Abstract
This study presents a mathematical model for the transport of non-Newtonian nanofluids in an inclined ciliated converging microchannel. The analysis focuses on the combined effects of cilia length variation, electroosmotic effect, and temperature-dependent viscosity and thermal conductivity. The governing equations were derived using the Debye-Hückel approximation along with lubrication theory. These equations were then solved semi-analytically using the Homotopy Perturbation Method (HPM) in MATHEMATICA. The resulting solutions were visualized by plotting graphs in MATLAB. The results indicate that increased cilia length leads to a reduction in axial velocity but lowers the external pressure required to maintain flow, allowing for precise adjustments to transport dynamics. Variable viscosity and thermal conductivity improve flow and heat transfer under mild obstruction. The applied electric field accelerates the fluid by offsetting the drag caused by cilia, thereby enhancing overall transport efficiency. These findings illustrate the capability of cilia to serve as moderators of flow and transport in applications like targeted drug delivery, lab-on-a-chip diagnostics, microscale heat exchangers, and bio-inspired pumping systems.