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.
Highlights
Paraffin waxes are interesting candidates as phase change materials (PCM)
The proposed method has the following advantages over the above described methods for the identification of enthalpy–temperature, apparent heat capacity–temperature, or heat flux–temperature curves: It generates phase fraction–temperature curves represented by smooth functions which accurately adapt to the shape of the measured peak signals, i.e., no prior assumptions need to be taken on the curve shape
As for the data generated by hf-differential scanning calorimetry (DSC), there is no clear start and end of the phase transition temperature range and simplifying assumption need to be taken for the values for csp and clp
Summary
Paraffin waxes are interesting candidates as phase change materials (PCM). They are commercially available for a wide range of melting temperatures, relatively low in cost and have a good thermal reliability [1,2]. Phase fraction–temperature curves can be generated by baseline construction [42,43] This method is usually applied for the analysis of thermal events in DSC heat capacity data, where the events are characterized by a peak in the recorded signal in a specific temperature range. The proposed method has the following advantages over the above described methods for the identification of enthalpy–temperature, apparent heat capacity–temperature, or heat flux–temperature curves: It generates phase fraction–temperature curves represented by smooth functions which accurately adapt to the shape of the measured peak signals, i.e., no prior assumptions need to be taken on the curve shape They predict the degree of conversion of the phase transition process, and are consistent with the two-phase apparent heat capacity modeling approach.
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