Two finite difference schemes to enhance nanofluid stability and heat transfer: Bioconvection with motile microorganisms in non-Darcy media

This study investigates steady magnetohydrodynamic bioconvective flow of a Prandtl-type nanofluid containing motile microorganisms over an inclined stretching sheet embedded in a non-Darcy porous medium. The governing nonlinear similarity equations incorporate magnetic effects, Brownian diffusion, thermophoresis, and Forchheimer drag, thus representing the coupled interaction between momentum, heat, nanoparticle concentration, and microorganism transport. The resulting boundary-value problem is solved using two independent numerical approaches: a collocation-based solver (bvp4c) and the Network Simulation Method (NSM), formulated through an electrical analogy framework. Grid refinement and cross-validation confirm numerical consistency between both methods. The results indicate that magnetic and porous resistance parameters suppress momentum transport while modifying thermal and microorganism distributions within the boundary layer. Variations in bioconvection and inclination parameters significantly influence surface shear stress, heat transfer, and mass diffusion characteristics. The study demonstrates that NSM provides a stable and conservative computational framework for strongly nonlinear multiphysics boundary-layer systems, thus supporting its applicability to complex bioconvective nanofluid configurations.