Analysis of Natural Convection in an Elliptical Cavity,Using a Dini Expansion

INTRODUCTIONNaturalconvectioninanellipticalcavityheatedfrombelowwastreatednumericallybyM..him.ull],usingaFourierspectralfinitedifferencemethod,anditseffectivenesswasshownasinRef.[2].AlsopossibilityoftheextensiontovarioustypesofboundaryconditionsforthespectralfinitedeferenceschemewasproposedinReL[2-3].HerethespectralfinitedifferenceschemeisbeingextendedtoadoptDimexpansions(akindofBesselexpansions).NUMERICALANAlySISBasicAssumptionsbleatedistransiellttwo--dimensionalnaturallaminarco…     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method

In this study, the lattice Boltzmann method was used to solve the turbulent and laminar natural convection in a square cavity. In this paper a fluid with Pr = 6.2 and different Rayleigh numbers (Ra = 10³, 10⁴,10⁵ for laminar flow and Ra = 10⁷, 10⁸,10⁹ for turbulent flow) in the presence of a magnetic field (Ha = 0, 25, 50, and 100) was investigated. (Results show that the magnetic field drops the heat transfer in the laminar flow as the heat transfer behaves erratically toward the presence of a magnetic field in a turbulent flow. Moreover, the effect of the magnetic field is marginal for a turbulent flow in contrast with a laminar flow.The greatest influence of the magnetic field is observed at Ra = 10⁵ from Ha = 0 to 100 as the heat transfer decreases significantly.     

封闭方腔自然对流换热的研究

论述和分析了封闭方腔自然对流换热的研究进展,研究了采用商业软件FLUENT对此模拟的方法以及换热规律研究的可行性,所获得的数值模拟结果与研究文献做了对比分析,其模拟结果是正确的,由此表明:采用FLUENT软件通过数值模拟方法不仅能获得封闭腔自然对流换热的结果,还能研究其换热规律,是解决封闭腔自然对流换热的有效工具。     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。     

Mixed convective cooling of a fin in a channel

Mixed convection heat transfer in an inclined parallel-plate channel with a transverse fin located at lower channel wall is investigated numerically. Employing the stream function vorticity transformation, solution of the transformed governing equations for the system is obtained by the control-volume method with non-uniform grid. The results indicate that the optimum aspect ratio of a fin corresponding to the fin with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed fin profile area. Also, the optimum aspect ratio increases with the inclination angle for Gr/Re² = 10; whereas the effects of orientation on the optimum aspect ratio is not pronounced for Gr/Re² < 1. In addition, the optimum aspect ratio of a fin with a smaller fin profile area and Re at Gr/Re² = 0.1 approaches that of analytical solution having the assumption of constant heat-transfer-coefficient.     

CFD Analysis of Steady Laminar Natural Convection Heat Transfer from a Pin Finned Isothermal Vertical Plate

Heat transfer behavior with both the conductive and nonconductive fins have been analyzed by examining variations of the local and average Nusselt numbers in two‐dimensional flow. The main objective of this study is to quantify and compare the natural convection heat transfer enhancement of fin array with different fin aspect ratio and at different angles of inclination. It is found that significant heat transfer augmentation is obtained for both conductive and nonconductive fins. For conductive fins 20% higher augmentation factor is obtained when the fin aspect ratio is 6, angle of inclination is 60° and the pitch‐to‐length ratio is 0.2. For nonconductive fins, 10% higher augmentation factor is obtained when fin aspect ratio is 8, angle of inclination is 45° and pitch‐to‐length ratio at 0.5. A general correlation has been developed to predict the average Nusselt number and heat transfer augmentation factor for conductive and nonconductive fin arrays as a function of different fin configurations.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

逆向流动边界下窄方腔内相变材料融化传热数值研究

为分析复杂流动边界条件对相变材料融化进程的影响,采用计算流体动力学方法进行数值模拟,研究了窄方腔内月桂酸在逆向流动边界中的融化传热特性。建立了填充有相变材料的窄方腔两侧流过参数相同但逆向的传热流体的物理模型。通过数值模拟得到了相变材料融化形态变化以及相对应的液体分数、温度、速度矢量分布等瞬态传热特性,从中总结出了腔体中相变融化机制和传热机理。选取雷诺数1×10⁴,3×10⁴,5×10⁴,7×10⁴和瑞利数3×10⁶,4×10⁶,5×10⁶,6×10⁶的7种工况,分析了不同边界条件对传热过程的影响。结果表明：腔内自然对流的产生大大增加了传热强度,导致顶部相变材料率先完全融化;融化阶段的传热方式依次为导热、导热与对流混合、对流主导传热;在两侧流体的共同传热作用下腔内外换热效果明显增强;雷诺数和瑞利数都对融化过程有积极的影响,但融化前期雷诺数影响较大,后期瑞利数逐渐起主导作用。     

On identical problems of natural convection in enclosures and applications of the identity character

In this paper, a concept of "identical problems" of natural convection in enclosures is presented. A pair of problems of natural convection in enclosures is said to be identical if they look different in appearance but with appropriate selection of coordinates and appropriate definition of dimensionless variables for each problem, they will have identical geometric configurations and identical dimensionless governing equations and related boundary conditions. The identical characteristics of a pair of problems of natural convection in enclosures with an internal isolated island are demonstrated via dimensionless mathematical formulation and flow visualization results. Numerical computations are performed and the predicted streamlines agree with the flow visualization results. A number of other possible pairs of identical problems are also presented. Applications of the identical character are provided and assumptions under which the identical problems may exist are discussed.     

