Nano-encapsulated phase change materials (NEPCMs) have advantages of both phase change materials as well as the proficiencies of nanoparticles, and they play a crucial role in enhancing thermal management across multiple industries. Polyethylene glycol + N-Nonadecane/Ethylene glycol-based nano-encapsulated phase change materials \(\left( {{\text{NEPCMs}}} \right)\) flow and heat transport efficiencies within a permeable enclosure with magnetic parameter, activation energy, radiation parameter, and Christov–Cattaneo heat flux are numerically scrutinized in this investigation. Finite element technique is implemented to solve the fluid equations along with boundary conditions. Patterns of motile and oxygen microorganisms, heat capacity ratio, temperature patterns, and velocity patterns for different influencing parameters are plotted and analyzed in detail. The values of Nusselt number are also scrutinized and illustrated for various parameters. Important findings of this analysis reveal that higher values of Cattaneo–Christov heat flux parameter leads to stronger velocity vortices inside the cavity. Rising values of porous parameter weakens the vortex circulation which leads to reduction in flow strength. As fusion parameter \(\left( {{\uptheta }_\text{f} } \right)\) intensifies from 0.1 to 0.9, the phase transition zone shrinks, accelerating the melting process of NEPCMs. Higher bio-convection Rayleigh number (Rb) enhances microorganism concentration patterns and introduces complex flow structures. Increasing Stefan number \(\left( {{\text{Ste}}} \right)\) broadens the transition zone, indicating stronger latent heat effects.
