Biological fluids often have complex properties due to the presence of tiny particles, cells, microbes, or large molecules. The Casson-Maxwell-Oldroyd-B (CMO) fluid model is a key tool for understanding the effects of non-Newtonian behaviour in biological processes like microbe movement, blood flow, and mucus transport. This research focuses on how microbes move in a reactive magnetised CMO nanofluid on a slanted elongated cylinder, considering entropy generation effects. It explores how factors like Arrhenius activation energy and specific boundary conditions influence this process. The CMO model helps clarify how non-Newtonian nanofluids behave in microbial migration. The study converts the model equations to a dimensionless form using similarity methods. The results are calculated using a combination of a shooting method and a fourth-order Runge-Kutta scheme in MATLAB, and presented in graphs and tables. The results show the impact of various factors: Lorentz force and porosity slow down the fluid, while higher temperatures speed it up. Higher activation energy increases concentration. The Casson-Oldroyd-B (CO) nanofluid has a lower Nusselt number than the Casson-Maxwell (CM) nanofluid. The presence and movement of microorganisms greatly affect entropy generation. This research is valuable for understanding biological fluids, which is essential in medical research, diagnostics, and the development of healthcare products.
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