Mathematical modeling of magneto-bioconvective Eyring-Powell nanofluid with activation energy and gyrotactic effects across various geometries

Abstract

This work formulates a mathematical framework to analyze the magneto-bioconvective transport of an Eyring-Powell nanofluid containing gyrotactic microorganisms over flat plate, wedge, and stagnation-point geometries embedded in a porous medium. The Eyring-Powell constitutive relation is represented through two material constants, namely the viscoelastic parameter (A1) and the nonlinear stretching parameter (A2), which determine the fluid's shear response. The model accounts for nonlinear thermal radiation, activation energy, variable thermal conductivity, internal heat generation, Brownian diffusion, thermophoretic motion, and chemical reaction effects. By applying similarity transformations, the governing nonlinear PDE system is converted into a set of coupled ODEs, which are solved numerically using a fourth-order Runge-Kutta method combined with the shooting technique. Numerical results highlight the strong sensitivity of transport characteristics to governing parameters. For instance, in the flat-plate case, increasing A1 from 0.1 to 0.7 enhances the skin-friction coefficient from 1.128 to 1.387, whereas the same variation in A2 reduces it slightly from 1.129 to 1.121. For wedge geometry, the local Nusselt number (Nux) decreases from 0.6164 to 0.6112 as A1 increases, while in stagnation-point flow, the Sherwood number (Shx) falls from 0.4838 to 0.4741. A rise in the magnetic parameter (M) from 0.2 to 0.6 lowers Nux by about 0.002 and simultaneously raises the skin-friction coefficient by approximately 0.21 in the plate configuration. Activation energy (E) significantly increases solutal concentration and microorganism density by more than 6%, whereas the reaction-rate constant (Kr) produces a nearly equivalent reduction. Brownian motion (Nb) and thermophoresis (Nt) elevate fluid temperature while decreasing Shx by over 0.01, and higher Peclet (Pe) and Schmidt (Sc) numbers reduce microorganism density and solute concentration by 5-10%. Overall, the developed formulation provides a predictive tool for applications such as bio-convective heat exchangers, microfluidic systems, and porous-medium transport under magnetic environments.