Freezing of Water in a Slab with Boundary Conditions of the Third Kind

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Melting of frozen, porous media contained in a horizontal or a vertical, cylindrical capsule

Melting of ice in porous media has been investigated experimentally and analytically for a horizontal and vertical cylindrical capsule. Quantitative results of the temperature distribution and solid-liquid interface motion and shape were obtained for inward melting with different size and types of spherical beads used as the porous media. Predictions from an analysis which considers conduction as the only mode of heat transfer in both the solid and liquid were compared to experimental data to show where natural convection becomes significant. It was found that the melting rate was augmented by natural convection in the liquid. For large differences in the thermal conductivity of the phase-change material and porous medium (e.g. water and aluminum), the effective thermal conductivity of the system was not predicted accurately by the model used, resulting in a further discrepancy between data and predictions. Moreover, the assumption of local temperature equilibrium between the void constituent and the porous medium becomes invalid for a water-aluminum bead system.     

Thermal radiation effects in phase-change energy-storage systems

A numerical model was developed to determine the transient temperature distribution, solid/liquid interface location, and energy-storage capacity of a semi-transparent phase-change medium. The medium is bounded between two concentric cylinders and internal energy transfer occurs simultaneously by conduction and thermal radiation. The radiation transport equation was coupled with the energy equation; both enthalpy and temperature were employed as dependent variables. The spherical harmonic approximation (P-N approximation) was used to obtain solutions for the radiative heat flux. The coupled conservation of energy and moment differential equations were solved by using iterative numerical finite-difference schemes with appropriate thermal and radiant boundary and interface conditions. The numerical model was used to study the effects of radiation on solidification (melting), transient temperature distribution and energy-storage capacity of an absorbing, emitting, and isotropically scattering, semi-transparent, gray medium contained in a cylindrical annulus. The results increase our understanding of internal energy transfer and show the effects of optical properties, conduction/radiation parameter, and geometric dimensions and should lead to better designs and optimization of phase-change energy-storage systems.     

HEAT TRANSFER OF SOLID–LIQUID PHASE-CHANGE MATERIAL SUSPENSIONS IN CIRCULAR PIPES: EFFECTS OF WALL CONDUCTION

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.     

Performance Analysis of Heat Sinks With Phase-Change Materials Subjected to Transient and Cyclic Heating

Phase-change cooling technique is a suitable method for thermal management of electronic equipment subjected to transient or cyclic heat loads. The thermal performance of a phase-change based heat sink under cyclic heat load depends on several design parameters, namely, applied heat flux, cooling heat transfer coefficient, thermophysical properties of phase-change materials (PCMs), and physical dimensions of phase-change storage system during melting and freezing processes. A one-dimensional conduction heat transfer model is formulated to evaluate the effectiveness of preliminary design of practical PCM-based energy storage units. In this model, the phase-change process of the PCM is divided into melting and solidification subprocesses, for which separate equations are written. The equations are solved sequentially and an explicit closed-form solution is obtained. The efficacy of analytical model is estimated by comparing with a finite-volume-based numerical solution for both transient and cyclic heat loads.     

Melting in a vertical cylindrical tube: Numerical investigation and comparison with experiments

The present work numerically investigates melting of a phase-change material (PCM) in a vertical cylindrical tube. The analysis aims at an investigation of local flow and thermal phenomena, by means of a numerical simulation which is compared to the previous experimental results .The numerical analysis is realized using an enthalpy–porosity formulation. The effect of various parameters of the numerical solution on the results is examined: in particular, the term describing the mushy zone in the momentum equation and the influence of the pressure–velocity coupling and pressure discretization schemes. PISO vs. SIMPLE and PRESTO! vs. Body-Force-Weighted schemes are examined. No difference is detected between the first two. However, considerable differences appear with regard to the last two, due to the mushy zone role.Image processing of experimental results from the previous studies is performed, yielding quantitative information about the local melt fractions and heat transfer rates. Based on the good agreement between simulations and experiments, the work compares the heat transfer rates from the experiments with those from the numerical analysis, providing a deeper understanding of the heat transfer mechanisms. The results show quantitatively that at the beginning of the process, the heat transfer is by conduction from the tube wall to the solid phase through a relatively thin liquid layer. As the melting progresses, natural convection in the liquid becomes dominant, changing the solid shape to a conical one, which shrinks in size from the top to the bottom.     

