Study of Peristaltic Transport of Dusty Fluids

Abstract

Dusty fluids are important due to their involvement and application in the environmental sciences, engineering and physical sciences. Examples of such fluids in different fields are fallouts of pollutants in air, mixture of micro molecules of fibers exclusions in paper making, ignition and impulsion in rockets, polluted water, many juice products with pulp, paints with different suspensions, impurified crude oil etc. Many industries also utilize peristaltic pumps at different situations while processing and dealing with such fluids. This dissertation focuses on the flow of dusty fluid flowing through different geometries such as symmetric channel, asymmetric channel, curved channel and tube. These channels are considered to be exhibiting peristaltic manner. Different body forces like MHD and porosity have been added to the momentum equation, to study the dusty fluid impact in different situations. Heat transfer analysis has also been investigated. A system of coupled equations for both fluid and solid particles are derived for each case. These equations are non-linear in nature thus stream function conversions have been taken into account. Different boundary conditions such as slip condition, no slip condition, wall properties have been employed for distinct situation. Regular perturbation technique has been implemented to get the solutions. Graphical representation of the results is included to demonstrate the solutions. Chapter one includes the basic definitions, laws and dimensionless numbers that have been used in this research. A brief literature review is also part of this chapter to give an insight to the concept of peristalsis and the related researches that have been done. vii Chapter two includes effect of wall properties on the dusty Walter’s B fluid model flowing through a symmetric passage. The results of the coupled equations are obtained by employing perturbation technique. The concluded outcomes are shown graphically. Impact of parameters on velocity, streamline patterns and flow rate are exhibited through graphs. This study can help researchers to understand the elastic properties of paints, polymers and molten plastic. The results obtained in this study are issued in the Journal of Brazilian Society of Mechanical Sciences and Engineering (2018) 40:368. Chapter three is about the second-grade dusty fluid flowing through an asymmetric porous channel. The coupled equations are modelled. Regular perturbation method has been imposed to the system of equations to get the solutions. Streamline patterns and pressure rise graphs are found to demonstrate the influence of distinct parameters. Outcomes of this study are publication in the Journal of Porous Media (2020) 23(9):883. Chapter four deals with the dusty Jeffrey fluid flowing past a symmetric passage under the influence of wall properties. The wave number in this study has been taken small, therefore the impact of both relaxation and retardation times are involved. In past, no effort is made to study the Jeffrey fluid with retardation time. Regular perturbation technique has been adopted to get the results for fluid and solid particles. Flow rate streamline patterns and velocity graphs are included to show the impact of different parameters. The results of this study are submitted in Arabian Journal for Science and Engineering. Chapter five is the extension of chapter two. The motivation of this study is to investigate the MHD impact on the dusty Walter’s B fluid model flowing through an viii inclined asymmetric channel. The impact of heat transfer on such fluid has also been examined. DSolver command in Mathematica has been used to get the results and has been demonstrated graphically. Influence of distinct parameters on velocity and pressure are shown through graphs. The results of research are published in Arabian Journal for Science and Engineering 44(9), 7799 – 7808 (2019). Chapter six is about the dusty second-grade fluid flowing past a tube. The tube is considered to be symmetric. Coupled equations have been solved by using build-in command DSolver in Mathematica. Influence of diverse parameters on the velocity, pressure rise, pressure gradient and streamline patterns have been shown. The outcomes of this research are published in Journal of Mechanical Engineering Research 11(2), 11 – 25 (2020). Chapter seven deals with the study of dusty fluid with variable density of dust particles. Till date, no research study has been conducted in which the dust particles’ number density is varying or not a constant. This research is conducted to note the behavior of dusty fluid with variable number density. The calculations of the coupled equations have been demonstrated through graphs. Slip condition is imposed to the boundaries to note down their behavior too. Streamline patterns and velocity graphs are included to validate the influence of parameters on such fluid. This research is accepted to be published in Arabian Journal for Science and Engineering (2020). Chapter eight deals with the dusty fluid flowing through an endoscope. No effort has been made till now, to observe the flow of dusty fluid in such situation. An initial insight has been obtained by using long wavelength approximation. The obtained results are illustrated through graphs. Velocity, pressure rise and streamline patterns ix graphs are included to show the effect of different parameters involved. This research study is accepted for publication in SN Applied Sciences. Chapter nine is about dusty second-grade fluid flowing through a curved asymmetric channel. In previously available research articles, no attempt has been made to study such fluid in a curved channel. This research can be helpful to know the behavior of dusty fluid flowing through the curved channel as many glandular ducts, tubes are curved in nature. The results are shown through graphs. Velocity and contour graphs show the effect of involved parameters. The outcomes of this study are submitted in Archive of Applied Mechanics.