Dhananjay Yadav, PhD, is an Associate Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has over 160 publications, including seven books and one patent. His research interests include fluid mechanics, thermal engineering, and computational fluid dynamics. Mukesh Kumar Awasthi, PhD, is an Assistant Professor in the Department of Mathematics at Babasaheb Bhimrao Ambedkar University. He has published more than 20 books and numerous research articles in international journals and conferences. His research focuses on heat and mass transfer, fluid mechanics, and computational fluid dynamics. Harith Mohamed Al-Azri, PhD, is an Assistant Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has published more than 25 articles in international journals. His research centers on experimental nuclear physics, radiation physics, and dosimetry.

• Contributing Author List xiiiAim & Scope xviiPreface xixAcknowledgement xxi1 Introduction to Non-Newtonian Fluids 1D. D. Ganji1.1 Overview 21.1.1 Definition 21.1.2 Importance of the Non-Newtonian Fluids 71.1.3 Governing Equations for the Newtonian Fluids 91.1.3.1 Vectorial Governing Equations for Newtonian Fluids 91.1.4 Governing Equations for the Non-Newtonian Fluids 161.1.4.1 Vectorial Governing Equations for Non-Newtonian Fluids 161.1.5 Recent Advances in Non-Newtonian Fluids 181.1.6 Summary 23References 252 Viscoelastic Fluid Models 29Mukesh Kumar Awasthi, Atul Kumar Shukla and Dhananjay Yadav2.1 Fluids 302.1.1 Molecular Perspective 302.1.2 Newtonian Fluids 302.1.3 Non-Newtonian Fluids 312.2 Viscoelastic Fluids 322.2.1 Differences between Newtonian, Non-Newtonian, and Viscoelastic Fluids 332.2.2 Real-World Examples and Applications 332.3 Viscoelastic Fluid Models 342.3.1 Rivlin–Ericksen Fluids 342.3.2 Reiner–Rivlin Fluids 362.3.3 Maxwell Fluids 372.3.4 Oldroyd Fluids 372.3.5 Power Law Fluids 382.3.6 Bingham Plastic Fluids 392.3.7 Ellis Fluids 402.3.8 Reiner–Philippoff Fluids 412.3.9 Prandtl Fluids 422.3.10 Eyring Fluids 422.3.11 Power–Eyring Fluids 432.3.12 Williamson Fluids 442.3.13 Walters’ B Fluids 452.4 Applications of Viscoelastic Fluids in Industry and Nature 452.4.1 Biomedical Engineering: Blood Flow and Circulatory Dynamics 452.4.2 Biomedical Innovations: Targeted Drug Delivery 462.4.3 Polymer Processing: Manufacturing and Material Design 462.4.4 Food Industry: Texture and Stability 462.4.5 Geophysical Flows: Lava, Glaciers, and Mudslides 472.4.6 Environmental Engineering: Oil Spills and Sediment Transport 472.4.7 Energy and Industrial Fluids: Hydraulic Fracturing and Drilling 472.4.8 Ecological Adaptations: Biological Fluids and Mucus 482.5 Recent Advances and Emerging Trends in Viscoelastic Fluid Flow 482.5.1 Machine Learning in Viscoelastic Flow Modeling 482.5.2 Data-Driven Constitutive Model Discovery 482.5.3 Multiscale Modeling: Bridging Molecular and Continuum Scales 492.5.4 Hybrid Approaches for Complex Flow Regimes 492.5.5 Cutting-Edge Experimental Techniques for Validation 502.5.6 Machine Vision and Real-Time Feedback Loops 502.5.7 Interdisciplinary Fusion and Future Directions 502.5.8 Sustainability and Industry 4.0 Applications 512.6 Conclusion 51References 513 Computational Fluid Dynamics (CFD) for Non-Newtonian Fluids 55K. Jyothi, Yeddula Rameswara Reddy, Ramachandra Reddy Vaddemani, Raghunath Kodi and Dhananjay Yadav3.1 Introduction 563.2 Mathematical Formulation of the Problem 583.3 Numerical Method of Solution 623.3.1 The Finite-Element Method 623.3.2 Variational Formulation 643.3.3 Finite-Element Formulation 643.4 Results and Discussions 723.5 Table Discussions 783.6 Conclusions 79References 80Nomenclature 824 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 85Sahin Ahmed, Bikash Das and Anil Nangkar4.1 Introduction 864.1.1 Research Questions 884.2 Mathematical Formulation 884.3 Research Methodology 924.4 Stability and Validation 