Unsteady reactive hybrid nanofluid flow between coaxial cylinders with variable transport properties and Einstein–Hamilton crosser model

This study investigates unsteady hybrid nanofluid flow between concentric stretched cylinders, incorporating homogeneous-heterogeneous (h–h) reactions. The SWCNTs/MWCNTs are selected as hybrid nanoparticles in a base fluid engine oil, with Newtonian heating at the inner wall. The shape factors of the nanoparticles were also considered, as they are important in the heat transfer rate of the system. Uniquely, in order to better explain the heat transfer phenomenon, the Hamilton-Crosser model and the Einstein model are used, which explain the variable temperature-dependent viscosity and variable temperature-dependent thermal conductivity in the present study. The presumed model is represented by Partial differential equations. The governing equations are transformed into nonlinear ODEs by similarity transformation and then solved numerically using the bvp4c method. Key findings reveal that radial velocity increases with the unsteadiness parameter, whereas axial velocity near the outer cylinder decreases. Rising variable viscosity reduces radial velocity, while variable thermal conductivity enhances temperature profiles. Wall friction at the outer cylinder increases with unsteadiness, but decreases at the inner cylinder, and the Nusselt number drops on both walls, signifying reduced heat transfer. Model validation is also included, endorsing the proposed framework. This analysis with an annular geometries model provides critical insights for optimizing thermal systems in many engineering applications where precise flow control is essential.