ReLU-activated deep learning approach for simulating and sensitivity of casson hybrid nanofluid dynamics with...

This study focuses on the Casson Hybrid Nanofluid (CHNF) flow behavior over a stretching surface with thermal radiation, with a base fluid of blood and using gold (Au) and silver (Ag) as the nanoparticles. The nonlinear partial differential equations (PDEs) that govern the flow are simplified using similarity transformations to a set of ordinary differential equations (ODEs), which were solved using Python's solve_bvp method. To distinguish between classical methods for the calculation of non-dimensional velocity and temperature functions, a supervised deep learning neural network that employs the Rectified Linear Unit (ReLU) as its activation function and is trained using the Adam algorithm was developed in Python and applied to the solution of the PDEs. In addition to how an external magnetic field (M), the Casson parameter (β), the thermal radiation (Rd), the Eckert number (Ec), and the Prandtl number (Pr) influence the non-dimensional velocity and temperature component of the CHNF will also be presented. We observe that M and β suppressed the velocity component, while M, Rd, Eu and β increased temperature. However, larger Prandtl numbers can diminish thermal behavior as well. The neural model also demonstrates good fidelity and a mean square error (MSE) of 10^-2 to 10^-5 and reliable regression fit between 0 and 1 of R² up to 0.9949. Sensitivity is evidenced by smooth convergence curves, balanced derived gradients, and tightly fit regression. The study shows that the addition of AI to classical modeling is a valid method for predicting CHNF in biomedical and thermal engineering contexts.