Oscillatory Channel Flow for Newtonian and Non- Newtonian Fluids

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.