Abstract The study of thin liquid films on spinning disks has attracted significant attention due to their diverse industrial and biomedical applications. This work investigates the transient bio‐nano‐convective flow, heat, nanoparticle volume fraction (NPVF), and microorganism transport past a thin finite liquid film along an extendable rotating disk under the influence of Stefan blowing. The Buongiorno nanofluid model incorporating Brownian motion and thermophoresis effects is adopted to characterize a dilute bio‐nano‐polymer suspension, while the unsteadiness number governs the film thickness variation. The nonlinear coupled equations are solved numerically using MATLAB's bvp4c solver. The results reveal that radial skin friction decreases by 38% and tangential skin friction increases by 45% as the unsteadiness parameter A rises from 0.2 to 1.0. The Nusselt and Sherwood numbers increase by 62% and 49%, respectively, with higher Lewis number and Brownian motion parameters, indicating improved thermal and mass transfer. Conversely, the thermophoretic parameter suppresses heat and mass transport by up to 25%, while motile microorganism density grows by 40% with intensified suction and bioconvection effects. These findings demonstrate that unsteadiness, suction, and Brownian motion synergistically enhance energy and mass transport, whereas thermophoresis opposes them. The present outcomes offer predictive insights for coating processes, bio‐reactor design, and nanofluid film management in rotating disk systems.
Uddin et al. (Sun,) studied this question.