Effects of coagulation on the two-phase peristaltic pumping of magnetized prandtl biofluid through an endoscopic annular geometry containing a porous medium

In this article, motivated by more accurate simulation of electromagnetic blood flow in annular vessel geometries in intravascular thrombosis, a mathematical model is developed for elucidating the effects of coagulation (i.e., a blood clot) on peristaltically induced motion of an electrically-conducting (magnetized) Prandtl fluid physiological suspension through a non-uniform annulus containing a homogenous porous medium. Magnetohydrodynamics is included owing to the presence of iron in the hemoglobin molecule and also the presence of ions in real blood. Hall current which generates a secondary (cross) flow at stronger magnetic field is also considered in the present study. A small annular tube (endoscopic) with sinusoidal peristaltic waves traveling along the inner and outer walls at constant velocity with a clot present is analyzed. The governing conservation equations which comprise the continuity and momentum equations for the fluid phase and particle phase are simplified under lubrication approximations (long wavelength and creeping flow conditions). The moving boundary value problem is normalized and solved analytically (with appropriate wall conditions) for the fluid phase and particle phase using the homotopy perturbation method (HPM) with MATHEMATICA software. Validation is conducted with MAPLE numerical quadrature. A parametric study of the influence of clot height (δ), particle volume fraction (C), Prandtl fluid material parameters (α, β), Hartmann number (M), Hall parameter (m), permeability parameter (k), peristaltic wave amplitude (φ) and wave number (δ¯) on pressure difference and wall shear (friction forces) is included. Pressure rise is elevated with clot height, medium permeability and Prandtl rheological material parameters whereas it is reduced with increasing particle volume fraction and magnetic Hartmann number. Friction forces on the outer and inner tubes of the endoscope annulus are enhanced with clot height and particle volume fraction whereas they are decreased with Prandtl rheological material parameters, Hall parameter and permeability parameter. The simulations provide a good benchmark for more general computational fluid dynamics studies of magnetic endoscopic multi-phase peristaltic pumping.