MHD nanofluid bioconvection with gyrotactic microorganisms under Cattaneo–Christov heat–mass flux in rotating frame using Keller–Box and artificial neural network analysis

Purpose This study aims to investigate magnetohydrodynamic bioconvection induced by gyrotactic microorganisms in nanofluid flow over a rotating frame. Adding gyrotactic microorganisms to nanoparticles improves heat transfer in systems like microbial fuel cells, bacteria-powered micromixers, microfluidic devices, enzyme biosensors and chip-based microsystems. Design/methodology/approach The Buongiorno nanofluid model is used to incorporate Brownian motion and thermophoresis. The classical Fourier and Fick laws are generalized using the Cattaneo–Christov heat and mass flux theory to incorporate thermal and solutal relaxation phenomena. The governing partial differential equations are reduced to ordinary differential equations by using similarity transformations. The Keller–Box method has been used to solve these equations. The system is first converted into first-order form, then discretized with central differences and linearized using Newton’s method. A block tridiagonal matrix algorithm is used to obtain the numerical solution. This implicit scheme is stable, accurate and efficient. The numerical solutions are used to train an artificial neural network model with the Levenberg–Marquardt algorithm. Findings The results show that Coriolis and Lorentz forces reduce the velocity field, while thermal relaxation suppresses energy transport. Skin friction coefficient decays as the rotation and magnetic parameter values are increased. The model achieves high accuracy, with absolute errors between 10−4 and 10−5. Originality/value The proposed hybrid numerical–machine learning framework provides an accurate and computationally efficient approach for analyzing complex bioconvective nanofluid systems.