Laminar Flow Analysis

LAMINAR FLOW ANALYSIS
by
David F. Rogers

TABLE of CONTENTS

Preface		xi
Chapter 1	Derivation of the Navier-Stokes Equations	1
1-1	Introduction	1
1-2	Stress-Rate-of-Strain Relation	7
1-3	Angular Velocity and Fluid Deformation	8
1-4	The Viscosity Coefficients of Fluids	12
1-5	The Momentum Equation	12
1-6	Derivation of the Energy Equation	13
1-7	Boundary Conditions	20
1-8	Equation of State and the Relation of the
	Transport Properties to the State Variables	21
1-9	Special Forms of the Navier-Stokes Equations	21
1-10	Classification	22

Chapter 2	Exact Solutions of the Navier-Stokes Equations	23
2-1	Introduction	23
2-2	Analytical Solutions	23
2-3	Parallel Flow Through a Straight Channel	24
2-4	Couette Flow	26
2-5	The Suddenly Accelerated Plane Wall	28
2-6	Similarity Analysis	31
2-7	Two-dimensional Stagnation Point Flow	35
2-8	Iteration Scheme	40
2-9	Numerical Solution	41
2-10	Axisymmetric Stagnation Point Flow	44

Chapter 3	Boundary Layer Theory	53
3-1	Concept of a Boundary Layer	53
3-2	Derivation of the Boundary Layer Equations	54
3-3	The Flow Past a Flat Plate - Blasius Solution	60
3-4	The General Two-dimensional Incompressible
	Boundary Layer - The Falkner-Skan Equations	65
3-5	Group Properties of the Blasius Equation	69
3-6	Numerical Integration of the Falkner-Skan Equation	70
3-7	Skin Friction, Displacement and Momentum Thickness	77
3-8	Physical Interpretation of the Falkner-Skan Equation	81
3-9	Axisymmetric Boundary Layers -
	The Mangler Transformation	84
3-10	Boundary Layers with Mass Transfer	90
3-11	Nonsimilar Boundary Layers	93
3-12	Locally Nonsimilar Boundary Layer Method	96

Chapter 4	Thermal Layers and Forced Convection Boundary Layers	105
4-1	Introduction	105
4-2	General Characteristics of Thermal Layers	105
4-3	Simple Couette Flow	110
4-4	Nonsimple Couette Flow	115
4-5	Flow in a Channel with Straight Parallel Walls -
	Poiseuille Flow	119
4-6	The Energy Equation for the Boundary Layer	122
4-7	Forced Convection Boundary Layer -
	Parallel Flow Past a Flat Plate	127
4-8	Forced Convection Boundary Layer Flows with
	Pressure Gradient and Nonisothermal
	Surface Conditions	136
4-9	Numerical Integration of the Energy Equation
	for a Forced Convection Boundary Layer	139
4-10	Forced Convection Boundary Layer Flows
	with Mass Transfer	147
4-11	Nonsimilar Forced Convection Boundary Layer	154

Chapter 5	Free Convection Boundary Layers	159
5-1	Introduction	159
5-2	Free Convection Boundary Layers	159
5-3	Numerical Integration of the Free Convection
	Boundary Layer Equations	164
5-4	Results for a Free Convection Boundary Layer
	on an Isothermal Vertical Flat Plate	164
5-5	Results for a Free Convection Boundary Layer
	on a Nonisothermal Vertical Flat Plate	170
5-6	Free Convection Boundary Layer on a Nonisothermal
	Vertical Flat Plate with Mass Transfer	173
5-7	Nonsimilar Free Convection Boundary Layer	178
5-8	Nonsimilar Free Convection Boundary Layer
	with Mass Transfer	182
5-9	Combined Forced and Free Convection Boundary
	Layer Flows on a Nonisothermal Surface	183
5-10	Numerical Integration of the Governing Equations
	for Combined Forced and Free Convection	186
5-11	Nonsimilar Combined Forced and Free Convection
	Boundary Layers	190

Chapter 6	The Compressible Boundary Layer	195
6-1	Introduction	195
6-2	Variation of Transport Properties	195
6-3	Analytical Solutions of the Compressible
	Navier-Stokes Equations - Couette Flow	199
6-4	Compressible Boundary Layer	208
6-5	Transformation of the Compressible
	Boundary Layer Equations	210
6-6	The Low Speed Compressible Boundary Layer	223
6-7	The Compressible Boundary Layer on a Flat Plate	225
6-8	The Similar Compressible Boundary Layer
	with Unit Prandtl Number	230
6-9	The Similar Hypersonic Compressible Boundary
	Layer with Nonunit Prandtl Number	232
6-10	Displacement and Momentum Thickness in a
	Compressible Boundary Layer	234
6-11	Numerical Integration of the Compressible
	Boundary Layer Equations	236
6-12	Results for the Low Speed Compressible
	Boundary Layer	237
6-13	Results for the Compressible Boundary Layer
	with Unit Prandtl Number	241
6-14	Results for the Similar Hypersonic Compressible
	Boundary Layer with Nonunit Prandtl Numbers	257
6-15	The Similar Compressible Boundary Layer
	with Mass Transfer	261
6-16	Results for the Similar Compressible Boundary Layer
	with Mass Transfer	262
6-17	Hypersonic Shock Wave-Boundary Layer Interaction	270
6-18	The Nonsimilar Compressible Boundary Layer	276

	References	283

	Appendix A Runge-Kutta Integration Scheme	289
	Appendix B Satisfaction of Asymptotic Boundary Conditions	299
	Appendix C Numerical Results for the Boundary Layer Flows	321
	Appendix D General Boundary Layer Program	353
	Appendix E Problems	381

	Index	411

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