MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: <italic>Electromagnetic therapy simulation</italic>.

Abstract\nCULMINATIONSThe ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system.  This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional <italic>via</italic> appropriate scaling transformations. A numerical solution is achieved <italic>via</italic> BVP4C MATLAB quadrature.  Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter (ζ), Hartmann number (<italic>M</italic>), Prandtl number (<italic>Pr</italic>), Weissenburg number (<italic>We</italic>), particle volume fraction (<italic>C</italic>), Eckert number (<italic>Ec</italic>), Soret number (<italic>Sr</italic>), Schmidt number (<italic>Sc</italic>). <italic>The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously</italic>. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.A detailed new formulation is given for magnetohydrodynamic (MHD) two-phase Williamson non-Newtonian ureteral transport with mass diffusion, Soret cross diffusion, viscous heating and peristaltic wave propulsion.We compute numerically the pressure gradient, skin friction, Nusselt number, and wall shear stress in a planar channel with flexible walls, which serves as a model for the ureter under a transverse magnetic field.We also investigate the impact of Hartmann number and Weissenberg non-Newtonian number on fluid and particle phase velocities.The present work reveals some interesting insights into electromagnetic ureteral peristaltic multi-phase non-Newtonian thermo-solutal transport phenomena via extensive visualization.There is a strong suppression in the ureteral fluid phase velocity for greater magnetic field confirming the excellent flow control abilities of Magnetic Ureteral Therapy (MUT).A detailed new formulation is given for magnetohydrodynamic (MHD) two-phase Williamson non-Newtonian ureteral transport with mass diffusion, Soret cross diffusion, viscous heating and peristaltic wave propulsion.We compute numerically the pressure gradient, skin friction, Nusselt number, and wall shear stress in a planar channel with flexible walls, which serves as a model for the ureter under a transverse magnetic field.We also investigate the impact of Hartmann number and Weissenberg non-Newtonian number on fluid and particle phase velocities.The present work reveals some interesting insights into electromagnetic ureteral peristaltic multi-phase non-Newtonian thermo-solutal transport phenomena via extensive visualization.There is a strong suppression in the ureteral fluid phase velocity for greater magnetic field confirming the excellent flow control abilities of Magnetic Ureteral Therapy (MUT). [ABSTRACT FROM AUTHOR]