Solid-liquid Phase Change Heat Transfer Research Articles

Effect of contact thermal resistance and skeleton thermodynamic properties on solid-liquid phase change heat transfer in porous media: A simulation study

Phase change materials (PCMs) have the potential for heat storage and release, but low thermal conductivity limits their wide application in thermal systems. This work proposes a mathematical model to simulate the freezing process of water in porous media. Unlike traditional methods that solve for two temperatures in different materials, the hybrid finite element method computes a single temperature satisfying the jump on the interface. The effect of contact thermal resistance and skeleton parameters on solid-liquid phase change heat transfer was investigated. This model was validated by experiments in reference. Results show that increased contact thermal resistance decreases temperature gradient, phase interface deflection and freezing rate. Specifically, with contact thermal resistance of 0.0001 K/W, 0.0005 K/W, and 0.001 K/W, freezing rates decrease by 36.4 %, 52.35 %, and 54.14 %, respectively, compared to the case without resistance. Although the contact thermal resistance reduced the temperature gradient, it stabilized the phase change process. Moreover, higher thermal conductivity of the skeleton enhances the freezing rate. However, after a certain value is reached, the rate increases only marginally. Skeletons with lower density and specific heat capacity are favorable to enhancing phase change heat transfer.

Phase change in a one-dimensional functionally graded material

Functionally graded materials (FGMs) are a class of materials with engineered microstructure to achieve spatial variation in properties so as to serve a desired function. While FGMs have been well-researched for their structural properties, there is a lack of investigation of FGMs in solid-liquid phase change heat transfer processes. A well-designed functionally graded phase change material (FG-PCM) may overcome some of the well-known limitations of the phase change process. In order to investigate this possibility, this work presents a theoretical model to predict phase change propagation in a one-dimensional FG-PCM containing an arbitrary spatial variation in thermal conductivity, thermal diffusivity and latent heat. The problem is solved using the method of eigenfunction expansion to determine the temperature distribution, wherein, spatial variation in thermophysical properties listed above is accounted for by deriving a first-order matrix ordinary differential equation in the coefficients of the series solution. Results are found to correctly reduce to the well-known Stefan solution under special conditions. The impact of variation in thermophysical properties is investigated in detail. It is found that while spatial variation in thermal conductivity and latent heat has a significant effect on the rate of phase change, the impact of the thermal diffusivity function is negligible for realistic values of the Stefan number. The effect of the Stefan number governing this problem on the rate of melting is investigated. The nature of phase change under linear (1+aξ), polynomial (1+aξn) and exponential (eaξ) functional forms of thermophysical properties is investigated. It is shown that an appropriate choice of these spatial functions may help overcome the well-known self-limiting nature of phase change and produce a nearly-linear phase change propagation curve. For example, results show 33% increase in phase change propagation for a linear (1+5ξ) variation in thermal conductivity compared to baseline. The theoretical tools developed here may help design and optimize functionally graded PCMs towards improved phase change heat transfer in applications of practical interest.

Analytical modeling of phase change in a composite wall comprising two distinct phase change materials in series

Most of the past literature on solid-liquid phase change heat transfer modeling focuses on a single phase change material (PCM), whereas, a sandwich of two or more PCMs arranged in series may be of interest in several applications. The modeling of heat transfer and phase change in such a system is complicated by the presence of multiple phase change fronts propagating at the same time. This work presents a theoretical analysis of the problem of melting of a two-PCM stack being heated from one end. Depending on whether the lower-melting PCM is located next to or away from the heat source, two distinct cases are considered. The propagation of the phase change fronts in each case is divided into several stages, each of which is characterized by a distinct phase change and/or sensible heating processes. The transient temperature field in each stage is determined in the form of infinite series solutions, and the propagation of phase change front over time is then determined using energy conservation at the phase change interface. In this manner, explicit expressions are derived for the time taken for each layer to completely melt. Results are shown to be in good agreement with finite-element simulations, and with the exact Stefan solution under special conditions. Key non-dimensional parameters that influence the nature of the two-PCM phase change process are identified, and their impact on phase change performance is analyzed. Quantitative predictions are presented for the conditions under which both PCMs finish melting at the same time, which is a favorable outcome for efficient energy storage.

