Numerical marching techniques for fluid flows with heat transfer

목차 (Table of Contents)

• CONTENTS
• PREFACE = ⅲ
• 1 INTRODUCTION = 1
• 1.1 HISTORICAL BACKGROUND OF MARCHING PROCEDURES = 1
• 1.2 RANGE OF APPLICABILITY OF MARCHING PROCEDURES = 2
• 1.3 STABILITY, CONSISTENCY, AND CONVERGENCE = 3
• 1.4 EXPLICIT AND IMPLICIT DIFFERENCE REPRESENTATIONS = 4
• 1.5 CHOICE OF MESH SIZE = 7
• REFERENCES = 8
• 2 BOUNDARY LAYERS = 11
• 2.1 TWO-DIMENSIONAL BOUNDARY LAYERS = 11
• 2.1.1 Incompressible Constant Property Flow-Velocity Solution = 11
• 2.1.2 Incompressible Constant Property Flow-Temperature Solution = 16
• 2.1.3 Incompressible Constant Property Flow-Heat Transfer Solutmn = 20
• 2.1.4 Compressible Flow-Velocity and Temperature Solutions = 21
• 2.1.5 Compressible Flow-Tonlinear Finite Difference Representation = 28
• 2.1.6 Compressible Flow-Heat Transfer Solution = 29
• 2.2 AXISYMMETRIC BOUNDARY LAYERS = 30
• 2.2.1 Incompressible Constant Property Flow-Velocity Solution = 30
• 2.2.2 Incompressible Constant Property Flow-Temperature Solution = 36
• 2.2.3 Incompressible Constant Property Flow-Heat Transfer Solution = 39
• 2.2.4 Compressible Flow-Velocity and Temperature Solutions = 39
• 2.2.5 Compressible Flow-Heat Transfer Solution = 48
• 2.3 OTHER PROBLEMS WITH A SIMILAR FORMULATION = 48
• 2.3.1 Wake Behind a Flat Plate = 48
• 2.3.2 Two-Dimensional or Axisymmetric Body With Suction or Injection at the Surface = 50
• 2.3.3 Tangential Jet Adjacent to a Wall = 50
• 2.3.4 Boundary Layer Flows With Body Forces (MHD,EHD, etc.) = 51
• 2.4 EXAMPLE PROBLEM-FLAT PLATE BOUNDARY LAYER = 52
• REFERENCES = 55
• 3 JETS = 57
• 3.1 PLANE JETS = 57
• 3.1.1 Incompressible Constant Property Flow-Velocity Solution = 57
• 3.1.1.1 Highly implicit difference representation valid/or small secondary velocities = 59
• 3.1.1.2 Implicit formulation valid only for large secondary velocities = 63
• 3.1.2 Incompressible Constant Property Flow-Temperature Solution = 65
• 3.1.3 Compressible Flow-Velocity and Temperature Soluions = 67
• 3.1.3.1 Highly implicit representation, valid for small secondary velocities = 69
• 3.1.3.2 Implicit representation valid only for large secondary velocities = 73
• 3.2 AXISYMMETRIC JETS = 77
• 3.2.1 Incompressible Constant Property Flow-Velocity Solution = 77
• 3.2.1.1 Highly implicit difference representation valid for small secondary velocities = 78
• 3.2.1.2 Implicit difference representation valid only for large secondary velocities = 82
• 3.2.2 Incompressible Constant Property Flow-Temperature Solution = 84
• 3.2.3 Compressible Flow-Velocity and Temperature Solutions = 87
• 3.2.3.1 Highly implicit difference representation valid for small secondary velocities = 89
• 3.2.3.2 Implicit difference representation valid only for large secondary velocities = 94