Coupled radiation and solidification heat transfer inside a graded index medium by finite element method

Effects of thermal radiation on solidification heat transfer must be considered inside semitransparent media. This paper investigates coupled heat transfer of solidification and radiation within a two-dimensional rectangular semitransparent medium having gradient index. Solidification process is supposed to happen at some temperature range, and accordingly three zones including liquid-, solid- and mushy-zones exist in phase-change media. In different phase field, parameters of thermophysical property are assumed different and those of radiative property are assumed same. Governing equation includes conduction, radiation and phase-change terms, and radiation and phase-change are treated as source terms in the equation, respectively. A Galerkin finite element method is used to solve energy equation of coupled radiation and phase-change heat transfer. This paper analyzes effect of thermal radiation on phase-change heat transfer and those of refractive index distributions on temperature fields and liquid fraction distributions during radiation–solidification coupled heat transfer. From the results, we can find that refractive index gradient has a major influence on phase-change process and compared with the case of smaller index gradient, bigger gradient can speed up phase-change heat transfer in semitransparent media.     

Numerical and experimental study of melting in a spherical shell

The present study explores numerically and experimentally the process of melting of a phase-change material (PCM) in spherical geometry. Its properties used in the simulations, including the melting temperature, latent and sensible specific heat, thermal conductivity and density in solid and liquid states, are based on a commercially available paraffin wax, which is manufactured to be used mainly in latent-heat-based heat storage systems. A detailed parametric investigation is performed for melting in spherical shells of 40, 60, and 80 mm in diameter, when the wall-temperature is uniform and varies from 2 °C to 20 °C above the mean melting temperature of the PCM. Transient numerical simulations are performed using the Fluent 6.0 software. These simulations show the melting process from the beginning to the end, and incorporate such phenomena as convection in the liquid phase, volumetric expansion due to melting, sinking of the solid in the liquid, and close contact melting. The results of the experimental investigation, which included visualization, compare favorably with the numerical results and thus serve to validate the numerical approach. The computational results show how the transient phase-change process depends on the thermal and geometrical parameters of the system, including the temperature difference between the wall and the mean melting temperature, and the diameter of the shell. Dimensional analysis of the results is performed and presented as the mean Nusselt numbers and PCM melt fractions vs. an appropriate combination of the Fourier, Stefan, and Grashof numbers. This analysis leads to generalization which encompasses the cases considered herein.     

A comparative study on the performances of different shell-and-tube type latent heat thermal energy storage units including the effects of natural convection

Numerical modeling was performed to simulate the melting process of a fixed volume/mass phase-change material (PCM) in different shell-and-tube type latent thermal energy storage units with identical heat transfer area. The effect of liquid PCM natural convection (NC) on the latent heat storage performance of the pipe and cylinder models was investigated using a 3D numerical model with FLUENT software. Result shows that NC can cause a non-uniform distribution of the solid–liquid interface, which accelerates PCM melting rate. The PCM melting rate and heat storage rate in the horizontal cylinder model are higher than those in the horizontal pipe model because of the combined effects of heat conduction and NC. A comparative study was conducted to determine the effects of horizontal and vertical shell-and-tube models with different heat transfer fluid (HTF) inlets including the effects of NC. The results indicate that the vertical model with an HTF inlet at the bottom exhibits the highest PCM melting rate and heat storage rate for the pipe models. For the cylinder models, the horizontal model and the vertical model with an HTF inlet at the bottom can achieve nearly the same completed melting time. In addition, NC has minimal effect on any model with an HTF inlet at the top.     

Modeling of a heat exchanger utilizing a phase-change material for short-term storage

A computer program was proposed to simulate the behavior of a low-temperature phase-change material (PCM) in a heat exchanger for short-term storage. An experimental set-up of mainly a heat exchanger with a staggered tube arrangement and air temperature control unit were used. In the modeling approach, the PCM in the tube was divided into 10 concentric cells of equal mass, and was logically treated in terms of energy balance. Experimental inlet air temperature (at three different flow rates) was utilized as input data to test the model output results and their reliability. Excellent agreement was obtained for the outlet air temperature when compared with the experimental measurements, and differences did not exceed 0.5°C over the simulated period. The predicted PCM average temperature history showed good agreement with the experimental ones, and differences did not exceed 2° at the highest applied air flow rate. This modeling approach can be used for any PCM, provided that its thermophysical properties are available. The transient moving front for freezing or melting can be predicted, and consequently the mass fraction of either liquid or solid phase to the total PCM mass can be predicted as well.     

