Computational Analysis of Flow and Thermal Characteristics Across Elongating Cylinders Immersed in Newtonian and Non-Newtonian Fluids

Abstract

Boundary layer flows occurring along flat or curved surfaces have been extensively studied in the past, since these are encountered in variety of technical applications. Moreover, fluids treated in many of the engineering applications are non-Newtonian such as managing heat transfer in metal extrusion process, glass manufacturing, polymer processing, coating applications to name a few. This thesis investigates momentum and thermal transport around stretching cylinders immersed in non-Newtonian fluids through various rheological models. Initially, viscoelastic effects are analyzed using the well-known second-grade and Jeffrey models. Then, the Reiner-Rivlin model is investigated, capable of representing the flow behavior of diverse substances, including granular materials. The primary emphasis in these studies is on examining the heat transfer mechanisms influenced by frictional heating, a factor often overlooked in non-Newtonian flow situations. Also, a comparative analysis of how varying physical properties affect heat transfer in a Newtonian fluid-filled annulus between coaxial cylinders is investigated. This problem compares the two viscosity models which are widely adopted in the literature. This study enlightens the impact of gap size between the cylinders on subtle fluid dynamics variables. Preferred computational methods are the MATLAB built-in package bvp4c and Optimal Homotopy Analysis Method (OHAM). The obtained results are subjected to discussions, analysis and physical interpretations to come up with significant conclusions. Firstly, the impacts of partial slip boundary on the viscoelastic motions obeying second grade and Jeffrey models are investigated. Notably, incorporating slip boundary assumption gives a nonlinear Robin-type condition, even after applying boundary layer approximations. Furthermore, the role of viscoelasticity in heat generation through viscous dissipation is preserved. For the second-grade model, the effects of normal stress differences and slip boundary conditions on the flow characteristics around a stretching cylinder are clarified, while the Jeffrey model is employed to analyze the intriguing phenomena of relaxation and retardation times. Secondly, an investigation of the influence of Darcy-Forchheimer porous space on second-grade fluid motion with coupled heat and mass transport over an elongating cylinder is made. In this problem, the aspects of non-uniform heat source/sink as well as Soret effect are accounted in the transport equations. Acknowledging the importance of stagnation-point flows in diverse engineering applications, this thesis utilizes the Reiner-Rivlin model to investigate a non-Newtonian stagnation-point flow over an elongating cylinder, considering the influence of both heat and mass transfer. It includes the dissipation effects, heat source/sink and chemical reactions. The results show that the Reiner-Rivlin fluid properties, combined with viscous dissipation, Soret effects, heat source/sink and entropy generation affect both flow and thermal characteristics. The study investigates the generation of entropy in the flow induced over the cylinder by presenting graphical results of the entropy production rate. Additionally, it explores the Bejan number, which offers an intriguing comparison between entropy generated through heat transfer and that arising from viscous dissipation. The research further explores flow within an annular region formed by stretching of inner cylinder and an outer stationary cylinder, incorporating variable physical properties. Building on the approach from a previous study, a set of transformations is introduced to develop a model that assesses the impact of changing gap size on the velocity and temperature fields. Two distinct models of variable viscosity are employed for computational analysis, allowing for a comprehensive examination of how variable fluid properties influence flow characteristics between cylinders.