Natural convection in a cavity with time-dependent flux boundary

Numerical simulations have been carried out to investigate the unsteady natural convection flow in a cavity subjected to a sidewall heat flux varying sinusoidally with time. With all walls non-slip and the upper and lower boundaries and the other sidewall adiabatic, the heating and cooling produces an alternating direction natural convection boundary layer that discharges hot fluid to the top and cold fluid to the bottom of the cavity, generating a time-varying thermal stratification in the cavity interior. Scaling analysis has been conducted for different flow regimes based on the forcing frequency, with the characteristic time scales being the forcing period and the boundary layer development time. The scaling relations are then verified using the simulations, with the results showing overall good agreement with the derived scaling relations.     

Mathematical simulation of conjugate mixed convection in a rectangular region with a heat source

Conjugate convective-conductive heat transfer in a rectangular region with forced flow and a heat source is simulated numerically. Distributions of the thermal and hydrodynamic characteristics of the flow regimes studied are obtained. The evolution of the process analyzed is shown. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 69–81, November–December, 2008     

Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium

An analysis is presented for the calculation of heat transfer due to free convective flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface heat flux. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of ordinary differential equations. Numerical solutions are presented for these equations which represent universal functions and several computational examples are provided.     

矩形倾斜腔体中的两种对流斑图和分区

为了研究矩形倾斜腔体中普朗特数Pr=0.72的流体对流斑图和分区,本文基于流体力学方程组进行了数值模拟。在相对瑞利数r=6.0的情况下,观察了倾角θ=10°和θ=60°时对流斑图随着时间的发展,发现系统存在单圈型对流和多圈型对流两种斑图。流线随着倾角的变化说明:随着倾角增加,对流圈数逐渐减少,对流波长逐渐增加,对流波数减小;然后,随着对流圈数显著地减少,系统由多圈型对流过渡到单圈型对流。根据模拟计算结果,给出了多圈型对流过渡到单圈型对流的临界倾角θc随着相对瑞利数r变化的关系曲线。对流在θ-r平面上分为两个区域:θ<θc时系统是单圈型对流,θ>θc时系统是多圈型对流。对流最大振幅A和努塞尔数Nu随着倾角θ的变化曲线被临界倾角θc分成两段,它们有不同的变化规律。因此,临界倾角也可以由对流最大振幅A或努塞尔数Nu的变化曲线来确定。     

Mass and heat transfer by natural convection in a vertical cavity

This paper reports a fundamental study of laminar natural convection in a rectangular enclosure with heat and mass transfer from the side, when the bouyancy effect is due to density variations caused by either temperature or concentration variations. In the first part of the study scale analysis is used to determine the scales of the flow, temperature and concentration fields in boundary layer flow for all values of Prandtl and Lewis numbers. In particular, scale analysis shows that in the extreme case where the flow is driven by bouyancy due to temperature variations, the ratio of mass transfer rate divided by heat transfer rate scales as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ only if (Pr > 1, Le < 1) or (Pr < 1, Sc < 1), and as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ if (Pr > 1, Le > 1) or (Pr < 1, Sc > 1). In the second part of the study, the boundary layer scales derived in the first part are used to determine the heat and mass transport characteristics of a vertical slot filled with fluid. Criteria for the existence of distinct thermal and concentration boundary layers in the slot are determined. Numerical solutions for the flow and concentration fields in a slot without distinct thermal boundary layers are reported. These solutions support further the method of scale analysis employed in the first part of the study     

On natural convection from a vertical plate with a prescribed surface heat flux in porous media

This paper presents a theoretical and numerical investigation of the natural convection boundary-layer along a vertical surface, which is embedded in a porous medium, when the surface heat flux varies as (1 +x ²)), where is a constant andx is the distance along the surface. It is shown that for > -1/2 the solution develops from a similarity solution which is valid for small values ofx to one which is valid for large values ofx. However, when -1/2 no similarity solutions exist for large values ofx and it is found that there are two cases to consider, namely < -1/2 and = -1/2. The wall temperature and the velocity at large distances along the plate are determined for a range of values of .Notation g Gravitational acceleration - k Thermal conductivity of the saturated porous medium - K Permeability of the porous medium - l Typical streamwise length - q _w Uniform heat flux on the wall - Ra Rayleigh number, =gK(q _w /k)l/(v) - T Temperature - Too Temperature far from the plate - u, v Components of seepage velocity in the x and y directions - x, y Cartesian coordinates - Thermal diffusivity of the fluid saturated porous medium - The coefficient of thermal expansion - An undetermined constant - Porosity of the porous medium - Similarity variable, =y(1+x ) ^/3/x ^1/3 - A preassigned constant - Kinematic viscosity - Nondimensional temperature, =(T – T )Ra^1/3 k/qw - Similarity variable, = =y(log_e x)^1/3/x ^2/3 - Similarity variable, =y/x ^2/3 - Stream function     

Three-dimensional convection regimes in a cubical cavity

Nonlinear three-dimensional convection regimes in a cubical cavity heated from below are studied numerically for small and moderate supercriticalities and different values of the Prandtl number Pr. The cases of adiabatic and perfectly heat-conducting lateral cavity boundaries are considered. The structure of different supercritical motions and their stability are investigated. The existence of different kinds of convective structures is detected over a wide range of governing parameters.     

