Contributing Author List xiii Aim & Scope xvii Preface xix Acknowledgement xxi 1 Introduction to Non-Newtonian Fluids 1 D. D. Ganji 1.1 Overview 2 1.1.1 Definition 2 1.1.2 Importance of the Non-Newtonian Fluids 7 1.

1.3 Governing Equations for the Newtonian Fluids 9 1.1.3.1 Vectorial Governing Equations for Newtonian Fluids 9 1.1.4 Governing Equations for the Non-Newtonian Fluids 16 1.1.

4.1 Vectorial Governing Equations for Non-Newtonian Fluids 16 1.1.5 Recent Advances in Non-Newtonian Fluids 18 1.1.6 Summary 23 References 25 2 Viscoelastic Fluid Models 29 Mukesh Kumar Awasthi, Atul Kumar Shukla and Dhananjay Yadav 2.1 Fluids 30 2.1.

1 Molecular Perspective 30 2.1.2 Newtonian Fluids 30 2.1.3 Non-Newtonian Fluids 31 2.2 Viscoelastic Fluids 32 2.2.1 Differences between Newtonian, Non-Newtonian, and Viscoelastic Fluids 33 2.

2.2 Real-World Examples and Applications 33 2.3 Viscoelastic Fluid Models 34 2.3.1 Rivlin-Ericksen Fluids 34 2.3.2 Reiner-Rivlin Fluids 36 2.3.

3 Maxwell Fluids 37 2.3.4 Oldroyd Fluids 37 2.3.5 Power Law Fluids 38 2.3.6 Bingham Plastic Fluids 39 2.3.

7 Ellis Fluids 40 2.3.8 Reiner-Philippoff Fluids 41 2.3.9 Prandtl Fluids 42 2.3.10 Eyring Fluids 42 2.3.

11 Power-Eyring Fluids 43 2.3.12 Williamson Fluids 44 2.3.13 Walters'' B Fluids 45 2.4 Applications of Viscoelastic Fluids in Industry and Nature 45 2.4.1 Biomedical Engineering: Blood Flow and Circulatory Dynamics 45 2.

4.2 Biomedical Innovations: Targeted Drug Delivery 46 2.4.3 Polymer Processing: Manufacturing and Material Design 46 2.4.4 Food Industry: Texture and Stability 46 2.4.5 Geophysical Flows: Lava, Glaciers, and Mudslides 47 2.

4.6 Environmental Engineering: Oil Spills and Sediment Transport 47 2.4.7 Energy and Industrial Fluids: Hydraulic Fracturing and Drilling 47 2.4.8 Ecological Adaptations: Biological Fluids and Mucus 48 2.5 Recent Advances and Emerging Trends in Viscoelastic Fluid Flow 48 2.5.

1 Machine Learning in Viscoelastic Flow Modeling 48 2.5.2 Data-Driven Constitutive Model Discovery 48 2.5.3 Multiscale Modeling: Bridging Molecular and Continuum Scales 49 2.5.4 Hybrid Approaches for Complex Flow Regimes 49 2.5.

5 Cutting-Edge Experimental Techniques for Validation 50 2.5.6 Machine Vision and Real-Time Feedback Loops 50 2.5.7 Interdisciplinary Fusion and Future Directions 50 2.5.8 Sustainability and Industry 4.0 Applications 51 2.

6 Conclusion 51 References 51 3 Computational Fluid Dynamics (CFD) for Non-Newtonian Fluids 55 K. Jyothi, Yeddula Rameswara Reddy, Ramachandra Reddy Vaddemani, Raghunath Kodi and Dhananjay Yadav 3.1 Introduction 56 3.2 Mathematical Formulation of the Problem 58 3.3 Numerical Method of Solution 62 3.3.1 The Finite-Element Method 62 3.3.

2 Variational Formulation 64 3.3.3 Finite-Element Formulation 64 3.4 Results and Discussions 72 3.5 Table Discussions 78 3.6 Conclusions 79 References 80 Nomenclature 82 4 Exploring Heat and Mass Diffusion in Non-Newtonian Fluid Flow over a Stretching Surface in a Non-Darcy Variable Porous Medium: An Analysis by Finite Difference Scheme 85 Sahin Ahmed, Bikash Das and Anil Nangkar 4.1 Introduction 86 4.1.

1 Research Questions 88 4.2 Mathematical Formulation 88 4.3 Research Methodology 92 4.4 Stability and Validation 93 4.5 Results and Discussion 94 4.6 Conclusions 98 Nomenclature 98 References 100 5 Exploring Non-Newtonian Fluid Dynamics in Porous Media: A CNT-Water Diven Analytical Approach in Vertical Channels 103 Sahin Ahmed, Nava Jyoti Hazarika, Eny Tayang and Dhananjay Yadav Nomenclature 104 5.1 Introduction 105 5.2 Mathematical Formulation 109 5.

3 Validity and Accuracy 114 5.4 Results and Discussion 115 5.5 Conclusion 120 Bibliography 121 6 Non-Newtonian Fluid Flow in Porous Media 125 Yeddula Rameswara Reddy, Damodara Reddy Annapureddy, K. Jyothi, Raghunath Kodi, Dhananjay Yadav and Ramachandra Reddy Vaddemani 6.1 Introduction 126 6.2 Problem Formulation 129 6.3 Physical Quantities 132 6.4 Code Validation 132 6.

