The current study aims to investigate the use of a water-based tri-hybrid nanofluid for advanced cooling in permeable cavities. The role of porous media governed by Darcy–Forchheimer’s model is considered that ensure the inclusion of viscous shearing in natural convective heat transfer. It makes the direct implication of the study with design of heat exchangers, radiators, various thermal management systems like solar panels, and heating, ventilation, and air conditioning (HVAC) systems. The nanofluid utilised in the current investigation consists of three different shaped nanoparticles: spherical aluminium oxide
, cylindrical carbon nanotubes (CNT), and platelet-shaped graphene. The novelty of the present work is related to the thermal analysis of the tri-hybrid nanofluid particles. By studying the tri-hybrid nanofluid, we are exploring that the efficiency of these systems can be increased by modifying the nanofluids as suggested in the article. The current investigation reveals that this advanced water-based tri-hybrid nanofluids exhibit a significant improvement in heat transfer rate, indicating a highly favourable thermal performance. The current issue is expressed as momentum and energy equations in the form of partial differential equations, accompanied by certain boundary conditions. The penalty finite element method (PFEM) is utilised to get precise results by varying key parameters. In addition, we have used nanoparticles in various proportions and discovered intriguing outcomes that can be employed in diverse engineering challenges, particularly in the cooling procedure.