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.     

Analysis of natural convection melting inside isothermally heated horizontal rectangular capsule

Melting characteristics of phase change material by natural convection heat transfer inside horizontal rectangular capsules are examined experimentally. The capsules are heated isothermally and three kinds of aspect ratios (qH/W=3, 1 and 1/3) are provided. Octadecane and ice are used, respectively, as the phase change material. A method of analysis applying the empirical correlations for natural convection heat transfer in a vertical or horizontal enclosure to the melting in the rectangular capsules is presented. The predicted results show good agreement with the experimental data. For the melting of octadecane and ice, it is found that the effect of aspect ratio on the melting process is not significant for the range ofB=1/3 to 3.     

Melting process with solid-liquid density change and natural convection in a rectangular cavity

This paper presents a numerical method that simulates the melting process in the presence of solid-liquid density change and natural convection in the melt. The physical model concerned is two-dimensional melting of a phase-change material, initially at its fusion temperature, charged in a rectangular cavity with isothermally heated side walls and an adiabatic bottom wall. The presence of the density change brings no change into the basic form of governing equation, so it is considered through the reformulation of boundary conditions. Difficulties associated with the complex time-dependent melt region, whose shape is also a part of the solutions, are overcome by employing the boundary-fitted coordinate system. Comparison with other works validates the present numerical model and reveals the effects of density change qualitatively. Also, it is confirmed that the present method is preferable to others with natural convection only. Computed results for interesting cases are shown in forms of transient position of the interface, temperature distribution, flow pattern, heat transfer coefficient, and melting fraction as a function of time. Closer examination on melting patterns allows a correlation to be made between the melting fraction and a new independent variable Ste·Fo·Ra^1/4.     

Solidification and melting heat transfer to an unfixed phase change material (PCM) encapsulated in a horizontal concentric annulus

The solidification and melting process of an unfixed PCM between two isothermal concentric horizontal cylinders was investigated by experimental techniques and by a combined analytical and numerical method. During the solidification process concentric solid PCM layers form at both tube walls, growing slowly into the annulus. Assuming quasi-steady heat conduction, this process is described by a simple analysis. The melting PCM reveals a different behaviour. Due to gravitational forces the solid phase moves downwards. Experiments prove that the solid retains contact with the lower part of the outer tube as well as with the upper part of the inner tube. In this process thin liquid films form between the solid body and the heated walls and heat transfer by conduction is the dominating mechanism during melting. Heat transfer by natural convection causes the melting at the upper interface. There, the melting rates, however, are comparatively small. The theoretical approach and the numerical analysis are based on a balance of the pressure forces in the thin liquid films and of the gravitational force acting on the solid material. As a result melting rates and heat fluxes may be predicted. For practical application a Nusselt correlation is derived.     

Experimental study of enhanced heat transfer by addition of CuO nanoparticle

An energy storage system has been designed to study the thermal characteristics of paraffin wax with an embedded nano size copper oxide (CuO) particle. This paper presents studies conducted on phase transition times, heat fraction as well as heat transfer characteristics of paraffin wax as phase change material (PCM) embedded with CuO nanoparticles. 40?nm mean size CuO particles of 2, 5 and 10% by weight were dispersed in PCM for this study. Experiments were performed on a heat exchanger with 1.5–10?l/min of heat transfer fluid (HTF) flow. Time-based variations of the temperature distributions are revealed from the results of observations of melting and solidification curves. The results strongly suggested that the thermal conductivity enhances 6, 6.7 and 7.8% in liquid state and in dynamic viscosity it enhances by 5, 14 and 30% with increasing mass fraction of the CNEPs. The thermal conductivity ratio of the composites can be augmented by a factor up to 1.3. The heat transfer coefficient during solidification increased about 78% for the maximum flow rate. The analysis of experimental results reveals that the addition of copper oxide nanoparticles to the paraffin wax enhances both the conduction and natural convection very effectively in composites and in paraffin wax. The paraffin wax-based composites have great potential for energy storage applications like industrial waste heat recovery, solar thermal applications and solar based dynamic space power generation with optimal fraction of copper oxide nanoparticles.     

Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above

A two-dimensional numerical simulation of natural convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurry with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations have been done using the finite volume method. Both natural convection and heat transfer characteristics are discussed about natural convection with PCM microcapsulate slurry, which exhibits the pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity with latent heat. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of phase-change material, the mass concentration, and the aspect ratio Ar on the natural convection heat transfer are described, respectively. By comparing with the results of microcapsule slurry without phase change, the enhancement in heat transfer is found in microcapsule slurry with phase change during the phase change temperature range. Numerical simulations are performed in the following parametric ranges: the width–height aspect ratio of the enclosure Ar from 2 to 20, the mass concentrations C _m of the slurry from 10 to 40%, power law index n of the slurry from 0.89 to 1.0 and Rayleigh numbers Ra ranges from 10³ to 10⁷.     

