A one-step method for producing microencapsulated phase change materials

This short communication reports our recent work on the synthesis and characterisation ofmicrocapsules of phase change materials using silica as the shell material through a one-step method. The method uses no surfactants or dispersants for stabilising the capsules. The results show that the one-step method allows the tuning of the size and polydispersity of the capsules, and the use of different core materials. Analyses of the capsules show that they contain about 65% phase change materials. The results also suggest no need for a stabilising agent due to self-stabilisation by the amine groups. Further work is underway to investigate the mechanical and thermal properties of the microcapsules and the scale-up of the method.     

Convective heat transfer characteristics of microencapsulated phase change material suspensions in minichannels

A comparative experimental study was conducted in order to investigate the convective heat transfer characteristics of water-based suspensions of microencapsulated phase change material (MEPCM) flowing through rectangular copper minichannels. The hydraulic diameter of the channels was 2.71 mm. MEPCM particles with an average size of 4.97 μm were used to form suspensions with mass concentrations ranging from 0 to 20%. The comparative experiments were performed for varying mass flow rates in the laminar region and varying thermal conditions. The cooling performance of the MEPCM suspensions strongly depended on the mass flow rate and the MEPCM mass concentration. The 5% suspension always showed a better cooling performance than water resulting in lower wall temperatures and enhanced heat transfer coefficients within the whole range of mass flow rates. The suspensions with higher mass concentrations, however, were more effective only at low mass flow rates. At higher mass flow rates they showed a less effective cooling performance than water.     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

A limiting “viscosity” approach to the Riemann problem for materials exhibiting change of phase

Dedicated to Bernard Coleman on the occasion of his sixtieth birthday     

Natural convection in composite systems with phase change materials

In this study, we carried out a numerical simulation of transient heat transfer in a composite passive system consisting of air–phase change material–air, arranged as a rectangular enclosure. The vertical boundaries of the enclosure are isothermal and the horizontal ones adiabatic. The enthalpy formulation with a fixed grid is used to study the process of phase change with liquid–solid interface zone controlled by natural convection. The flow in this zone is simulated by a model based on the Darcy porous medium. The numerical solution of the mathematical model is done using finite difference–control volume algorithm. The influence of the geometrical and thermal parameters is studied. It is found that subcooling coefficient is the most important parameter influencing heat transfer, and for a given subcooling, there is an optimum phase change partition thickness.     

A reference solution for phase change with convection

A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.     

A preparation method of functionally graded materials with phase transition under shock loading

The propagation of phase boundary in a material undergoing shock induced irreversible phase transition is studied theoretically using a model based on simple-mixture rule. It is found that along with the decay of the phase boundary, a functionally graded material (FGM) forms in the mixed-phase region. Such FGMs are composed of parent phase and product phase, and the composition and physical properties are changing continuously without apparent macro-interfaces. The effect of stress boundary conditions on formation of the FGM is investigated in detail with a numerical method. The possibility of producing FGMs with impact method is proposed and the limit of this method is discussed.     

A limiting “viscosity” approach to the Riemann problem for materials exhibiting a change of phase(II)

Communicated by C. Dafermos     

Radial integral boundary element method for simulating phase change problem with mushy zone

A radial integral boundary element method(BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including the solid phase, the liquid phase, and the mushy zone, are considered in the phase change problem. First, according to the continuity conditions of temperature and its gradient on the liquid-mushy interface, the mushy zone and the liquid phase in the simulation can be considered as a whole part, namely, the non-solid phase, and the change of latent heat is approximated by heat source which is dependent on temperature. Then, the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone, respectively. Moreover, an iterative predictor-corrector precise integration method(PIM) is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary. According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone, the front-tracking method is used to track the move of the interface. The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field.Finally, four numerical examples are provided to assess the performance of the proposed numerical method.     

Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change

Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes. The multi-relaxation-time lattice Boltzmann method(MRT-LBM) shows great numerical performance during simulation;however, the value method of the relaxation parameters needs to be specified. Therefore,in this study, a random forest(RF) model is used to discriminate the importance of different relaxation parameters to the convergence, and a support vector machine(SV...     

