Bioconvective radiative unsteady Casson nanofluid flow across two concentric stretching cylinders with variable viscosity and variable thermal conductivity

The role of variable viscosity and variable thermal conductivity in nanofluid flows is significant, as they can strongly influence the flow behavior and heat transfer performance of nanofluids. Keeping in mind the importance of these effects of variable characteristics, our motivation in this study is to investigate the role of nonlinear radiative heat flux on unsteady Casson nanofluid flow across two concentric stretched cylinders in the presence of temperature-dependent viscosity and thermal conductivity. A convective condition on the inner cylinder wall is also considered. In addition, the nanofluid is immersed with microorganisms that can swim and move independently. The addition of microorganisms has a significant role in the stability of the nanofluid flow. The influence of thermophoresis and Brownian motion on the flow, heat, mass, and microorganisms are scrutinized by employing the Buongiorno model. The governing flow equations are converted into a system of differential equations engaging similarity transformations, and the bvp4c method is employed to solve it numerically. Engineering parameters are computed and tabulated numerically. The findings demonstrate that as the unsteadiness parameter upsurges, the radial profile intensifies while the axial profile diminishes near the outer cylinder surface. It is also comprehended that both Lewis and bioconvective Lewis numbers reduce the motile density profiles. The accuracy of the presented model is also given in a graphical illustration by comparing it with a published result in a limiting case.