An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications

Since its introduction in the 1980\u27s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender\u27s delta-perturbation method

Numerical and experimental investigations of the acoustic standing wave resonator, pump, and micropump

The interactions of acoustic waves and thermoviscous fluids in closed cavities lead to some important physical phenomena such as, linear and nonlinear acoustic standing waves, and acoustic streaming which are very important in a wide range of engineering applications. The present dissertation is focused on the detailed investigation of standing wave dynamics in closed cavities. As a part of this research, novel numerical and experimental techniques are developed to analyze different phenomena caused by acoustic-fluid interaction. Using these techniques, the behavior of pressure, acoustic and streaming velocity fields inside the standing wave resonator, as well as the valveless acoustic pump and micropump are investigated. A new sixth-order accurate compact finite difference method for solving the Helmholtz equation with Neumann boundary conditions is developed. This scheme showed a better performance at higher wave numbers than the finite element method. A new fourth-order numerical scheme is also developed for solving highly nonlinear standing wave equations with no restriction on nonlinearity level and type of fluid. For highly nonlinear waves, the simulation results show the presence of a wavefront that travels along the resonator with very high pressure and velocity gradients. The slopes of the traveling velocity and pressure gradients, and the asymmetry in the pressure waveform are higher for CO 2 than those for air. The spatial and temporal variations of the nonlinear pressure and particle velocity fields inside a resonator are experimentally investigated at different frequencies and intensities. The effects of the excitation frequency and displacement on the streaming structure are also studied. It is found that, the classical streaming is not developed for Re s 1 50. Acoustic streaming patterns are also found to be significantly affected by transverse temperature gradient. A valveless acoustic standing wave pump is developed and the velocity fields inside this novel pump are analyzed. It is found that, the net flow rate of the pump increases with an increase in the pressure amplitude. The behavior of a novel acoustic micropump is also studied at a high frequency. The effect of the diffuser geometry on the pump performance is investigated. The results show that the maximum diffuser efficiency is achieved at the diffuser-nozzle element's half-angle of approximately 45

Advanced Topics in Mass Transfer

This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics

Proceedings of the First International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics

1st International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Kruger Park, 8-10 April 2002.This lecture is a principle-based review of a growing body of fundamental work stimulated by multiple opportunities to optimize geometric form (shape, structure, configuration, rhythm, topology, architecture, geography) in systems for heat and fluid flow. Currents flow against resistances, and by generating entropy (irreversibility) they force the system global performance to levels lower than the theoretical limit. The system design is destined to remain imperfect because of constraints (finite sizes, costs, times). Improvements can be achieved by properly balancing the resistances, i.e., by spreading the imperfections through the system. Optimal spreading means to endow the system with geometric form. The system construction springs out of the constrained maximization of global performance. This 'constructal' design principle is reviewed by highlighting applications from heat transfer engineering. Several examples illustrate the optimized internal structure of convection cooled packages of electronics. The origin of optimal geometric features lies in the global effort to use every volume element to the maximum, i.e., to pack the element not only with the most heat generating components, but also with the most flow, in such a way that every fluid packet is effectively engaged in cooling. In flows that connect a point to a volume or an area, the resulting structure is a tree with high conductivity branches and low-conductivity interstices.tm201

Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Numerical and Analytical Methods in Electromagnetics

Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics

Proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress

Published proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress, hosted by York University, 27-30 May 2018