934.5 Results and Discussion 944.6 Conclusions 98Nomenclature 98References 1005 Exploring Non-Newtonian Fluid Dynamics in Porous Media: A CNT-Water Diven Analytical Approach in Vertical Channels 103Sahin Ahmed, Nava Jyoti Hazarika, Eny Tayang and Dhananjay YadavNomenclature 1045.1 Introduction 1055.2 Mathematical Formulation 1095.3 Validity and Accuracy 1145.4 Results and Discussion 1155.5 Conclusion 120Bibliography 1216 Non-Newtonian Fluid Flow in Porous Media 125Yeddula Rameswara Reddy, Damodara Reddy Annapureddy, K. Jyothi, Raghunath Kodi, Dhananjay Yadav and Ramachandra Reddy Vaddemani6.1 Introduction 1266.2 Problem Formulation 1296.3 Physical Quantities 1326.4 Code Validation 1326.5 Result and Discussion 1326.6 Conclusion 141References 1427 Effect of Couple Stresses on Thermal Convection of Navier–Stokes–Voigt Fluid in Porous Media 147Sunil, Sweta Sharma, Deepak Kumar and Poonam Sharma7.1 Introduction 1487.2 Geometrical Configuration and Mathematical Formulation 1537.2.1 Governing Equations 1537.2.2 Basic State and Perturbation Equations 1557.2.3 Dimensionless Perturbation Equations 1567.2.4 Boundary Conditions 1587.3 Nonlinear Analysis 1587.3.1 Conditional Energy Stability 1597.3.2 Variational Principle 1617.4 Linear Analysis 1637.4.1 Principle of Exchange of Stabilities 1647.5 Solution Methodology 1657.6 Results and Discussion 1677.7 Conclusions 1707.8 Applications 171References 1738 Convective Heat Transfer and Subcritical Dynamics in Rotating Ferrofluids with Couple Stresses in Porous Media Under Non-Equilibrium Conditions 177Sunil, Akanksha Thakur and Reeta Devi8.1 Introduction 1788.2 Formulation of the Problem 1818.2.1 Geometrical Configuration and Governing Equations 1818.2.2 Basic State 1838.2.3 Nondimensionalized Perturbation Equations 1838.3 Nonlinear Analysis 1868.3.1 Generalized Energy Functional 1888.4 Variational Principle 1918.5 Method of Solution 1938.5.1 Free–Free Boundaries 1948.5.2 Rigid–Rigid Boundaries 1958.6 Results and Discussion 1958.6.1 Effect of Couple Stresses 1968.6.2 Effect of Magnetization 1988.6.3 Effect of Medium Permeability 1998.6.4 Effect of Rotation 2008.6.5 Effect of Porosity–Modified Conductivity Ratio 2018.6.6 Effect of Heat Transfer Coefficient 2028.7 Conclusions 2038.8 Applications 204References 2059 Non-Newtonian Casson Fluid through a Porous Rotating Channel with Seepage Flow 209Abdul Faiz Ansari, Sameera Iqram, Vinod Y., Mohd. Asif and Piyush Jaiswal9.1 Introduction 2109.2 Problem Formulation 2129.3 Solution of Problem 2139.4 Results and Discussion 2159.5 Conclusion 219References 22010 Stationary Thermosolutal Convection of a Rotating Walters’ (Model B’) Nanofluid in a Porous Medium Under Rigid–Rigid and Rigid–Free Boundary Conditions 223Pushap Lata Sharma, Praveen Lata, Ajit Kumar, G.C. Rana and Dhananjay Yadav10.1 Introduction 22410.2 Mathematical Model 22510.2.1 Governing Equations 22610.2.2 Basic State Solutions 22910.2.3 Perturbation Solutions 23010.2.4 Normal Mode Analysis 23110.3 Linear Stability Analysis 23210.3.1 For Rigid–Rigid Boundaries 23210.3.1.1 Stationary Convection 23210.3.2 For Rigid–Free Boundaries 23310.3.2.1 Stationary Convection 23410.4 Result and Discussion 23510.5 Conclusion 240References 24111 Study of Two-Phase Flow Characteristics Due to Stretching Sheet 243Aswin Kumar RautaNomenclature 24411.1 Introduction 24511.2 Modeling of the Problem 24711.3 Flow Analysis and Coordinate System 24811.4 Solution Method 25111.5 Discussion 25211.6 Conclusions 258References 25912 Thermophoresis and Brownian Movement Impact on Maxwell Fluid Flow Over Permeable Stretching Sheet with Variable Magnetic Field 263S.M. Sachhin, G. M. Sachin, K. R. Harshitha, U.S. Mahabaleshwar and M. K. Awasthi12.1 Introduction 26412.2 Mathematical Analysis 26612.3 Numerical Method and Solution 26812.4 Results and Discussion 27012.5 Conclusion 276References 