Unsteady flow of gyrotactic microorganisms with hybrid nanofluid and higher order slips using modified Buongiorno model

In this work, we investigate the unsteady flow of gyrotactic microorganisms over a shrinking surface in the presence of hybrid Ag-TiO2/H2O nanofluid. The hybrid nanofluid considered in our analysis comprises nanoparticles with distinct properties, improving the fluid's thermal and transport characteristics. Additionally, we incorporate higher-order slip conditions to capture the complex interfacial dynamics. The mathematical model governing the flow is formulated using the Buongiorno-Tiwari-Das nanofluid framework or modified Buongiorno's nanofluid model, which accounts for the impact of Brownian motion and thermophoresis on the nanoparticle distribution. The resulting nonlinear ordinary differential equations, which were derived from a set of partial differential equations by a similarity transformation technique, are solved via bvp4c method in MATLAB. We present a detailed parametric study to elucidate the influence of various physical parameters on the flow and microorganisms' behavior. Our analysis reveals two distinct solutions when shrinking parameter lambda < 0, as well as the intricate interplay between gyrotaxis microorganisms, nanoparticle migration, unsteadiness flow, and slip effects on the current model. The presence of the Brownian motion constant was observed to enhance the heat transfer rate, nanofluid concentration and the mobility of microorganisms near the wall. The shrinking parameter was also found to increase the heat transfer rate, while the second-order slip parameter had a diminishing effect. Further, suction parameter and nanoparticle volume fraction positively influenced the velocity profiles. Prior to identifying dual solutions, a temporal stability analysis is performed, justifying the stability of the first solution.