The effects of casting speed on steel continuous casting process

A three dimensional simulation of molten steel flow, heat transfer and solidification in mold and “secondary cooling zone” of Continuous Casting machine was performed with consideration of standard k−ε model. For this purpose, computational fluid dynamics software, FLUENT was utilized. From the simulation standpoint, the main distinction between this work and preceding ones is that, the phase change process (solidification) and flow (turbulent in mold section and laminar in secondary cooling zone) have been coupled and solved jointly instead of dividing it into “transient heat conduction” and “steady fluid flow” that can lead to more realistic simulation. Determining the appropriate boundary conditions in secondary cooling zone is very complicated because of various forms of heat transfer involved, including natural and forced convection and simultaneous radiation heat transfer. The main objective of this work is to have better understanding of heat transfer and solidification in the continuous casting process. Also, effects of casting speed on heat flux and shell thickness and role of radiation in total heat transfer is discussed.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

Numerical modelling of a melting-solidification cycle of a phase-change material with complete or partial melting

A high accuracy numerical model is used to simulate an alternate melting and solidification cycle of a phase change material (PCM). We use a second order (in time and space) finite-element method with mesh adaptivity to solve a single-domain model based on the Navier-Stokes-Boussinesq equations. An enthalpy method is applied to the energy equation. A Carman-Kozeny type penalty term is introduced in the momentum equation to bring the velocity to zero inside the solid region. The mesh is dynamically adapted at each time step to accurately capture the interface between solid and liquid phases, the boundary-layer structure at the walls and the multi-cellular unsteady convection in the liquid. We consider the basic configuration of a differentially heated square cavity filled with an octadecane paraffin and use experimental and numerical results from the literature to validate our numerical system. The first study case considers the complete melting of the PCM (liquid fraction of 95%), followed by a complete solidification. For the second case, the solidification is triggered after a partial melting (liquid fraction of 50%). Both cases are analysed in detail by providing temporal evolution of the solid-liquid interface, liquid fraction, Nusselt number and accumulated heat input. Different regimes are identified during the melting-solidification process and explained using scaling correlation analysis. Practical consequences of these two operating modes are finally discussed.     

Lattice Boltzmann investigation for enhancing the thermal conductivity of ice using Al2O3 porous matrix

An enthalpy-based Lattice Boltzmann method (LBM) with double-distribution function (DDF) model is used to investigate numerically the effects of inserting a porous matrix on the heat transfer performance of the phase change material (PCM). Simulations are carried out for melting of ice in saturated Al₂O₃ porous matrix encapsulated in a concentric annulus. The process is considered as a conduction/convection controlled phase change problem at a representative elementary volume (REV) scale. The present results are validated by previous published numerical simulations of melting with and without porous media. In this research paper, the effects of decreasing the porosity on the temperature contours, flow patterns within the melt zone, complete melting time of the PCM and average Nusselt number are discussed qualitatively and quantitatively.     

A two-phase,two-component model for natural convection in a porous medium

A numerical study of natural convection in a two-phase, two-component flow in a porous medium heated from below is presented. Interphase mass and energy transfer, latent heat and bouyancy effects are major physical features. This study extends earlier studies of natural convection based on single-phase, saturated porous medium models. The appearance of two-phase heat pipe zones in the flow has a marked effect on the fluid and heat flows as well as on the performance of the numerical methods. The numerical techniques for handling phase change, Jacobian construction and time step selection are discussed.     

Theoretical study and experimental verification of the behaviour of a passive conditioning system for electronic components

 The paper describes the theoretical determination of the flow and the temperature distribution in a water natural circulation loop for passive conditioning of a big shelter for electronic components. A cylinder filled with phase change material in thermal connection with the inner of the shelter and with the ambient by a water natural circulation loop forms the system. The system operates in natural convection, consequently during the daytime the water flow in the exchanger is stopped because the external temperature is greater then the melting temperature. During the night the situation is reversed, thus the convective flow begins allowing the water circulating and exchanging heat with the ambient. The paper presents a simulation model which describes the flow and the temperature field of the water in the loop during the night. Moreover the theoretical values of temperature are compared with the experimental data obtained in a climatic chamber. Received on 17 January 2000     

A finite element thermally coupled flow formulation for phase‐change problems

A finite element, thermally coupled incompressible flow formulation considering phase‐change effects is presented. This formulation accounts for natural convection, temperature‐dependent material properties and isothermal and non‐isothermal phase‐change models. In this context, the full Navier–Stokes equations are solved using a generalized streamline operator (GSO) technique. The highly non‐linear phase‐change effects are treated with a temperature‐based algorithm, which provides stability and convergence of the numerical solution. The Boussinesq approximation is used in order to consider the temperature‐dependent density variation. Furthermore, the numerical solution of the coupled problem is approached with a staggered incremental‐iterative solution scheme, such that the convergence criteria are written in terms of the residual vectors. Finally, this formulation is used for the solutions of solidification and melting problems validating some numerical results with other existing solutions obtained with different methodologies. Copyright © 2000 John Wiley & Sons, Ltd.     