27613 Arrhenius Activation Energy and Viscosity Ratio Impact on Casson Fluid Flow Across Porous Stretching Surface with Variable Magnetic Field 279S.M. Sachhin, G. M. Sachin, U.S. Mahabaleshwar and M. K. Awasthi13.1 Introduction 28013.2 Mathematical Analysis 28213.3 Numerical Method and Solution 28413.4 Results and Discussion 28613.5 Conclusion 294References 29514 Computational Fluid Dynamics Examination of Non‐Newtonian Fluid Flows over an Exponentially Extending Surface with Thermal Source/Sink 297Priyanka Chandra and Raja Das14.1 Introduction 29814.2 Mathematical Formulation 30014.3 Computational Fluid Dynamic Tools: FEM 30314.3.1 Variational Formulation 30414.3.2 Finite-Element Formulation 30514.4 Results Analysis 30614.5 Conclusion 314Acknowledgement 315References 31515 Non-Newtonian Fluids in Environmental Engineering 319Abdulhalim Musa Abubakar, Suleiman A. Wali, Abubakar Mohammed and Vivek Kumar Pandey15.1 Introduction 32015.2 Characteristics of Non-Newtonian Fluids 32115.3 Modeling Non-Newtonian Fluids 32315.4 Case Studies 32415.4.1 Sediment Transport in Rivers and Estuaries 32415.4.2 Impact of Non-Newtonian Behavior on Deposition and Erosion 32515.4.3 Biofilm Development in Wastewater Treatment 32615.4.4 Implications for Nutrient and Pollutant Removal 32715.5 CFD Simulation Techniques 32815.6 Challenges in Measurement and Modeling 33015.6.1 Difficulties in Assessing Non-Newtonian Properties 33015.6.2 Environmental Factors Affecting Fluid Behavior 33015.7 Applications in Environmental Engineering 33215.8 Conclusion 332References 33616 Non-Newtonian Fluid Dynamics in Additive Manufacturing and 3D Printing 355Gandhimathi G., Chellaswamy C., Geetha T. S. and Awad M. M.16.1 Introduction to Non-Newtonian Fluids in Additive Manufacturing 35616.1.1 Overview of Additive Manufacturing and 3D Printing Technologies 35616.1.2 Importance of Non-Newtonian Fluid Behavior in 3D Printing 35716.1.3 Comparison of Newtonian vs. NNF in Printing Applications 35716.2 Rheology and Material Behavior in 3D Printing 35916.2.1 Shear-Thinning and Shear-Thickening Effects in Printing Fluids 35916.2.2 Viscoelasticity and Its Impact on Printability 36016.2.3 Yield Stress Behavior in Paste-Like Printing Materials 36016.2.4 Thixotropy and Structural Recovery During Deposition 36116.2.5 Types of Non-Newtonian Materials in Additive Manufacturing 36116.3 Deposition Techniques for Non-Newtonian Fluids 36216.3.1 Flow Behavior and Nozzle Design Considerations 36216.3.2 Resin Viscosity and Curing Dynamics 36316.3.3 Droplet Formation and Spreading for High-Precision Deposition 36416.3.4 Interaction of Binders and Powder Flowability 36416.4 Computational Modeling and Simulation 36516.4.1 Governing Equations for Non-Newtonian Fluid Flow in 3D Printing 36516.4.2 Momentum Equation (Navier–Stokes for NNF) 36716.4.3 Temperature Distribution in Thermoresponsive Nanofluid 37016.4.4 Case Study 1 37416.4.5 Case Study: 2 37816.5 Conclusion and Future Scope 379References 380About the Editors 383Index 385

Dhananjay Yadav, PhD, is an Associate Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has over 160 publications, including seven books and one patent. His research interests include fluid mechanics, thermal engineering, and computational fluid dynamics. Mukesh Kumar Awasthi, PhD, is an Assistant Professor in the Department of Mathematics at Babasaheb Bhimrao Ambedkar University. He has published more than 20 books and numerous research articles in international journals and conferences. His research focuses on heat and mass transfer, fluid mechanics, and computational fluid dynamics. Harith Mohamed Al-Azri, PhD, is an Assistant Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has published more than 25 articles in international journals. His research centers on experimental nuclear physics, radiation physics, and dosimetry.

