FINITE ELEMENT STUDY OF TRANSPORT PHENOMENA IN COMPLEX FLUIDS

Abstract

The exhaustive knowledge of the dynamics of fluids is necessary due to its innumerable applications in surrounding natural and technical environment. The natural environment means the fluid flow in human body and plants, atmospheric flow and flow in lakes, rivers and seas. On the other hand, in the technical environment, the fluids are used in all technological devices manufactured either inside it or somewhere in its design e.g. different types of machines are lubricated by fluids, all vehicles engine get power through fluids, aeroplane and ships move in fluids. The flow behaviour and attributes of fluids may be simple or complex, but the proper understanding of fluids and their flow characteristics is an essential requirement for handling them properly as these fluids have practical application in several industries such as chemical, food processing, plastic manufacturing, biomathematics, automotive and hydraulic, slider and lubrication bearing, textile and fabrics industries. The simple fluids follow Newton’s law of viscosity. So, these are also called newtonian fluids. In contrast, complex or non-newtonian fluids do not obey this rule. So, these fluids have dissimilarity with simple fluids and have different flow behaviour and properties. The growing prospect of Complex fluids like polymer melts, emulsions and suspensions, molten plastics, lubricants, biological fluids, has attracted the researchers due to their uncounted engineering, science and technological applications such as manufacturing of plastic sheets, textile and fibre processing, lubricants execution, motion of biological fluids and food preparation and preservation. The classification of complex fluids is based on their flow aspect i and these fluids are used according to their applications in relevant industries. It is quite interesting to study the flow behaviour and transport phenomenon of complex fluids over the plane surfaces. The four different type of complex fluids are employed in the present research work namely Power-Law Non-Newtonian Fluid, Eyring Powell Fluid, Viscoelstic Second Grade Fluid, Viscoelstic Third Grade Fluid. The present study aims to contribute to the revealing and concretizing the lack of information about complex fluids with different type of condition imposed on the surfaces under different physical scenario. The Galerkin Finite Element method is used to solve the problems as this method has been so well established now-a-days that it is regarded as one of the best methods for solving a broad variety of practical problems especially Boundary Value Problems. The thesis consists of eight chapters. A brief chapter-wise description of the problems, worked out in the thesis, is presented below. Chapter 1 is the introductory chapter of the thesis, containing some basic fundamentals of fluid dynamics like continuity, momentum and heat transfer fluid flow equations. The basic overview of the complex fluids, employed in the present work, is also described with their specific properties. A brief review of the existing work is summarized. Chapter 2 describes the steady, laminar boundary layer flow of an incompressible Eyring Powell fluid over a horizontal flat permeable plate. The bottom surface of the plate is heated by convection from a hot fluid. A convective surface boundary condition in taken into consideration in order to define thermal boundary condition. The influence of Biot number, Prandtl number, eyring powell fluid parameters and suction/injection parameter on the velocity and temperature profiles is shown graphically. It is observed that as much as eyring powell fluid parameter decreases, the fluid have a tendency to behave as a newtonian fluid. i.e. the fluid can easily flow so when the values of eyring powell fluid parameter decreases, the velocity increases in boundary layer regime. An increase in the Biot number leads to increase in fluid ii temperature. Also, the rate of heat transfer at the surface increases with increasing values of Biot number implies that the heat transfer is enhanced by convection. Chapter 3 deals with the study of free convection MHD boundary layer flow of an incompressible viscoelastic fluid along an inclined moving plate and heat transfer characteristics with prescribed quadratic power-law surface temperature. The numerical results for the dimensionless velocity and temperature profiles are displayed graphically for various physical parameters such as viscoelasticity, Prandtl number, angle of inclination parameter, magnetic and buoyancy parameter. A rise in viscoelastic parameter enhances the velocity in boundary layer regime because viscoelastic parameter causes the decrease in viscosity so velocity increases. It is observed that the fluid velocity decreases with increase in the inclination angle from vertical. This is because inclination angle decreases the effect of the buoyancy force due to the gravity component. As, the buoyancy parameter