Natural convection heat transfer and entropy generation in a novel complex cavity with rectangular fin containing Nano-encapsulated phase change materials

Efficient thermal energy management is essential for sustainable technologies such as energy storage systems, cooling of electronic devices, solar energy and battery thermal management, etc. This study investigates natural convection (NC) heat transfer (HT), entropy generation (E_gen), Bejan number (Be), and thermal performance criterion (TPC) in a novel complex cavity with a rectangular fin containing nano-encapsulated phase change materials (NEPCMs), aiming to enhance HT performance while minimizing E_gen. It focuses on the impact of the Rayleigh number (Ra), Stefan number (Ste), fusion temperature θf[jls-end-space/], and NEPCM concentration φ[jls-end-space/]. Numerical solutions are obtained using the Galerkin finite element weighted residual method to solve the two-dimensional continuity, momentum, and energy equations. The research examines a broad range of key parameters including 10³ ≤ Ra ≤ 10⁶, 0.2 ≤ Ste.≤ 0.9, 0.05 ≤ θf[jls-end-space/] ≤ 0.95 and 0 ≤ φ[jls-end-space/] ≤ 5% with a fixed Prandtl number (Pr) = 6.2, the number of thermal conductivity, Nc=3.0[jls-end-space/], the number of dynamic viscosity, Nv=3.0[jls-end-space/], and the sensible heat capacity ratio λ=0.4[jls-end-space/]. The results indicate that an increases in Ra and φ enhances the HT rate and E_gen, whereas Be decreases. At Ra = 10⁶, increasing φ from 0% to 5% reduces the TPC by 21.14%, highlighting the significance of NEPCM concentration in minimizing the energy loss of the system. At φ=5%[jls-end-space/], with increasing Ra from 10³ to 10⁶, the HT rate increases from 3.2302 to 16.47, E_gen increases from 3.5965 to 610.24, and TPC increases from 1.1134 to 37.051, respectively. At θf=0.5[jls-end-space/], reducing Ste from 0.9 to 0.2, the HT rate leads to a local minimum but E_gen and TPC decrease by 17.86% and 22.15% respectively, whereas Be increases by approximately 28.28%. From this analysis, θf = 0.5 provides the optimal configuration for the energy storage systems. Therefore, the present research offers valuable insights into sustainable energy storage systems, highlighting the crucial role of the novel complex cavity model and rectangular fin and by providing guidelines for minimizing energy loss in terms of TPC.