Double diffusive convection of anomalous density fluids in a porous cavity

A numerical study has been performed to analyze the combined effect of temperature and species gradients on the buoyancy-driven natural convection flow of cold water near its density extremum contained in a porous cavity. The governing equations are descretized using the finite volume method. The results of the investigation are presented in the form of steady-state streamlines, velocity vectors, isotherms, and isoconcentrationlines. The results are discussed for different porosities, Darcy numbers, and Grashof numbers. The heat and mass transfer rates calculated are found to behave nonlinearly with hot wall temperature. The heat and mass transfer are increased with increasing Darcy number and porosity. It is found that the convective heat and mass transfer rate are greatly affected by the presence of density maximum.     

Effects of walls temperature variation on double diffusive natural convection of Al2O3–water nanofluid in an enclosure

The effect of wall temperature variations on double diffusive natural convection of Al₂O₃–water nanofluid in a differentially heated square enclosure with constant temperature hot and cold vertical walls is studied numerically. Transport mechanisms of nanoparticles including Brownian diffusion and thermophoresis that cause heterogeneity are considered in non-homogeneous model. The hot and cold wall temperatures are varied, but the temperature difference between them is always maintained 5 °C. The thermophysical properties such as thermal conductivity, viscosity and density and thermophoresis diffusion and Brownian motion coefficients are considered variable with temperature and volume fraction of nanoparticles. The governing equations are discretized using the control volume method. The results show that nanoparticle transport mechanisms affect buoyancy force and cause formation of small vortexes near the top and bottom walls of the cavity and reduce the heat transfer. By increasing the temperature of the walls the effect of transport mechanisms decreases and due to enhanced convection the heat transfer rate increases.     

Transient conjugate mixed convection from a sphere in a porous medium saturated with cold pure or saline water

In this paper, a numerical investigation of the transient conjugate mixed convection flow about a sphere embedded in a porous medium saturated with pure or saline water is carried out. The effect of density extremum is considered by using the nonlinear dependence of density on the temperature. The salinity effects are considered by assuming uniform saline concentration over the domain considered. The direction of the natural convection is changed either to aiding or to opposing the upcoming flow direction simulating the sphere is either hot or cold relative to the surrounding temperature. Results show that the initial temperature differences as well as the saline concentration alter the transient heat transfer rate in conceivable degree. It was found that the heat capacity ratio between the sphere and the surrounding media has more significant effect on the calculated heat transfer rate than the thermal conductivity ratio. The study is performed by using six nondimensional parameters and results are discussed in detail. Received on 10 November 1997     

Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity

In this study, a transient heat transfer process of freezing water inside a two-dimensional square cavity has been investigated numerically. Water was used as a phase-change medium, and the numerical model has been created with control volume approach by using C++ programming language. To be able to accelerate the numerical calculations, CUT (Consistent-Update-Technique) algorithm has been implemented in the numerical code. Span-wise variations of the vertical component of the velocity have been represented in comparison with the experimental measurements from the literature at various vertical positions to examine the accuracy of the numerical scheme. The influence of natural convection has been considered by comparing the conduction and convection dominated solidification under same boundary conditions. Comparative results have been obtained regarding time-wise variations of the cold wall temperature and the dimensionless effectiveness. Moreover, the streamlines and isotherms have been represented to understand the differences between the conduction and convection driven phase change processes.Results indicate that natural convection becomes remarkable and has different forms at the initial periods of the phase change process. Increasing the effect of natural convection in the cavity increases the cooling rate of water. Near the density inversion temperature of water (4°C), temperature variations fluctuate and counter currents observed in the domain.     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-B?NARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM

为了解具有密度极值流体瑞利-贝纳德对流特有现象和规律,利用有限容积法对长方体腔内关于密度极值温度对称加热-冷却时冷水瑞利-贝纳德对流的分岔特性进行了三维数值模拟,得到了不同条件下的对流结构型态及其分岔序列,分析了密度极值特性、瑞利数、热边界条件以及宽深比对瑞利-贝纳德对流的影响. 结果表明:具有密度极值冷水瑞利-贝纳德对流系统较常规流体更加稳定,且流动型态及其分岔序列更加复杂;相同瑞利数下多种流型可以稳定共存,各流型在相互转变中存在滞后现象;随着宽深比的增加,流动更易失稳,对流传热能力增强;系统在导热侧壁时比绝热侧壁更加稳定,对流传热能力有所减弱;基于计算结果,采用线性回归方法,得到了热壁传热关联式.     

Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface

An experimental and analytical investigation pertaining to the effect of density inversion of water on the free convective heat transfer and the onset of free convection in a horizontal melt layer of ice heated by upper rigid surface is carried out. Temperatures of the upper surface are varied from 1°C to 15°C, with Rayleigh number ranging from 2 × 10² to 1 × 10⁵. From the present study, it can be demonstrated both experimentally and analytically that the density inversion of water plays an influential role in such a melt layer and the onset of free convection and the free convective heat transfer are considerably affected by the temperature of upper rigid surface T₂, in the case of T₂ ≤ 8° C, unlike the results obtained for common fluids without density inversion.     

Heat transfer during the melting of ice around a horizontal,isothermal cylinder

An experimental investigation of the melting of ice around a horizontal, isothermal cylinder is performed. Emphasis is placed on interpreting the heat transfer mechanisms which control solid-liquid interface position. Flow visualization and interferometric techniques are employed to study the transient flow patterns and corresponding temperature distributions in the melted region. It has been determined that density inversion plays an important role in the melting of water. The location of the maximum density surface in the liquid has a significant effect on natural convection, and hence on the shape and size of the melted region. Local Nusselt numbers at the surface of the cylinder and at the solid-liquid interface are determined and found to be complicated functions of time and imposed thermal conditions. Average Nusselt numbers at the solid-liquid interface and at the surface of the cylinder decrease with time and quasi-steady conditions are not reached.     

Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation

We consider unsteady laminar natural convection flow of water subject to density inversion in a rectangular cavity formed by isothermal vertical walls with internal heat generation. The top and bottom horizontal walls are considered to be adiabatic, whereas the temperature of the left vertical wall is assumed to be greater than that of the right vertical wall. The equations are non-dimensionalized and are solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of both heat generation and variations in the aspect ratio on the streamlines, isotherms and the rate of heat transfer from the walls of the enclosure are presented. Investigations are performed for water taking Prandtl number to be Pr=11.58 and the Rayleigh number to be Ra=10⁵.     

Influence of Density Inversion on Thawing Around a Cylinder in a Frozen Saturated Porous Medium

An analytical study is made of the convective flow field produced when a warm cylinder maintained at a fixed temperature above freezing is buried in saturated frozen porous medium. The flow field is shown to have a double cell pattern due to the density inversion of water at ~ 4°C, with downward convection of heat dominating at cylinder temperatures of below ~ 10°C and upward heat convection dominating at temperatures greater than this. The analysis uses a perturbation technique to determine the first-order convective correction to the flow and temperature fields around the cylinder for a quasi-static case. It demonstrates that the porous medium permeability and the cylinder temperature are the dominant factors in determining the point at which convection heat transfer becomes significant, with convection expected to be insignificant for Darcy permeabilies lower than 10⁻⁵ m/s. The analysis also gives an indication of the rates of thawing occurring in different directions without resorting to numerical methods. The practical implications of a thawing pattern significantly different to that predicted by conduction theory only are discussed briefly with respect to the problem of differential thaw settlement of arctic pipelines.     