• Contributing Author List xiiiAim & Scope xviiPreface xixAcknowledgement xxi1 Introduction to Non-Newtonian Fluids 1D. D. Ganji1.1 Overview 21.1.1 Definition 21.1.2 Importance of the Non-Newtonian Fluids 71.1.3 Governing Equations for the Newtonian Fluids 91.1.3.1 Vectorial Governing Equations for Newtonian Fluids 91.1.4 Governing Equations for the Non-Newtonian Fluids 161.1.4.1 Vectorial Governing Equations for Non-Newtonian Fluids 161.1.5 Recent Advances in Non-Newtonian Fluids 181.1.6 Summary 23References 252 Viscoelastic Fluid Models 29Mukesh Kumar Awasthi, Atul Kumar Shukla and Dhananjay Yadav2.1 Fluids 302.1.1 Molecular Perspective 302.1.2 Newtonian Fluids 302.1.3 Non-Newtonian Fluids 312.2 Viscoelastic Fluids 322.2.1 Differences between Newtonian, Non-Newtonian, and Viscoelastic Fluids 332.2.2 Real-World Examples and Applications 332.3 Viscoelastic Fluid Models 342.3.1 Rivlin–Ericksen Fluids 342.3.2 Reiner–Rivlin Fluids 362.3.3 Maxwell Fluids 372.3.4 Oldroyd Fluids 372.3.5 Power Law Fluids 382.3.6 Bingham Plastic Fluids 392.3.7 Ellis Fluids 402.3.8 Reiner–Philippoff Fluids 412.3.9 Prandtl Fluids 422.3.10 Eyring Fluids 422.3.11 Power–Eyring Fluids 432.3.12 Williamson Fluids 442.3.13 Walters’ B Fluids 452.4 Applications of Viscoelastic Fluids in Industry and Nature 452.4.1 Biomedical Engineering: Blood Flow and Circulatory Dynamics 452.4.2 Biomedical Innovations: Targeted Drug Delivery 462.4.3 Polymer Processing: Manufacturing and Material Design 462.4.4 Food Industry: Texture and Stability 462.4.5 Geophysical Flows: Lava, Glaciers, and Mudslides 472.4.6 Environmental Engineering: Oil Spills and Sediment Transport 472.4.7 Energy and Industrial Fluids: Hydraulic Fracturing and Drilling 472.4.8 Ecological Adaptations: Biological Fluids and Mucus 482.5 Recent Advances and Emerging Trends in Viscoelastic Fluid Flow 482.5.1 Machine Learning in Viscoelastic Flow Modeling 482.5.2 Data-Driven Constitutive Model Discovery 482.5.3 Multiscale Modeling: Bridging Molecular and Continuum Scales 492.5.4 Hybrid Approaches for Complex Flow Regimes 492.5.5 Cutting-Edge Experimental Techniques for Validation 502.5.6 Machine Vision and Real-Time Feedback Loops 502.5.7 Interdisciplinary Fusion and Future Directions 502.5.8 Sustainability and Industry 4.0 Applications 512.6 Conclusion 51References 513 Computational Fluid Dynamics (CFD) for Non-Newtonian Fluids 55K. Jyothi, Yeddula Rameswara Reddy, Ramachandra Reddy Vaddemani, Raghunath Kodi and Dhananjay Yadav3.1 Introduction 563.2 Mathematical Formulation of the Problem 583.3 Numerical Method of Solution 623.3.1 The Finite-Element Method 623.3.2 Variational Formulation 643.3.3 Finite-Element Formulation 643.4 Results and Discussions 723.5 Table Discussions 783.6 Conclusions 79References 80Nomenclature 824 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 85Sahin Ahmed, Bikash Das and Anil Nangkar4.1 Introduction 864.1.1 Research Questions 884.2 Mathematical Formulation 884.3 Research Methodology 924.4 Stability and Validation 934.5 Results and Discussion 944.6 Conclusions 98Nomenclature 98References 1005 Exploring Non-Newtonian Fluid Dynamics in Porous Media: A CNT-Water Diven Analytical Approach in Vertical Channels 103Sahin Ahmed, Nava Jyoti Hazarika, Eny Tayang and Dhananjay YadavNomenclature 1045.1 Introduction 1055.2 Mathematical Formulation 1095.3 Validity and Accuracy 1145.4 Results and Discussion 1155.5 Conclusion 120Bibliography 1216 Non-Newtonian Fluid Flow in Porous Media 125Yeddula Rameswara Reddy, Damodara Reddy Annapureddy, K. Jyothi, Raghunath Kodi, Dhananjay Yadav and Ramachandra Reddy Vaddemani6.1 Introduction 1266.2 Problem Formulation 1296.3 Physical Quantities 1326.4 Code Validation 1326.5 Result and Discussion 1326.6 Conclusion 141References 1427 Effect of Couple Stresses on Thermal Convection of Navier–Stokes–Voigt Fluid in Porous Media 147Sunil, Sweta Sharma, Deepak Kumar and Poonam Sharma7.1 Introduction 1487.2 Geometrical Configuration and Mathematical Formulation 1537.2.1 Governing Equations 1537.2.2 Basic State and Perturbation Equations 1557.2.3 Dimensionless Perturbation Equations 1567.2.4 