Shape-factor effect on melting in an elliptic capsule

An approximate mathematical model of contact melting of an unfixed material in an elliptical capsule is developed. The main characteristic scales and non-dimensional parameters which describe the principal features of the melting process are found. Choosing a special heat flux distribution on the wall of the capsule allows us to derive a closed-form evolution equation for the motion of the solid accounting for the energy convection in the liquid, expressed through the non-linearity of the temperature distribution across the molten layer. It is shown that the melting rate of the solid depends on the shape of the capsule. Generally, elliptical capsules show higher rate of melting than circular ones. Elongated capsules provide more effective melting than oblate ones, even though they have the same aspect ratios and vertical cross-sectional areas. This phenomenon is caused by the fact, that the pressure necessary to support the solid is larger for the elongated capsules than that for oblate ones, which leads to thinning of the molten layer along with the increase of the heat flux across it. The time required for complete melting can be achieved by the right choice of the shape of the capsule, which is specified by the value of the aspect ratio. The found influence of the capsule shape on the melting rate can be used for design and optimization of practical latent-heat-thermal-energy systems.     

Study of contact melting inside isothermally heated vertical cylindrical capsules

Close-contact melting processes of phase change material (PCM) inside vertical cylindrical capsule are studied. PCM are heated by the capsule isothermally at the bottom and side. The theoretical formulas of the melting rate and thickness of liquid layer during the heat transfer process are obtained by analysis, which are convenient for engineering predictions. Finally, the factors that affect melting are discussed, and conclusions are drawn.     

Effect of internal void placement on the heat transfer performance – Encapsulated phase change material for energy storage

The effect of an internal air void on the heat transfer phenomenon within encapsulated phase change material (EPCM) is examined. Heat transfer simulations are conducted on a two dimensional cylindrical capsule using sodium nitrate as the high temperature phase change material (PCM). The effects of thermal expansion of the PCM and the buoyancy driven convection within the fluid media are considered in the present thermal analysis. The melting time of three different initial locations of an internal 20% air void within the EPCM capsule are compared. Latent heat is stored within an EPCM capsule, in addition to sensible heat storage. In general, the solid/liquid interface propagates radially inward during the melting process. The shape of the solid liquid interface as well as the rate at which it moves is affected by the location of the internal air void. The case of an initial void located at the center of the EPCM capsule has the highest heat transfer rate and thus fastest melting time. An EPCM capsule with a void located at the top has the longest melting time. Since the inclusion of a void space is necessary to accommodate the thermal expansion of a PCM upon melting, understanding its effect on the heat transfer within an EPCM capsule is necessary.     

Analysis of contact melting of phase change materials inside a heated rectangular capsule

Close-contact melting processes of phase change material (PCM) inside a horizontal rectangular capsule are studied. The PCM is heated by the capsule at constant heat flux at the top and isothermally at the bottom, and the sides are adiabatic. The theoretical formulas of the dimensionless melting rate and the thickness of the liquid layer during the heat transfer process are obtained by analysing, which is convenient for engineering predictions. Finally, the influences on the melting process are discussed, and conclusions are drawn.     

Melting of a vertical plate in porous medium controlled by forced convection of a dissimilar fluid

In this paper a boundary layer analysis is presented for the problem of melting of a flat plate embedded in a porous medium. The melting phenomenon is induced by forced convection of the ambient fluid. The ambient fluid and the melt are dissimilar. The density difference between the melt and the ambient fluid is responsible for the boundary layer flow in the melt region. The results of this paper document the dependence of the temperature and flow fields in the system, as well as the dependence of the local heat transfer rate at the solid/ melt interface on the dimensionless groups describing the physics of the problem.     

Numerical simulation of contact melting using the cell-splitting modified enthalpy method

The present work deals with the numerical simulation of contact melting using a cell-splitting enthalpy method, which is an improvement over the conventional enthalpy-porosity method. It is demonstrated that such a method is far superior to the enthalpy-porosity method which not only is unable to capture the interface precisely but is also unable to capture the melt rates, unless the coefficients are back-fitted with the experimental data. In contact melting, the contact layer is thin and hence to resolve the flow, fine grids have to be used. A novel integral model is proposed where a single control volume is used in the contact layer. A parametric study is performed for contact melting in a square geometry and a correlation is evolved for the melt rates. The shapes of the solid during contact and noncontact melting are discussed and the physical mechanisms that decide the evolution are articulated.     

