Forecasting heat and mass transfer enhancement in magnetized non-Newtonian nanofluids using Levenberg-Marquardt algorithm: influence of activation energy and bioconvection

A literature review shows that nanofluids are more effective for heat transfer than traditional fluids. However, our understanding of current methods to enhance heat transfer in nanofluids still needs to be completed, necessitating further research. This study explores the combined effects of magnetized surface and Maxwell–Sutterby–Casson nanofluid inside a stretchy sheet, taking into account the effects of Joule heating, variable thermal conductivity, and thermal radiation. The research examines activation energy, heat sources/sinks, bioconvection, and gyrotactic microbes, considering Brownian motion and thermophoresis effects. Using similarity functions, the boundary layer ODEs are created from PDEs. The shooting strategy is used to solve these altered equations numerically. A supervised Levenberg–Marquardt backpropagation algorithm and BVP5C built-in function of MATLAB are utilized to generate datasets for developing continuous neural network mappings. Analytical approaches like regression-based statistical and error histogram graphs are utilized to assess the precision of the existing method. The study provides graphical and numerical evaluations of the distributions of motile microorganisms, temperature, velocity, and concentration for various parameters when Casson parameters \(\beta \)=\(\infty \) and \(\beta \)=1.1. The findings indicate that the velocity profile rises with a higher magnetic parameter but falls with an increase in the magnetic parameter. The heat flux distribution improves when the thermophoresis and magnetic parameters are increased. On the other hand, when the Prandtl number and Brownian motion parameter increase, the energy profile falls. The spread of motile microorganisms decreases as the Peclet and bioconvection Lewis numbers rise. On the other hand, when the Prandtl number and Brownian motion parameter increase, the energy profile falls. The spread of motile microorganisms decreases as the Peclet and bioconvection Lewis numbers rise. Table: 1 compares Artificial Neural Networks (ANN) results and numerical results driven in the present study.