Heat transfer and thermal management of electric vehicle batteries with phase change materials

This paper examines a passive thermal management system for electric vehicle batteries, consisting of encapsulated phase change material (PCM) which melts during a process to absorb the heat generated by a battery. A new configuration for the thermal management system, using double series PCM shells, is analyzed with finite volume simulations. A combination of computational fluid dynamics (CFD) and second law analysis is used to evaluate and compare the new system against the single PCM shells. Using a finite volume method, heat transfer in the battery pack is examined and the results are used to analyse the exergy losses. The simulations provide design guidelines for the thermal management system to minimize the size and cost of the system. The thermal conductivity and melting temperature are studied as two important parameters in the configuration of the shells. Heat transfer from the surroundings to the PCM shell in a non-insulated case is found to be infeasible. For a single PCM system, the exergy efficiency is below 50%. For the second case for other combinations, the exergy efficiencies ranged from 30–40%. The second shell content did not have significant influence on the exergy efficiencies. The double PCM shell system showed higher exergy efficiencies than the single PCM shell system (except a case for type PCM-1). With respect to the reference environment, it is found that in all cases the exergy efficiencies decreased, when the dead-state temperatures rises, and the destroyed exergy content increases gradually. For the double shell systems for all dead-state temperatures, the efficiencies were very similar. Except for a dead-state temperature of 302 K, with the other temperatures, the exergy efficiencies for different combinations are well over 50%. The range of exergy efficiencies vary widely between 15 and 85% for a single shell system, and between 30–80% for double shell systems.     

Optimization of size and shape of composite heat sinks with phase change materials

A composite heat sink is one in which a phase change material is interspersed with a high thermal conductivity base material to maximize the thermal performance of the device. Unlike constant area fins considered in literature, this work considers a repeating elemental composite heat sink (ECHS) with variable area fins. The base material is aluminium and the phase change material is n-Eicosane. An in house code was developed in MATLAB© to determine the time of operation for a vertical fins ECHS for a one dimensional approximation. This was followed by a two dimensional analysis of the problem using FLUENT 6.3. The effects of the shape of the interface surface on the time of operation and overall heat dissipated are determined and design modifications for the composite Heat Sinks based on the results obtained are suggested.     

Experimental study on the convective heat transfer behavior of microencapsulated phase change material suspensions in rectangular tube of small aspect ratio

An experimental study on the heat transfer performance of microencapsulated phase change material suspensions flowing in the rectangular tube of small aspect ratio (b/a = 0.14) is presented in this work. The slurry of higher MPCM concentration shows better cooling performance in the most section of dimensionless axial distance whereas worse in a small section at the beginning. Up to 20.6% of the dimensionless wall temperature was decreased by the 20 wt% MPCM suspension as compared to water.     

模拟相变问题的精细积分边界元法

将精细积分边界元法和界面追踪法相结合求解相变问题。因为边界元法只需要将待求解空间域的边界离散,方便连续追踪移动界面位置和重构网格,所以边界元法适合应用于移动边界问题的模拟。首先,利用精细积分边界元法在固相区域和液相区域分别求解相应的瞬态热传导控制方程,从而求得温度场和边界热流密度。然后,根据固-液相变界面上的能量平衡方程,利用热流密度求得相变界面的移动速度,再采用界面追踪法预测移动相变界面的位置变化。最后,给出了几个数值算例,并通过与参考解的对比验证本文方法的准确性。     

A real-space phase field model for the domain evolution of ferromagnetic materials

A real-space phase field model based on the time-dependent Ginzburg–Landau (TDGL) equation is developed to predict the domain evolution of ferromagnetic materials. The phase field model stems from a thermodynamic theory of ferromagnetic materials which employs the strain and magnetization as independent variables. The phase field equations are shown to reduce to the common micromagnetic model when the magnetostriction is absent and the magnitude of magnetization is constant. The strain and magnetization in the equilibrium state are obtained simultaneously by solving the phase field equations via a nonlinear finite element method. The finite-element based phase field model is applicable for the domain evolution of ferromagnetic materials with arbitrary geometries and boundary conditions. The evolution of magnetization domains in ferromagnetic thin film subjected to external stresses and magnetic fields are simulated and the magnetoelastic coupling behavior is investigated. Phase field simulations show that the magnetization vectors form a single magnetic vortex in ferromagnetic disks and rings. The configuration and size of the simulated magnetization vortex are in agreement with the experimental observation, suggesting that the phase field model is a powerful tool for the domain evolution of ferromagnetic materials.     

Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations, the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1] to characterize discontinuous cracks in brittle materials. This method can well describe the crack initiation and propagation without assuming the shape, size and orientation of the initial crack in advance. In this paper, a phase field method based on Miehe's approach [Miehe et al., Comp. Meth. App.Mech. Eng.(2010)] is applied to simulate different crack propagation problems in twodimensional(2 D), isotropic and linear elastic materials. The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM). The validity, accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature. Several numerical examples are presented to show the effects of the loading type(tension and shear), boundary conditions, and initial crack location and orientation on the crack propagation path and force-displacement curve. Furthermore, for a single edge-cracked bi-material specimen, the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed. It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials, and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.