Two-dimensional problem of natural convection in a rectangular domain with local heating and heat-conducting boundaries of finite thickness

Time-dependent natural convective heat transfer in a closed rectangular domain with heat-conducting boundaries of finite thickness is investigated numerically in the case of local heating on the inner side of the vertical wall. Convection-radiation heat transfer takes place on one of the outer boundaries of the solution domain. The inhomogeneous temperature distribution in the gas cavity is clearly manifested when the Grashof number Gr > 10⁶. Circulation flows can be distinguished in various zones of the solution domain on the basis of the numerical investigations carried out. These flows are due to the effect of the heat-release source, the propagation of perturbations induced by elements of the rigid wall, and the dynamics of conductive heat transfer in the solid material. The scales of the effect of the Grashof number on the hydrodynamic and thermal characteristics are indicated.     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

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.      

Forced convection heat transfer at the boundary layer of a packed bed

Numerical investigations of the nature of the fluid flow pattern and heat transfer at the boundary layer of a packed bed are reported. A volume averaged Navier-Stokes equation is used to predict the fluid flow and a volume averaged heat balance equation the heat transfer. A variable porosity in the packing is assumed in the region near the wall. Simulations are performed using a modified penalty Galerkin finite element method. The case of fully developed hydrodynamic flow and developing thermal flow is studied. The Nusselt number is found to depend on the Reynolds number, Graetz number and ratio of thermal conductivity of the solid and fluid phases. Comparison is made to some experimental literature values.Nomenclature A constant - [A] Navier-Stokes type matrix - B constant - [B] divergence matrix - C _p constant pressure heat capacity - d characteristic length - D _p particle diameter - D _t tube diameter - {F} solicitation vector - Gz Graetz number, z D _t ^–1 Pr _f Re _p - k permeability term - k _f Thermal conductivity of the fluid phase - k _s Thermal conductivity of the solid phase - [K] coefficient matrix for temperature equation - n normal vector - P pressure - Pr _f Prandtl number for the fluid _f C _p k _f ^-1 - r radial coordinate - R _t tube radius - R residual - R _m residual - Re _p Reynolds number for particle, - t tortuosity factor - T temperature - interstitial velocity - z axial coordinate - effective thermal conductivity - penalty parameter - boundary of solution domain - porosity - viscosity - density - test function - solution domain - test function     

Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number

Finite element predictions of two-dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half-divider in water for Rayleigh number up to 10¹¹ and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.     

Three dimensional finite element analysis for Rayleight-Benard convection in rectangular enclosures

The pattern of Rayleigh-Benard convection of air in a rectangular box heated-from-below is studied by numerically solving the three-dimensional time-dependent Navier-Stokes equations under the Boussinesq approximation. Slightly supercritical Rayleigh number was adopted to track the evolutions of flow structure as a function of enclosure's aspect ratio (A=L/H). The flow will asymptotically evolve to different patterns, among which, two possible types of flow pattern are found. One consists of the pair of straight vortex rolls and the other appears as closed vortex rings. The transition between the flow patterns indicates that there exists a flow bifurcation with the variation of container's aspect ratio. In addition, both steady and oscillatory flows have been observed, corresponding to the pair of straight vortex rolls and the vortex ring, respectively. The complexity of flow structure tends to increase with the increasing aspect ratio of the rectangular enclosure. The project supported by the National Natural Science Foundation of China (19889210), the National Distinguished Young Fund (10125210), the Hundred Talents Program of CAS, and the Training Program for the Trans-Century Outstanding Young of MOE     

A boundary layer analysis of combined heat and mass transfer by natural convection from a concentrated source in a saturated porous medium

A boundary layer analysis was carried out to investigate the coupled phenomena of heat and mass transfer by natural convection from concentrated heat and mass sources embedded in saturated porous media. Both line and point source problems were treated. The boundary layer equations based on Darcy's law and Boussinesq approximation were solved by means of similarity transformation to obtain the details of velocity, temperature and concentration distributions above a concentrated heat source. Two important parameters, namely the Lewis number Le and the buoyancy ratioN were identified to conduct a series of numerical integrations. For the case of small Le, a substance diffuses further away from the plume centerline, such that the mass transfer influences both velocity and temperature profiles over a wide range. For large Le, on the other hand, the substance diffuses within a narrow range along the centerline. Naturally, the influence of mass transfer is limited to the level of the centerline velocity, so that a peaky velocity profile appears for positiveN whereas a velocity defect emerges along the centerline for negativeN. For such cases of large Le, the temperature profiles are found to be fairly insensitive to Le.     

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Enhancement of natural convection heat transfer from a fin by triangular perforation of bases parallel and toward its tip

This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations （their bases parallel and toward the fin tip） under natural convection. The fin＇s heat dissipation rate is compared to that of an equivalent solid one. The parameters considered are geometrical dimensions and thermal properties of the fin and the perforations. The gain in the heat transfer enhancement and the fin weight reduction due to the perforations are considered. The study shows that the heat dissipation from the perforated fin for a certain range of triangular perforation dimensions and spaces between perforations result in improvement in the heat transfer over the equivalent solid fin. The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thickness are increased.