**Applications of Heat, Mass and Fluid Boundary Layers**

Edited by R.O. Fagbenle, O.M. Amoo, S. Aliu and A. Falana

**Contents**

Preface xvii

Acknowledgments xix

1 Physics of fluid motion 1

O.C. Okoye, B.O. Bolaji

1.1 Introduction 1

1.2 The basic equations of viscous flow 2

1.3 Momentum equation 6

1.4 Velocity slip and temperature jump 19

References 20

2 Mechanisms of heat transfer and boundary layers 23

Sufianu Aliu, O.M. Amoo, Felix Ilesanmi Alao, S.O. Ajadi

2.1 Introduction 23

2.2 Heat transfer 23

2.3 Modes of heat transfer 24

2.4 The boundary layer equations 29

2.5 Internal boundary layer flows 40

2.6 External boundary layer flows 40

2.7 Wake and jet boundary layers 42

2.8 Hydrodynamic boundary layer stability 43

2.9 Practical applications of boundary layer flow 48

2.10 Conclusions 52

References 52

3 On some basics of compressible fluid flows 55

Felix Ilesanmi Alao, Samson Babatunde

Nomenclature 55

3.1 Introduction 56

3.2 Fundamental assumption 57

3.3 Basic equations of compressible fluid flow 58

3.4 Entropy factors 63

3.5 A note on applications of compressible fluid flow 65

References 65

4 Boundary layer equations in fluid dynamics 67

Hafeez Y. Hafeez, Chifu E. Ndikilar

4.1 The continuity equation 67

4.2 The momentum equations 68

4.3 Coutte flow 70

4.4 Plane Poiseuille flow 71

4.5 Hagen Poiseuille flow (pipe flow) 72

4.6 Flow over porous wall 74

4.7 Flow between plates with bottom injection and top suction 75

4.8 Flow in a porous duct 78

4.9 Approximate analytic solution (perturbation) 81

4.10 Numerical solution 84

4.11 The boundary-layer equations 85

4.12 Influence of boundary layer on external flow 87

4.13 The flat-plate boundary layer 91

References 94

5 The Merk–Chao–Fagbenle method for laminar boundary layer analysis 95

R. Layi Fagbenle, Leye M. Amoo, S. Aliu, A. Falana

5.1 Introduction 95

5.2 Historical perspectives of series-based methods and the

Merk–Chao–Fagbenle (MCF) procedure 97

5.3 Mathematical formulations of the Merk–Chao–Fagbenle method 101

5.4 Forced convection flow over a sphere 119

5.5 Forced convection over sears’ airfoils 121

5.6 Consideration in forced convection (nonisothermal) boundary layer transfer 124

5.7 Consideration in mixed convection boundary layer transfer 127

5.8 Consideration for nanofluids and other extensions of the methodology 127

5.9 Conclusion 128

References 128

6 The spectral-homotopy analysis method (SHAM) for solutions of

boundary layer problems 133

S.S. Motsa, Z.G. Makukula

6.1 Introduction 133

6.2 The spectral-homotopy analysis method (SHAM) 133

6.3 Examples 137

6.4 Pros and Cons of the SHAM 146

6.5 Conclusion 147

References 147

7 On a new numerical approach of MHD mixed convection flow with

heat and mass transfer of a micropolar fluid over an unsteady

stretching sheet in the presence of viscous dissipation and thermal

radiation 149

S. Shateyi, G.T. Marewo

Nomenclature 149

7.1 Introduction 150

7.2 Mathematical formulation 152

7.3 Similarity analysis 153

7.4 Methods of solution 155

7.5 Results and discussion 159

7.6 Conclusion 172

Acknowledgment 175

References 175

8 On the bivariate spectral quasilinearization method for

**nonlinear**

boundary layer partial differential equations 177

Vusi M. Magagula, Sandile S. Motsa, Precious Sibanda

8.1 Introduction 177

8.2 Bivariate interpolated spectral quasilinearization method 179

8.3 Results and discussion 183

8.4 Conclusion 188

Acknowledgments 189

References 189

9 Mixed convection heat transfer in rotating elliptic coolant channels 191

Olumuyiwa Ajani Lasode

9.1 Introduction 191

9.2 Governing equations for horizontal elliptic duct rotating in

parallel mode 194

9.3 Governing equations for vertical elliptic duct rotating in parallel

mode 199

9.4 Parameter perturbation analysis for horizontal elliptic ducts in

parallel mode rotation 201

9.5 Parameter perturbation analysis for vertical elliptic ducts in

