In order to avert the impending international energy crisis and foster the sustainable and robust development of the economy and society, two crucial strategies have surfaced as imperative measures for overcoming energy-related challenges: enhancing the efficiency of primary energy utilization in traditional sources and addressing the supply-demand imbalance in renewable energy [1,2]. Renewable sources like solar, wind, and tidal energy have gained widespread attention due to their attributes of abundant reserves, easy accessibility, and sustainability. However, their intermittent and unstable nature, significantly influenced by factors such as geographical distribution, seasonality, and climate, imposes limitations on their broad application. As a result, energy storage systems have become pivotal for the large-scale integration of renewable energy. At present, energy storage technologies can be broadly classified based on storage mechanisms into physical storage [3], electromagnetic storage [4], chemical storage [5], and thermal storage [[6], [7], [8]]. Given its high energy density, consistent temperature during the heat exchange process, and the capacity for repeated cyclic utilization, LHS has emerged as an effective means to ensure the sustainable utilization of societal energy resources. It finds extensive applications in diverse fields such as solar power generation [9], waste heat recovery [10], building energy conservation [11], biomedical applications [12], peak shaving in power plants, and space station [13]. Extensive scholarly investigations [14] have revealed that shell-and-tube LHS units are considered the most promising compared to rectangular and spherical counterparts. This is attributed to their superior integrative and economic performance, as well as the broader heat exchange space internally, enabling the maximal reduction of heat losses to the surroundings. However, it is noteworthy that LHS units face inherent deficiencies in the form of low thermal conductivity and the inefficiency of the heat exchange process in PCMs. Therefore, in recent years, scholars have dedicated significant research efforts to improving the heat exchange efficiency of LHS, with considerable attention directed towards enhancing the heat exchange efficiency between PCMs and heat exchange fluids, and optimizing the spatial configuration of LHS units to maximize heat exchange.

To broaden and deepen the application scope of LHS in renewable energy, there is a pivotal focus on enhancing heat transfer efficiency during the melting and solidification processes. Numerous scholars have concentrated on directly improving the thermal conductivity of PCMs to boost the heat transfer efficiency of LHS. This involves methods such as incorporating foam metals [15,16], expanded graphite [17,18], and nanoparticles [19,20]. However, LHS units with added high-conductivity materials may exhibit poor stability after multiple cycles of charging and discharging. Consequently, increasing the heat exchange area on the surface of heat exchange tubes with fins, offering a larger area, ease of installation, and requiring less operational maintenance, becomes a preferable choice. Fins, based on their spatial configuration, can be categorized into rectangular fins [21], annular fins [22], helical fins [23], and needle-shaped fins [24]. In early practical engineering applications, it was observed that the heat exchange efficiency of LHS units with poor spatial structure filling performance was relatively low. Although the addition of fins can improve the heat exchange efficiency to some extent, it often falls short of meeting the extensive demands in the field of renewable energy. Consequently, scholars have explored innovative spatial structures to enhance heat exchange efficiency. Fortunately, effective heat transfer is abundantly observed in nature, and scholars have keenly recognized the efficiency of tree-shaped structures (see Fig. 1(a)) in energy transfer. Due to the superior spatial uniformity and larger specific surface area of tree-shaped structures, they possess advantages in point-to-surface-to-volume heat transfer processes [25,26]. Bejan [27] initially proposed the incorporation of tree-shaped fins in LHS units. Despite the increased complexity and cost, the improvement in heat exchange efficiency is significant. Consequently, this approach has found widespread applications in renewable fields such as solar thermal storage [28,29], radiators [30,31], and embedded thermal storage devices [32,33]. Given the advantageous heat transfer characteristics of tree-shaped structures, many scholars have introduced them into the field of heat exchange. Zhang et al. [34] conducted a numerical simulation to analyze the aspect ratio of tree-shaped structures, optimizing the heat transfer pathways. The results indicated that an increased aspect ratio of tree-shaped fins has a promoting effect on the heat exchange efficiency of LHS units, shortening the complete solidification time by 66.2 % compared to rectangular fins. Zheng et al. [35] utilized numerical simulation to optimize and analyze tree-shaped structures with different numbers of layers, revealing the impact of tree-shaped branching structures on heat transfer. The results showed that with four layers of tree-shaped branches, the complete solidification time could be shortened by 53 % compared to rectangular fins. Huang et al. [36,37] studied the effects of different angles of tree-shaped fins, heat exchange fluid directions, and various flow rates on LHS units through experiments and numerical simulations. The results indicated that the inclination angle and upward flow of the heat exchange fluid have a greater impact on melting than solidification, while downward flow contributes to enhancing the efficiency of the solidification process. In comparison to rectangular fins, the inclination angle and downward heat exchange fluid direction shortened the complete solidification time by 21.7 % and 49.2 %, respectively. Huang et al. [38] proposed a novel gradient tree-shaped fin through numerical simulation and experiments, considering the weaker natural convection in the lower part of tree-shaped fins. Non-uniformly distributed tree-shaped fins were adopted for the lower part. The research results showed that the gradient fins shortened the complete melting time by 9 % compared to rectangular fins. However, the non-uniform distribution had a significant impact on thermal conduction, thus extending the complete solidification time by 57.4 %. Huang et al. [39] studied a novel layered tree-shaped fin through numerical simulation, improving the thermal conductivity performance in the later stages of LHS unit melting. The results indicated that, compared to tree-shaped fins, layered fins reduced the complete melting time by 41.1 %.

