David F. Rogers

Preface xi
Chapter 1 Derivation of the Navier-Stokes Equations1
1-2Stress-Rate-of-Strain Relation7
1-3Angular Velocity and Fluid Deformation8
1-4The Viscosity Coefficients of Fluids12
1-5The Momentum Equation12
1-6Derivation of the Energy Equation13
1-7Boundary Conditions20
1-8Equation of State and the Relation of the 
     Transport Properties to the State Variables21
1-9Special Forms of the Navier-Stokes Equations21
Chapter 2  Exact Solutions of the Navier-Stokes Equations23
2-2Analytical Solutions23
2-3Parallel Flow Through a Straight Channel24
2-4Couette Flow26
2-5The Suddenly Accelerated Plane Wall28
2-6Similarity Analysis31
2-7Two-dimensional Stagnation Point Flow35
2-8Iteration Scheme40
2-9Numerical Solution41
2-10Axisymmetric Stagnation Point Flow44
Chapter 3  Boundary Layer Theory53
3-1Concept of a Boundary Layer53
3-2Derivation of the Boundary Layer Equations54
3-3The Flow Past a Flat Plate - Blasius Solution60
3-4The General Two-dimensional Incompressible 
     Boundary Layer - The Falkner-Skan Equations65
3-5Group Properties of the Blasius Equation69
3-6Numerical Integration of the Falkner-Skan Equation70
3-7Skin Friction, Displacement and Momentum Thickness77
3-8Physical Interpretation of the Falkner-Skan Equation81
3-9Axisymmetric Boundary Layers - 
     The Mangler Transformation84
3-10Boundary Layers with Mass Transfer90
3-11Nonsimilar Boundary Layers93
3-12Locally Nonsimilar Boundary Layer Method96
Chapter 4  Thermal Layers and Forced Convection Boundary Layers105
4-2General Characteristics of Thermal Layers105
4-3Simple Couette Flow110
4-4Nonsimple Couette Flow115
4-5Flow in a Channel with Straight Parallel Walls - 
     Poiseuille Flow119
4-6The Energy Equation for the Boundary Layer122
4-7Forced Convection Boundary Layer - 
     Parallel Flow Past a Flat Plate127
4-8Forced Convection Boundary Layer Flows with 
     Pressure Gradient and Nonisothermal 
     Surface Conditions136
4-9Numerical Integration of the Energy Equation 
     for a Forced Convection Boundary Layer139
4-10Forced Convection Boundary Layer Flows 
     with Mass Transfer147
4-11Nonsimilar Forced Convection Boundary Layer154
Chapter 5  Free Convection Boundary Layers159
5-2Free Convection Boundary Layers159
5-3Numerical Integration of the Free Convection 
     Boundary Layer Equations164
5-4Results for a Free Convection Boundary Layer 
     on an Isothermal Vertical Flat Plate164
5-5Results for a Free Convection Boundary Layer 
     on a Nonisothermal Vertical Flat Plate170
5-6Free Convection Boundary Layer on a Nonisothermal 
     Vertical Flat Plate with Mass Transfer173
5-7Nonsimilar Free Convection Boundary Layer178
5-8Nonsimilar Free Convection Boundary Layer 
     with Mass Transfer182
5-9Combined Forced and Free Convection Boundary 
     Layer Flows on a Nonisothermal Surface183
5-10Numerical Integration of the Governing Equations 
     for Combined Forced and Free Convection186
5-11Nonsimilar Combined Forced and Free Convection 
     Boundary Layers190
Chapter 6  The Compressible Boundary Layer195
6-2Variation of Transport Properties195
6-3Analytical Solutions of the Compressible 
     Navier-Stokes Equations - Couette Flow199
6-4Compressible Boundary Layer208
6-5Transformation of the Compressible 
     Boundary Layer Equations210
6-6The Low Speed Compressible Boundary Layer223
6-7The Compressible Boundary Layer on a Flat Plate225
6-8The Similar Compressible Boundary Layer 
     with Unit Prandtl Number230
6-9The Similar Hypersonic Compressible Boundary 
     Layer with Nonunit Prandtl Number232
6-10Displacement and Momentum Thickness in a 
     Compressible Boundary Layer234
6-11Numerical Integration of the Compressible 
     Boundary Layer Equations236
6-12Results for the Low Speed Compressible 
     Boundary Layer237
6-13Results for the Compressible Boundary Layer 
     with Unit Prandtl Number241
6-14Results for the Similar Hypersonic Compressible 
     Boundary Layer with Nonunit Prandtl Numbers257
6-15The Similar Compressible Boundary Layer 
     with Mass Transfer261
6-16Results for the Similar Compressible Boundary Layer 
     with Mass Transfer262
6-17Hypersonic Shock Wave-Boundary Layer Interaction270
6-18The Nonsimilar Compressible Boundary Layer276
  Appendix A    Runge-Kutta Integration Scheme289
  Appendix B    Satisfaction of Asymptotic Boundary Conditions299
  Appendix C    Numerical Results for the Boundary Layer Flows 321
  Appendix D    General Boundary Layer Program353
  Appendix E    Problems381
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