Numerical investigation of a PCM-based heat sink with internal fins

The present study explores numerically the process of melting of a phase-change material (PCM) in a heat storage unit with internal fins open to air at its top. Heat is transferred to the unit through its horizontal base, to which vertical fins made of aluminum are attached. The phase-change material is stored between the fins. Its properties used in the simulations, including the melting temperature of 23-25 °C, latent and sensible specific heat, thermal conductivity and density in solid and liquid states, are based on a commercially available paraffin wax.A detailed parametric investigation is performed for melting in a relatively small system, 5-10 mm high, where the fin thickness varies from 0.15 mm to 1.2 mm, and the thickness of the PCM layers between the fins varies from 0.5 mm to 4 mm. The ratio of the PCM layer to fin thickness is held constant. The temperature of the base varies from 6 °C to 24 °C above the mean melting temperature of the PCM.Transient three- and two-dimensional simulations are performed using the Fluent 6.0 software, yielding temperature evolution in the fins and the PCM. The computational results show how the transient phase-change process, expressed in terms of the volume melt fraction of the PCM, depends on the thermal and geometrical parameters of the system, which relate to the temperature difference between the base and the mean melting temperature, and to the thickness and height of the fins.In search for generalization, dimensional analysis of the results is performed and presented as the Nusselt numbers and melt fractions vs. the Fourier and Stefan numbers and fin parameters. In some cases, the effect of Rayleigh number is significant and demonstrated.     

Free convection heat and mass transfer during pool penetration into a melting miscible substrate

A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.     

Melting of a vertical ice cylinder inside a rotating cylindrical cavity filled with binary aqueous solution

The melting of a vertical ice cylinder into a homogeneous calcium chloride aqueous solution inside a rotating cylindrical cavity with several rotating speeds is considered experimentally. The melting mass and temperature are measured on four initial conditions of the solution and four rotating speeds of the cavity. The temperature of the liquid layer becomes uniform by the mixing effect resulting from cavity rotation and it enhances the melting rate of the ice cylinder. As the cavity‐rotating speed increases, the melting rate increases. The dimensionless melting mass is related to the Fourier number and the rotating Reynolds number in each initial condition, therefore an experimental equation that is able to quantitatively calculate the dimensionless melting mass is presented. It is seen that the melting Nusselt numbers increase again in the middle of the melting process. The ice cylinder continues to melt in spite of the small temperature difference between the ice cylinder and the solution. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 359–373, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20211     

Analysis of Partial Melting in Metal Powder Bed with Constant Heat Flux

Rapid melting of a subcooled single-component metal powder bed in Selective Laser Sintering (SLS) is analyzed in this paper. Under irradiation of a pulse laser beam, the surface of the powder particle is molten first while the core of the particle remains solid. The temperature of the liquid layer is higher than the melting point, while the temperature of the solid core is below the melting point. Therefore, the mean temperature of the partially molten particle is within a range of temperature adjacent to the melting point. In addition, the powder bed experiences a significant density change during melting because the interstitial gas initially in the pore space is driven out as melting progresses. Melting in SLS of single-component metal powder can therefore be modeled as that occurring in a range of temperature with significant density change. The temperature distributions in the solid, liquid, and mushy zones and locations of the various interfaces are obtained by using an integral approximate method. The effects of initial porosity, dimensionless initial temperature, and dimensionless thermal conductivity of the interstitial gas on the surface temperature and locations of the interfaces are investigated.     

水平圆管内相变材料接触熔化分析

研究相变材料在水平圆管内的接触熔化过程,考虑了圆管表面与接触熔化固液相界面法向角度的不同,给出新的物理模型,应用边界层理论推导得熔化过程所应该满足的基本方程,用数值方法求得了新的边界层厚度、压力分布、熔化率、熔化结束时间、努谢尔特数,以及熔化、液面高度的变化规律,并进行了分析讨论,与相关文献的解析结果进行了比较。     

An analytical solution of the heat transfer process during contact melting of phase change material inside a horizontal elliptical tube

Close-contact melting processes of phase change material (PCM) inside a horizontal elliptical tube are studied. The theoretical formulas of the melting rate, thickness of liquid layer, elapsed time of solid PCM and Nusselt number during the heat melting process are obtained by analyzing. The results include those of contact melting inside a horizontal cylinder. Finally, the influences of elliptical compression coefficient and temperature difference in melting are discussed, and useful conclusions are drawn. © 1998 by John Wiley & Sons, Ltd.     

