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.