Boundary Conditions 1587.3 Nonlinear Analysis 1587.3.1 Conditional Energy Stability 1597.3.2 Variational Principle 1617.4 Linear Analysis 1637.4.1 Principle of Exchange of Stabilities 1647.5 Solution Methodology 1657.6 Results and Discussion 1677.7 Conclusions 1707.8 Applications 171References 1738 Convective Heat Transfer and Subcritical Dynamics in Rotating Ferrofluids with Couple Stresses in Porous Media Under Non-Equilibrium Conditions 177Sunil, Akanksha Thakur and Reeta Devi8.1 Introduction 1788.2 Formulation of the Problem 1818.2.1 Geometrical Configuration and Governing Equations 1818.2.2 Basic State 1838.2.3 Nondimensionalized Perturbation Equations 1838.3 Nonlinear Analysis 1868.3.1 Generalized Energy Functional 1888.4 Variational Principle 1918.5 Method of Solution 1938.5.1 Free–Free Boundaries 1948.5.2 Rigid–Rigid Boundaries 1958.6 Results and Discussion 1958.6.1 Effect of Couple Stresses 1968.6.2 Effect of Magnetization 1988.6.3 Effect of Medium Permeability 1998.6.4 Effect of Rotation 2008.6.5 Effect of Porosity–Modified Conductivity Ratio 2018.6.6 Effect of Heat Transfer Coefficient 2028.7 Conclusions 2038.8 Applications 204References 2059 Non-Newtonian Casson Fluid through a Porous Rotating Channel with Seepage Flow 209Abdul Faiz Ansari, Sameera Iqram, Vinod Y., Mohd. Asif and Piyush Jaiswal9.1 Introduction 2109.2 Problem Formulation 2129.3 Solution of Problem 2139.4 Results and Discussion 2159.5 Conclusion 219References 22010 Stationary Thermosolutal Convection of a Rotating Walters’ (Model B’) Nanofluid in a Porous Medium Under Rigid–Rigid and Rigid–Free Boundary Conditions 223Pushap Lata Sharma, Praveen Lata, Ajit Kumar, G.C. Rana and Dhananjay Yadav10.1 Introduction 22410.2 Mathematical Model 22510.2.1 Governing Equations 22610.2.2 Basic State Solutions 22910.2.3 Perturbation Solutions 23010.2.4 Normal Mode Analysis 23110.3 Linear Stability Analysis 23210.3.1 For Rigid–Rigid Boundaries 23210.3.1.1 Stationary Convection 23210.3.2 For Rigid–Free Boundaries 23310.3.2.1 Stationary Convection 23410.4 Result and Discussion 23510.5 Conclusion 240References 24111 Study of Two-Phase Flow Characteristics Due to Stretching Sheet 243Aswin Kumar RautaNomenclature 24411.1 Introduction 24511.2 Modeling of the Problem 24711.3 Flow Analysis and Coordinate System 24811.4 Solution Method 25111.5 Discussion 25211.6 Conclusions 258References 25912 Thermophoresis and Brownian Movement Impact on Maxwell Fluid Flow Over Permeable Stretching Sheet with Variable Magnetic Field 263S.M. Sachhin, G. M. Sachin, K. R. Harshitha, U.S. Mahabaleshwar and M. K. Awasthi12.1 Introduction 26412.2 Mathematical Analysis 26612.3 Numerical Method and Solution 26812.4 Results and Discussion 27012.5 Conclusion 276References 27613 Arrhenius Activation Energy and Viscosity Ratio Impact on Casson Fluid Flow Across Porous Stretching Surface with Variable Magnetic Field 279S.M. Sachhin, G. M. Sachin, U.S. Mahabaleshwar and M. K. Awasthi13.1 Introduction 28013.2 Mathematical Analysis 28213.3 Numerical Method and Solution 28413.4 Results and Discussion 28613.5 Conclusion 294References 29514 Computational Fluid Dynamics Examination of Non‐Newtonian Fluid Flows over an Exponentially Extending Surface with Thermal Source/Sink 297Priyanka Chandra and Raja Das14.1 Introduction 29814.2 Mathematical Formulation 30014.3 Computational Fluid Dynamic Tools: FEM 30314.3.1 Variational Formulation 30414.3.2 Finite-Element Formulation 30514.4 Results Analysis 30614.5 Conclusion 314Acknowledgement 315References 31515 Non-Newtonian Fluids in Environmental Engineering 319Abdulhalim Musa Abubakar, Suleiman A. Wali, Abubakar Mohammed and Vivek Kumar Pandey15.1 Introduction 32015.2 Characteristics of Non-Newtonian Fluids 32115.3 Modeling Non-Newtonian Fluids 32315.4 Case Studies 32415.4.1 Sediment Transport in Rivers and Estuaries 32415.4.2 Impact of Non-Newtonian Behavior on Deposition and Erosion 32515.4.3 Biofilm Development in Wastewater Treatment 32615.4.4 Implications for Nutrient and Pollutant Removal 32715.5 CFD Simulation Techniques 32815.6 Challenges in Measurement and Modeling 33015.6.1 Difficulties in