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Chapter 5 Numerical study of coupled partial differential equations in heat transfer problems with imprecisely defined parameters

  • Sudipta Priyadarshini and Sukanta Nayak
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Flow Dynamics and Heat Transfer
This chapter is in the book Flow Dynamics and Heat Transfer

Abstract

The epistemic-type uncertaintiesuncertainties are the main focus in connection with the heat transfer problems. The same are arising due to imprecise involved parameters, boundary conditions, experimental errors, and material properties. This chapter includes the numerical approach to investigate heat transfer problems in presence of uncertainties. In addition, to quantify the impreciseness, fuzzy numberfuzzy number is used. Using the fuzzy number with the concept of finite element method (FEMfinite element method (FEM)), fuzzy finite element method (FFEMfuzzy finite element method (FFEM)) is developed and the same is discussed in detail. Then a case study is illustrated using FFEMfuzzy finite element method (FFEM) to quantify the velocity and temperature profiles. The Rayleigh numberRayleigh number ( R a ) and radiation parameterradiation parameter ( R d ) are considered as fuzzy. Here, the modelled coupled algebraic equations are simplified through Gauss-Seidel (GS) iterative techniqueGauss-Seidel (GS) iterative technique. Further, convergence analysisconvergence analysis of the different profiles is discussed and the sensitiveness of the same is analyzed. Finally, using the obtained results the efficiency and usefulness of the FFEMfuzzy finite element method (FFEM) is depicted.

Abstract

The epistemic-type uncertaintiesuncertainties are the main focus in connection with the heat transfer problems. The same are arising due to imprecise involved parameters, boundary conditions, experimental errors, and material properties. This chapter includes the numerical approach to investigate heat transfer problems in presence of uncertainties. In addition, to quantify the impreciseness, fuzzy numberfuzzy number is used. Using the fuzzy number with the concept of finite element method (FEMfinite element method (FEM)), fuzzy finite element method (FFEMfuzzy finite element method (FFEM)) is developed and the same is discussed in detail. Then a case study is illustrated using FFEMfuzzy finite element method (FFEM) to quantify the velocity and temperature profiles. The Rayleigh numberRayleigh number ( R a ) and radiation parameterradiation parameter ( R d ) are considered as fuzzy. Here, the modelled coupled algebraic equations are simplified through Gauss-Seidel (GS) iterative techniqueGauss-Seidel (GS) iterative technique. Further, convergence analysisconvergence analysis of the different profiles is discussed and the sensitiveness of the same is analyzed. Finally, using the obtained results the efficiency and usefulness of the FFEMfuzzy finite element method (FFEM) is depicted.

Chapters in this book

  1. Frontmatter I
  2. Contents V
  3. Aim and scope VII
  4. Preface IX
  5. Acknowledgments
  6. About editors XIII
  7. List of contributing authors XV
  8. Chapter 1 Introduction to flow dynamics and heat transfer 1
  9. Chapter 2 Compressible fluid flow and heat transfer 29
  10. Chapter 3 Non-Newtonian fluid flow and heat transfer 59
  11. Chapter 4 Heat transfer in forced and natural convection 81
  12. Chapter 5 Numerical study of coupled partial differential equations in heat transfer problems with imprecisely defined parameters 91
  13. Chapter 6 Numerical approach to study the effect of uncertain spectrum of field variables in a porous cavity 107
  14. Chapter 7 Investigation of the thermal fluid system using direct numerical simulation 123
  15. Chapter 8 Dynamics of shock-accelerated V-shaped gas interface 139
  16. Chapter 9 Nonlinear and linear analyses of partially ionized plasma 155
  17. Chapter 10 Thermo-fluid behavior of electroosmotic flow in a hydrophobic microchannel under Joule heating and external fields 185
  18. Chapter 11 The study of oscillating water column energy device in a two-layer fluid system of finite impermeable depth 219
  19. Chapter 12 Data-driven prediction of thermal conductivity ratio in nanoparticle-enhanced 60:40 EG/water nanofluids 239
  20. Chapter 13 Industrial applications of flow dynamics and heat transfer 261
  21. Chapter 14 Optimization techniques in flow dynamics and heat transfer 301
  22. Chapter 15 Advanced optimization methods in flow dynamics 335
  23. Index 353
  24. De Gruyter Series in Advanced Mechanical Engineering
https://doi.org/10.1515/9783111661674-005

Chapters in this book

  1. Frontmatter I
  2. Contents V
  3. Aim and scope VII
  4. Preface IX
  5. Acknowledgments
  6. About editors XIII
  7. List of contributing authors XV
  8. Chapter 1 Introduction to flow dynamics and heat transfer 1
  9. Chapter 2 Compressible fluid flow and heat transfer 29
  10. Chapter 3 Non-Newtonian fluid flow and heat transfer 59
  11. Chapter 4 Heat transfer in forced and natural convection 81
  12. Chapter 5 Numerical study of coupled partial differential equations in heat transfer problems with imprecisely defined parameters 91
  13. Chapter 6 Numerical approach to study the effect of uncertain spectrum of field variables in a porous cavity 107
  14. Chapter 7 Investigation of the thermal fluid system using direct numerical simulation 123
  15. Chapter 8 Dynamics of shock-accelerated V-shaped gas interface 139
  16. Chapter 9 Nonlinear and linear analyses of partially ionized plasma 155
  17. Chapter 10 Thermo-fluid behavior of electroosmotic flow in a hydrophobic microchannel under Joule heating and external fields 185
  18. Chapter 11 The study of oscillating water column energy device in a two-layer fluid system of finite impermeable depth 219
  19. Chapter 12 Data-driven prediction of thermal conductivity ratio in nanoparticle-enhanced 60:40 EG/water nanofluids 239
  20. Chapter 13 Industrial applications of flow dynamics and heat transfer 261
  21. Chapter 14 Optimization techniques in flow dynamics and heat transfer 301
  22. Chapter 15 Advanced optimization methods in flow dynamics 335
  23. Index 353
  24. De Gruyter Series in Advanced Mechanical Engineering
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