• 3.3 OTHER PROBLEMS WITH A SIMILAR FORMULATION = 99
• 3.3.1 Jets With Bodv Forces = 99
• 3.3.2 Jet Mixing When Primary and Secondary Streams Are Different Compressible Fluids = 99
• 3.4 EXAMPLE PROBLEM-TWO-DIMENSIONAL JET = 111
• REFERENCES = 114
• 4 FREE CONVECTION = 115
• 4.1 FLOW ON A VERTICAL HEATED PLATE = 115
• 4.1.1 Velocity and Temperature Solutions = 115
• 4.1.2 Heat Transfer Solution = 121
• 4.2 OTHER PROBLEMS WITH SIMILAR FORMULATION = 122
• 4.2.1 Combined Free and Forced Convection on a Vertical Heated Plate = 122
• 4.2.2 Free Convection With Wall Temperature or Wall Heat Flux a Function of Position = 123
• 4.2.3 Free Convection With MHD or EHD Body Forces = 126
• 4.3 EXAMPLE PROBLEM-FREE CONVECTION FROM A HEATED VERTICAL PLATE = 126
• REFERENCES = 128
• 5 TIME DEPENDENT BOUNDARY LAYERS = 129
• 5.1 PLANE TRANSIENT BOUNDARY LAYER = 129
• 5.1.1 Incompressible Flow-Velocity Solution = 129
• 5.1.1.1 Explicit representation = 131
• 5.1.1.2 Implicit representation = 133
• 5.1.2 Incompressible Flow-Temperature Solution = 135
• 5.1.2.1 Explicit representation = 137
• 5.1.2.2 Implicit representation = 138
• 5.1.3 Incompressible Flow-Heat Transfer Solution = 140
• 5.1.4 Compressible Flow-Velocity and Temperature Solutions = 140
• 5.1.5 Compressible Flow-Heat Transfer Solution = 148
• 5.2 OTHER PROBLEMS WITH SIMILAR FORMULATIONS = 148
• 5.3 EXAMPLE PROBLEM-OSCILLATING BOUNDARY LAYER ON A FLAT PLATE = 149
• REFERENCES = 151
• 6 PARALLEL PLATE CHANNEL = 153
• 6.1 ENTRANCE FLOW AND HEAT TRANSFER IN A PARALLEL PLATE CHANNEL = 153
• 6.1.1 Incompressible Constant Property Flow-Velocity Solution = 153
• 6.1.2 Incompressible Constant Property Flow-Temperature Solution = 160
• 6.1.3 Incompressible Constant Property Flow-Heal Transfer Solution = 165
• 6.1.4 Compressible Flow-Velocity and Temperature Solutions = 167
• 6.1.5 Compressible Flow-Heat Transfer Solution = 178
• 6.2 OTHER PROBLEMS WITH A SIMILAR FORMULATION = 181
• 6.2.1 Flow in Parallel Plate Channels With Porous Walls = 181
• 6.2.2 Developing Confined Free Convection Flow Between Parallel Plates = 185
• 6.2.3 Flow in a Parallel Plate Channel With Body Forces = 191
• 6.3 EXAMPLE PROBLEM - INCOMPRESSIBLE ENTRANCE FLOW IN A PARALLEL PLATE CHANNEL = 191
• REFERENCES = 194
• 7 CIRCULAR TUBE = 195
• 7.1 ENTRANCE FLOW AND HEAT TRANSFER IN A CIRCULAR TUBE = 195
• 7.1.1 Incompressible Constant Property Flow-Velocity Solution = 196
• 7.1.2 Incompressible Constant Property Flow-Temperature Solution = 202
• 7.1.3 Incompressible Constant Property Flow-Heat Transfer Solution = 206
• 7.1.4 Compressible Flow-Velocity and Temperature Solutions = 208
• 7.1.5 Compressible Flow-Heat Transfer Solution = 219
• 7.2 OTHER PROBLEMS WITH A SIMILAR FORMULATION = 221
• 7.2.1 Flow in Circular Tubes With Porous Walls = 221
