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For calculating the thermal storage time for an annular tube with phase change material (PCM), a novel method is proposed. The method is suitable for either low-temperature PCM or high-temperature PCM whose initial temperature is near the melting point. The deviation fit is smaller than 8% when the time is below 2×104 s. Comparison between the predictions and the reported experimental data of thermal storage time at same conditions is investigated and good agreements have been got. Based on this method, the performance of the thermal storage unit and the role of natural convection are also investigated. Results show a linear relation between the maximum amount of stored heat and thermal storage time, and their ratio increases with the height of the thermal storage unit. As the thickness of the cavity increases, natural convection plays an increasingly important role in promoting the melting behavior of paraffin. When the thickness of the cavity is small, natural convection restrains the melting behavior of paraffin.