Natural convection heat transfer on surfaces of copper micro-wires

The natural convection heat transfer characteristics and mechanism for copper micro-wires in water and air were investigated experimentally and numerically. The wires with diameters of 39.9, 65.8 and 119.1 μm were placed horizontally in water inside of a sealed tube and in air of a large room, respectively. Using Joule heating, the heat transfer coefficients and Nusselt numbers of natural convection for micro-wires in ultra pure water and air were obtained. A three dimensional incompressible numerical model was used to investigate the natural convection, and the prediction with this model was in reasonable accordance with the experimental results. With the decrease of micro-wire diameter, the heat transfer coefficient of natural convection on the surface of micro-wire becomes larger, while the Nu number of natural convection decreases in water and air. Besides, the change rate of Nu number in water decreases apparently with the increase of heat flux and the decrease of wire diameter, which is larger than that in air. The thickness of boundary layer on the wall of micro-wire becomes thinner with the decrease of diameter in both water and air, but the ratio of boundary layer thickness in water to the diameter increases. However, there is almost no change of this ratio for natural convection in air. As a result, the proportion of conduction in total heat transfer of natural convection in water increases, while the convective heat transfer decreases. The velocity distribution, temperature field and the boundary layer in the natural convection were compared with those of tube with conventional dimension. It was found that the boundary layer around the micro-wire is an oval-shaped film on the surface, which was different from that around the conventional tube. This apparently reduces the convection strength in the natural convection, thus the heat transfer presents a conduction characteristic.     

Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium

The current study addresses the mathematical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a lid-driven differentially heated cavity in presence of radiatively absorbing, emitting and scattering gray medium. The walls of the enclosure are considered to be opaque, diffusive and gray. Mixed convection is the outcome of the interaction of forced convection induced by the moving vertical hot and cold wall with the natural convection induced due to the differentially heated enclosure. Two different orientations of the wall movement have been considered to simulate opposing and aiding mixed convection phenomenon and to study its interaction with radiation. Vorticity-stream function formulation of N–S equation has been employed. The discrete ordinate method has been used in modeling the radiative transport equation followed with finite volume method as discretisation technique. The effect of influencing parameters on fluid flow and heat transfer has been studied.     

Onset of Rayleigh–Bénard convection in cold water near its density maximum in vertical annular containers

A set of three-dimensional numerical simulations of Rayleigh–Bénard convection in cold water near its density maximum in vertical annular containers is performed with the aim of determining the critical Rayleigh number at the onset of convection and the primary flow patterns for different geometric dimensions and density inversion parameters. The Prandtl number of cold water is about 11.57. The annular container is heated from below and cooled from above. The inner and outer sidewalls are considered to be perfectly adiabatic. The results obtained show that the critical Rayleigh number at the onset of convection increases with increase in the density inversion parameter and the radius ratio and with decrease in the aspect ratio. When the radius ratio is small, the flow patterns in vertical annular containers are similar to those in cylindrical containers. At large radius ratios the flow pattern is relatively simple, with several convective rolls observable along the azimuthal direction and similar with those characteristic of Rayleigh–Bénard convection in the Boussinesq fluid. The stratified flow phenomenon is found to exist at moderate values of the density inversion parameter. The results are compared with those obtained in the Boussinesq fluid to reveal the effect of the density inversion parameter.     

Heat transfer enhancement for laminar natural convection along a vertical plate due to sub-millimeter-bubble injection

Sub-millimeter-bubble injection is one of the most promising techniques for enhancing heat transfer for the laminar natural convection of liquids. However, flow and heat transfer characteristics for laminar natural convection of water with sub-millimeter bubbles have not yet been fully understood. The purpose of this study is to experimentally clarify the effects of sub-millimeter-bubble injection on the laminar natural convection of water along a heated vertical plate. The use of thermocouples and a particle tracking velocimetry (PTV) technique are applied to temperature and velocity measurements, respectively. The temperature measurement shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection increases with an increase in the bubble flow rate or a decrease in the wall heat flux and that the ratio ranges from 1.35 to 1.85. Moreover, it is concluded from simultaneous measurement of temperature and velocity that the heat transfer enhancement is directly affected by flow modification due to bubbles rising near the heated vertical plate.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

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.