Dual-sided melting of a one-dimensional composite wall comprising two distinct phase change material (PCM) layers

Past literature on theoretical modeling of solid-liquid phase change heat transfer mostly addresses a single phase change material (PCM), whereas, a series combination of two or more PCMs is often used in practical applications. This work presents an approximate analytical model for the melting/freezing of a one-dimensional composite of two PCMs being heated/cooled from both ends. It is shown that up to three phase change fronts may simultaneously exist in this problem. In addition to direct melting/freezing from the respective walls, it is shown that each PCM may also melt/freeze due to heat transfer through the other PCM. Using a quasi-stationary assumption, temperature field during the multi-stage phase change process is approximated by solving a multilayer transient thermal conduction problem using eigenfunction expansion. Good agreement with numerical simulations, and with the Stefan solution for a special case is demonstrated. The impact of key non-dimensional parameters on performance metrics including total time for phase change is determined. A quantitative prediction of conditions leading to the thermodynamically favorable situation of simultaneous completion of phase change of two commonly used PCMs is carried out. This work improves the theoretical understanding of phase change in composite PCMs, leading to optimization of practical thermal systems.

Review of phase change heat transfer enhancement by metal foam

• Enhancement characteristics of metal foam on solid-liquid phase change heat transfer and liquid-gas phase change heat transfer are reviewed. • The mechanism of metal foam enhancing phase change heat transfer and the factors affecting the phase change heat transfer process are comprehensively discussed. • Existing methods for optimizing phase change heat transfer performance within metal foam are classified and evaluated. • The practical applications of metal foam enhanced phase change heat transfer in recent years are summarized and compared. • This review will lead to a better understanding on the designing and applying of efficient metal foam-phase change heat transfer systems. Metal foam is a novel multifunctional material with high porosity, high surface density, and excellent heat transfer performance. Embedding metal foams into phase change heat transfer systems can be used to improve the comprehensive heat transfer performance, which is receiving increasing attention in the field of thermal management. This paper focuses on the lasted advances in solid-liquid phase change heat transfer and liquid-gas phase change heat transfer within metal foams, and specifically analyzes the influencing factors on phase change heat transfer performance as well as the mechanism of metal foam effects on phase change heat transfer. Different optimized techniques for improving phase change heat transfer within metal foams and the current state of metal foam engineering applications for improving phase change heat transfer are reviewed and discussed. It is concluded that the addition of metal foam can significantly enhance the heat transfer performance of solid-liquid phase change systems and liquid-gas phase change systems, but it is accompanied by an inhibitory effect on natural convection, an obstructive effect on bubble overflow and an elevated effect on pressure drop. The application of gradient porous structure, metal foam fins, V-groove structure or changing the surface wettability of metal foam is a feasible way to alleviate the above problems. Meanwhile, it is pointed out that the heat transfer performance of phase change within metal foam is influenced by the interaction of various factors, and some key issues regarding the influence mechanism of PCM-device orientation, pore distribution, surface wettability, and structural properties on heat transfer performance still need to be studied to develop more efficient and compact heat sinks.

An enthalpy-based cascaded lattice Boltzmann method for solid-liquid phase-change heat transfer

• The CLB method is extended to simulate solid-liquid phase-change problems. • The unphysical numerical diffusion can be effectively eliminated by the CLB method. • The CLB method can achieve better numerical stability due to the enhanced Galilean invariance. In this paper, a cascaded lattice Boltzmann (CLB) method for investigating solid-liquid phase-change heat transfer is developed. In the CLB method, the enthalpy methodology is adopted to capture the solid-liquid phase interface implicitly. Mesoscopically, the enthalpy is defined as the basic evolution variable of the CLB equation of the temperature field so as to consider the phase-change effect in simulations without iteration procedure, and to achieve this purpose, the cascaded collision process is artfully designed by modifying the shifting procedure. Numerical results demonstrate that the enthalpy-based CLB method can serve as an accurate and reliable numerical tool for simulating solid-liquid phase-change heat transfer.

Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditions

Solid-liquid phase change heat transfer problems appear in a broad variety of engineering systems, such as thermal management and latent energy storage. Boundary conditions in such systems often vary with time, for example, due to sinusoidal heating, or step changes in externally applied temperature or heat flux. Unfortunately, phase change problems with time-dependent boundary conditions do not generally admit an exact solution, and therefore, approximate analytical solutions are of much interest. This paper presents an eigenfunction expansion based technique for solving one-dimensional phase change heat transfer problems with time-dependent temperature or heat flux boundary conditions. The temperature field is expressed as a series solution of appropriate eigenfunctions, and with time-dependent coefficients, which are determined by deriving and solving an ordinary differential equation that accounts for the time-dependent nature of the boundary condition. Solutions for Cartesian, cylindrical and spherical problems are derived. Results are found to be in excellent agreement with past work and numerical simulations. The effect of Stefan problem on the nature of phase change propagation is studied. Two practical problems involving sinusoidal and step function boundary conditions are also solved and analyzed in detail. In addition to improving the fundamental understanding of phase change heat transfer, this work may also contribute towards design and optimization of practical engineering problems involving phase change heat transfer.

Simulating Solid-Liquid Phase-Change Heat Transfer in Metal Foams via a Cascaded Lattice Boltzmann Model.

A cascaded lattice Boltzmann (CLB) model is constructed for simulating heat transfer in metal-foam-based solid-liquid phase change materials (PCMs). The present model captures the phase interface implicitly via the enthalpy methodology, and to avoid iterations in simulations, the CLB equation of the PCM employs the enthalpy as the basic evolution variable through modifying the cascaded collision process. Numerical results demonstrate the effectiveness and practicability of the CLB model for investigating heat transfer in solid-liquid PCMs with metal foams. The effects of the inertial coefficient, permeability and porosity on the melting process are investigated. The results indicate that the empirical correlations of inertial coefficient and permeability based on packed beds overestimate the melting rate at high porosities. Moreover, the porosity has significant impact on phase-change processes. The melting rate increases as the porosity of the metal foam decreases since heat conduction through high thermal conductive metal foam dominates the total heat transfer.

Experimental investigation on melting heat transfer of an organic material under electric field

In this paper the melting heat transfer process of n-octadecane when confined in a cylinder-cubic cavity under the influence of an electric field is experimentally investigated. n-octadecane is a typical organic phase change material (PCM) and possesses a well-defined melting point. The cylinder is subject to the simultaneous actions of electric potential and heating, while the bottom wall or the four sidewalls of cavity are grounded. The effects of the voltage's magnitude and polarity on the solid–liquid phase change heat transfer performance are studied. The dynamic evolutions of the melting front and liquid fractions, the measurement of velocity field and electric current–voltage characteristics, and the distribution of electric field are presented to understand the physical mechanism. It is observed that when the applied voltage is higher than a certain threshold charge injection at the cylinder takes places, and the resulting strong Coulomb force promotes melting. In addition, heat transfer enhancement is more significant when the charge injection takes place at a negative voltage. The strong electric field that surrounds the whole cylinder with the four grounded sidewalls would facilitate injection and accelerate phase change. In this case, the melting time can be reduced by up to 68.0% when the −25.0 kV is applied.

Intelligent optimization of horizontal fins to improve the melting performance of phase change materials in a square cavity with isothermal vertical wall

A new combination mode of genetic algorithm (GA) and computational fluid dynamics (CFD) is proposed to solve optimization problems of fins for the enhancement of solid-liquid phase change heat transfer performance. In this optimization problem, some horizontal straight fins are installed on a vertical wall of a two-dimensional square cavity filled with PCM. The total cross-sectional area of fins is set as constraint, and the number, location and length/thickness of fins are selected as variables. The effect of natural convection on the melting characteristic of PCM is considered. The optimization results showed that fin length should be as long as possible and the fins should be arranged uniformly if the fin thickness is free. The existence of natural convection may slightly move fin downward to shorten the total melting time and increase the thermal energy storage rate. When the fin thickness is limited, the optimal number of fins depends on the total length of fins. One fin is suggested when the total length is smaller than 1.3, two fins when between 1.3 and 2.6, three fins when between 2.6 and 3.6, and four fins when greater than 3.6. Within the parameter range in this study, the thermal conductivity of fin material and fin thickness have ignorable effects on the critical values of total length, while the effects of natural convection should not be neglected. The critical length will increase with the increase of the Rayleigh number.