The comprehensive literature review above highlights the considerable progress made by researchers in enhancing heat transfer through tree-shaped structures. This improvement is achieved by optimizing the spatial structure arrangement of tree-shaped fins to enhance their thermal conduction. However, this optimization primarily focuses on the spatial configuration of tree-shaped structures, neglecting the crucial role of natural convection in the melting and solidification processes of LHS units. Due to the uniformity of tree-shaped fins, they exert a suppressing effect on naturally induced convection during the heat exchange process of LHS units. Therefore, a key challenge addressed in this study is how to maintain the excellent thermal conductivity of tree-shaped structures while simultaneously enhancing natural convection. Taking inspiration from the evolution observed in nature, exemplified by Monstera friedrichsthalii in Fig. 1(b), this plant efficiently transfers energy through its veins while facilitating fluid flow in the surrounding space through holes on its leaves. Currently, many researchers have applied perforations to LHS. Karami et al. [40] experimentally perforated vertical shell-and-tube circular fins to enhance the impact of natural convection on the heat exchange process of LHS units. The results demonstrated a 7 % reduction in the complete melting time compared to non-perforated circular fins. Modi et al. [41] conducted experiments to investigate the impact of perforations on the performance of rectangular fins in LHS units. The results indicated that perforations with a large diameter weaken the thermal conductivity of the fins, while small-diameter perforations significantly improve the heat transfer performance. Perforated rectangular fins exhibited a 12.65 % reduction in complete melting time compared to non-perforated fins. Li et al. [42] studied vertically arranged shell-and-tube circular perforated fins in LHS units through numerical simulation. The results suggested that increasing the size of perforations has a more pronounced impact on natural convection, with the optimal perforation size being 3 mm, resulting in a 5.49 % reduction in the complete melting time compared to non-perforated fins. Presently, there is limited research on perforated tree-shaped fins. Consequently, investigating perforated tree-shaped fins holds great significance for LHS.

In the pursuit of enhancing the heat transfer efficiency of horizontal shell-and-tube LHS units, this study introduces an innovative tree-shaped perforated fin structure inspired by the botanical configuration of Monstera friedrichsthalii. The design aims to preserve the high thermal conductivity of the tree-shaped structure while simultaneously fostering the initiation of natural convection. A transient model for the solidification process of tree-shaped perforated fins in LHS units is established, offering an in-depth analysis of the coupled heat transfer mechanisms involving conduction and convection during solidification. A comprehensive analysis and comparison are conducted, considering parameters such as liquid fraction, heat exchange, radial and circumferential temperature distributions, and the overall average temperature of the PCM for fins with no perforations, rectangular fins, tree-shaped fins, and tree-shaped fins with various layers of perforations. Furthermore, employing a multi-objective optimization approach [[43], [44], [45]] based on Computational Fluid Dynamics (CFD), RSM, and Genetic Algorithm (GA), the study explores the relationship between the diameter and quantity of perforations in three layers of tree-shaped fins and the filling amount of PCM, as well as the solidification time of the LHS unit. Through correlation fitting, highly accurate predictive relationships are obtained, facilitating the optimization of horizontal shell-and-tube LHS units with increased filling capacity and reduced solidification time.