Direct contact melting with asymmetric load

In this study, direct contact melting with an asymmetric load was investigated both experimentally and by numerical analysis. A rectangular parallelepiped solid on a heating surface was melted under various asymmetric loads, while total load acting on the solid and brine temperature were kept constant. In the numerical analysis, the melting process keeping the force balance between the pressure in the liquid film and the loads at all times was calculated. It was found that the average heat flux into the solid was independent of the moment acting on the solid. Analytical results of the time dependencies of the amount of melting and the inclination of the solid agreed with experimental ones for each condition.     

Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index

Radiative heat transfer in semitransparent phase-change media is of great interest in many engineering fields. Its essence is the transient coupled heat transfer of radiation and conduction along with liquid–solid phase change. The difficulty is to solve radiative heat transfer with the consideration of time–space dependent radiative properties. Especially when the refractive index is considered to vary with space and time in phase change, the problem becomes more complicated. This paper investigates the problem of the variable radiative properties with space and time during phase change in semitransparent media. The phase-change medium is assumed to have solid, mushy and liquid zones, and the solid/mushy and liquid/mushy interfaces are considered to be semitransparent and diffuse reflecting. In different zones, there are different physical property parameters. Phase interfaces are always moving in phase change, while the interfaces of control volumes are fixed. Therefore, the interfaces of control volumes and phase interfaces are not always coincided, which will bring errors into the simulation of radiative transfer in phase-change media. However, the errors can be reduced by dividing the medium into enough sub-layers. As long as the number of sub-layers is big enough, the errors can be limited in a very small range. Then using the multilayer radiative transfer model, we can solve the radiative transfer problem in the semitransparent phase-change medium. Considering time–space dependent refractive index, this paper analyzes coupled radiative and conductive heat transfer in semitransparent solidifying media. The results show that the effects of variable refractive index with time and space on transient coupled heat transfer are significant and could not be neglected inside the semitransparent phase-change medium under some conditions.     

Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)

In this paper the experimental investigation on the solid/liquid phase change (melting and solidification) processes have been carried out. Paraffin wax RT58 is used as phase change material (PCM), in which metal foams are embedded to enhance the heat transfer. During the melting process, the test samples are electrically heated on the bottom surface with a constant heat flux. The PCM with metal foams has been heated from the solid state to the pure liquid phase. The temperature differences between the heated wall and PCM have been analysed to examine the effects of heat flux and metal foam structure (pore size and relative density). Compared to the results of the pure PCM sample, the effect of metal foam on solid/liquid phase change heat transfer is very significant, particularly at the solid zone of PCMs. When the PCM starts melting, natural convection can improve the heat transfer performance, thereby reducing the temperature difference between the wall and PCM. The addition of metal foam can increase the overall heat transfer rate by 3-10 times (depending on the metal foam structures and materials) during the melting process (two-phase zone) and the pure liquid zone. The tests for investigating the solidification process under different cooling conditions (e.g. natural convection and forced convection) have been carried out. The results show that the use of metal foams can make the sample solidified much faster than pure PCM samples, evidenced by the solidification time being reduced by more than half. In addition, a two-dimensional numerical analysis has been carried out for heat transfer enhancement in PCMs by using metal foams, and the prediction results agree reasonably well with the experimental data.     

Numerical and experimental investigation for heat transfer in triplex concentric tube with phase change material for thermal energy storage

This paper addresses a numerical and experimental investigation of a thermal energy storage unit involving phase change process dominated by heat conduction. The thermal energy storage unit involves a triplex concentric tube with phase change material (PCM) filling in the middle channel, with hot heat transfer fluid (HHTF) flowing outer channel during charging process and cold heat transfer fluid (CHTF) flowing inner channel during discharging process. A simple numerical method according to conversation of energy, called temperature & thermal resistance iteration method has been developed for the analysis of PCM solidification and melting in the triplex concentric tube. To test the physical validity of the numerical results, an experimental apparatus has been designed and built by which the effect of the inlet temperature and the flow rate of heat transfer fluid (HTF, including HHTF and CHTF) on the thermal energy storage has been studied. Comparison between the numerical predictions and the experimental data shows good agreement. Graphical results including fluid temperature and interface of solid and liquid phase of PCM versus time and axial position, time-wise variation of energy stored/released by the system were presented and discussed.     

Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface

Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet’s free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120 °C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet’s evaporation rate is predicted using a model based on Fick’s law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid–gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.     

一种余热利用相变石蜡储热过程的数值模拟

基于一种相变储热石蜡,考虑熔化过程中液相的自然对流情况,建立了矩形腔内石蜡熔化过程的数学模型,并利用该模型进行了数值模拟,分析了石蜡熔化过程中的温度场变化、流场变化、相界面移动情况。通过采用铝制翅片的方式强化传热,并分析了翅片位置对该石蜡熔化时间的影响。模拟结果表明,在y=0.1、y=5、y=10、y=15mm时,与不采用翅片相比,储热时间分别缩短了43.1%、52.0%、38.3%、22.2%。研究结果对相变储热器的优化设计有一定意义。     

The correlation between the number of fins and the discharge time for a finned heat pipe latent heat storage system

The concept of a solar energy heat pipe latent heat storage system is presented. In order to assure large charging and discharging rates, finned heat pipes are used to transfer heat to and from the phase-change material (paraffin in this case). The evolution of the solid - liquid interface is studied by considering the radial heat transfer (due to the heat pipe wall) and the angular one (due to the fin). Two mathematical models, corresponding to exponential, respectively polynomial functions describing the fin temperature profile are presented and the results are compared. The two models allow the evaluation of the discharge time of the storage unit for a certain number of fins for a single heat pipe. When the discharge time has a fixed value, the methods presented in the paper allow to conclude whether the number of fins is sufficiently large to assure the complete solidification of the phase-change material.     

An analytical solution for the coupled heat and mass transfer during the freezing of high-water content materials

The coupled problem of heat and mass transfer during the solidification of high-water content materials like soils, foods, tissues and phase-change materials is developed. Assuming quasi-steady heat conduction in the frozen region, the system leads to a set of coupled ordinary differential equations. The model takes into account the influence of material characteristics and process variables on the advance of the freezing and sublimation fronts, temperature and water vapour profiles and weight loss. It was validated against the analytical solution of the freezing (without surface ice sublimation) of a semi-infinite medium and was extensively used to perform a parametric study.     

Numerical heat transfer and thermal engineering of AdBlue (SCR) tanks for combustion engine emission reduction

In the automotive industry the selective catalytic reduction (SCR), which converts nitrogen oxides into nitrogen and water in the presence of a reducing agent, namely the so-called AdBlue urea–water solution, becomes major importance as a powerful emission reduction technique. Thermal engineering of SCR-tanks is a great challenge due to the melting and freezing behaviour of the AdBlue-fluid. In this paper, an efficient use of computational fluid dynamics and numerical heat transfer methods is presented for developing and optimising automotive SCR-tank systems. These thermal simulations include the phase change (melting and freezing), heat conduction, power generation, and natural convection effects within the liquid. The accuracy of the numerical scheme is assessed by comparisons with benchmark cases and experimental data. Typical industrial application examples are presented.     

Numerical and Experimental Investigation on Heat Transfer Performance of a Solar Single Storage Tank

The single-tank latent heat thermal energy storage(LHTES) of solar energy mainly consists of two modules: the first one is the phase change material(PCM) module heated by solar energy; the second is a module of heat transfer between melted PCM and the user's low-temperature water. This paper mainly focuses on the former one. To investigate the heat transfer performance of the paraffin-based solar single storage tank and find a more suitable experimental configuration, as basic research work, we established a single-tank thermal storage platform and then conducted a numerical simulation on the heat transfer process with Fluent. The result of numerical simulation shows that the test situation was basically reflected and the data agreed well with the experiment results. The numerical simulation analysis is accurate and the method is reliable. To obtain the heat transfer performance of paraffin in a single tank and strengthen heat transfer, the aspect ratio, the melting temperature of paraffin, and the heating power of the electric heater were analyzed based on simulation. The results show that the heat transfer gets more uniform when the aspect ratio is lower. This results in an increase in the liquid fraction of 61.83% to 76.47% one hour after heating when the aspect ratio of the tank reduced from 2.8 to 1.1. The higher the melting temperature of paraffin, the longer it takes for PCM to reach a stable state. And the curvature of liquid heating is greater than that of solid heating at the bottom layer. Under the constant total work, the heating power has little effect on the heat transfer performance of the paraffin. This study will provide some reference value for the optimization design of single-tank LHTES systems in the future.