Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary

Abstract

Abstract In this paper, a mathematical model for the steady laminar, incompressible and Newtonian fluid flow in a proximal renal tubule is presented. In this, the tubule is considered as a tapered tube with double constriction and permeable boundary. The impact of the fluid reabsorption across the tubule wall is assumed as the occurrence of exponentially decreasing flow at each cross-section. The present model is formulated through the Navier–Stokes equations, under the appropriate boundary conditions. A regular perturbation technique is used to obtain the approximate solutions. This study brings out the significant impacts of reabsorption coefficient (α) and tapered angle (ϕ) on the flow variables such as velocities, the drop in pressure, and wall shear stress are discussed through graphs. The streamlines are also plotted to understand the influence of the reabsorption and tapering phenomena on the flow.