Estimation of time-dependent Darcy-forchheimer flow through artificial intelligence-based technique for chemically reactive trihybrid nanofluid configured by rotating sphere invoked bioconvection analysis

In this work, the application of Levenberg–Marquardt backpropagation scheme is used to demonstrate the importance of viscous dissipation, Joule heating, and magnetic field on the stagnation point Darcy–Forchheimer flow of ternary hybrid nanofluid around a rotating sphere containing oxytactic and gyrotactic microorganisms. The present analysis additionally includes higher-order biochemical reactions and heat generating effects. In this paper, the performance of each nanofluid is compared using the Hamilton–Crosser model. This model can be using to optimize and construct complex cooling systems. The result is a statistical matrix data set and a linear graphical representation of the established model on several parameters. The results are thoroughly verified and cross-checked until they align with the Levenberg–Marquardt backpropagation model, utilizing a stochastic, artificial intelligent driven neural network approach. This blend of artificial intelligence allows for precise predictions of nonlinear flow parameters and is beneficial for applications in both biomedical and industrial heat transfer systems. An analysis of the findings indicates that an increase in the Forchheimer and Darcy parameters lowers primary velocity and that a stronger magnetic field boosts the velocity. Changing the Prandtl number leads to temperature decreasing in the profile and changing the Schmidt and chemistry parameters tends to reduce the concentration profile. The profiles of gyrotactic and oxytactic microorganisms are reduced as the Schmidt numbers grow larger. The model is very accurate, reaching values close to zero regression and having a mean square error of 10⁻⁶, confirming it is effective for predicting complicated fluid movements.