Integrate mathematical modeling for heat dynamics in two-phase casson fluid flow through renal tubes with variable wall properties

Urine consists of cells and many chemicals, and its complex rheological characteristics can be accurately explained using non-Newtonian fluid models. A theoretical study is conducted on the peristaltic pumping of a Casson fluid through inclined tapering wavy walls of the ureter containing debris. The Casson fluid serves as the base liquid in which homogeneous and spherical solid particles are suspended. In order to simulate the motion of both fluids and particles, non-linear partial differential equations were employed. The flow through the ureter is exposed to evenly distributed magnetic field in the transverse direction. To calculate the flow-anchored equations, we assume a low Reynolds number and deliberate over long wavelengths. The resulting exact solutions were obtained using the Matlab software to determine the fluid temperature, contour pattern, velocity of the deposited particles, and fluid. We investigate the effects of wavy tapered walls with variable wall characteristics, thermal radiation and variable heat source on the flow of a non-Newtonian Casson fluid in an inclined channel. The particle phase models the behavior of stiff calculi suspensions due to lack of filtration process. The simulations illustrate that electromagnetic radiation can effectively manipulate the pumping properties in urology. The originality of this study lies in the concurrent examination of a generalised two-phase model, partial wall slip, non-Newtonian fluid properties, cross diffusion, magnetic body force, elastic wall behaviour in the presence of debris, and curvature effects in peristaltic urological transport, a comprehensive approach not previously explored. This text highlights several novel aspects of the dynamics of the ureter in two-phase conditions, which are relevant to the usage of magnetic therapy and thermal radiation techniques. The study also considers the impact of radiation and the visualisation of wall tension parameter using contour plots. More thermal energy is contributed due to radiation causing a reduction in the velocity of the fluid. Fluctuations in the thermal radiation parameter (Rn) suggest the presence of localized inflammation or infection, specifically called urinary tract infections (UTIs) or ureteral inflammation (ureteritis). Enhancement in particle volume fraction tends to a reduction in the rate of peristaltic pumping. An elevation in the Hall current parameter leads to a reduction in the growth of the bolus in the channel, as well as a drop in the velocity of the particle phase. The heat transfer rate intensified as the values of the Casson parameter of the non-Newtonian fluid and magnetic parameter were raised. Both the wall tension and wall mass parameters on the profiles exhibit behaviours that are qualitatively comparable to one another.