Effective magnetisation and chemotaxis impact on controlled flow: A study using optimization and Jacobi-Bernstein polynomial collocation

The present article explores the impact of bioconvection, a low oscillating magnetic field, Dufour and Soret effects on the flow of fluid between two parallel revolving non-expandable disks with the passive and active control of nanoparticles. The low-oscillating magnetic field is advantageous for particle management, enhancing fluid and rheological stability and optimizing heat transfer. The Jacobi-Bernstein polynomial collocation method is used to obtain the solution. Additionally, the artificial neural network is employed to study the energy and concentration profiles, and the Taguchi method is employed to study the rate of heat transfer. The analysis of variance results indicate that the radiation parameter contributes 63.25% of the total variation, followed by thermophoresis with 28.62% and the Brownian motion parameter with 4.68%. The regression model for this case yields R-Sq = 96.55% and R-Sq(adj) = 91.37%, which indicates a good fit between the predicted and observed responses. The study demonstrates that active control enhances the role of nanoparticle transfer mechanisms, particularly thermophoresis, whereas radiation effects primarily dominate passive control. This shift in parameter dominance highlights the sensitivity of the heat transfer process to the imposed control mechanism and emphasizes the importance of selecting appropriate control strategies for optimizing thermal performance.