Preface
More and more researchers are using non-Newtonian fluids for a variety of
geometries. Plastic production, lubrication theory, the paint industry, and food
processing are just a few of the many industries where non-Newtonian fluids play
an important role. Because of their wide range of uses, these fluids have been
utilized by a large number of researchers [1-4]. Examples of flows through
permeable barriers that have gotten a lot of attention recently because of their
multiple uses in biosciences are human blood desalination in hemodialysis using an
artificial kidney, blood flow and renal proximal tubule flow while in engineering
few of many examples are transpiration cooling, insulation of buildings and geo
thermal energy extraction etc. [5-8]. There is a fluid model called Johnson-Segalman
that was created to accommodate non-affine deformations. The purpose of this
model is to forecast non-Newtonian effects [9-12]. Some of the numerous uses for
creeping flow via porous limits include ultrafiltration, proximal tubule flow, reverse
osmosis, and the kidneys themselves. They studied slip creeping flow via a
permeable slit and found that the slip coefficient had an influence. Haroon et al.
[13] studied the creeping flow of Newtonian fluid permeable slit by considering
exponential reabsorption and slip effects. Matteo Gorgone et al. [14] proposed
approximate invariant solutions of creeping flow. According to Siddiqui et al. [15],
who studied creeping circulation in a circular vessel with lower permeability porous
material, fluid velocity decreases along the axial coordinate, while only a tiny shift
occurs along the radial coordinate.
This thesis comprises of three chapters. Chapter 1 gives introduction of basic laws
and definitions of fluid flows, fluid types and solution methodology.
Chapter 2 is review work [16] in which creeping flow for Maxwell fluid through
uniformly porous slit is studied. Langlois Recursive approach is used to solve
nonlinear equations. Graphical study is carried out for different phenomena.
Chapter 3 is the study of Slow Flow of Johnson-Segalman fluid model thorough a
permeable slit. Slow flow and slip conditions are used on general Continuity and
Momentum equations. The resulting nonlinear equations are solved through
Langlois Recursive Approach.