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This paper studies the enhanced heat transfer of adding longitudinal fins in a horizontal shell-and-tube heat storage unit. A two-dimensional numerical model is established and validated through comparing with experimental data in literature. Under the same ratio of fin volume to phase change materials (PCMs), the melting thermal performance is optimized by changing the fin thickness, interval and the number. Results demonstrate that adding longitudinal fins is a simple and effective method to enhance the thermal energy storage efficiency. The number of fins greatly affects the complete melting time, and the maximum time difference caused by the number of fins is as high as 72.85% under the same phase change material (PCM) filling mass. At the same time, increasing the number of fins will weaken the local natural convection. In this paper, the optimal number of fins in the limited research range is given, and the effectiveness of longitudinal fins in improving melting speed is quantified, which has certain practical significance for the engineering application research of phase change energy storage. © 2021 Elsevier B.V.