# 2D Conduction Simulation of a PCM Storage Coupled with a Heat Pump in a Ventilation System
## 5 Conclusions  
A numerical model of heat conduction in a PCM device has been constructed to predict the behaviour of a full-scale experimental component containing paraffin. The PCM was modelled using an equivalent heat capacity during the phase transition, and a variable thermal conductivity as a function of temperature. Both 2D and 1D pure conductive models were considered in order to demonstrate and evaluate the importance of edge effects. Hysteresis effects were also taken into account by adopting different curves of equivalent heat capacity for heating and cooling modes (based on DSC data). The overall behaviour of the PCM storage unit was well described by the model. Some quantitative discrepancy was observed between the models and data however, both during melting and solidification. This error was reduced by adopting the mean value of the curves during the melting phase. The origin of the model-data disparity was found to be different rates of temperature change during experiments.  
The work presented in this paper offers answers to the some of the general questions that be posed before beginning a numerical study of PCM heat storage. Critically, it is important to model thermal conduction through the PCM slabs for configurations with Biot numbers greater then unity. A 2D model gives better results than a 1D description for systems where the material used for the container has a very different thermal conductivity to the PCM. Hysteresis phenomena related to DSC characterisation (generally in paraffin) was not found to be a significant source of error. Where both heating and cooling DSC curves are available, better with low temperature evolution range, it is recommended to consider the mean value of the two results. In particular, as novelty, two peaks of equivalent heat capacity have been observed with DSC when the rate is very low instead of only one peak using current rate, which explains the real behaviour in the experiments.  
For the present study, this was found to improve model accuracy both in terms of temperature variation and heat flux density, even if convection should be considered for better results.  
**Acknowledgments:** The experimental results used in this work have been obtained with the support of the French ANR project STOCKAIR2 with the reference: ANR-2010-STKE-010.  
**Author Contributions:** [PERSON] conceived, designed and performed the experiments and developed the main analysis. [PERSON] performed the numerical simulations. The paper was written equally by both the authors.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\begin{tabular}{l l} \(Bi\) & Biot number \\ \(c_{p}\) & heat capacity (kJ\(\cdot\) kg\({}^{-1}\cdot\) K\({}^{-1}\)) \\ \(e\) & thickness (m) \\ \(h_{c}\) & convective heat transfer coefficient (W\(\cdot\) m\({}^{-2}\cdot\) K\({}^{-1}\)) \\ \(P\) & heating power (W) \\ \(Q_{V}\) & airflow rate (m\({}^{3}\cdot\) s\({}^{-1}\)) \\ \(S\) & surface exchange with air of the containers (m\({}^{2}\)) \\ \(T\) & temperature (\({}^{\circ}\)C) \\ \(t\) & time (s) \\ \end{tabular}