Assessing Non-Newtonian Properties 33015.6.2 Environmental Factors Affecting Fluid Behavior 33015.7 Applications in Environmental Engineering 33215.8 Conclusion 332References 33616 Non-Newtonian Fluid Dynamics in Additive Manufacturing and 3D Printing 355Gandhimathi G., Chellaswamy C., Geetha T. S. and Awad M. M.16.1 Introduction to Non-Newtonian Fluids in Additive Manufacturing 35616.1.1 Overview of Additive Manufacturing and 3D Printing Technologies 35616.1.2 Importance of Non-Newtonian Fluid Behavior in 3D Printing 35716.1.3 Comparison of Newtonian vs. NNF in Printing Applications 35716.2 Rheology and Material Behavior in 3D Printing 35916.2.1 Shear-Thinning and Shear-Thickening Effects in Printing Fluids 35916.2.2 Viscoelasticity and Its Impact on Printability 36016.2.3 Yield Stress Behavior in Paste-Like Printing Materials 36016.2.4 Thixotropy and Structural Recovery During Deposition 36116.2.5 Types of Non-Newtonian Materials in Additive Manufacturing 36116.3 Deposition Techniques for Non-Newtonian Fluids 36216.3.1 Flow Behavior and Nozzle Design Considerations 36216.3.2 Resin Viscosity and Curing Dynamics 36316.3.3 Droplet Formation and Spreading for High-Precision Deposition 36416.3.4 Interaction of Binders and Powder Flowability 36416.4 Computational Modeling and Simulation 36516.4.1 Governing Equations for Non-Newtonian Fluid Flow in 3D Printing 36516.4.2 Momentum Equation (Navier–Stokes for NNF) 36716.4.3 Temperature Distribution in Thermoresponsive Nanofluid 37016.4.4 Case Study 1 37416.4.5 Case Study: 2 37816.5 Conclusion and Future Scope 379References 380About the Editors 383Index 385

Dhananjay Yadav, PhD, is an Associate Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has over 160 publications, including seven books and one patent. His research interests include fluid mechanics, thermal engineering, and computational fluid dynamics. Mukesh Kumar Awasthi, PhD, is an Assistant Professor in the Department of Mathematics at Babasaheb Bhimrao Ambedkar University. He has published more than 20 books and numerous research articles in international journals and conferences. His research focuses on heat and mass transfer, fluid mechanics, and computational fluid dynamics. Harith Mohamed Al-Azri, PhD, is an Assistant Professor in the Department of Mathematics, College of Arts and Sciences, University of Nizwa. He has published more than 25 articles in international journals. His research centers on experimental nuclear physics, radiation physics, and dosimetry.

• Contributing Author List xiiiAim & Scope xviiPreface xixAcknowledgement xxi1 Introduction to Non-Newtonian Fluids 1D. D. Ganji1.1 Overview 21.1.1 Definition 21.1.2 Importance of the Non-Newtonian Fluids 71.1.3 Governing Equations for the Newtonian Fluids 91.1.3.1 Vectorial Governing Equations for Newtonian Fluids 91.1.4 Governing Equations for the Non-Newtonian Fluids 161.1.4.1 Vectorial Governing Equations for Non-Newtonian Fluids 161.1.5 Recent Advances in Non-Newtonian Fluids 181.1.6 Summary 23References 252 Viscoelastic Fluid Models 29Mukesh Kumar Awasthi, Atul Kumar Shukla and Dhananjay Yadav2.1 Fluids 302.1.1 Molecular Perspective 302.1.2 Newtonian Fluids 302.1.3 Non-Newtonian Fluids 312.2 Viscoelastic Fluids 322.2.1 Differences between Newtonian, Non-Newtonian, and Viscoelastic Fluids 332.2.2 Real-World Examples and Applications 332.3 Viscoelastic Fluid Models 342.3.1 Rivlin–Ericksen Fluids 342.3.2 Reiner–Rivlin Fluids 362.3.3 Maxwell Fluids 372.3.4 Oldroyd Fluids 372.3.5 Power Law Fluids 382.3.6 Bingham Plastic Fluids 392.3.7 Ellis Fluids 402.3.8 Reiner–Philippoff Fluids 412.3.9 Prandtl Fluids 422.3.10 Eyring Fluids 422.3.11 Power–Eyring Fluids 432.3.12 Williamson Fluids 442.3.13 Walters’ B Fluids 452.4 Applications of Viscoelastic Fluids in Industry and Nature 452.4.1 Biomedical Engineering: Blood Flow and Circulatory Dynamics 452.4.2 Biomedical Innovations: Targeted Drug Delivery 462.4.3 Polymer Processing: Manufacturing and Material Design 462.4.4 Food Industry: Texture and Stability 462.4.5 Geophysical Flows: Lava, Glaciers, and Mudslides 472.4.6 Environmental Engineering: Oil Spills