Metachronal wave analysis for magnetized Williamson fluid through a ciliated curved channel

Cilia play an important role in many psychological processes such as locomotion, alimentation, circulation, respiration, and reproduction. Therefore, the present investigation is modeled to study the impact of velocity slip on the cilia motion of electrically conducting Williamson fluid in a curved channel. The walls of the channel are carpeted with cilia such that their coordinated beatings produce a metachronal wave. Moreover, the viscous dissipation effect is also observed through the heat transfer mechanism. The governing system of coupled partial differential equations with highly nonlinear terms is simplified using the long wavelength and low Reynolds number approximations. The numerical solutions of simplified normalized equations are obtained using the finite difference method with an incorporating relaxation algorithm. The outcomes regarding the influences of several physical parameters on the temperature, velocity, pumping characteristics, and stream function are examined through graphs. Furthermore, the skin friction and Nusselt number at the channel walls are determined for a variety of critical parameter assessments. It is concluded that the fluid velocity is diminished at the lower wall of the channel and enhanced at the upper wall of the channel by enhancing the values of the Weissenberg number. The Brickman number shows a stronger viscous dissipation effect, leading to an increase in the liquid temperature.