The effect of carbon nanotubes in enhancing the thermal transport properties of PCM during solidification

This study is aimed to prepare a novel class of nanofluid phase change material (NFPCM) by dispersing a small amount of multi-walled carbon nanotubes (MWCNT) in liquid paraffin, to enhance the heat transfer properties and examine the characteristics of the NFPCM during the solidification process. The stable NFPCMs are prepared by dispersing the MWCNT in liquid paraffin at 30°C with volume fractions of 0.15, 0.3, 0.45 and 0.6% without any dispersing agents. The rheology measurement illustrates the Newtonian fluid behavior in the shear stress range of 1–10?Pa. The differential scanning calorimetric results showed that there is no observable variation in the freezing/melting temperature of the NFPCM, and only a small observable change in the latent heat values. The thermal conductivity of various NFPCM is measured. The enhancement in thermal conductivity increases with the increased volume fraction of the MWCNT, and shows a weak dependence on the temperature. Further, for the NFPCM with a volume fraction of 0.6%, there is an appreciable increase in heat transfer with a reduction in the solidification time of 33.64%. The enhancement in the heat transfer performance would alleviate the major problems that have been encountered in the conventional phase change materials since several years.     

Inward solidification of a superheated liquid in a cooled horizontal tube

Inward solidification has been studied experimentally and analytically under conditions where the liquid phase is above the fusion temperature (i.e., superheated). The liquid was housed in a horizontal circular tube in which the surface was maintained at a uniform, time-invariant temperature during test runs. Three phase change materials (n-heptadecane,n-octadecane, and water) were used in the tests. Both analysis and experiments have established that for inward solidification, natural convection in a superheated liquid is not important in controlling the solidliquid interface motion for Stefan numbers less than unity. The interface velocity is determined primarily by the thermal resistance across the solid layer. Good agreement has been obtained between experimentally measured and analytically predicted solid-liquid interface positions when the density differences between the phases were accounted for.     

横向磁场下侧壁加热方腔熔化的数值模拟研究

磁场下的固-液相变过程在电磁冶金和增材制造等工程应用中广泛存在,其中的熔化过程和流动机理尚未完全探究清楚.方腔熔化是研究固-液相变过程的基础模型,具有良好的普适性,研究磁场对其流动的影响可以为其他复杂相变过程提供参考.本文基于焓方法开展了固-液相变的数值模拟研究,得到了垂直主环流方向的横向磁场对侧壁加热方腔中流动、传热和熔化过程的影响.首先,对于无磁场时的方腔熔化问题,通过与已有的实验结果和数值结果进行对比,证实了文献中方腔宽度对固-液界面的形状及位置影响不能忽视的结论.随后,对小磁场情况下的三维工况进行了直接数值模拟,发现此时磁场效应主要表现为对混乱三维流动产生整流作用,使流动趋于二维化.但由于固-液界面的存在,主流区的速度在趋于一致的同时也会反作用于界面,其形状随磁场增强而逐渐转变为二维结构.最后,本文采用准二维模型分析了更强磁场时的情形,讨论了不同参数对传热效率及界面形状的影响,并发现了横向磁场作用下的垂直最大速度仍满足磁对流中的无量纲参数标度律关系.     

Convection-dominated melting of phase change material in partially heated cavity: lattice Boltzmann study

Heat transfer and fluid flow processes of natural convection melting of a phase change material are simulated numerically inside a partially heated square cavity. The momentum and energy equations are solved by using enthalpy-based lattice Boltzmann method combined with multi distribution function model. In this communication, the dependence of liquid fraction, temperatures of vertical nodes and average Nusselt number on the positions of heated plates is investigated quantitatively.     

Network simulation method for solving phase-change heat transfer problems with variable thermal properties

 The transient heat conduction equation in a finite slab undergoing phase change (two-phase problem of melting and solidification), with isothermal, adiabatic or convective boundary conduction is studied by the network simulation method; solid phase conductivity and specific heat are assumed to be dependent on temperature. Ablation, as a particular case, is also analysed. A network model is established for a cell and boundary conditions are added to complete the whole network model. No restrictions exist, as to the kinds of linear and non-linear boundary conditions, Stefan number values or the initial conditions (when hypotheses concern of the Stefan problem, numerical and exact solutions are compared for a large interval of Stefan numbers; simulation values show good agreement). Movement of the solid–liquid boundary and thermal fields are determined in all cases. Received on 10 May 2000 / Published online: 29 November 2001     

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.