On peristaltic activity in channels

Abstract

Phenomenon of peristalsis coordinating rhythmic contraction and relaxation of esophageal muscle is used in transport of food bolus in digestive tract. Human body involves peristalsis for the transfusion of blood via pumping, transport of ovum in fallopian tube and vasomotion of small blood vessels such as arterioles, capillaries and venules. Locomotion in living organisms such as earthworms, transport of corrosive fluid, sanitary fluid transport and blood transport in an open heart surgery are few industrial examples of peristaltic pumping. Such technique is very useful in transportation of nuclear material where contamination and applied stresses may be avoided at every cost. It is noted that peristaltic applications found in industries are carried out in a straight channel. However to capture the real effect of peristalsis in human body and transportation of biofluid in other living organisms, one should assume curved channel as blood vessels in such organisms are not straight. For this purpose, curvilinear coordinates are more appropriate choice. For arteries and gastrointestinal tract, endoscope refers to a flexible tube with an attached camera. This instrument allows examination of internal human organs, injuries, biopsy and targeted drug delivery without surgery. Such applications may be interest to researchers for peristaltic flow with an endoscope. Many applications are analyzed when the channel rotates. Rotation is largely used in study of stellar dynamics, ocean circulation, flight dynamics and geophysics. Peristaltic transport in the presence of rotation is seen in arterioles, intestines and ureters. This thesis studies peristaltic phenomenon with compliant channel walls. Compliance in channel specifies the change in volume subjected to varying pressure. In fluid flow problems this impact is involved via spring stiffness, elasticity and damping of peristaltic walls. The objective of this thesis is to capture the peristaltic phenomenon in different geometries. To capture a more realistic approach to real applications, the heat and mass transfer phenomena are also involved. Explicitly this thesis is structured as follows: Fundamental expressions and review literature are presented in chapter one. Chapter two examines peristaltic activity in a symmetric channel. Fluid saturates porous medium. Sutterby fluid under the impact of magnetohydrodynamics is considered. Modified Darcy’s law is used to capture porous medium effect. Thermal field of problem is subject to dissipation and Joule heating. Convective heat and mass transfer conditions are utilized. Channel walls are compliant in nature. . The relevant observations are published in Results in Physics 7 (2017) 762-768. Chapter three aims to analyze the impact of porosity in the presence of Soret and Dufour effects. An incompressible Williamson fluid is considered. Effect of magnetic field is also retained. Boundary conditions are set so that slip effects are not ignored. Lubrication approach is used to simplify the problem. The contents of this chapter are published in Results in Physics 10 (2018) 751-759. Chapter four investigates peristaltic activity of Sutterby fluid in an inclined channel. Walls of channel are compliant. Energy equation is studied with Joule heating and radiation. Soret and Dufour effects are also considered. The problem is simplified by applying long wavelength and low Reynolds number. NDSolve is employed for computation. Material of this chapter are published in Journal of Thermal Science and Engineering Applications 10 (2018) DOI: 10.1115/1.4038564. Chapter five examines buoyancy effect on peristalsis of Johnson-Segalman fluid in an inclined geometry. MHD is employed along with Hall current and radiation. Flexible channel walls are considered. Furthermore slip effect is not ignored. Results are found via numerical technique. The contents of this chapter are published in Results in Physics 233 (2017) 131-138. Purpose of chapter six is to model the peristaltic flow of Ellis fluid in curved channel. Comparison between curved and planar channels is also made. The channel boundaries satisfy convective conditions of heat and mass transfer. The problem formulation is developed for radially imposed magnetic field and mixed convection. Further the analysis includes thermal radiation and chemical reaction aspects. Perturbation technique is used to obtain solutions for obtained system of equations. The contents of this chapter are submitted to AIP Advances. Chapter seven investigates homogeneous-heterogeneous reactions on peristaltic flow of Ellis fluid in a curved configuration. MHD and porous medium effects are taken. Flow properties are discussed subject to viscous dissipation. Compliance of channel walls is considered. Solutions are obtained for variables of interest. Main conclusions are presented. Observations of this chapter are published in Results in Physics 9 (2018) 1455-1461. Chapter eight is designed to investigate peristalsis of MHD third grade nanofluid in a curved channel with wall properties. Gravitational and mixed convection are analyzed. Chemical reaction and radiation in energy and concentration expressions are included. No-slip effect for velocity, temperature and nanoparticle volume fraction is studied. The nonlinear, coupled system is solved by using lubrication approach. The contents of this chapter are published in Results in Physics 7 (2017) 3687-3695. Chapter nine addresses channel flow of Ree-Eyring nanofluid of variable viscosity in a curved channel. Flow problem is studied under the impact of viscous dissipation and chemical reaction. Keeping in mind the blood circulatory system in living organisms the compliance of channel walls is also considered. Buongiorno model is implied to capture nanofluid aspect. Velocity, temperature, heat transfer rate and nanoparticle concentration are discussed. The conclusions of this chapter have been submitted to Brazlian Society of Mechanical Sciences. In Chapter ten the flow problem of couple-stress fluid is elaborated in the presence of homogeneous-heterogeneous reactions. Effectiveness of buoyancy is executed via mixed convection. Geometry of channel is curved. Non-linear radiation is involved. Following lubrication approach, the flow problem is solved numerically and streamlines are captured. Results through physical insights are presented. The contents of this chapter are submitted to Int. J. Chemical Reactor Engineering. Chapter eleven explores impacts of thermophoresis and Brownian motion on peristaltic flow problem. Carreau-Yasuda nanofluid is studied in a tubular structure. Energy equation for the given flow problem also includes the impacts of Joule heating, viscous dissipation, nonlinear radiation and heat source/sink. Quantities like velocity, temperature, concentration, heat transfer rate and trapping are addressed. Observations of this chapter are submitted to J. Mechanics. Chapter twelve captures the effect of rotation on peristaltic flow of silver-water nanofluid. Maxwell model is used to explore the impacts of nanoparticles. Convective conditions are employed for heat transfer analysis. Entropy generation phenomena is also discussed. Numerical results are obtained and discussed for velocity, heat transfer, streamlines and entropy generation. These contents are submitted to Physics and Chemistry of Solids.