Abstract:
Oscillatory Channel Flow for Newtonian and Non-Newtonian
Fluids
The flow between parallel porous plates may be driven by the uniform suction/injection
at the permeable walls or by the movement of the walls. Sometimes, this flow can also be
induced due to the pressure gradient. In this thesis, we have examined the flow between
parallel plates and cylindrical tubes due to the uniform suction/injection at the walls with
oscillatory pressure gradient. The oscillatory flow inside a channel/tube has many
applications in industrial and engineering processes. Understanding the physics of
oscillatory or transient flows in small channels is of fundamental interest for many
biological and industrial applications. For example, the quasi-periodic blood flow in the
cardiovascular diseases are described by the frequency components of the pressure and
flow rate pulses, and many vascular diseases are associated with disturbances of the local
flow conditions in the blood vessels. Furthermore, it has applications in modeling of
respiratory
functions
in
lungs,
modeling
of
chemical/blood
dispensing
in
biochemistry/clinical labs etc. The oscillatory channel flow have special relevance in
vibrating media with applications in oil drilling, control of blood flow during surgical
operations, manufacturing and processing of foods and paper, oil exploration and paper
industry. Some other applications of value are to detect the intensity of underground
explosions, chemicals and material processing, isotope separation, irrigation systems,
rocket propulsion, filtration mechanism, sweat cooling, cooling of electronic device, heat
exchanger and many others.
Most of the theoretical work undertaken in oscillatory channels and tubes is for viscous
fluids. Nothing or very little has been said for non-Newtonian fluids.
Motivated by these considerations, we extend the analysis of oscillatory channel and tube
flows from clear Newtonian fluid to Newtonian fluid in porous medium and non-
Newtonian second grade and Jeffery fluids. The flow in the channel is driven by suction
ixat the permeable walls while time harmonic pressure waves are responsible for
oscillations in the velocity field. The analytic solutions of the corresponding boundary
value problems for Newtonian (porous medium) and non-Newtonian fluids are
established. The combined effects of porosity of the medium and the fluid oscillations on
the oscillatory axial velocity between porous channels are investigated for the case of a
Newtonian fluid. Further investigations are made for a second grade fluid in a channel
and a cylindrical tube. The effects of wall suction, the second grade fluid parameter on
the amplitude and penetration depth of the oscillatory axial velocity are determined. The
oscillatory channel flow is also discussed for Jeffery fluid and the effects of
relaxation/retardation time parameters and Deborah number are examined.