Overview
- Provides a complement to the author’s earlier book, “Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists”
- Goes beyond the traditional Pi Theorem method to apply dimensional analysis to gas dynamics and thermal hydraulics, in addition to both laminar and turbulent fluids
- Includes specific examples demonstrating how dimensional analysis can shed light on applications of various Heat and Mass Transfer problems
- Includes supplementary material: sn.pub/extras
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable.
A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers.
In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials.
Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Dimensional Analysis Beyond the Pi Theorem
Authors: Bahman Zohuri
DOI: https://doi.org/10.1007/978-3-319-45726-0
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2017
Hardcover ISBN: 978-3-319-45725-3Published: 09 December 2016
Softcover ISBN: 978-3-319-83359-0Published: 28 June 2018
eBook ISBN: 978-3-319-45726-0Published: 02 November 2016
Edition Number: 1
Number of Pages: XIX, 266
Number of Illustrations: 42 b/w illustrations, 36 illustrations in colour
Topics: Mathematical and Computational Engineering, Engineering Thermodynamics, Heat and Mass Transfer, Engineering Fluid Dynamics