A comprehensive analysis on obstacle-driven flow reconfiguration inclined MHD thermo-bioconvection: A porous cavity study with Galerkin finite element method and XGBoost machine learning surrogates

A unified approach using a combination of inclined MHD effects and thermo-bioconvection in a porous cavity is presented in this work, along with the quantification of insert-geometry control using high-fidelity Galerkin finite element method (FEM) supported by an XGBoost surrogate to predict the main results more quickly. The results elucidate that increasing the Richardson number and having a favorable inclination promotes both convection and heat transfer, while decreasing the Darcy number and increasing the Hartmann number limits circulation and promotes conduction-dominant behavior; at the same time, an increase in the Peclet number strengthens the transport by advection and increases the motile density response. The use of internal obstacles leads to a gradual reduction in the overall heat transfer rate, from flow obstruction and the formation of stagnant zones, with the most modulation of thermal dynamics being shown by the cruciform insert. The findings provide important design aspects in porous thermal and bio-transport apparatuses such as bioreactors, microfluidic platforms, and magnetically controlled heat/mass transfer modules.