Cover -- Half Title Page -- Title Page -- Copyright -- Contents -- About the Cover Image -- Foreword -- Preface -- Acknowledgements -- Notation -- 1. Essentials of Continuum Framework -- Introduction -- 1.1 Measurements of the Continuum Field -- 1.2 Geometric Interpretation of Vectors -- 1.3 Algebraic Properties of the Vectors -- 1.3.1 Scalar Multiplication with Vectors -- 1.3.2 Addition of the Vectors -- 1.3.3 Scalar Product of Vectors -- 1.3.4 Cross Product of Vectors -- 1.3.5 Scalar Triple Product -- 1.3.6 Vector Triple Product -- 1.4 Tensors

1.5 Algebraic Properties of Tensor Operations -- 1.5.1 Linearity in Addition -- 1.5.2 Properties of Dyadic -- 1.5.3 Dyadic Product of Vectors -- 1.5.4 Single Index Contraction Products of Dyadic and Vectors -- 1.5.5 Tensor Double Dot Contraction -- 1.5.6 Magnitude of Vectors and Tensors -- 1.6 Eigenvalues and Eigenvectors -- 1.7 Vector Calculus -- 1.7.1 Time Derivative -- 1.7.2 Spatial Derivatives -- 1.7.3 Gradient of the Field Variables -- 1.7.4 Divergence of the Field Variables -- 1.7.5 Curl of the Field Variables -- 1.7.6 The Laplacian of Field Variables -- 1.8 Divergence Theorem

1.9 Stokes' Theorem -- 1.10 Green's Theorem -- 1.11 Leibniz Theorem for Differentiation Under Integral Sign -- 1.12 Closure -- 2. Kinematics of Flow Transport -- Introduction -- 2.1 A Quantitative Measure of the Continuum Hypothesis -- 2.2 The Continuum Density of the Fluid -- 2.3 Representation of the Fluid Motion -- 2.4 Flow Field Visualization -- 2.4.1 Pathlines -- 2.4.2 Streamlines -- 2.4.3 Streaklines -- 2.5 Strains and Deformation in Fluid Flow -- 2.6 The Time Rate of Change Following a Moving Fluid Element -- 2.7 Closure -- 3. Dynamics of Transport Phenomena -- Introduction

3.1 Forces and Stresses in Fluids -- 3.1.1 Long-range/Body Forces -- 3.1.2 Short-range/Surface Forces -- 3.1.3 Line Force in Fluids (Surface Tension -- 3.2 Conservation Laws for Continuum Field Variables -- 3.3 Reynolds Transport Theorem -- 3.4 Conservation of the Mass: Continuity Equation -- 3.5 Conservation of Linear Momentum -- 3.5.1 Pressure Poisson Equation -- 3.5.2 Stream Functions and Velocity Potentials -- 3.5.3 Navier-Stokes Equation in a Rotating Reference Frame -- 3.6 Closure -- 4. Governing Equations for Thermal Energy and Species Transpor -- Introduction

4.1 Recapitulation of Classical Thermodynamics -- 4.1.1 State of the Thermodynamic Systems -- 4.1.2 Concept of Heat and Work -- 4.1.3 The Zeroth Law of Thermodynamics -- 4.1.4 The First Law of Thermodynamics -- 4.1.5 Fluid Compressibility -- 4.1.6 Fluid Specific Heat -- 4.1.7 Directional Nature of the Interconversion: Second Law of Thermodynamics -- 4.1.8 Entropy and the Third Law -- 4.1.9 Free Energy in Thermodynamics -- 4.1.10 Generalized Thermodynamic Relationship -- 4.2 Conservation of Thermal Energy -- 4.3 Conservation Equation for Species Transport -- 4.4 Generic Transport Equation