Carreau–Yasuda fluid flow generated via metachronal waves of cilia in a micro-channel

The accretion of excessive bio-fluid in human tissues is triggered due to several reasons, such as pregnancy, local injuries, and allergic reactions or by using certain therapeutic drugs. Motivated by such numerous biomedical applications, this article aims to elaborate on the shear-dependent peristaltic flow of Carreau–Yasuda fluid inside the micro-channel by incorporating the ciliary walls. The long wavelength and the low Reynold's number approximation simplify the problem. Furthermore, the MATLAB-based algorithm known as the bvp5c is adopted for the problem's numerical solution. The impact of emerging parameters on the velocity, pressure gradient, and streamlines is examined through various graphs. The results reveal that while using Carreau–Yasuda fluid, the pumping apparatus performs better than Newtonian or Carreau fluid. The findings could aid our understanding of biofluid movement in the human body. Furthermore, it is believed that this solution has an important contribution in the biomedical industry for the advancement and improvement of several kinds of drug delivery devices.