Heat pipes with plate fins, which are a simple and effective technique for heat transfer enhancement, are extremely important for latent heat storage. However, the effect of fin geometry on the solid‒liquid phase transition is not fully understood, and correlations for describing the melting heat transfer process are rarely proposed. Here, experiments and numerical simulations were conducted on a reduced-scale model of a latent heat storage unit that used flat heat pipes and plate fins for charging. The evolution of the temperature pattern and solid‒liquid interface of the phase change material during melting and the performance of the flat heat pipe with and without fins were experimentally investigated in terms of heat transfer enhancement. Then, the latent heat storage unit was numerically simulated based on the enthalpy‒porosity model and the effective thermal conductivity method. The effects of the fin structure parameters and the input heat on the melting heat transfer mechanism of the phase change material were also studied. Finally, the overall results were generalized via multivariate nonlinear fitting, and the correlations of melting and heat transfer of the phase change material with plate fins were obtained. This research contributes to the study of latent heat storage by establishing the correlations of the melting process and heat transfer in confined spaces of plate fins using the Rayleigh number, Fourier number, Stefan number, fin length‒width ratio, height‒width ratio, and filling ratio of the fin.