• 7.2.2 Developing Confined Free Convection Flow in a Circular Tube = 225
• 7.2.3 Flow in a Circular Tube With Body Forces = 228
• 7.2.4 Entrance Flow and Heat Transfer in a Concentric Annulus = 228
• 7.2.4.1 Incompressible constant property flow-velocity solution = 228
• 7.2.4.2 Incompressible constant property flow-temperature solution = 231
• 7.2.4.3 Incompressible constant property flow-heat transfer = 233
• 7.3 EXAMPLE PROBLEM-INCOMPRESSIBLE FLOW IN THE ENTRANCE REGION OF A CIRCULAR TUBE = 235
• REFERENCES = 240
• 8 RECTANGULAR CHANNEL = 241
• 8.1 ENTRANCE FLOW AND HEAT TRANSFER IN A RECTANGULAR CHANNEL = 241
• 8.1.1 Incompressible Constant Property Flow-Velocity Solution-First Model = 242
• 8.1.2 Incompressible Constant Property Flow-Velocity Solution-Second Model = 252
• 8.1.3 Incompressible Constant Property Flow-Temperature and Heat Transfer Solutions = 255
• 8.1.3.1 Case 1-constant wall temperature = 257
• 8.1.3.2 Case 2-constant heat input per unit length, uniform peripheral temperature = 260
• 8.1.3.3 Case 3-constant heat input per unit area of duct surface = 264
• 8.1.4 Compressible Flow in the Entrance of a Rectangular Channel-Proposed Velocity and Temperature Solutions = 266
• 8.2 OTHER PROBLEMS WITH A SIMILAR FORMULATION = 271
• 8.2.1 Flow in Rectangular Channels With Porous Walls = 271
• 8.2.2 Entrance Flow in Channels With Cross Sections Composed of Rectangular Elements = 273
• 8.2.3 Flow With Body Forces in Rectangular Channels = 273
• 8.2.4 Confined Free Convection in a Vertical Rectangular Channel = 274
• 8.3 EXAMPLE PROBLEM-LAMINAR INCOMPRESSIBLE ENTRANCE FLOW IN A SQUARE DUCT = 276
• REFERENCES = 282
• 9 OTHER NONCIRCULAR AND VARYING AREA CHANNELS = 283
• 9.1 NONCIRCULAR CHANNELS OF CONSTANT AREA = 283
• 9.1.1 Alternating Direction Implicit (ADI) Techniques = 284
• 9.1.2 Irregular Boundaries = 287
• 9.1.3 Normal Gradient Boundary Conditions = 289
• 9.1.4 General Remarks = 290
• 9.2 CHANNELS OF VARYING CROSS-SECTIONAL AREA = 290
• 9.3 EXAMPLE PROBLEM-COMPRESSIBLE FLOW IN VARYING AREA CHANNELS = 293
• REFERENCES = 299
• APPENDIXES
• A SOLUTION FOR A SET OF LINEAR ALGEBRAIC EQUATIONS HAVING A TRIDIAGONAL MATRIX OF COEFFICIENTS = 301
• B FINITE DIFFERENCE REPRESENTATIONS, TRUNATION ERROR ANALYSIS, AND STABILITY ANALYSIS = 307
• B.1 FINITE DIFFERENCE REPRESENTATIONS = 307
• B.2 TRUNCATION ERROR AND A SAMPLE TRUNCATION ERROR ANALYSIS = 311
• B.3 GENERAL METHOD OF STABILITY ANALYSIS = 312
• B.4 SAMPLE STABILITY ANALYSIS = 316
• C ANALYSIS AND CORRECTION OF INHERENT ERROR IN FLOW RATE FOR CONFINED FLOW PROBLEMS IN CHANNELS OF CONSTANT AREA = 323
• D VARIABLE MESH SIZE TECHNIQUE = 329
• E GAUSS-JORDAN ELIMINATION ROUTINE = 333
• F SPECIFICATION OF TRANSVERSE VELOCITIES AT LEADING EDGES AND CHANNEL ENTRANCES = 337