Enthalpy porosity model for melting and solidification of pure-substances with large difference in phase specific heats

A modified enthalpy porosity formulation is introduced to capture melting and solidification of pure substances. When melting and solidification of pure substances are addressed by the fixed grid based volume averaging technique, it is possible to obtain two equivalent and interchangeable mathematical formulations of the energy conservation equation if the governing equation is expressed in terms of temperature as the primary dependent variable. Between these two formulations, only one form is shown to provide physically consistent numerical solutions when very large difference in specific heats for liquid and solid phases is involved. A modified enthalpy updating scheme is proposed to predict the solid/liquid fraction during melting and solidification process of pure substances having large difference in phase specific heats. The results from the proposed scheme are validated with the existing results from literature involving numerical prediction of freezing of water. The physical consistency of the simulation results obtained by solving two interchangeable forms of energy conservation equation is tested and compared considering a case study involving melting of ice. While one of the conservation forms fails to predict the melting process, the other conservation form successfully predicts physically consistent result. The proposed formulation is capable of predicting melting and solidification of all pure substances including those with large difference in phase specific heats such as water and paraffin wax.     

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 phase density based enthalpy model for laser assisted phase change process

Diffusion dominated laser assisted phase change process in a pure metal is numerically investigated using the enthalpy based fixed-grid approach. The single equation based on the total enthalpy (sensible and latent heat) is used in the whole domain (solid, liquid and vapor) to describe the transport processes in individual phases. To simulate in line with the experiment for laser drilled cavity in a cylinder, density variation due to change of phase has been taken into account in the proposed axisymmetric model. The proposed model also includes temperature dependent thermal properties. An iterative enthalpy update equation is developed to capture the evolution of the complicated melt as well as vapor front. To resemble a true laser beam, a Gaussian laser pulse is irradiated on the substrate surface. The drilled cavity depth predicted using the proposed model is compared with the available experimental results and a good agreement is found.     

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.     

Enhanced heat transfer in free convection-dominated melting in a rectangular cavity with an isothermal vertical wall

Free convection-dominated melting of a phase change material in a rectangular cavity with an isothermally heated vertical wall is simulated using the streamline upwind/Petrov–Galerkin finite element technique in combination with a fixed-grid primitive variable method. The enthalpy–porosity model is employed to account for the physics of the evolution of the flow at the solid/liquid interface. A penalty formulation is used to treat the incompressibility constraint in the momentum equations. Inverting of the container at an appropriate stage during the melting process is proposed as a simple but effective technique for enhancement of free convection-controlled heat transfer in the phase change material. The technique results in more than 50% increase of the energy charge rate during the melting process for some specific cases.     

A new model of phase change process for thermal energy storage

Thermal energy can be converted into mechanical energy through the melting process of a phase change material (PCM). A PCM mixed with an insoluble liquid has higher energy converting efficiency during the whole melting process, where the massive microvacuum formed during the freezing process is filled by the insoluble liquid, which increases utilization of the volume change. The traditional theoretical model of the phase change process is unable to sufficiently describe the mixed PCM; therefore, a new model aimed at analyzing the characteristics of the volumetric change rate, as well as the freezing and melting times of the mixed PCM, is theoretically constructed. In this paper, the effective heat capacity method is used, and the effects of porosity are considered when the PCM is in the solid state. Comparisons of this model with the traditional model are carried out using both simulations and experiments for different pressures and geometric structures. Our results indicate that the introduced model has better accuracy when describing the phase change process of the pure PCM mixed with an insoluble liquid.     

Numerical analysis of melting with constant heat flux heating in a thermal energy storage system

Melting in a finite slab with a second kind boundary condition is studied numerically in order to simulate the charging process of a thermal energy storage system. A dimensionless model is given, from which it is concluded that the main factors that influence the melting process are the dimensionless heating flux, the modified Stefan number, the relative thermal diffusivity and the relative thermal conductivity. The influence of preheating or solid subcooling is studied. It is found that though preheating does not have very important effects on the melting time, it does influence the interface marching velocity significantly. The melt fraction and the melting time are calculated extensively for various dimensionless numbers. The numerical results show that the ratio of the thermal conductivity of the solid to that of the liquid has little effect on the melting time, and the time for finishing melting can be expressed as a function of the dimensionless heating flux, the modified Stefan number and the relative thermal diffusivity, and the possible function form is suggested.