Charter 1 Introduction.- 2 Dimensional Analysis and the Pi Theorem Units and Dimensions.- 2-1 Units and Dimensions.- 2-2 Types of Quantities Appearing in Physical Equations.- a. Primary and Secondary Quantities.- b. Physical Constants and Independent Dimensions.- c. Nondimensional Quantities.- 2-3 Dimensional Homogeneity of Physical Equations.- 2-4 Statement and Use of the Pi Theorem.- 2-5 Rationale of the Pi Theorem.- 2-6 Huntley’s Addition.- 2-7 Examples of Application of Dimensional Analysis.- 2-8 Summary.- 3 Method of Similitude and Introduction to Fractional Analysis of Overall Equations.- 3-1 Introduction.- 3-2 Method of Similitude.- a. Use of Force Ratios.- b. Generalization of the Method of Similitude.- c. Some Energy Ratios of Heat Transfer.- 3-3 Direct Use of Governing Overall Equations.- 3-4 Concluding Remarks.- 4 Fractional Analysis of Governing Equations and Conditions.- 4-1 Introduction.- 4-2 Normalization of the Governing Equations.- a. A Procedure for Normalization.- b. Meaning of Normalized Governing Equations.- 4-3 Conditions Required for Rigorous Solution of the Canonical Problem of Similitude and Dimensional Analysis Using Normalized Governing Equations.- 4-4 Basis of Improved Correlations.- a. General Basis.- b. Homogeneous Equations.- 4-5 Relations among Elementary Processes.- a. Model Laws, Similitude, and Analogues.- b. An Alternative Procedure.- c. A Remark on Force Ratios.- d. Relation among Dimensional Analysis, Governing Equations, and Boundary Conditions; Internal and External Similarity.- 4-6 Approximation Theory.- a. Extension to New Classes of Information by Approximation Theory.- b. Classification of Problems and Difficulties in Approximation Theory.- c. Conditions Required for Approximation Theory.- 4-7 Some Problems Involving Uniform Behavior.- 4-8 Nonuniform Behavior—Boundary Layer Methods.- a. Use of Physical Data Alone.- b. Zonal Estimates.- 4-9 Nonuniform Behavior—Expansion Methods and Uniformization.- a. Poincaré’s Expansion.- b. Lighthill’s Expansion.- c. WKBJ Expansion.- d. Inner and Outer Expansions.- 4-10 Processes Involving Transformations of Variables.- a. Absorption of Parameters and Natural Coordinates.- b. Supersonic and Transonic Similarity Rules.- c. Reduction in Number of Independent Variables — Separation and Similarity Coordinates 179.- 4-11 Summary and Conclusions.- a. Classification of Types of Similitude—Information Achievable from Fractional Analysis of Governing Equations.- b. Various Viewpoints—Relations among Invariance, Transformations, and Similitude.- c. Final Remarks.- 5 Summary and Comparison of Methods.- 5-1 Introduction.- 5-2 Summary of Methods.- a. The Pi Theorem.- b. The Method of Similitude.- c. Use of Governing Equations.- 5-3 Comparison of Methods.- a. Power.- b. Rigor.- c. Accuracy.- d. Simplicity.- e. Input Information.- 5-4 Concluding Remarks.- a. Utility of Various Methods.- b. Implications in Teaching.- c. Possible Further Development.- d. Final Remark.- References.
