A two layer analytical study of MHD Jeffrey blood flow in a porous non uniform channel with multiple stenoses

The flow through microvessels with stenosis is controlled by several factors: fluid rheology, vessel geometry, wall slip, magnetic forces, and porous-medium properties. To investigate these coupled effects, a two-layer analytical model is formulated to analyse the flow of magnetohydrodynamic (MHD) Jeffrey fluid through a non-uniform vessel with multiple mild stenoses filled with porous media. The blood-filled core is represented by Jeffrey fluid, which is compatible with its viscoelastic properties, and cell-free periphery is Newtonian fluid. Using the mild-stenosis and lubrication approximations, the governing equations are simplified and solved analytically with the slip boundary conditions. The velocity distribution, volumetric flow rate, effective viscosity, normalized core haematocrit and normalized mean haematocrit are obtained. The results show that the effective viscosity as well as the normalized core haematocrit and mean haematocrit increases with the increase of Jeffrey parameter, magnetic parameter and slip parameter. The results indicate that the effective viscosity and the normalized core haematocrit and mean haematocrit increase with the increase in Jeffrey parameter, magnetic parameter and slip parameter. On the other hand, higher Darcy number can result in higher permeability of the porous medium and thus reduce blood flow resistance. The microcirculatory hemodynamics also are markedly different as a result of vessel size and stenosis height variation. The model mimics the Fåhræus–Lindqvist effect and offers a complete analytical tool for the study of combined effects of multiple stenoses, vessel non-uniformity, porous-medium effects, MHD forces, wall slip and Jeffrey fluid rheology on microvascular blood flow.