Thermally driven two-phase shear thinning non-Newtonian fluid through the renal tube induced by electric double layer effects with variable wall properties

Peristaltic flow in the ureter is a highly controlled biological process crucial for the efficient movement of urine from the kidneys to the bladder. Accordingly, this article analyses the unsteady pseudoplastic viscous fluid flow that is influenced by the combined effects of electro-osmosis and peristalsis in a tapered wavy channel.

Overview of the objectives

The purpose of this article is to conduct an analytical analysis of the movement of dissolved substances along with urinary flow inside ureter, which is considered to be flow with slip conditions imposed on non-uniform compliant channel.

Methodology

The governing equation of the Casson fluid model for both the fluid phase and solid phase has been derived by ignoring the effects of inertial forces and making the assumption of long wavelength. Closed-form solutions are obtained for the non-dimensional boundary conditions of the symmetric channel.

Key findings

The results suggest that velocity exhibits parabolic behaviour towards the centre, while a combination of behaviours is exhibited around the edges. It can also be observed that the tapering parameter (${\eta }^{\prime }$) has a significant impact on the velocity. Streamline representation demonstrates that the amount of trapped bolus is reduced as the thickness of the electric double layer (EDL) increases, as well as with a stronger external electric field. Simultaneous approach of skin friction drag and heat transfer coefficient impacted by magnetic body force.

Significance of the study

The uniqueness of this investigation lies in the concurrent examination of a generalised two-phase model, wall slip, non-Newtonian properties of Casson fluid, electric double layer effects (L), viscous dissipation, Hall effect (m), magnetic body force (M), Helmholtz-Smoluchowski velocity $\left(U_{hs}\right)$, Joule heating, and curvature effects in peristaltic urological transport, such comprehensive approach that has not been previously explored. Electroosmosis may promote urine flow or facilitate drug delivery, whereas magnetic therapy may break down kidney stones or guide therapeutic nanoparticles to the stone's location, facilitating stone removal.