Bioconvection in Maxwell nanofluids with gyrotactic microorganisms: A comprehensive review of viscoelastic flow dynamics, parametric influences, and emerging applications

• Bioconvection enhances heat transfer in Maxwell nanofluids with microorganisms. • Deborah number and thermophoresis increase thermal boundary layer thickness. • Magnetic fields stabilize flow and influence microorganism distribution. • Applications include bio-MEMS, nano-bioreactors, and thermal regulation systems. Bioconvection within viscoelastic Maxwell nanofluids that encompass gyrotactic microorganisms has emerged as a pivotal domain of inquiry owing to its significance in biomedical microfluidics, thermal regulation in lab-on-chip systems, and energy transport mechanisms. These nanofluids, distinguished by their memory-dependent flow characteristics and superior thermophysical attributes, engage with the upward locomotion of microorganisms such as Chlamydomonas nivalis to establish organized convection rolls that markedly affect heat and mass transfer phenomena. This review synthesizes literature from the years 2019 to 2024, encompassing mathematical formulations, similarity transformations, and numerical simulations employing Runge–Kutta (RK4) shooting methodologies, MATLAB's BVP4c solver, and finite element analytical techniques. A particular focus is directed toward linearly stretching surface configurations, along with cylindrical and inclined geometries, to elucidate the governing roles of viscoelastic effects, thermophoresis, Brownian motion, magnetic fields, and microorganism motility on flow dynamics. Documented findings indicate substantial enhancements in thermal transport, with Nusselt numbers varying from 1.8 to 4.2 across diverse configurations, a reduction exceeding 25% in wall shear stress under magnetic influence, and the emergence of sharper, convection-driven microbial plumes at elevated motility levels. Practical ramifications are underscored for bio-MEMS devices, targeted drug delivery mechanisms, and nanobioreactors, wherein the regulation of heat and mass transport is of paramount importance. The review distinctively amalgamates discussions pertaining to hybrid nanofluid design, artificial intelligence (AI), and machine learning (ML)-based predictive modeling for the optimization of parameters and pathways for experimental validation utilizing micro-PIV and holographic velocimetry, thereby providing a strategic framework for the application of theoretical insights into advanced thermal-fluid and biomedical innovations.