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This study presents a novel mathematical investigation of peristaltic transport in electroosmotic-driven micropolar bio-nanofluids containing gyrotactic microorganisms within a magnetized microchannel. The current study addresses the effects of Joule heating, viscous dissipation, first-order chemical reactions, as well as Soret and Dufour impacts. The governing nonlinear differential equations are derived under the assumptions of low Reynolds numbers and long-wavelength approximation and are numerically solved using the parametric NDSolve function in MATHEMATICA software. The influence of key parameters such as Helmholtz–Smoluchowski velocity, electroosmotic parameter, magnetic field strength, thermophoresis, and Brownian motion on the velocity, temperature, concentration, microrotation, and motile microorganism density is thoroughly analyzed. Trapping phenomena are also examined, revealing sensitivity to electrokinetic parameters. Notably, increasing the electroosmotic parameter andUHS{U}_{{\rm{HS}}}enhances the fluid flow and mass transmission, while the bioconvection Peclet number and coupling number influence motility distribution and microrotation behavior. Furthermore, improving the Brownian diffusion parameterNb{N}_{{\rm{b}}}from 0.1 to 1.0 results in a 60% increase in microorganism density, while a higher thermophoresis parameterNt{N}_{{\rm{t}}}reduces it by approximately 45%. The heat transfer rate is found to increase by 35% when the magnetic parameterMMincreases from 1 to 4. The results highlight potential applications in targeted drug delivery and microscale fluid handling systems, offering insights into the design of advanced electrokinetic microfluidic devices.

open physics

Advanced mathematical analysis of heat and mass transfer in oscillatory micropolar bio-nanofluid flows  via  peristaltic waves and electroosmotic effects