Thermal expansion effects on the one-dimensional liquid-solid phase transition in high temperature phase change materials (original) (raw)
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Applications of Mathematics, 2011
We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the wellknown and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the balance of the momentum of the system influences significantly the numerical solution and is necessary in order to get a better match with the experimental observations. Here an up-to-date list of the most meaningful mathematical models and numerical simulations of this test is discussed and the need is shown of an accurate revision of the numerical simulations of melting/solidification processes of pure materials (e.g. artificial crystal growth) produced in the last thirty years and not accounting for the solid phase mechanics.
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The phase diagram of elemental liquids has been found to be surprisingly rich, including variations in the melting curve and transitions in the liquid phase. The effect of these transitions in the liquid state on the shape of the melting curve is analysed. First-order phase transitions intersecting the melting curve imply piecewise continuous melting curves, with solid-solid transitions generating upward kinks or minima and liquid-liquid transitions generating downward kinks or maxima. For liquid-liquid phase transitions proposed for carbon, phosphorous selenium and possibly nitrogen, we find that the melting curve exhibits a kink. Continuous transitions imply smooth extrema in the melting curve, the curvature of which is described by an exact 2 thermodynamic relation. This expression indicates that a minimum in the melting curve requires the solid compressibility to be greater than that of the liquid, a very unusual situation. This relation is employed to predict the loci of smooth maxima at negative pressures for liquids with anomalous melting curves. The relation between the location of the melting curve maximum and the two-state model of continuous liquid-liquid transitions is discussed and illustrated by the case of tellurium.
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Physical Review B, 1980
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Thermal behaviour of materials in interrupted phase change
Journal of Thermal Analysis and Calorimetry, 2019
The most critical part and barrier of phase change material (PCM) applications are the accuracy of simulations and the control of the process. The state of the PCM and the momentarily stored energy cannot be estimated easily unless numerous temperature sensors are used. There are a lot of models used by researchers, but most of them focus solely on the full charging or discharging of the PCM thermal energy storage. In a real working environment, the phase change is often interrupted so this phenomenon should also be modelled with high accuracy. The aim of this paper is to present the newly developed diagonal model validated by differential scanning calorimetry measurements, which can model what occurs inside the hysteresis of the solid-liquid two-phase state. The model was created and validated by using paraffin wax (P53) and was further tested with coconut oil (C.oil20), which has a very wide hysteresis. The modelling accuracy of the different models was compared with each other, and the evaluations were carried out. Keywords Phase change materials (PCM) Á Differential scanning calorimetry (DSC) Á Enthalpy-temperature curves Á Phase transition Á Interrupted melting/solidification List of symbols c Specific heat capacity (kJ kg-1 K-1) c app Apparent heat capacity of the PCM during melting (kJ kg-1 K-1) f Liquid fraction of PCM (1) H Enthalpy (kJ kg-1) L f Latent heat of fusion (kJ kg-1) T Temperature (°C)
High-Pressure Melting Curves and Liquid–Liquid Phase Transition
Advanced Science Letters, 2010
Breaks on the melting lines in the pressure-temperature (P T m) space are often handled as a hallmark of a liquid-liquid phase transition in pure materials. In this paper it is shown that there is no one-to-one agreement between these virtual breaks and liquid-liquid transitions. Four melting curve is analyzed; selenium, phosphorus, carbon and nitrogen. It is shown that a modified form of the Simon-Glatzel equation can describe experimental data, without introducing any break, demonstrating that the shape of the melting line is not an evidence for any further phase transition.
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