Eigenfunction-based solution for one-dimensional solid-liquid phase change heat transfer problems with advection

Heat transfer problems involving solid-liquid phase change occur in a wide variety of engineering applications. Most phase change heat transfer problems do not admit an exact analytical solution, and therefore, development of approximate analytical methods is of much interest. This work analyzes a one-dimensional phase change heat transfer problem in the presence of advection due to fluid flow. An approximate, eigenfunction-based solution for the temperature distribution and propagation of the phase change front with time is derived, which may be interpreted as a generalization of the classical quasistationary method. It is shown that even a single term of this series offers improved accuracy compared to the classical quasistationary solution. The method is shown to retain good accuracy even at large values of the Stefan number where approximate analytical methods usually lose accuracy. Results are shown to be in good agreement with numerical simulation results. As expected, in the absence of advection, results are shown to reduce to well-known Neumann and Stefan solutions. The impact of various problem parameters, including Stefan and Peclet numbers on the rate of phase change front propagation is investigated. The theoretical treatment presented here can also be used to solve similar mass transfer problems with a chemical reaction front where species advection may play a key role. This work improves the theoretical understanding of phase change heat transfer in the presence of advection, and may find applications in the design and optimization of engineering processes and systems involving phase change.

Experimental investigation on the melting characteristics of n-octadecane with electric field inside macrocapsule

Experiments on the melting characteristics of n-octadecane with electric field inside a cavity are carried out. The classical differentially heated cavity is considered to explore the effect of electric field on solid-liquid phase change heat transfer. The influence of the applied voltage's polarity and magnitude on the melting process of n-octadecane is investigated. The dynamic evolution of the liquid fraction and solid-liquid interface positions with melting time are reported. The velocity fields and electric current-voltage curves are also presented for understanding the physical mechanism. Results show that Coulomb force plays the central role in affecting the melting heat transfer process. The electric field would hinder or accelerate the melting process depending on the strength of electric field. When the applied voltage set to the right wall that is cold is larger than 10.0kV, the electric field would obviously accelerate the melting process. For a cavity with the length of 40.0 mm, the charge injection is hardly taken place when the maximum DC voltage of 20.0kV is applied, so the free charge carriers are mainly generated by conduction mechanism.

Comparison of LBM and FVM for Simulation of Solid-Liquid Phase Change Problem with Natural Convection

Phase change materials (PCM) are wildly investigated and used in the fields of thermal energy storage and thermal control of electronics. Numerical simulation is an important method in the research, development, analysis and design of PCM based systems. At present, there are two main numerical methods for the simulation of solid-liquid phase transition problems with natural convection: the finite volume method (FVM) based on macroscopic scale continuity equations, and the lattice Boltzmann method (LBM) based on mesoscopic scale lattice Boltzmann equation. In this paper, the calculation characteristics, speed, efficiency, and accuracy of the two numerical methods are compared, with the classical solid-liquid phase change heat transfer experimental results as benchmark reference. The results obtained in this paper can be used as valuable reference for the selection and use of numerical simulation methods in the study of solid-liquid phase transition problems.

Numerical modeling of solid-liquid phase change under the influence an external electric field

Recent experimental results demonstrate that electric field can effectively decrease the melting time of dielectric Phase Change Materials (PCMs). In this study, a Finite-Volume Method (FVM) based numerical model for the solid-liquid phase change heat transfer of dielectric PCM under the influence of electric field is presented. Fully coupled governing equations of electric potential, charge transport, Navier–Stokes equations, and the energy equation are implemented in the finite-volume framework of OpenFOAM®. The numerical model is first validated against the analytical solutions for several test cases in the hydrostatic regime. Results from the numerical model exhibit good agreement with the analytical solutions. The numerical model presented in this work is capable of capturing the sudden step change in the charge density distribution and electric field due to the discontinuity of the physical properties at the interface. A numerical analysis of EHD assisted melting of a dielectric PCM inside a rectangular cavity is considered. Effects of electric Rayleigh number T and Stefan number St on the rate of melting are discussed. The transient evolution of the EHD assisted melting process which includes different flow stages is analyzed. It is found that the electric Rayleigh number T has a notable effect on the rate of melting and its influence is more pronounced at lower values of St. A maximum of 56.10% reduction in total melting time is achieved at T=3000 and St=0.01, for the flow configuration considered here.

