Mathematical Analysis of Blood Flow in Porous Tubes: A Comparative Study

Abstract

The steady flow of Herschel-Bulkley and Casson fluids for blood flow in tubes filled with homogeneous porous medium with (i) constant and (ii) variable permeability is analyzed. The expression for the shear stress is obtained first by general iteration method and then using numerical integration; the solutions for velocity and flow rate are obtained. It is noticed that the shear stress and plug core radius are considerably higher in the case of variable permeability than those of the constant permeability case. The velocity and flow rate of both the fluids increase considerably with the increase in the permeability factor and they decrease with the increase in the yield stress of the fluids. The velocity and flow rate of Herschel-Bulkley fluid are considerably higher than those of Casson fluid. Aforesaid flow quantities are significantly higher for flow in tubes with variable permeability than for flow in tubes with constant permeability.