Exploring entropy production in metachronal wave motion of Carreau fluid in a channel under lubrication hypothesis

The energy loss associated with the beating of cilia in the human stomach, leading to acidity in the blood flow under certain conditions, has become a critical topic in modern medical research. This study investigates entropy generation in the flow of cilia-generated metachronal waves of Carreau fluid through a channel, incorporating the effects of viscous dissipation and an externally applied magnetic field. The flow is governed by metachronal wave propagation along the ciliated channel walls. Using the lubrication hypothesis, the governing equations are normalized and solved analytically via the integration technique. Graphical representations illustrate the impact of key physical parameters on the flow behavior, providing a deeper physical interpretation of the system dynamics. Special emphasis is placed on analyzing pumping efficiency and trapped bolus formation in Carreau fluid due to ciliary metachronism. The results indicate that fluid velocity increases with higher values of the power-law index parameter and eccentricity parameter. Additionally, fluid temperature rises with an increasing Brinkman number but decreases as the Weissenberg number increases. These findings offer valuable insights into the optimization of biomedical microfluidic devices, particularly in the design of magnetic micro-bots for targeted medical applications.