and Sediment Transport 472.4.7 Energy and Industrial Fluids: Hydraulic Fracturing and Drilling 472.4.8 Ecological Adaptations: Biological Fluids and Mucus 482.5 Recent Advances and Emerging Trends in Viscoelastic Fluid Flow 482.5.1 Machine Learning in Viscoelastic Flow Modeling 482.5.2 Data-Driven Constitutive Model Discovery 482.5.3 Multiscale Modeling: Bridging Molecular and Continuum Scales 492.5.4 Hybrid Approaches for Complex Flow Regimes 492.5.5 Cutting-Edge Experimental Techniques for Validation 502.5.6 Machine Vision and Real-Time Feedback Loops 502.5.7 Interdisciplinary Fusion and Future Directions 502.5.8 Sustainability and Industry 4.0 Applications 512.6 Conclusion 51References 513 Computational Fluid Dynamics (CFD) for Non-Newtonian Fluids 55K. Jyothi, Yeddula Rameswara Reddy, Ramachandra Reddy Vaddemani, Raghunath Kodi and Dhananjay Yadav3.1 Introduction 563.2 Mathematical Formulation of the Problem 583.3 Numerical Method of Solution 623.3.1 The Finite-Element Method 623.3.2 Variational Formulation 643.3.3 Finite-Element Formulation 643.4 Results and Discussions 723.5 Table Discussions 783.6 Conclusions 79References 80Nomenclature 824 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 85Sahin Ahmed, Bikash Das and Anil Nangkar4.1 Introduction 864.1.1 Research Questions 884.2 Mathematical Formulation 884.3 Research Methodology 924.4 Stability and Validation 934.5 Results and Discussion 944.6 Conclusions 98Nomenclature 98References 1005 Exploring Non-Newtonian Fluid Dynamics in Porous Media: A CNT-Water Diven Analytical Approach in Vertical Channels 103Sahin Ahmed, Nava Jyoti Hazarika, Eny Tayang and Dhananjay YadavNomenclature 1045.1 Introduction 1055.2 Mathematical Formulation 1095.3 Validity and Accuracy 1145.4 Results and Discussion 1155.5 Conclusion 120Bibliography 1216 Non-Newtonian Fluid Flow in Porous Media 125Yeddula Rameswara Reddy, Damodara Reddy Annapureddy, K. Jyothi, Raghunath Kodi, Dhananjay Yadav and Ramachandra Reddy Vaddemani6.1 Introduction 1266.2 Problem Formulation 1296.3 Physical Quantities 1326.4 Code Validation 1326.5 Result and Discussion 1326.6 Conclusion 141References 1427 Effect of Couple Stresses on Thermal Convection of Navier–Stokes–Voigt Fluid in Porous Media 147Sunil, Sweta Sharma, Deepak Kumar and Poonam Sharma7.1 Introduction 1487.2 Geometrical Configuration and Mathematical Formulation 1537.2.1 Governing Equations 1537.2.2 Basic State and Perturbation Equations 1557.2.3 Dimensionless Perturbation Equations 1567.2.4 Boundary Conditions 1587.3 Nonlinear Analysis 1587.3.1 Conditional Energy Stability 1597.3.2 Variational Principle 1617.4 Linear Analysis 1637.4.1 Principle of Exchange of Stabilities 1647.5 Solution Methodology 1657.6 Results and Discussion 1677.7 Conclusions 1707.8 Applications 171References 1738 Convective Heat Transfer and Subcritical Dynamics in Rotating Ferrofluids with Couple Stresses in Porous Media Under Non-Equilibrium Conditions 177Sunil, Akanksha Thakur and Reeta Devi8.1 Introduction 1788.2 Formulation of the Problem 1818.2.1 Geometrical Configuration and Governing Equations 1818.2.2 Basic State 1838.2.3 Nondimensionalized Perturbation Equations 1838.3 Nonlinear Analysis 1868.3.1 Generalized Energy Functional 1888.4 Variational Principle 1918.5 Method of Solution 1938.5.1 Free–Free Boundaries 1948.5.2 Rigid–Rigid Boundaries 1958.6 Results and Discussion 1958.6.1 Effect of Couple Stresses 1968.6.2 Effect of Magnetization 1988.6.3 Effect of Medium Permeability 1998.6.4 Effect of Rotation 2008.6.5 Effect of Porosity–Modified Conductivity Ratio 2018.6.6 Effect of Heat Transfer Coefficient 2028.7 Conclusions 2038.8 Applications 204References 2059 Non-Newtonian Casson Fluid through a Porous Rotating Channel with Seepage Flow 209Abdul Faiz Ansari, Sameera Iqram, Vinod Y., Mohd. Asif and Piyush Jaiswal9.1 Introduction 2109.2 Problem Formulation 2129.3 Solution of Problem 2139.4 Results and Discussion 2159.5 Conclusion 219References 22010 Stationary Thermosolutal Convection of a Rotating Walters’ (Model B’) Nanofluid in a Porous Medium Under Rigid–Rigid and Rigid–Free Boundary Conditions 223Pushap