Intelligent computing analysis of radiative heat transfer in magnetized bio-convective Williamson fluid flow over a curved elongated surface

Considering diverse applications of bioconvective nanofluid in bio-medical and other relevant of science and technology, strive is made to explore Williamson nanofluid using bioconvection for the swimming motion gyrotactic microorganisms in a stretched curved surface. A mathematical model is presented, yielding PDES, which are subjected to similarity transformations for simplification. The solution for the radiative induced nanofluid is explored with BVP5C solution which is validated using Artificial Neural Network (ANN) based Levenberg–Marquardt backpropagation. Outstanding unanimity of BVP5C solution is revealed with ANN, showing precision and accuracy of the solution scheme. The present study examines rheological nanofluid transport over a curved stretching sheet, incorporating key effects such as thermophoresis, Brownian motion, velocity and concentration slip, and motile microorganism density. The nonlinear system is solved numerically using by employing robust BVP5C method and validated through an ANN based on the Levenberg–Marquardt algorithm. The influence of governing parameters on velocity, temperature, concentration, skin friction, Sherwood number, and microorganism density is analyzed. The outcomes of investigation indicate that curvature and magnetic effects hinder fluid motion, while increased curvature enhances gyrotactic microorganism density. Higher radiation raises fluid temperature and thickens the thermal boundary layer, whereas thermal slip reduces heat transfer near the wall. Increasing the Prandtl number suppresses thermal diffusion, leading to a thinner thermal boundary layer. The strong agreement between numerical and ANN results confirms the model’s accuracy. These findings of the reported fluidic scheme cover diverse applications in biomedical engineering, microfluidics, and biotechnology, including drug delivery and bioconvective flow control.