Creeping Flow Through Porous Slit with Application to Renal Tubule

Abstract

In this thesis, the creeping flow of linearly viscous (Newtonian) fluid through a porous slit is studied with various forms of reabsorption across the walls. These reabsorptions include the types, where the transverse velocity across the walls, remains fixed, varies linearly, periodically, hyperbolically and exponentially. The transport equations are exactly solved in term of stream function using the inverse method with the appropriate boundary conditions. Dimensional forms of stream function, velocity components, pressure distribution, flow rate, pressure drop, fractional reabsorption, wall shear stress and leakage flux are obtained. Using the physiological data of rat kidney available in the literature, the quantitative values of uniform, linear, periodic, hyperbolic and exponential parameters for 50%, 60%, 70% and 80% fractional reabsorption are tabulated. The effects of these parameters are studied graphically using dimensionless quantities. Further, the comparisons of uniform reabsorption across the walls with linear, periodic, hyperbolic and exponential reabsorptions across the walls are highlighted. It is observed that the obtained theoretical results provide a good foundation and specialist knowledge in the field of bio-mathematics, especially, in analyzing the behavior of glomerular filtrate during the process of reabsorption through the renal tubule in normal and pathological conditions.