A deep neural network model for heat transfer in darcy-forchheimer hybrid nanofluid flow with activation energy.

This paper investigates the magnetohydrodynamic (MHD) flow along with heat and mass transfer behavior of Casson-type hybrid nanofluid through aluminum oxide ([Formula: see text]) as well as titanium dioxide ([Formula: see text]) nanoparticles dispersed throughout engine oil, a thermally stable functioning fluid that is used in utmost industrialized thermal exchanger applications. The advanced model incorporates the collective influences of heat radiation, Darcy-Forchheimer permeable media resistance, magnetic field-heating, and activation energy under nonlinear chemical reaction circumstances. Employing similarity transformations, the intricate governing equations are streamlined to ordinary differential equations (ODEs) that are numerically solved by means of the Bvp4c solver. The numerical solutions attained via the Bvp4c algorithm are employed for training a Morlet Wavelet Neural Network with Particle Swarm Optimization as well as Neural Network Algorithm (MWNN-PSO-NNA), through improving prediction robustness as well as generality behavior. The results show that strengthening the magnetic field leads to a decrease in the velocity distribution whereas thermal radiation growth in temperature, via variations falling within the range of 15-25% across the flow domain. Raising activation energy nearly 30% is observed to regulate species concentration as well as promote a more controlled thermal response inside the porous structure. In comparison with the base fluid and single-nanoparticle suspensions, the hybrid nanofluid exhibits superior thermal performance. Moreover, the MWNN-PSO-NNA outcomes remain in close agreement with the numerical solutions, yielding error levels of the order 10⁻