Hybrid numerical–artificial neural network modeling of bioconvection in MHD nanofluids with gyrotactic microorganisms

This study presents a comprehensive numerical investigation into the effects of thermal radiation and chemical reactions on magnetohydrodynamic (MHD) nanofluid bioconvection influenced by gyrotactic microorganisms, with direct applications in bioreactors, heat exchangers, smart cooling, and bioengineered fluid systems. The complex interplay among thermal gradients, magnetic fields, nanoparticle motion, and microorganism activity is modelled through governing equations for velocity, temperature, concentration, and microorganism density, transformed via similarity techniques and solved using the classical fourth-order Runge–Kutta (RK4) method coupled with the shooting technique. Key numerical findings reveal that increasing Brownian motion enhances thermal uniformity, while more substantial gyrotactic effects intensify bioconvection by concentrating microorganisms near the boundary layer. According to parametric analysis, increasing the Hartmann number (Ha) from 0 to 3 reduces skin friction at the wall and suppresses nanofluid velocity by approximately 22% and the Nusselt number by approximately 15%, due to Lorentz force damping. Heating is intensified by thermal radiation (R); an increase in R from 0.5 to 1.5 results in a temperature increase of about 21%. While thermophoresis (Nt) encourages particle migration to cooler locations, lowering the Sherwood number by up to 14%, the Brownian motion parameter (Nb) increases nanoparticle diffusion, increasing temperature profiles by $$\approx $$ 12% but decreasing near-wall concentration by $$\approx $$ 8%. While higher Peclet numbers (Pe) reinforce bioconvection currents and increase microorganism clumping by approximately 17%, higher Lewis numbers (Le) steepen microorganism density gradients near the wall. By increasing the density of microorganisms close to the wall by approximately 18%, the gyrotactic parameter ( $$\Omega $$ ) improves bioconvective mixing. An artificial neural network (ANN) with the Levenberg–Marquardt algorithm for training backpropagation is employed to enhance forecasting capability, achieving $$R^2=0.9996$$ with mean squared errors $$< 10^{-5}$$ for skin friction, Nusselt number, and Sherwood number. These results provide design insights for applications in microfluidics and thermal systems by establishing quantitative correlations between governing factors and transport characteristics, demonstrating the potential of the ANN for intelligent and optimized control of MHD nanofluid bioconvection systems.