The physical characteristics of a heated non-Newtonian Eyring–Powell fluid in a conduit with sinusoidally moving ciliated walls are highlighted in this analytical study. The impact of mass transmission is considered in this model. The dimensional form of the governing equations is simplified using the long-wavelength estimation and suitable transformations to produce a set of dimensionless partial differential equations with pertinent boundary conditions. To solve it, the perturbation technique is utilized applying polynomial solutions. The solutions of temperature, concentrations, and velocity profiles are obtained, and then are further analyzed through graphical results. An accurate mathematical solution for the pressure gradient is achieved by integrating the velocity profile over the elliptic cross-section. The non-Newtonian Eyring–Powell fluid flows quicker through this vertical ciliated elliptic duct than the Newtonian fluid. Moreover, the cilia elliptic movement eccentricity and the wave number for metachronal wave have a dual effect on the velocity profile. Increasing the dimensionless flow rate and occlusion leads to an increase in closed contour size, as seen in the streamline description.
N. M. Hafez (Sun,) studied this question.