An analytical exploration of low Reynolds number cilia-driven flow of Johnson-Segalman fluid with heat transfer effects

This article discusses the properties of heat transfer on Johnson-Segalman fluids in a complex wavy channel made of metachronal wavy cilia. Such complex wall structures can be used in the design of biomimetic systems. The movement of fluid through a two-dimensional complex wave channel produced by the metachronal wave of cilia is characterized as laminar and incompressible. Firstly, the system of equations is transformed from a fixed frame of reference to a wavy frame of reference. Secondly, the system of equations of motion (EOM) is transformed into a non-dimensional form by using the scaling factors. Mathematical analysis has been conducted using long wavelength as well as low Reynold numbers assumptions. The perturbation approach is used to solve the simplified governing equations for the axial velocity, temperature, stream function, pressure rise, and heat transfer coefficients. The equations representing axial velocity, pressure rise, and the streaming function are illustrated, and the reason for observed changes in different physical aspects are explained using basic theoretical principles. A solution for small values of the Weissenberg numbers is generated for the resulting nonlinear system. The current study investigates the effects of different boundaries and rheology on fluid flow.

The velocity profile increases near the channel center with higher Q (time-mean flow rate) and $\overline{e}$ (slip parameter), but decreases with greater Weissenberg number (We). The Brinkman number (Br), Q, and $\overline{e}$ directly influence the temperature distribution, while we have the opposite effect. The size and number of trapped boluses increase with higher Q but decrease with rising We and $\overline{e}$. It is noteworthy that the overall number of trapped zones rises throughout the complex wavy path.