Examining ciliary flow of hyperbolic tangent fluid with heat transfer effects

The objective of this work is to investigate the dynamics of the cilia-driven flow of non-Newtonian fluids inside a wavy channel with heat transfer. The hyperbolic tangent fluid model approximates non-Newtonian mucus, which is a viscous and slippery fluid that plays important roles in protection, lubrication, and particle trapping in the digestive and respiratory systems. Laminar and incompressible flow is the term used to describe fluid flow in the two-dimensional complicated wavy channel that is created through metachronal waves produced by beating cilia. First, an oscillating frame of reference is created from the set of equations' stationary frame of reference. Additionally, scaling factors are used to transform the system of equations of motion into a non-dimensional form. The equations that govern for velocity profile, temperature, pressure rise, stream function, and heat transfer coefficients are solved by employing the perturbation approach. The impacts of several pertinent variables on the flow are investigated with graph plotting. Additionally, the phenomenon of trapping is also investigated. Moreover, a comparative analysis of flow behavior in a complex and simple wavy channel is also presented.