Lata Sharma, Praveen Lata, Ajit Kumar, G.C. Rana and Dhananjay Yadav10.1 Introduction 22410.2 Mathematical Model 22510.2.1 Governing Equations 22610.2.2 Basic State Solutions 22910.2.3 Perturbation Solutions 23010.2.4 Normal Mode Analysis 23110.3 Linear Stability Analysis 23210.3.1 For Rigid–Rigid Boundaries 23210.3.1.1 Stationary Convection 23210.3.2 For Rigid–Free Boundaries 23310.3.2.1 Stationary Convection 23410.4 Result and Discussion 23510.5 Conclusion 240References 24111 Study of Two-Phase Flow Characteristics Due to Stretching Sheet 243Aswin Kumar RautaNomenclature 24411.1 Introduction 24511.2 Modeling of the Problem 24711.3 Flow Analysis and Coordinate System 24811.4 Solution Method 25111.5 Discussion 25211.6 Conclusions 258References 25912 Thermophoresis and Brownian Movement Impact on Maxwell Fluid Flow Over Permeable Stretching Sheet with Variable Magnetic Field 263S.M. Sachhin, G. M. Sachin, K. R. Harshitha, U.S. Mahabaleshwar and M. K. Awasthi12.1 Introduction 26412.2 Mathematical Analysis 26612.3 Numerical Method and Solution 26812.4 Results and Discussion 27012.5 Conclusion 276References 27613 Arrhenius Activation Energy and Viscosity Ratio Impact on Casson Fluid Flow Across Porous Stretching Surface with Variable Magnetic Field 279S.M. Sachhin, G. M. Sachin, U.S. Mahabaleshwar and M. K. Awasthi13.1 Introduction 28013.2 Mathematical Analysis 28213.3 Numerical Method and Solution 28413.4 Results and Discussion 28613.5 Conclusion 294References 29514 Computational Fluid Dynamics Examination of Non‐Newtonian Fluid Flows over an Exponentially Extending Surface with Thermal Source/Sink 297Priyanka Chandra and Raja Das14.1 Introduction 29814.2 Mathematical Formulation 30014.3 Computational Fluid Dynamic Tools: FEM 30314.3.1 Variational Formulation 30414.3.2 Finite-Element Formulation 30514.4 Results Analysis 30614.5 Conclusion 314Acknowledgement 315References 31515 Non-Newtonian Fluids in Environmental Engineering 319Abdulhalim Musa Abubakar, Suleiman A. Wali, Abubakar Mohammed and Vivek Kumar Pandey15.1 Introduction 32015.2 Characteristics of Non-Newtonian Fluids 32115.3 Modeling Non-Newtonian Fluids 32315.4 Case Studies 32415.4.1 Sediment Transport in Rivers and Estuaries 32415.4.2 Impact of Non-Newtonian Behavior on Deposition and Erosion 32515.4.3 Biofilm Development in Wastewater Treatment 32615.4.4 Implications for Nutrient and Pollutant Removal 32715.5 CFD Simulation Techniques 32815.6 Challenges in Measurement and Modeling 33015.6.1 Difficulties in Assessing Non-Newtonian Properties 33015.6.2 Environmental Factors Affecting Fluid Behavior 33015.7 Applications in Environmental Engineering 33215.8 Conclusion 332References 33616 Non-Newtonian Fluid Dynamics in Additive Manufacturing and 3D Printing 355Gandhimathi G., Chellaswamy C., Geetha T. S. and Awad M. M.16.1 Introduction to Non-Newtonian Fluids in Additive Manufacturing 35616.1.1 Overview of Additive Manufacturing and 3D Printing Technologies 35616.1.2 Importance of Non-Newtonian Fluid Behavior in 3D Printing 35716.1.3 Comparison of Newtonian vs. NNF in Printing Applications 35716.2 Rheology and Material Behavior in 3D Printing 35916.2.1 Shear-Thinning and Shear-Thickening Effects in Printing Fluids 35916.2.2 Viscoelasticity and Its Impact on Printability 36016.2.3 Yield Stress Behavior in Paste-Like Printing Materials 36016.2.4 Thixotropy and Structural Recovery During Deposition 36116.2.5 Types of Non-Newtonian Materials in Additive Manufacturing 36116.3 Deposition Techniques for Non-Newtonian Fluids 36216.3.1 Flow Behavior and Nozzle Design Considerations 36216.3.2 Resin Viscosity and Curing Dynamics 36316.3.3 Droplet Formation and Spreading for High-Precision Deposition 36416.3.4 Interaction of Binders and Powder Flowability 36416.4 Computational Modeling and Simulation 36516.4.1 Governing Equations for Non-Newtonian Fluid Flow in 3D Printing 36516.4.2 Momentum Equation (Navier–Stokes for NNF) 36716.4.3 Temperature Distribution in Thermoresponsive Nanofluid 37016.4.4 Case Study 1 37416.4.5 Case Study: 2 37816.5 Conclusion and Future Scope 379References 380About the Editors 383Index 385