Latent heat thermal energy storage (LHTES) based on phase change material (PCMs) is an interesting solution to be used for mitigating the mismatch between energy demand and supply that affects various kinds energy systems. The advance of LHTES technology requires to overcome the limitations posed by the poor thermal conductivity of most of the PCMs. Thus, a large scale utilization of LHTES system strongly depends on the development of efficient heat transfer enhancement techniques. In this paper the use of tree shaped fins is proposed to enhance the performance of a shell-and-tube LHTES unit. The study is performed through a numerical model that takes into account of the thermal behaviour of the system. The geometry of Y-shaped fins with one and two bifurcations are optimized through the combined use of CFD modelling and response surface method. The results show that an increase of 24% of the system efficiency can be achieved by the optimized unit. Another relevant result arises from the analysis: the optimal fin design depends on the operating time of the LHTES unit. For short operating times Y-shaped fins with wide angles between branches are preferable. On the contrary, smaller angles are necessary for long operating times. To summarize, this work presents for the first time a shape optimization strategy for the improvement of a system involving transient operating conditions. This is a key feature of the paper and an innovative effort to tackle optimization problems involving energy systems that show unsteady state behaviour. (C) 2014 Elsevier Ltd. All rights reserved.