Electro-osmotic peristaltic streaming of a fractional second-grade viscoelastic nanofluid with single and multi-walled carbon nanotubes in a ciliated tube

Mathematical modeling of carbon nanotubes (CNTs) in biological fluids is essential for drug delivery, biosensing, and targeted therapy. This study explores the transport dynamics of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) based nanofluids under electro-osmotic peristaltic flow influenced by ciliary motion. A microfluidic channel lined with cilia, hair-like structures found in human airways and reproductive tracts, is considered. The coordinated beating of cilia generates a wavelike motion that propels the surrounding biological fluid. When an electric field is applied across the channel, electro-osmotic forces further modify the flow, affecting velocity and temperature distribution. A nanofluid, consisting of CNTs suspended in a base fluid, flows through this cilia-driven microchannel. The transport process is governed by electro-osmosis, heat transfer, and thermal radiation effects, with simplifications based on long-wavelength and low Reynolds number assumptions. The Caputo fractional model and Debye–Hückel linearization are used to analyze the interaction between electro-osmotic forces and thermal-mechanical effects. The results reveal that the negative Helmholtz-Smoluchowski parameter (Uhs) reduces the axial velocity in the core whereas it increases in the periphery of the channel, while the opposite trend is observed for positive Uhs. Longer cilia (β) and higher electro-osmotic parameter (m) slow the core flow while accelerating peripheral transport. Thermal effects indicate that an increased heat source (B) raises temperature and axial velocity, whereas a higher nanotube volume fraction (ϕ) enhances axial velocity but reduces temperature. Notably, MWCNTsexhibit superior axial velocity and temperature enhancement compared to SWCNTs. These outcomes provide valuable insights into electro-osmotic cilia-driven nanofluid transport, offering a theoretical foundation for optimizing microfluidic and biomedical applications.