increases, the rate of heat transfer increases. Chapter 4 presents the oblique stagnation-point flow of an incompressible viscoelastic fluid impinging on an infinite vertical plate and heat transfer characteristics with variable thermal conductivity. The streamline patterns and numerical results for the dimensionless velocity and temperature profiles are displayed graphically for various physical parameters such as Prandtl number, Weissenberg number, thermal conductivity parameter. When orthogonal stagnation point flow is combined with shear flow, the oblique flow is produced. It is observed from the streamline patterns that as a result of oblique flow, the dividing streamline does not change its shape but makes an oblique angle with the wall and the stagnation point of attachment shifts along the wall. The stagnation-point flow describes the fluid motion near the stagnation region. The stagnation region deals with the region of highest temperature. Chapter 5 is based on an unsteady boundary layer flow of laminar, free convective, incompressible third-grade fluid past an infinite vertical porous plate with the iii temperature dependent fluid properties by taking into account the effect of viscous dissipation. The results demonstrating the effects of various pertinent parameters like Grashof number, Prandtl number, Eckert number, third grade parameters, viscosity variation parameter, thermal conductivity variation parameter on dimensionless velocity and temperature distributions are studied in detailed through graphs and tables. It is found that the velocity of fluid increases with the increasing values of third-grade parameter and viscosity variation parameter because both of the parameter reduces the viscosity. On increasing the values of thermal conductivity variation parameter, the velocity increase correspondingly since thermal conductivity variation parameter enhances the thermal conductivity. Chapter 6 demonstrates the phenomena of the heat and mass transfer in an unsteady boundary layer flow of an incompressible, laminar, natural convective thirdgrade fluid. The flow is taken over a semi-infinite vertical porous plate with the temperature dependent fluid properties by taking into account the effect of variable suction. The effect of various significant parameters such as Grashof number, Prandtl number, Eckert number, Solutal Grashof number and Schmidt number on dimensionless velocity, temperature and concentration profiles is presented graphically. It is observed that velocity increases with the increasing values of Grashof number. As Grashof number increases, the viscous force i.e. restraining force due to viscosity of the fluid decreases. Hence the velocity of the fluid increases with increasing Grashof number. It is found that the Nusselt number is the the decreasing function of Prandtl number. Chapter 7 describes the laminar steady boundary layer flow of an incompressible MHD Power-Law fluid past a continuously moving surface. The study involves the influence of surface slip and non-uniform heat source/sink on the flow and heat transfer. The impact of different involved physical parameters is exhibited on the dimensionless velocity profile, temperature distributions and rate of heat transfer in form of graphical and tabular presentation for Pseudo-plastic and Dilatant fluids iv both. It is observed that the fluid temperature as well as rate of heat transfer increases due to the presence of the heat source in the boundary layer as the heat source generates energy. The presence of heat sink causes the temperature fall as well as reduction in rate of heat transfer in the boundary layer as the energy is absorbed during the heat sink effect. The heat sources are used to heat up the system whereas the heat sinks are used to cool down the system. In chapter 8, the two-dimensional laminar steady incompressible natural convection flow and heat transfer under the influence of magnetic field is examined in a tilted rectangular enclosure filled with non-newtonian power-law fluid. The left wall of enclosure is subjected to spatially varying sinusoidal temperature distribution and right wall is cooled isothermally while the upper and lower walls are retained to be adiabatic. The exhaustive flow pattern and temperature fields are displayed through streamlines and isotherm contours for various parameters namely Prandtl Number, Rayleigh Number, Hartmann Number by considering different power-law index, inclination angle and aspect ratio. The study results the potential vortex flow with elliptical core. As the inclination angle increases, the intensity of the flow field decreases due to the strengthening of the buoyancy forces. It is observed that the circulation strength decreases when the aspect ratio is increased. This happens due to the reduction in flow circulation area. The thesis ends with a brief discussion on the scope for further work, Appendix A providing closer insight to incorporated numerical technique Galerkin Finite Element Method and bibliography