5 Result and Discussion 132 6.6 Conclusion 141 References 142 7 Effect of Couple Stresses on Thermal Convection of Navier-Stokes-Voigt Fluid in Porous Media 147 Sunil, Sweta Sharma, Deepak Kumar and Poonam Sharma 7.1 Introduction 148 7.2 Geometrical Configuration and Mathematical Formulation 153 7.2.1 Governing Equations 153 7.2.2 Basic State and Perturbation Equations 155 7.

2.3 Dimensionless Perturbation Equations 156 7.2.4 Boundary Conditions 158 7.3 Nonlinear Analysis 158 7.3.1 Conditional Energy Stability 159 7.3.

2 Variational Principle 161 7.4 Linear Analysis 163 7.4.1 Principle of Exchange of Stabilities 164 7.5 Solution Methodology 165 7.6 Results and Discussion 167 7.7 Conclusions 170 7.8 Applications 171 References 173 8 Convective Heat Transfer and Subcritical Dynamics in Rotating Ferrofluids with Couple Stresses in Porous Media Under Non-Equilibrium Conditions 177 Sunil, Akanksha Thakur and Reeta Devi 8.

1 Introduction 178 8.2 Formulation of the Problem 181 8.2.1 Geometrical Configuration and Governing Equations 181 8.2.2 Basic State 183 8.2.3 Nondimensionalized Perturbation Equations 183 8.

3 Nonlinear Analysis 186 8.3.1 Generalized Energy Functional 188 8.4 Variational Principle 191 8.5 Method of Solution 193 8.5.1 Free-Free Boundaries 194 8.5.

2 Rigid-Rigid Boundaries 195 8.6 Results and Discussion 195 8.6.1 Effect of Couple Stresses 196 8.6.2 Effect of Magnetization 198 8.6.3 Effect of Medium Permeability 199 8.

6.4 Effect of Rotation 200 8.6.5 Effect of Porosity-Modified Conductivity Ratio 201 8.6.6 Effect of Heat Transfer Coefficient 202 8.7 Conclusions 203 8.8 Applications 204 References 205 9 Non-Newtonian Casson Fluid through a Porous Rotating Channel with Seepage Flow 209 Abdul Faiz Ansari, Sameera Iqram, Vinod Y.

, Mohd. Asif and Piyush Jaiswal 9.1 Introduction 210 9.2 Problem Formulation 212 9.3 Solution of Problem 213 9.4 Results and Discussion 215 9.5 Conclusion 219 References 220 10 Stationary Thermosolutal Convection of a Rotating Walters'' (Model B'') Nanofluid in a Porous Medium Under Rigid-Rigid and Rigid-Free Boundary Conditions 223 Pushap Lata Sharma, Praveen Lata, Ajit Kumar, G.C.

Rana and Dhananjay Yadav 10.1 Introduction 224 10.2 Mathematical Model 225 10.2.1 Governing Equations 226 10.2.2 Basic State Solutions 229 10.2.

3 Perturbation Solutions 230 10.2.4 Normal Mode Analysis 231 10.3 Linear Stability Analysis 232 10.3.1 For Rigid-Rigid Boundaries 232 10.3.1.

1 Stationary Convection 232 10.3.2 For Rigid-Free Boundaries 233 10.3.2.1 Stationary Convection 234 10.4 Result and Discussion 235 10.5 Conclusion 240 References 241 11 Study of Two-Phase Flow Characteristics Due to Stretching Sheet 243 Aswin Kumar Rauta Nomenclature 244 11.

1 Introduction 245 11.2 Modeling of the Problem 247 11.3 Flow Analysis and Coordinate System 248 11.4 Solution Method 251 11.5 Discussion 252 11.6 Conclusions 258 References 259 12 Thermophoresis and Brownian Movement Impact on Maxwell Fluid Flow Over Permeable Stretching Sheet with Variable Magnetic Field 263 S.M. Sachhin, G.

M. Sachin, K. R. Harshitha, U.S. Mahabaleshwar and M. K. Awasthi 12.

1 Introduction 264 12.2 Mathematical Analysis 266 12.3 Numerical Method and Solution 268 12.4 Results and Discussion 270 12.5 Conclusion 276 References 276 13 Arrhenius Activation Energy and Viscosity Ratio Impact on Casson Fluid Flow Across Porous Stretching Surface with Variable Magnetic Field 279 S.M. Sachhin, G. M.

Sachin, U.S. Mahabaleshwar and M. K. Awasthi 13.1 Introduction 280 13.2 Mathematical Analysis 282 13.3 Numerical Method and Solution 284 13.

4 Results and Discussion 286 13.5 Conclusion 294 References 295 14 Computational Fluid Dynamics Examination of NonNewtonian Fluid Flows over an Exponentially Extending Surface with Thermal Source/Sink 297 Priyanka Chandra and Raja Das 14.1 Introduction 298 14.2 Mathematical Formulation 300 14.3 Computational Fluid Dynamic Tools: FEM 303 14.3.1 Variational Formulation 304 14.3.

2 Finite-Element Formulation 305 14.4 Results Analysis 306 14.5 Conclusion 314 Acknowledgement 315 References 315 15 Non-Newtonian Fluids in Environmental Engineering 319 Abdulhalim Musa Abubakar, Suleiman A. Wali, Abubakar Mohammed and Vivek Kumar Pandey 15.1 Introduction 320 15.2 Characteristics of Non-Newtonian Fluids 321 15.3 Modeling Non-Newtonian Fluids 323 15.4 Case Studies 324 15.

4.1 Sediment Transport in Rivers and Estuaries 324 15.4.2 Impact.