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In this paper, the melting and solidification behaviours of the PCM in an indirect contact mobilized thermal energy storage (ICM-TES) container were numerically investigated to facilitate the further understanding of the phase change mechanism in the container. A 2D model was built based on the simplification and assumptions of experiments, which were validated by comparing the results of computations and measurements. Then, three options, i.e., a high thermal conductivity material (expanded graphite) addition, the tube diameter and the adjustment of the internal structure of the container and fin installation, were analyzed to seek effective approaches for the improvement of the ICM-TES performance. The results show that the optimal parameters of the three options are 10vol.% (expanded graphite proportion), 22mm (tube diameter) and 0.468m2 (fin area). When the three options are applied simultaneously, the charging time is reduced by approximately 74% and the discharging time by 67%.