Identification of Phase Fraction–Temperature Curves from Heat Capacity Data for Numerical Modeling of Heat Transfer in Commercial Paraffin Waxes

Abstract

The area-proportional baseline method generates phase fraction–temperature curves from heat capacity data of phase change materials. The curves describe the continuous conversion from solid to liquid over an extended temperature range. They are consistent with the apparent heat capacity and enthalpy modeling approach for the numerical solution of heat transfer problems. However, the curves are non-smooth, discrete signals. They are affected by noise in the heat capacity data and should not be used as input to continuous simulation models. This contribution proposes an alternative method based on spline approximation for the generation of consistent and smooth phase fraction–temperature, apparent heat capacity–temperature and enthalpy–temperature curves. Applications are presented for two commercial paraffins from Rubitherm GmbH considering heat capacity data from Differential Scanning Calorimetry and 3-layer-calorimetry. Apparent heat capacity models are validated for melting experiments using a compact heat exchanger. The best fitting models and the most efficient numerical solutions are obtained for heat capacity data from 3-layer-calorimetry using the proposed spline approximation method. Because of these promising results, the method is applied to melting data of all 44 Rubitherm paraffins. The computer code of the corresponding phase transition models is provided in the supplementary information.

Comparison of Two CFD Approaches Using Constant and Temperature Dependent Heat Capacities during the Phase Transition in PCMs with Experimental and Analytical Results

“…An example of a heat capacity curve of a technical grade paraffin (trade name RT64HC from Rubitherm Technologies) based on previous work by [13] with its significant peak due to the phase transition enthalphy is shown in Figure 1a. While the solidification and melting (SM) model takes into account a linear relationship of the liquid fraction between the solidus and liquidus temperatures T sol and T liq , the apparent heat capacity model has no clearly defined information about the liquid fraction curve.…”

“…There are different ways to model the liquid fraction in the mushy zone [13]. The most easy approach is to assume a linear behavior between the solidus and the liquidus temperature, which is implemented in the Ansys Fluent solidification and melting model [10].…”

“…In previous work, Barz et al [13] identified phase fraction-temperature curves for commercial phase change materials in order to detect the peak shape and location of the heat capacity data. The identified phase fraction-temperature curves are shape-preserving and only need the following input: Heat capacity in the solid and liquid state, phase change enthalpy, and melting range.…”

“…The model showed good agreement with experimental data from 3-layer-calorimetry and the computer code is publicly available. Further details can be found in [13]. The chosen melting ranges, liquid fraction curves, and thus the heat capacity curves in this work follow this approach.…”

“…To the authors knowledge, only a few publications discuss applying the apparent heat capacity (AHC) method in Ansys Fluent. The solidification and melting model applies a linear relationship of the liquid fraction between solidus and liquidus temperature although it is known that the phase transition follows a non-linear behavior [13]. This behavior can be captured using the AHC method as the curve shape and location of the specific heat capacity contain information about the nature of phase transition behavior.…”