parallel mode rotation 221

9.6 Discussion and conclusions of the effects of the variables on fluid

flow and heat transfer 225

References 230

10 Numerical techniques for the solution of the laminar boundary layer

equations 233

O.M. Amoo, A. Falana

10.1 Introduction – laminar boundary layer equations 233

10.2 Numerical methods – general background and the most important

techniques in the context of the laminar boundary layer ODEs 235

10.3 Application of different numerical methods for the solution of the

Blasius equation 241

10.4 Implementation of the shooting method for the solution of the

Blasius equation 249

10.5 Application of the finite-element method for one-dimensional

unsteady heat equation 253

10.6 Practical implementation of the finite-element method for

one-dimensional unsteady heat equation 254

10.7 Summary and outlook 256

References 258

11 On a selection of convective boundary layer transfer problems 259

Anselm Oyem

11.1 Introduction 259

11.2 Viscous dissipation and magnetic field effects on convection flow

over a vertical plate 259

11.3 Free convection mhd flow past a semiinfinite flat plate 263

11.4 Convection of non-darcy flow, Dufour and Soret effects past a

porous medium 265

11.5 Unsteady mhd convective flow with thermophoresis of particles

past a vertical surface 268

11.6 Thermal conductivity effects on compressible boundary layer flow

over a vertical plate 274

11.7 Conclusion 278

References 278

12 Advanced fluids – a review of nanofluid transport and its

applications 281

Leye M. Amoo, R. Layi Fagbenle

12.1 Introduction 281

12.2 Current understanding of nanofluids 285

12.3 Classes of nanofluids 289

12.4 Thermophysical properties of nanofluids 324

12.5 Convective heat transfer of nanofluids 332

12.6 Global nanofluid research – developments, policy perspectives,

and patents 344

12.7 Applications of nanofluids 345

12.8 Research gaps and outlook 354

12.9 Conclusion 355

References 357

13 On a selection of the applications of thermodynamics 383

L.M. Amoo

13.1 Introduction 383

13.2 Internal combustion engines – Otto and Diesel cycles 383

13.3 Electrical power generation – ideal basic Rankine cycle 388

13.4 Refrigeration systems – ideal vapor compression refrigeration cycle 391

13.5 Gas turbine systems – ideal air-standard Brayton cycle 394

13.6 Desiccant and subcooling dehumidification 398

13.7 Evaporative cooling 402

13.8 Entropy generation in boundary layer flow and heat transfer 406

13.9 Conclusions 410

References 410

14 Overview of non-Newtonian boundary layer flows and heat transfer 413

Leye M. Amoo, R. Layi Fagbenle

14.1 Introduction 413

14.2 Background 413

14.3 A note on current research status and applications of

non-Newtonian fluids 428

14.4 Future directions 432

References 432

15 Climate change in developing nations of the world 437

Leye M. Amoo, R. Layi Fagbenle

15.1 Introduction 437

15.2 Climate change 438

15.3 Anthropogenic influences on climate change 440

15.4 Greenhouse gases (GHGs) 442

15.5 Earth’s energy budget 444

15.6 Some climate change trends 444

15.7 Climate change and the transport sector 446

15.8 Climate change and the industrial sector 447

15.9 Climate change mitigation and adaptation 447

15.10 Climate change and conflict 449

15.11 Climate change and agriculture 449

15.12 The role and integration of renewable energy technologies 451

15.13 Climate changes in China 453

15.14 Climate changes in Malaysia 454

15.15 Climate changes in Nigeria 457

15.16 Climate changes in Brazil 459

15.17 Climate changes in India 460

15.18 Climate changes in South Africa 462

15.19 Climate changes in Ecuador 464

15.20 Conclusion 465

References 466

A Some mathematical background of fluid mechanics 473

Felix Ilesanmi Alao, Samson Babatunde, Zounaki Ongodiebi

References 488

B Some fundamentals of fluid mechanics 491

Zounaki Ongodiebi

B.1 Types of fluid flow 491

B.2 Flow visualization 493

References 495

Index 497