# 2D Conduction Simulation of a PCM Storage Coupled with a Heat Pump in a Ventilation System
## 1 Introduction  
The adoption of thermal energy storage systems (TESS) technologies is an effective solution for building energy management that makes good use of the energy potential of the local environment. Concepts involving phase change material (PCM) are now technically mature for incorporation into buildings, and among the existing concepts of TESS, PCM-to-air thermal storage can readily be integrated into ventilation systems as a means to shave peak heating loads [1]. Similar systems have been proposed for cooling purposes, as presented in [2]. We have developed a PCM storage component presented in [3, 4], which comprises a set of PCM elements embedded in metallic plates and separated by fins. The component was designed to store heat during off-peak hours by means of heat pump that drives hot air through the attached heat exchanger. The stored energy can then be released during the peak period to provide heat and thus reduce the heating load of the building. To be an effective solution, the system must fully compensate for the heat pump so that it can be deactivated withoutconsequence to indoor thermal comfort. To meet this requirement the component was sized to deliver a steady 1 kW supply of heat during a period of 2 h. A full scale arrangement of the component was constructed and instrumented for testing under laboratory conditions. We have taken the experimental results as basis for considering the strategies in simulating such type of PCM storage. The work presented in this paper offers answers to some of the general questions that be posed before beginning a numerical study of PCM heat storage and adopt the simplest one according to the precision required. This is generally not provided in the articles presenting PCM storage modelling. Efforts to simulate heat transfer in a PCM (Phase Change Material) storage device are generally led by considerations of Biot number and material thickness, of 2D versus 1D representation, and of possible hysteresis effects arising from the characterisation of the PCM using differential scanning calorimetry (DSC). The PCM was modelled adopting equivalent thermophysical properties during the phase change. An equivalent heat capacity and thermal conductivity were provided for an appropriate description of energy release and storage in the process of solidification and melting. The geometry of the metal container induces 2D effects that are generally neglected in the numerical modelling. The thickness of the plates (about 2 cm) is sufficiently large to require the modelling of conduction in the PCM, but can also induce convection. Experimental results are presented and compared for both a 1D and 2D model of the PCM device. It was concluded that a 2D representation is essential for configurations, like the case study and geometry we had, with a large difference in thermal conductivity between PCM and metal casing. Two curves of equivalent heat capacity (measured via DSC) were introduced for heating and cooling phases. Comparisons to experimental results indicated significant errors in the models during melting and solidification of the PCM, which could be reduced by instead adopting the mean of the two heat capacity curves. The rate of temperature change during the experiments and for the DSC characterisation was analysed and found to explain well the observations. 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: and that explains the real behaviour in the experiments. The remainder of this paper is structured as follows. In Section 2, the storage system is presented in detail, with particular attention made to its geometry, and the PCM it contains (Mikrotek 37 paraffin [5]). In Section 3, 1D and 2D numerical models of the system are introduced. Comparisons of predicted behaviour to experimental data are presented for a typical charging and discharging cycle in Section 4.