On Peristaltic Transport with Heat Transfer and Rotation Aspects.

Abstract

Importance of peristalsis is recognized for numerous physiological and industrial applications which include swallowing food through oesophagus, capillaries and arterioles, in the vasomotion of venules, in sanitary fluid transportation, toxic liquid transport in the nuclear industry, digestive system catastalsis, ureteral tract, carrying of bile from gallbladder to duodenum, blood pumping, ovum transport, peristaltic pumps, locomotion of worms, roller and finger pumps etc. The waves of constant wavelength and amplitude (periodic waves) traveling along the tube give rise peristaltic excitation in human physiology. Further peristaltic transport of fluid with heat transfer is quite significant in oxygenation, hemodialysis, conduction of tissues, radiation between environment and its surface and heat convection for blood flow from the pores of tissues. As heat transfer fundamentally refers to the exchange of thermal energy between the different components of a physical system. Heat transfer rate depends upon temperature of different components and the physical properties of the medium through which heat transfer takes place. Heat transfer is further important in many processes including the design of chemical processing equipment, food processing and cooling towers, power generation, distribution of moisture over grove fields and many others. Further in rotating frame the study of fluid flow has vital applications in astronomy, geophysics, atmospheric science, stellar dynamics and earth sciences. Phenomenon of rotation can be understood by ocean circulation, flight dynamics, formation of galaxies and amusement rides, which gives rise to the effects of Coriolis and centrifugal force in addition to inertial forces. Peristalsis in presence of rotation has relevance with saline water, blood and bio fluid such as intestines, arterioles and ureters. Keeping all such facts in mind, the objective here is to develop fluid flows through periodic wave transport in channels. Such considerations are focused particularly for human tubular organs functioning to inspect the outcomes of different effects. Modeling and analysis are carried out by using basic laws and different techniques. Finally the present thesis is structured as follows: Chapter one provides literature review for peristaltic mechanism under different aspects. This chapter also consists of fundamental expressions. The peristaltic flow of viscous fluid in a rotating channel is discussed in chapter two.Channel walls are compliant. MHD effect is present. Hall current and Joule heating are taken into account. Convective conditions for heat transfer in the formulation are adopted. Lubrication approach is followed. Axial and secondary velocities are computed and analyzed. Results of this chapter are published in Results in Physics 7 (2016) pp. 2831-2836. Chapter three extends the research work of chapter two for heat and mass transfer. Thermophoresis, chemical reaction heat source/sink and thermal radiation are considered. Exact solutions to resulting problems invoking lubrication approach are established. The axial and secondary velocities and temperature are analyzed. Graphs are sketched for a parametric study for effects of thermophoretic, chemical, non-uniform heat source/sink, radiation and rotation parameters. The findings of this chapter are published in Results in Physics 6 (2016) pp. 1044-1050. Chapter four aims to examine the magnetohydrodynamic (MHD) peristaltic transport of Prandtl fluid in a rotating medium. The channel walls satisfy wall properties. The relevant formulation is made on the basis of long wavelength approximations. Numerical solutions for axial and secondary velocities, temperature and heat transfer coefficient are presented. The contents of this chapter are published in Computers in Biology and Medicine 79 (2016) pp. 215-221. Chapter five examines peristalsis transport of Prandtl fluid in a rotating channel. In fact results of chapter four here are modified for Soret and Dufour effects. The governing equations have been modeled and simplified using lubrication approach. The solution expressions are approximated numerically for the graphical results. The findings of this chapter have been published in Results in Physics 8 (2018) 1291-1300. The purpose of chapter six is twofold. Firstly to explore peristaltic flow of an incompressible Ree-Eyring fluid. Secondly to inspect non--uniform heat source/sink effect. Convective conditions for heat transfer in the formulation are also adopted. Closed form solutions for axial and secondary velocities, pressure rise per wavelength, flow rate due to secondary flow and temperature are obtained by considering small Reynolds number and long wavelength approximation. The results obtained in this chapter are published in Chinese Journal of Physics 55 (2017) pp. 1894-1907. The objective of chapter seven is to analyze peristalsis of Ree-Eyring fluid in a rotating channel. Interest here is covered by three concepts. Firstly to examine the influence of Hall current and ion slip effects. Secondly to examine the influence of heat transfer with viscous and Ohmic dissipation. Thirdly to address the impact of convective conditions. The relevant problems are formulated. Out coming problems through lubrication approach are solved. Attention is focused to the temperature, velocities and heat transfer coefficient. Material of this chapter is submitted for publication in Journal of Theoretical and Applied Mechanics. Chapter eight investigates the peristalsis Couple stress fluid in a non-uniform rotating channel. The generation of fluid temperature due to thermal radiation and non-uniform heat source/sink effects is recorded. The flow and heat transfer are discussed in presence of wall slip conditions. Numerical technique is applied to solve the non-linear system. Attention is focused for the temperature, both axial and secondary velocities, heat transfer coefficient and streamlines. The research presented in this chapter is published in Results in Physics 7 (2017) pp. 2865-2873. Chapter nine is intended to study effects of heat transfer in peristaltic flow when both the system and fluid are rotating. Third grade fluid is taken in convectively heated channel. Nonlinear radiation is discussed. This study is motivated towards investigating the physiological flows in rotating frame. Lubrication approach is adopted for problem formulation. Impact of various emerging physical parameters on the velocity, temperature and heat transfer coefficient is described. Estimated results are discussed in graphical representation. Material of this chapter is published in Canadian Journal of Physics. In thermal engineering processes many researchers have shown that second law of thermodynamics is more efficient in optimizing the system than first law. Since first law of thermodynamics does not determine the fluctuations in energy and only manipulates the accounting of energy. Therefore in chapter ten we analyze the entropy generation on the peristaltic flow of Casson fluid in a symmetric rotating channel. Heat transfer is examined for thermal radiation and viscous dissipation effects. Velocity and thermal slip effects at the channel boundaries are also considered. The fluid parameter, Taylor and Brinkman number, radiation and wall parameters effects on the axial and secondary velocities, temperature and entropy generation are discussed in detail. Main points of the resulting problem have been highlighted. The contents of this chapter are published in Results in Physics 7 (2017) pp. 3668-3677.