An improved layered thermal resistance model for solid-liquid phase change time estimation

This work improves a layered thermal resistance (LTR) model for the prediction of phase change times in solid-liquid phase change heat transfer. A combination of analytical and numerical approaches is applied in 1-D and 2-D solidification problems where heat conduction is dominant. In the improved layered thermal resistance (ILTR) model, the domain is discretized to layers. Based on its thermal resistance, the solidification time of each discrete layer is obtained by calculating the heat flux across the boundaries and the sensible and latent heat transfer. Unlike the quasi-steady heat conduction approach and linear temperature distribution assumption in the LTR model, the ILTR model considers transient heat conduction in each layer thus providing a better estimation of the average temperature distribution. The total solidification time is obtained by adding the solidification time of all the discrete layers. In several validations, the ILTR model shows a good agreement with the exact solution (1-D), experimental results (1-D), and numerical results (2-D). It is demonstrated that the ILTR model provides better predictions of phase change times than the LTR model, particularly under large Stefan numbers. This model could be further developed for more complicated (geometry or boundary conditions) phase change problems.

Conjugate solid-liquid phase change heat transfer in heatsink filled with phase change material-metal foam

The conjugate flow and heat transfer of phase change materials (PCMs)-metal foam confined between two annuli is addressed. A pulse heat load is employed at the inner surface of annuli, while the outer surface is subject to convection cooling. The enthalpy-porosity approach is utilized to model the phase change, and the natural convection in the porous medium is taken into account using Darcy-Brinkman model. The governing equations are transformed into non-dimensional form and solved by the finite element method. The finite element method is employed to solve the governing equations in the non-dimensional form. An automatic grid adaptation technique is employed to capture the phase change interface. The results are compared with theoretical and experimental studies available in the literature and found in good agreement. The steady-state solution and transient characteristics are addressed. The results demonstrate that the heatsink filled with PCM-metal foam can enhance the heat transfer at the hot surface, particularly at low external cooling power (Biot number < 0.2). The results reveal that the fusion temperature of phase change material is the key parameter on temperature controlling of the hot surface. Using the phase change heatsink results in a cooling power four times higher than that of pure external convection during the pulse load.

Microstructural evolution within mushy zone during paraffin’s melting and solidification

Mushy zone refers to the two-phase mixed region appearing between the solid and liquid region during solid-liquid phase change. The microstructural evolution within mushy zone is tightly coupled with the fluid flow, heat transfer and phase transition, as well as the related latent heat storage performance. In this paper, the microscopic structural evolution during paraffin’s melting and solidification was observed in real time using a confocal optical microscope equipped with a thermal stage. Based on image postprocessing, the evolving features of the mushy zone are quantified, including the characteristic length of the interphase liquid, solid/liquid fraction, solid/liquid formation rate, and latent heat evolution. Our results indicate that three regions, i.e. the solid region, the mushy zone and the liquid region, can be distinctly identified during both the melting and solidification processes. Meanwhile, it is found that the microstructure within mushy zone during melting evolves quite differently from that in solidification process, implying that the former is not just a simple reverse process of the latter. In addition, the mushy zone constant, coming from the enthalpy-porosity method that simulates the macroscale heat transfer of solid-liquid phase change, was evaluated according to the measured microstructure feature. These results provide physical insights into the nature of mushy zone during both the melting and solidification processes, and also offer instructive guidelines for accurate modelling of macroscale solid-liquid phase change heat transfer.