高封闭方腔自然对流换热特性数值模拟研究

采用ANSYS Fluent 17. 0中的标准k-ε湍流模型对高度、深度及宽度比为28. 7∶6. 8∶1,瑞利数分别为0. 86×10~6、1. 10×10~6和1. 43×10~6的高方腔内的空气自然对流传热进行分析研究,结果显示:温度场及速度场在几何上呈现出良好的中心对称结构;随着瑞利数增大,自然对流增强,努塞尔数增大;在冷、热壁面附近区域,温度梯度大,热量传递以导热为主,越靠近中心区域,对流传热占总的传热比例增加;方腔顶部区域,冷板侧的传热相对更强,而在贴近底板区域,热板侧的传热相对更强。分析结果经过与实验结果对比,具有很好的一致性,模拟结果和方法可作为该类问题模拟分析的参考。     

封闭方腔内叉排管间熔融盐自然对流换热

以硝酸锂熔融盐为流体介质,对封闭方腔内交叉排布的四根热管间的介质自然对流换热进行了数值模拟,研究了热管不同位置和不同瑞利数对方腔内介质自然对流换热特性的影响。结果表明:管间距ε=0.5时,腔体内温度场和流场的对称性开始打破;ε=0.4和0.5时,下管及左右两管产生的热羽流冲刷上管热边界层,使上管局部Nu_φ分别在圆周角φ=180°、φ=280°和φ=80°处出现增强;ε=0.6时,上管不再受下管羽流影响。随着管间距增大,上管平均Nu_m越来越小,下管Nu_m越来越大;ε=0.4~0.6时,管间距对左右两管Nu_m影响很小,但ε=0.7时,左右两管平均换热均明显增强。     

二阶全展开ETG有限元方法在方腔自然对流模拟中的应用

应用二阶全展开ETG有限元方法离散求解N-S方程和能量方程,并以零初值方腔自然对流问题为例进行了数值模拟。计算了不同瑞利数条件下方腔自然对流的流场和温度场,最终达到的稳态结果与标准数值解符合很好,并且较好地反映了流场和温度场的时间演化过程,特剐是捕捉到了分叉前后流场中涡结构的变化。结果表明二阶全展开ETG有限元方法有较好的稳定性和较高的精度,在计算温度场和流场的时间演化过程方面有一定优点。     

Double-diffusive natural convection in a porous medium under constant heat and mass fluxes

Double-diffusive natural convection in a rectangular fluid-saturated porous medium has been studied analytically and numerically. The analysis reveals that there is a range of buoyancy ratios N in which one obtains two types of solutions or oscillating convection. In the case of 0.4 < N < 1.0, there exist two analytical solutions when R_c = 100 and Le = 30. In that case, two solutions, temperature-dominated and concentration-dominated solutions, are calculated when the aspect ratio is small. It is found that the oscillation is due to a temporal formation of a two-roll flow pattern in the cavity when the aspect ratio is sufficiently large. The oscillation of time-dependent Nusselt number and flow patterns are shown. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 255–265, 1999     

Effects of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls

This paper describes the effect of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls numerically and experimentally. In the numerical analysis, fluid flow and temperature distributions for Ri=1.61, Pr=6.99, Re=100 and aspect ratio, Ar=0.2–10, were obtained by solving dimensionless governing equations using the SIMPLE procedure. The QUICK scheme was applied to the convective term of these equations. In the experimental analysis, the flow behavior for A_r=0.5–2 was visualized by the dye‐injection method. Numerical results showed that the swirl flow was generated along the flow direction, and its pitch length was influenced by A_r. The pitch length was the shortest when A_r=0.5–1, and this tendency was the same in numerical results and experimental results. The heat transfer behavior was also discussed corresponding to the flow, and the heat transfer ratio was highest at A_r=1 in 0.2 ≤ A_r ≤ 10. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20391     

冷热房间之间隔门通风性能的数值分析

应用数值模拟方法,对冷热房间之间隔门通风情况进行了分析。三维模拟区域主要运用稳态湍流和Boussinesq模型进行模拟,并着重对不同隔门高度和外部条件下流动换热情况作了对比研究。研究表明,两个墙壁间的温差及其引起的密度差是形成温度和速度分布的主要原因。隔门使两个房间之间形成对流,右侧高温房间下部有冷气流进入,而左侧低温房间有热气流由上方进入。当隔门高度降低时,零压差线的相对高度不断升高,对流效应减弱。