Effect of adiabatic wall on the natural convection heat transfer from a wavy surface created by attached horizontal cylinders

The effect of a vertical adiabatic wall on the natural convection heat transfer from vertical array of attached cylinders, which can be considered as wavy surface, was investigated experimentally and numerically. The experiments were carried out using Mach-Zehnder interferometer and the commercial FLUENT code was used for numerical study. This paper focuses on the effect of wall-wavy surface spacing and Rayleigh number variation on the local and average free convection heat transfer coefficients from the each cylinder and the wavy surface. Rayleigh number ranges from 2400 to 10,000 and from 300,000 to 1,250,000 based on cylinder diameter and wavy surface height respectively. The local and average Nusselt numbers were determined for the different Rayleigh numbers, and the ratio of wall- wavy surface spacing to cylinder diameter 0.75, 1, 1.5, 2, 3, 4, 5, and ∞. Results are indicated with a single correlation which gives the average Nusselt number as a function of the ratio of the wall-wavy surface spacing to cylinder diameter and the Rayleigh numbers. There is an optimum distance between the wall and wavy surface in which the Nusselt number attain its maximum value. This optimum distance depends on the Rayleigh number.     

Natural convection heat transfer along vertical rectangular ducts

Experimental investigations have been reported on steady state natural convection from the outer surface of vertical rectangular and square ducts in air. Seven ducts have been used; three of them have a rectangular cross section and the rest have square cross section. The ducts are heated using internal constant heat flux heating elements. The temperatures along the vertical surface and the peripheral directions of the duct wall are measured. Axial (perimeter averaged) heat transfer coefficients along the side of each duct are obtained for laminar and transition to turbulent regimes of natural convection heat transfer. Axial (perimeter averaged) Nusselt numbers are evaluated and correlated using the modified Rayleigh numbers for laminar and transition regime using the vertical axial distance as a characteristic length. Critical values of the modified Rayleigh numbers are obtained for transition to turbulent. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers and the area ratio for the laminar regimes. The local axial (perimeter averaged) heat transfer coefficients are observed to decrease in the laminar region and increase in the transition region. Laminar regimes are obtained at the lower half of the ducts and its chance to appear decreases as the heat flux increases.     

The Prandtl number effect near the onset of Bénard convection in a porous medium

This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Ra_c) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid.     

Heat transfer by conduction,natural convection and radiation across a rectangular cellular structure

This paper describes results on the effects of wall conduction and radiation heat exchange among surfaces on laminar natural convection heat transfer in a two-dimensional rectangular cavity modelling a cellular structure. Parametric heat transfer calculations have been performed, and numerical results are presented in graphical and tabular form. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The findings suggest that the local or the average Nusselt number is one of many parameters that control conjugate heat transfer problems. The results indicate that natural convection heat transfer in the cavity is reduced by heat conduction in the walls and radiation exchange among surfaces. The results obtaibed for the total heat transfer rate through the system using the two-dimensional model are compared with those based on a one-dimensional model.     

Aspect ratio effect on natural convection in water near its density maximum temperature

The effect of the aspect ratio on natural convection in water subjected to density inversion has been investigated in this study. Numerical simulations of the two-dimensional, steady state, incompressible flow in a rectangular enclosure with a variety of aspect ratios, ranging from 0.125 to 100, have been accomplished using a finite element model. Computations cover Rayleigh numbers from 10³ to 10⁶. Results reveal that the aspect ratio, A, the Rayleigh number, Ra, and the density distribution parameter, R, are the key parameters to determine the heat transfer and fluid flow characteristics for density inversion fluids in an enclosure. A new correlation for predicting the maximum mean Nusselt number is proposed in the form of , with the constants a and b depending on density distribution number R. It is demonstrated that the aspect ratio has a strong impact on flow patterns and temperature distributions in rectangular enclosures. The stream function ratio Ψ_inv/|Ψ_reg| is introduced to describe quantitatively the interaction between inversional and regular convection. For R=0.33, the density inversion enhancement is observed in the regime near A=3.     

Numerical investigation of natural convection inside an inclined parallel‐walled channel

Steady two‐dimensional natural convection in an inclined parallel‐walled channel was investigated numerically. The full elliptic forms of conservation equations were solved together and the velocity vectors, temperature contours and local and average Nusselt number distribution were obtained. The comparisons of local and average Nusselt number with published experimental and numerical results indicate very good agreement. Results are presented for a single aspect ratio, L/b=24, over the range of Rayleigh number of 3–1000 and angle of inclination 0–90°. The results indicate that the overall channel average Nusselt number is reduced as the inclination angle is increased. Significant reductions in the overall Nusselt number are exhibited at high angle of channel inclination. Copyright © 2005 John Wiley & Sons, Ltd.     

