Analytical Investigation of Carreau–Yasuda Fluid Flow in a Ciliated Channel

Abstract Ciliary transport is a fundamental mechanism for moving biological fluids through channels lined with cilia, with direct relevance to mucus clearance, reproductive transport, and other physiological processes. This study investigates the thermal and flow characteristics of Carreau–Yasuda fluid driven by metachronal ciliary beating in a two-dimensional channel. Under the lubrication approximation, with a small Weissenberg number and low Reynolds number, the governing nonlinear equations are reduced to a stream-function formulation and solved using a regular perturbation technique. The influence of key parameters — the Carreau–Yasuda index, Weissenberg number, power-law index, Brinkman number, Biot number, time-mean volumetric flow rate, and cilia length — is examined on the streamline topology, pressure distribution, velocity field, and temperature profile. Results show that increasing cilia length enhances the time-mean volumetric flow rate and horizontal velocity in the channel core, while producing a marked reduction in velocity near the ciliated boundary. The shear-thinning behavior captured by the Carreau–Yasuda model is shown to modulate trapping-bolus formation and heat transfer rates in ways that purely Newtonian or power-law models cannot resolve. These results extend the analytical framework for cilia-driven transport and clarify the role of the Yasuda parameter in shaping thermofluidic behavior in bio-inspired non-Newtonian systems.