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

Deepalakshmi, P.; Siva, E. P.; Tripathi, D.; Bég, O. Anwar; Kuharat, S.


P. Deepalakshmi

E. P. Siva

D. Tripathi



The 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 biomagnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on 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 is generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted comprising the electromagnetic urological viscous fluid phase and 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 via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter (), Hartmann number (M), Prandtl Number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). 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. 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 in urological pumping characteristics can be achieved with electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted of relevance to magnetic therapy techniques which will be beneficial to clinicians.


Deepalakshmi, P., Siva, E. P., Tripathi, D., Bég, O. A., & Kuharat, S. (2024). MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation. Numerical Heat Transfer, Part A Applications, 1-24.

Journal Article Type Article
Acceptance Date Mar 13, 2024
Online Publication Date Apr 12, 2024
Publication Date Apr 1, 2024
Deposit Date Mar 14, 2024
Publicly Available Date Apr 2, 2025
Journal Numerical Heat Transfer, Part A: Applications
Print ISSN 1040-7782
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Pages 1-24
Keywords Condensed Matter Physics, Numerical Analysis