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。     

Numerical investigation of thermosolutal natural convection in a rectangular enclosure of an aspect ratio four with heat and solute sources

A numerical study of double-diffusive natural convection in an enclosure with a partial vertical heat and mass sources for an aspect ratio Ar = 4 has been carried out. The influence of various dimensionless parameters (Rayleigh number, buoyancy ratio, source location, Lewis number, and source length) on the flow behavior are investigated. Correlations of average Nusselt and Sherwood numbers are obtained as function of two parameters (Ra, d) and (Le, d), respectively.     

Laminar natural convection of Cu-water nanofluid in concentric annuli with radial fins attached to the inner cylinder

Laminar natural convection of Cu-water nano-fluid between two horizontal concentric cylinders with radial fins attached to the inner cylinder is studied numerically. The inner and outer cylinders are maintained at constant temperature. The governing equations in the polar two-dimensional space with the respective boundary conditions are solved using the finite volume method. The hybrid-scheme is used to discretize the convection terms. In order to couple the velocity field and the pressure in the momentum equations, the well known semi-implicit method for pressure linked equation reformed algorithm is adopted. Using the developed code, a parametric study is undertaken, and the effects of the Rayleigh number, Number of fins, length of the fins and the volume fraction of nano-particles on the fluid flow and heat transfer inside the annuli are investigated. In this study, two cases with different number of fins are considered. It is observed from the results that the average Nusselt number increases with increasing both the Rayleigh number and the volume fraction of the nano-particles. Moreover, the average Nusselt number decreases by increasing the fins’ length and the number of fins. Heat transfer rate increases by increasing the fins’ length at all Rayleigh numbers, but it increases by increasing the number of fins at high Rayleigh numbers.     

Thermal and dynamic optimization of the convective flow in Trombe Wall shaped channels by numerical investigation

Two-dimensional, laminar, transitional and turbulent simulations were obtained by solving the fully-elliptic governing equations of the motion established by natural convection in channels, with Trombe Wall configuration, for different geometrical parameters and symmetrical heating. In transitional and turbulent cases, the low-Re k−ω turbulence model has been employed. To validate the numerical results, some comparisons with experimental results taken from literature have been carried out. Numerical results for the average Nusselt number and the non-dimensional induced mass-flow rate have been obtained for a wide and not yet covered range of the Rayleigh number varying from 10⁵ to 10¹². Correlations for the thermal and the mass-flow optimum wall-to-wall spacing have been presented. Finally, additional configurations including discrete heat sources have been studied, in order to obtain thermal and dynamic improvements. These intermediate devices were tested as turbulence generators, in the transitional range of Rayleigh numbers.     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

Nonlinear Two-Dimensional Convection in a Nanofluid Saturated Porous Medium

In this article, we study the linear and nonlinear thermal instability in a horizontal porous medium saturated by a nanofluid. For this, the momentum equation with Brinkman model has been used. Also, it incorporates the effect of Brownian motion along with thermophoresis. The linear stability is based on normal mode technique, and for nonlinear analysis, the truncated Fourier series involving only two terms has been used. The expression of Rayleigh number for linear theory has been derived, and the effects of various parameters on Rayleigh number have been presented graphically. Weak nonlinear theory is used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated and depicted graphically, by solving the finite amplitude equations using a numerical method.     

Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer

The present study is concerned with buoyancy-driven convection experiments in a circular horizontal differentially heated layer of air. The radius-to-height ratio of 14, and Rayleigh numbers of 5,861 and 12,124 have been considered. A Mach–Zehnder interferometer has been used to visualize the convection patterns in the fluid layer. The fluid layer has been imaged at view angles of 0, 45 and 90°. Results obtained show that fringe patterns appropriate for a cavity square in plan are seen in the fluid layer during the early stages of the experiments. After the passage of the initial transients, steady fringes have been observed in the fluid layer for a Rayleigh number of 5,861. At Ra=12,124, a dominant pattern was detectable combined with mild unsteadiness. The steady thermal field at Ra=5,861 displayed symmetry with respect to the viewing angle. A stronger three dimensionality was seen at the higher Rayleigh number. The average steady state Nusselt numbers were found to vary with view angle from 1.91 to 2.04 at Ra=5,861 and 2.28 to 2.43 at Ra = 12,124. The cavity-averaged Nusselt numbers are in good agreement with the available correlations.     

Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures

Two-dimensional numerical studies of flow and temperature fields for turbulent natural convection and surface radiation in inclined differentially heated enclosures are performed. Investigations are carried out over a wide range of Rayleigh numbers from 10⁸ to 10¹², with the angle of inclination varying between 0° and 90°. Turbulence is modeled with a novel variant of the k–ε closure model. The predicted results are validated against experimental and numerical results reported in literature. The effect of the inclination of the enclosure on pure turbulent natural convection and the latter’s interaction with surface radiation are brought out. Profiles of turbulent kinetic energy and effective viscosity are studied to observe the net effect on the intensity of turbulence caused by the interaction of natural convection and surface radiation. The variations of local Nusselt number and average Nusselt number are presented for various inclination angles. Marked change in the convective Nusselt number is found with the orientation of enclosure. Also analyzed is the influence of change in emissivity on the flow and heat transfer. A correlation relevant to practical applications in the form of average Nusselt number, as a function of Rayleigh number, Ra, radiation convection parameter, N _RC and inclination angle of the enclosure, φ is proposed.     

Free convection heat transfer from the outer surface of vertically oriented helical coils in glycerol-water solution

Steady state natural convection heat transfer from vertical helical coiled tubes, in glycerol-water solution 57% (g/w) by mass, is studied experimentally. Average heat transfer coefficients were obtained for laminar and transition to turbulent natural convection. The experiments have been carried out for three coil diameter to tube diameter ratios, D/d_o, and for five and ten coil turns, N. Effects of Rayleigh number, D/d_o ratios, and N on the heat transfer behavior of the coils are investigated. Correlations are presented to calculate the average Nusselt number in terms of Rayleigh number, D/d_o ratios, and N. The results show that the heat transfer coefficient is enhanced either by reducing the diameter ratio or the number of coil turns. The overall correlations covering all the data points using the coil length as a characteristic length are also presented.     

Non-linear Convective Transport in a Binary Nanofluid Saturated Porous Layer

In this article, we study double-diffusive convection in a horizontal porous medium saturated by a nanofluid, for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Darcy model is used for the porous medium. The thermal energy equations include the diffusion and cross-diffusion terms. The linear stability is studied using normal mode technique and for non-linear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. For linear theory analysis, critical Rayleigh number has been obtained, while non-linear analysis has been done in terms of the Nusselt numbers.     

Numerical analysis of a symmetrically heated vertical channel with obstruction

 In this paper, a numerical investigation of laminar natural convection flows in a vertical channel with obstructions is carried out. The main purpose was to analyze the effects of the locations of symmetric obstructions. The computations were performed in a two-dimensional domain and a symmetric uniform wall temperature has been taken as thermal boundary condition. The governing equations were solved using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling was employed. The profiles of the local Nusselt number were given for three different locations of the obstructions. The variation of the average Nusselt number and inlet flow rate versus the modified Rayleigh number were investigated. The results demonstrated that the average Nusselt number decreases as the distance of the obstructions from the inlet increases. Received on 17 January 2000     

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     

Numerical investigation of transient laminar natural convection of air in a tall cavity

Transient laminar natural convection of air in a tall cavity has been studied numerically. The Navier-Stokes and Energy equations were solved by the accurate projection method (PmIII), in which the derived Poisson equation for pressure potential was solved by the approximate factorization one method (AF1). The aspect ratio of the tall cavity is 16, and the Prandtl number of air filled in the tall cavity is 0.71. To obtain the numerical results of heat transfer by natural convection of air in the tall cavity, the second order schemes for the space and time discretizations were utilized. The availability of the numerical algorithm was also assessed by considering the natural convection of air in a square cavity which is differentially heated from side walls. It was found that the overall Nusselt numbers for the Rayleigh numbers covering the range from 1000 to 100000 reveal a good agreement with measured data. When Ra takes the value in the range from 100000 to 600000, the overall Nusselt number have a relative deviation less than 18% from the experimental data. For the suddenly heating mode, the multicellular flow pattern occurs when Rayleigh number belongs to the range of Ra from 7000 to 20000. or greater than 115000. At the critical number of cats' eye instability, the cell distance is just twice of the cavity width. This is rather similar to the observed result for Bénard problem. When Ra is over 115000, a further increase of heat flux across the tall cavity causes serious cell-breaking. There are 8 cells when Ra = 600000.     

具有强SORET效应的充分发展的混合流体行进波对流

混合流体Rayleigh-Benard对流是研究对流稳定性,时空结构和非线性特性的典型模型之一。本文利用流体力学扰动方程组的数值模拟,讨论了偏离传导状态具有强SORET效应的混合流体行进波对流的温度场和浓度场的成长过程,分析了充分发展对流情况下的对流振幅,Nusselt数及混合参数与相对瑞利数的关系。并给出了行进波相速度对相对瑞利数的依赖关系。结果说明混合参数的曲线与行进波相速度的分布曲线是类似的。文末,给出了垂直速度,温度和浓度场的分布并讨论了相对瑞利数对场的分布及不同场之间的相位差的影响。