In this project, an experimental-designed vertical double-tube thermal energy storage (TES) system was employed to analyze the storing and releasing of energy by a novel bio-based phase change material (bio-PCM) and nano-based bio-PCM (bio-nPCM). The evaluation encompassed testing of the bio-PCM, comprising coconut oil and beeswax, and the bio-nPCM, incorporating 2 wt% Gr-Cu hybrid nanoparticles. Furthermore, a machine learning model based on an artificial neural network (ANN) was developed, utilizing 1566 data and 200 distinct structures. The outcomes of the experiments, in comparison with the contours of temperature, liquid fraction, and streamline derived from the modeling, demonstrated that natural convection primarily influences the melting of both bio-PCM and bio-nPCM. Whereas, conduction heat transfer was the dominant factor during the solidification. During the melting, both materials' temperatures revealed non-linear and stepwise changes in the gravity direction. Although bio-PCM's temperature changes were linear and layered in the solidification, for the bio-nPCM, the temperature reductions occurred non-linearly and step-wisely due to enhanced thermal conductivity. Also, the nanoparticles' introduction accelerated the melting and solidification rates by 67.59 % and 56.32 %, respectively. An ANN was developed based on inputs including seven different datasets of characteristics of both PCMs. Multilayer perceptron-based ANN, comprised two hidden layers and housing 20 and 15 neurons. The melting's liquid fraction and time were predicted with errors of ±4.55 % and ± 0.023 %, respectively. Also, the estimation of solidification's liquid fraction and time had errors of ±2.3 % and ± 0.013 %, respectively. The outcomes of this research provide a strategic framework for reducing the reliance on petroleum-based PCMs within renewable energy systems. Furthermore, integrating machine learning results offers an avenue for optimizing energy storage and release in TES systems. © 2024 Elsevier Ltd