mass accumulation and rise of pressure at the exit of the annulus. It also causes a decrease in liquid head in the cooling leg. An increase in the heat flux leads to an increase in the heat transfer coefficient and Nusselt number. As a result of the data analysis correlations for the average Nusselt number, Reynolds number and circulation rate have been developed in terms of the heat flux.     

Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.