Global mathematical correlations for heat pipe and nanofluid based thermal energy storage system: Dimensional analysis approach

This research article presents the development of a mathematical model for a nanofluid-based thermal energy storage (TES) system. The main objective of the study is to establish global correlations among various performance parameters of the TES system. The TES system considered in this research employs Al2O3/Soybean oil as the heat transfer fluid (HTF), and heat pipes are integrated to enhance heat transfer between the HTF and the phase change material. The mathematical model developed in this study is based on the Buckingham-pi theorem. The derived correlations encompass the Nusselt number, stored energy, and thermal efficiency. Validation of the model is conducted for the Nusselt number, and a regression analysis is performed to assess the accuracy level of the mathematical model. Using the derived mathematical models, several key parameters of the TES unit are calculated. The convective heat transmission coefficient is determined to be 364.07 W/m(2)K, indicating the efficiency of heat transfer within the system. The thermal efficiency is found to be 89.10%, which provides insights into the overall effectiveness of the TES unit. Additionally, the thermal storage capacity of the TES unit is calculated as 3425.68 kJ, representing the amount of energy that can be stored and retrieved by the system. By equating the dimensions of variables within an equation, it becomes possible to deduce the relationship between the unknown parameters and the known quantities. This enables estimation of the unknown parameters even when direct measurements are unavailable, thereby providing a useful method for obtaining crucial information in data-limited scenarios.