Fundamentals of Dimensional Analysis - Theory and Applications in Metallurgy

• Main Author: Conejo, Alberto N
• Format: eBook
• Language: English
• Published: Singapore Springer Nature 2021; Springer; Springer Singapore
• Edition: 1
• Subjects: Applications of Mathematics; Classical Mechanics; Dimensional analysis; Engineering; General References; Materials Science; Metals & Metallurgy; Structural Materials
• ISBN: 9789811616013; 9811616019
• DOI: 10.1007/978-981-16-1602-0

This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowled...

Table of Contents:

• Title Page Preface Table of Contents 1. Introduction 2. Origin and Historic Evolution of Dimensional Analysis 3. Units, Dimensions and Dimensional Homogeneity 4. Dimensionless Numbers 5. Rayleigh's Method 6. Buckingham's π Theorem 7. Step by Step Method (Ipsen's Method) 8. Matrix Method 9. Inspection Method 10. Engineering Problems with and without Experimental Data 11. Applications of Dimensional Analysis in Metallurgy 12. Scaling and Similarity 13. Non-Dimensionalization of Differential Equations Epilogue
• Intro -- Preface -- Contents -- About the Author -- 1 Introduction -- 1.1 Nature Is Dimensionless -- 1.2 Advantages and Disadvantages of Dimensional Analysis -- References -- 2 Origin and Historic Evolution of Dimensional Analysis -- 2.1 Origins of Dimensional Analysis -- 2.2 Historic Evolution of Dimensional Analysis -- References -- 3 Units, Dimensions and Dimensional Homogeneity -- 3.1 Units -- 3.1.1 Origin and Evolution of Units -- 3.1.2 Metric System, Base Units and SI -- 3.1.3 New Developments on the Definition of Units -- 3.1.4 Previous Systems of Units -- 3.1.5 Derived Units -- 3.2 Dimensions -- 3.3 Principle of Dimensional Homogeneity -- 3.3.1 Derivation of the Principle of Dimensional Homogeneity [16, 17] -- References -- 4 Dimensionless Numbers -- 4.1 Concept of a Dimensionless Number -- 4.2 Common Dimensionless Numbers -- References -- 5 Rayleigh's Method -- 5.1 John William Strutt [1-4] -- 5.2 Rayleigh's Method -- 5.3 Examples of Application of Rayleigh's Method -- References -- 6 Buckingham's π Theorem -- 6.1 Edgar Buckingham -- 6.2 General π-Theorem -- 6.3 Examples of Application of π-Theorem -- References -- 7 Step by Step Method (Ipsen's Method) -- 7.1 Step by Step Method -- 7.2 Examples of Application of the Step by Step Method -- References -- 8 Matrix Method -- 8.1 Matrix Algebra -- 8.2 Matrix Method -- 8.3 Examples of Application of Matrix Method -- References -- 9 Inspection Method -- 9.1 Inspection Method -- 9.2 Examples of Application of the Inspection Method -- Reference -- 10 Engineering Problems with and without Experimental Data -- 10.1 General Engineering Problems with and without Experimental Data -- 10.1.1 Bubble Shape Dynamics Rising in a Liquid -- 10.1.2 Motion of Non-Metallic Inclusions in Liquid Metals -- 10.1.3 Thermal Stresses in Continuous Casting -- 10.1.4 Mass Transfer Coefficient Under Natural Convection
• 13.2 Scaling Differential Equations -- 13.3 How to Decrease the Number of Dimensionless Groups -- 13.4 Discriminated Dimensional Analysis (DDA) -- References -- Epilogue
• 10.1.5 Blast Furnace Raceway Dimensions -- 10.2 Engineering Problems with Experimental Data -- 10.2.1 Deformation of an Elastic Ball Striking a Wall -- 10.2.2 Pressure Drop of a Fluid in a Long Circular Pipe -- References -- 11 Applications of Dimensional Analysis in Metallurgy -- 11.1 Slag Foaming -- 11.1.1 Introduction to the Problem -- 11.1.2 Experimental Data on Foaming Index from Fruehan et al.: [1-9] -- 11.1.3 Experimental Data Including the Effect of Bubble Diameter from Fruehan et al. [4, 5] -- 11.1.4 Experimental Data Including the Effect of Bubble Diameter from Ghag et al. [16, 17] -- 11.1.5 Experimental Database from Pilon et al. [18-22] -- 11.2 Slag Open Eye Area -- 11.2.1 Introduction to the Problem -- 11.2.2 Experimental Data from Yonezawa and Schwerdtfeger [24] -- 11.2.3 Experimental Data from Peranandhanthan and Mazumdar [25] -- 11.2.4 Ladle Eye as a Function of Nozzle Radial Position -- 11.3 Mixing Time in the Ladle Furnace -- 11.3.1 Experimental Data from Pan et al. [32] -- 11.3.2 Experimental Data from Mandal and Mazumdar [33, 34] -- 11.4 Entrainment of Iron Droplets at Liquid/Liquid Interfaces Due to Rising Gas Bubbles -- 11.5 Tundish Open Slag Eye (TOSE) -- 11.6 Liquid Steel Discharge from a Ladle to the Tundish Using a Protective Shroud [57-62] -- 11.7 Teeming of Liquid Steel -- 11.7.1 Experimental Work from Kuwana [65] -- 11.7.2 Experimental Work from Kamaraj et al. [66] -- 11.8 Rate of Consumption of Mold Fluxes -- 11.9 Penetration of a High-Velocity Gas Jet Through a Liquid Surface -- References -- 12 Scaling and Similarity -- 12.1 Introduction -- 12.2 Similarity Criteria -- 12.2.1 Geometric Similarity -- 12.2.2 Materials Similarity -- 12.2.3 Mechanical Similarity -- 12.2.4 Thermal Similarity -- 12.2.5 Chemical Similarity -- References -- 13 Non-dimensionalization of Differential Equations -- 13.1 Introduction