Three-dimensional multiple-relaxation-time lattice Boltzmann models for single-phase and solid-liquid phase-change heat transfer in porous media at the REV scale

In this paper, three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are developed for single-phase and solid-liquid phase-change heat transfer in porous media at the representative elementary volume (REV) scale. These models are developed in the framework of the double-distribution-function (DDF) approach: the flow field is solved by an isothermal MRT-LB model with the D3Q15 or D3Q19 lattice based on the generalized non-Darcy model, while the temperature field is solved by a thermal MRT-LB model with the D3Q7 lattice. In the 3D DDF-MRT model for solid-liquid phase-change heat transfer in porous media, the enthalpy method is employed to capture the solid-liquid phase interface in an implicit manner. Mesoscopically, the effective enthalpy is defined as the basic evolution variable of the enthalpy-based MRT-LB model, and as a result, the temperature and liquid-fraction fields can be solved without iteration procedure. The practicability and accuracy of the proposed models are demonstrated by numerical simulations of several 3D single-phase and solid-liquid phase-change heat transfer problems in porous media at the REV scale. It is shown that the 3D DDF-MRT models for convection heat transfer in porous media are second-order accurate in space. In addition, the influences of Darcy number and porosity on the melting (solidification) processes of 3D melting (solidification) with convection in a cubical porous cavity are investigated by the enthalpy-based DDF-MRT model.

Can the melting behaviors of solid-liquid phase change be improved by inverting the partially thermal-active rectangular cavity?

The solid-liquid phase-change melting of phase change material (PCM, paraffin wax) is simulated in a rectangular cavity with two isothermally partially active vertical walls. A concept of inverting the cavity at different stages during the melting process is proposed as a possible method for thermal behaviors enhancement in the latent heat thermal energy storage with PCM. The enthalpy-porosity model is employed to account for the corresponding phase change process and flow evolution at the PCM solid-liquid interface, and the numerical model is validated by the existing data in the literature. It is confirmed that inverting the cavity is an effective method to improve the PCM thermal behaviors, and the maximum ∼24.3% increase of the liquid fraction during the PCM melting process for the best case of inverting at 40% standard unit hour. On the other hand, the cavity inverted is also a simple technique to enhance the solid-liquid phase-change melting heat transfer as compared to the available techniques reviewed. Furthermore, the concluded way is also suggested to incline the PCM cavity by a few degrees if a full inversion is not available in some situations. In conclusion, this proof of concept is expected to provide a novel development field of thermal transport enhancement in latent heat thermal energy storage.

Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure

This paper details a numerical study of solid-liquid phase change heat transfer in a rectangular enclosure with the aim of optimizing the number, dimension, and positioning of fins in the enclosure. The enclosure is exposed on one side to a constant heat flux of 1000 W/m2 for 3 h and both the total fin mass and the PCM mass are kept constant in all simulated cases. The heat diffusion equation in the PCM uses the equivalent heat capacity method while natural convection driven PCM motion in the enclosure is modeled through the buoyancy force, using a modified viscosity and an additional volume force term in the Navier-Stokes momentum conservation equation. Three efficiency assessment parameters are used: (i) the height-averaged temperature of the front hot plate which should remain as low as possible for the longer possible time, (ii) the energy stored inside the PCM as a function of time, and (iii) the heat transfer rate and heat flux between the front plate and the PCM. For each simulated case, complementary data such as the standard deviation of temperature along the heated plate and the ratio of sensible heat to latent accumulation are also calculated. Results show that increasing the number of fins diminishes both the stabilization temperature and the stabilization time of the front plate during phase change, and accelerates the sensible and latent storage of energy in the PCM. Using thinner but longer fins provides the same impact except that the stabilization time also increases as the fin length is increased. Besides, at constant fin mass, varying fin spacing have marginal impact on the latent heat storage performance and on the hot plate temperature stabilization. The study also shows that the surface area plays the largest role in the increase of the heat transfer rate between the front plate and the PCM, while configurations which can promote stronger natural convection lead to higher heat flux. Finally, it was observed that systems allowing easier heat transfer to the back plate during melting provide a higher ratio of sensible heat to latent accumulation, while the standard deviation of the front plate temperature decreases as the number of fins or the spacing between fins increases.