Abstract: Based on the solidification/melting model of the enthalpy method, a melting model of a shell-and-tube type phase change heat exchanger is developed with consideration of natural convection, and the mechanism of the influence of tube fin layout and thermal boundary conditions on the transient melting behavior of the phase change material is investigated. We design an eccentric structure with a fluctuating heat source for a uniform tube fin layout and constant wall temperature thermal boundary conditions and compare and analyze the enhanced heat transfer law between them. The results show that the eccentric layout improves melting in the heat transfer blind area with the same heat transfer area, while the fluctuating heat source enhances natural convection in the central region of the premelting stage. The comparison of energy storage parameters shows that the eccentric layout structure or the fluctuating heat source reduces the melting time by 12.5% and 6.25%, respectively, compared to the original structure, and both the optimized heat source and structure reduce the melting time by 31.25%. The fluctuating heat source and eccentric structure can significantly improve the heat exchanger’s melting rate.