This study presents a comprehensive numerical investigation of two-phase boundary layer shear flows involving immiscible non-Newtonian Carreau and Tangent hyperbolic nanofluids incorporating motile microorganisms. The analysis explores the coupled effects of thermophoresis, Brownian motion, and thermal radiation on velocity, temperature, concentration, and microorganism density profiles across distinct shear regions. Incorporating microorganisms within nanofluids enhances thermal conductivity and stabilizes the flow structure, contributing to improved transport phenomena relevant to biomedical, energy, and environmental systems. The governing nonlinear differential equations are transformed into dimensionless form using similarity transformations and solved via the MATLAB bvp4c collocation method to ensure high numerical accuracy. A grid independence test confirms the convergence and stability of the scheme for all parametric variations. The results demonstrate that the Carreau fluid parameter promotes fluid velocity, while an increase in the viscosity ratio and shear strength ratio reduces it. Brownian motion and thermophoresis parameters suppress temperature near the interface, whereas thermal radiation enhances it. The density of motile microorganisms rises with higher bioconvection and Péclet numbers but decreases with increasing microorganism Schmidt number. Quantitative results for skin friction, Nusselt number, Sherwood number, and microorganism density validate the influence of these parameters in both regions. The findings provide valuable insights for optimizing microfluidic transport, bioconvective systems, and nanofluid-based heat exchangers where multi-phase shear interactions and microorganism activity are significant.
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