Entropy optimization in Casson tetra-hybrid nanofluid flow over a rotating disk with nonlinear thermal radiation: a Levenberg–Marquardt neural network approach

Abstract

Abstract This research employs a neural network, specifically the Levenberg–Marquardt algorithm, to characterize the entropy optimization performance in the electro-magneto-hydrodynamic flow of a Casson tetra-hybrid nanofluid over a rotating disk. The problem was formulated mathematically using equations for momentum, continuity, and temperature. This study converts ordinary differential equations (ODEs) into partial differential equations (PDEs) by a self-similarity transformation. The equations are resolved via the fourth-order Runge-Kutta method in combination with a shooting technique for obtaining the required datasets. Using the Levenberg-Marquardt algorithm (LMA), these datasets are characterised as training, testing, and validation. The proposed outcomes are presented in multiple tables and graphs. This trained neural network is then utilized to predict the heat flow velocity and Nusselt number of the rotating disk. The developed model was evaluated using mean square error, error analysis, and regression analysis, thereby confirming the consistency, accuracy, and reliability of the designed technique. The best validation performance for skin friction and the Nusselt number for the Casson tetra-hybrid nanofluid flow across a rotating disk is 8752e-05 at epoch 95 and 0.00033239 at epoch 37. Training, validation, testing, and all performance metrics of the artificial neural network model are close to unity. As magnetic field strength increases, temperature profiles rise in di-hybrid, ternary-hybrid, and tetra-hybrid nanoparticle scenarios. Tetra-hybrid nanofluids are considered superior fluids when compared to di-hybrid, ternary-hybrid, and tetra-hybrid nanofluids. This optimization method holds promise for diverse applications in biotechnology, microbiology, and medicine, offering significant potential for various fields.