In this study, melting process in a phase change material (PCM) filled annular closed space by using flexible fins is analyzed. Cases with different number of flexible fins and without fin are compared in terms of phase change dynamics while two-way fluid structure interaction analysis is used. Temperature differences of 30 °C and 60 °C are considered between the walls of the circular enclosure while flexible fin numbers are varied between 0 and 10. It is observed that the melting is significantly accelerated by using the elastic fins. Due to the deflection of the elastic fins, melt process dynamics is influenced by varying fin number and its elastic modulus. Further reduction in the full phase transition occurs when the temperature difference is increased. As compared to un-finned case at temperature difference of 30 °C by using 10 flexible fins at ∆ T = 60 °C, there is 87 % reduction in the complete phase transition time. The ANFIS (Adaptive Neuro-Fuzzy Interface System) based modeling approach is used for phase transition dynamics in circular enclosure equipped with flexible fins. • Melting process in a phase change material (PCM) filled annular closed space by using flexible fins is analyzed. • Cases with different number of flexible fins and without fin are compared in terms of phase change dynamics. • For un-finned case at temperature difference of 30 °C by using 10 flexible fins, there is 87 % reduction in transition time. • The ANFIS (Adaptive Neuro-Fuzzy Interface System) based modeling approach is also used.