This work tackles the issue of enhancing heat transmission and minimizing entropy formation in tiny enclosures pertinent to thermal energy storage. It looks at how magnetohydrodynamic (MHD), non-Darcian porous media, a ternary hybrid nanofluid composition (Fe3O4–hBN–CuO/water), and triangle corrugation work together in a corrugated rectangular cavity. The goal is to figure out how these things affect convection, entropy formation, and the overall efficiency of the thermodynamic system. Utilizing the Galerkin finite element technique (GFEM), we found numerical solutions to the mathematical models for momentum, energy, and entropy generation. The effects of the porosity parameter, ternary nanoparticle concentration, Hartmann number, Darcy number, and Rayleigh number were carefully studied for the cavities' flat and triangular corrugated walls. Artificial Neural Network (ANN) model was developed and trained to predict the average Nusselt number and total entropy generation with high precision, using fewer computational resources compared to conventional CFD approaches. It is observed that the ANN model is used mostly as an ancillary prediction instrument derived from FEM-generated data, rather than as the principal computational framework. The results show that corrugated shapes improve local heat transfer by increasing the surface area and causing flow disruptions. However, too many corrugations lower the average Nusselt numbers because they cause recirculation. Higher Rayleigh numbers make buoyancy-driven convection stronger, whereas larger magnetic fields make circulation weaker, which makes conduction-dominated transport more likely and lowers entropy generation. The porosity and Darcy number have a big effect on convective intensity and entropy formation. On the other hand, the right number of nanoparticles may boost thermal conductivity without making irreversibility too high. The ANN model showed great prediction ability (MSE≈1.12 × 10⁻⁷), which proved that it works well for quickly testing Multiphysics systems. These results show that integrating ternary nanofluids, controlling porous media, and changing the magnetic field may improve thermal performance in advanced applications, including solar collectors, cooling electronics, and thermal energy storage devices. Combining ANN prediction gives us a solid base for designing and improving next-generation heat management solutions in a way that works well.

Objective Magnetically influenced bioconvective flow of ternary nanofluid induced by the expansion of curved surface by incorporating thermophoresis, Brownian motion, chemical species, activation energy and motile microbes to elucidate complex thermal fluid transport phenomena. Method ology: The mathematical model describing flow mechanism was formulated in sense of PDEs (partial differential equations), which are converted in ODEs (ordinary differential equations) by employing similar set of variables. Numerical technique by integrating the shooting method and RK-4 approach is employed to obtain the outcomes of study. Afterwards, neuro-computing model is designed to forecast Nusselt number for mono, hybrid and ternary nanoparticles comparatively. Key findings Findings of the analysis indicate that velocity of fluid intensifies by uplifting curvature factor while thermal profile goes down. Thermophoretic and Brownian diffusion factors cause the temperature of the fluid to rise but lower the associated flux. Higher curvature and activation energy factors elevate concentration distribution, whereas microbe density depreciates versus Peclet and bioconvective Lewis numbers. The MSE values obtained during training (2.79e-08, 7.63e-08, and 1.55e-07) demonstrate the model's robustness. Applications It is concluded that heat and mass transportation phenomenon is superior with the induction of ternary nanoparticles as compared to mono and hybrid, giving valuable insights for the design of improved thermal energy storage and bioconvective transference mechanism in engineering and biomedicine utilizations.