The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides fundamental theory, concepts, modelling and analysis of the physical, mathematical, thermodynamical and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems involving phase-changes, such as from liquid to solid.
This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics and functional analysis, and is thoroughly enriched with many appropriate references for an in-depth background reading on theorems. This new edition includes more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems.
1. 4.1 Introduction - p. 81 2. 4.2 A Phase-Field Model for Solidification Using Landau–Ginzburg Free Energy Functional - p. 82 3. 4.3 Some Thermodynamically Consistent Phase-Field and Phase Relaxation Models of Solidification - p. 87 4. 4.4 Solidification of Supercooled Liquid Without Curvature Effect and Kinetic Undercooling: Analysis of the Solution - p. 98 5. 4.5 Analysis of SSPs With the Modified Gibbs–Thomson Relation - p. 106 6. Chapter 5: Superheating due to Volumetric Heat Sources: The Formulation and Analysis - p. 120 7. Chapter 6: Steady-State and Degenerate Classical Stefan Problems - p. 131 8. Chapter 7: Elliptic and Parabolic Variational Inequalities - p. 138 9. 7.1 Introduction - p. 139 10. 7.2 The Elliptic Variational Inequality - p. 140 11. 7.3 The Parabolic Variational Inequality - p. 159 12. 7.4 Some Variational Inequality Formulations of Classical Stefan Problems - p. 163 13. Chapter 8: The Hyperbolic Stefan Problem - p. 182 14. 8.1 Introduction - p. 183 15. 8.2 Model I: Hyperbolic Stefan Problem With Temperature Continuity at the Interface - p. 185 16. 8.3 Model II: Formulation With Temperature Discontinuity at the Interface - p. 193 17. 8.4 Model III: Delay in the Response of Energy to Latent and Sensible Heats - p. 201 18. Chapter 9: Inverse Stefan Problems - p. 207 19. 9.1 Introduction - p. 209 20. 9.2 Well-Posedness of the Solution - p. 210 21. 9.3 Regularization - p. 215 22. 9.4 Determination of Unknown Parameters in Inverse Stefan Problems - p. 227 23. 9.5 Regularization of Inverse Heat conduction Problems by Imposing Suitable Restrictions on the Solution - p. 231 24. 9.6 Regularization of Inverse Stefan Problems Formulated as Equations in the Form of Convolution Integrals - p. 234 25. 9.7 Inverse Stefan Problems Formulated as Defect Minimization Problems - p. 239 26. Chapter 10: Analysis of the Classical Solutions of Stefan Problems - p. 250 27. 10.1 One-Dimensional One-Phase Stefan Problems - p. 251 28. 10.2 One-Dimensional Two-Phase Stefan Problems - p. 276 29. 10.3 Analysis of the Classical Solutions of Multidimensional Stefan Problems - p. 290 30. Chapter 11: Regularity of the Weak Solutions of Some Stefan Problems - p. 295 31. Chapter 12: Quasi-Analytical Solutions and Methods - p. 310 32. 12.1 Introduction - p. 311 33. 12.2 Exact Analytical Solutions of Some Stefan and Stefan-Like Problems - p. 313 34. 12.3 Analytical Solutions of Stefan and Stefan-Like Problems in Series Form - p. 423 35. 12.4 Analytical-Numerical Solutions of Stefan Problems - p. 460 36. 12.5 Analytical-Numerical Solutions of Inverse Stefan Problem - p. 497 37. 12.6 Quasianalytical Solutions of Hyperbolic Stefan Problems - p. 511 38. 12.7 Solutions of Stefan Problems Using Conformal Transformation Method - p. 530 39. 12.8 Approximate Methods of Solutions of Stefan and Stefan-Like Problems - p. 550 40. 12.9 Review of Some Limited Number of Perturbation Methods and Solutions of Stefan and Stefan-Like Problems - p. 614 41. 12.10 Brief Reviews of Some Supplementary References Concerning This Chapter - p. 658 42. Appendix A: Preliminaries - p. 663 43. Appendix B: Some Function Spaces and Norms - p. 671 44. Appendix C: Fixed Point Theorems and Maximum Principles - p. 676 45. Appendix D: Sobolev Spaces - p. 678 46. Bibliography - p. 683 47. Index - p. 717
The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides fundamental theory, concepts, modelling and analysis of the physical, mathematical, thermodynamical and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems involving phase-changes, such as from liquid to solid.
This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics and functional analysis, and is thoroughly enriched with many appropriate references for an in-depth background reading on theorems. This new edition includes more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems.
1. 4.1 Introduction - p. 81 2. 4.2 A Phase-Field Model for Solidification Using Landau–Ginzburg Free Energy Functional - p. 82 3. 4.3 Some Thermodynamically Consistent Phase-Field and Phase Relaxation Models of Solidification - p. 87 4. 4.4 Solidification of Supercooled Liquid Without Curvature Effect and Kinetic Undercooling: Analysis of the Solution - p. 98 5. 4.5 Analysis of SSPs With the Modified Gibbs–Thomson Relation - p. 106 6. Chapter 5: Superheating due to Volumetric Heat Sources: The Formulation and Analysis - p. 120 7. Chapter 6: Steady-State and Degenerate Classical Stefan Problems - p. 131 8. Chapter 7: Elliptic and Parabolic Variational Inequalities - p. 138 9. 7.1 Introduction - p. 139 10. 7.2 The Elliptic Variational Inequality - p. 140 11. 7.3 The Parabolic Variational Inequality - p. 159 12. 7.4 Some Variational Inequality Formulations of Classical Stefan Problems - p. 163 13. Chapter 8: The Hyperbolic Stefan Problem - p. 182 14. 8.1 Introduction - p. 183 15. 8.2 Model I: Hyperbolic Stefan Problem With Temperature Continuity at the Interface - p. 185 16. 8.3 Model II: Formulation With Temperature Discontinuity at the Interface - p. 193 17. 8.4 Model III: Delay in the Response of Energy to Latent and Sensible Heats - p. 201 18. Chapter 9: Inverse Stefan Problems - p. 207 19. 9.1 Introduction - p. 209 20. 9.2 Well-Posedness of the Solution - p. 210 21. 9.3 Regularization - p. 215 22. 9.4 Determination of Unknown Parameters in Inverse Stefan Problems - p. 227 23. 9.5 Regularization of Inverse Heat conduction Problems by Imposing Suitable Restrictions on the Solution - p. 231 24. 9.6 Regularization of Inverse Stefan Problems Formulated as Equations in the Form of Convolution Integrals - p. 234 25. 9.7 Inverse Stefan Problems Formulated as Defect Minimization Problems - p. 239 26. Chapter 10: Analysis of the Classical Solutions of Stefan Problems - p. 250 27. 10.1 One-Dimensional One-Phase Stefan Problems - p. 251 28. 10.2 One-Dimensional Two-Phase Stefan Problems - p. 276 29. 10.3 Analysis of the Classical Solutions of Multidimensional Stefan Problems - p. 290 30. Chapter 11: Regularity of the Weak Solutions of Some Stefan Problems - p. 295 31. Chapter 12: Quasi-Analytical Solutions and Methods - p. 310 32. 12.1 Introduction - p. 311 33. 12.2 Exact Analytical Solutions of Some Stefan and Stefan-Like Problems - p. 313 34. 12.3 Analytical Solutions of Stefan and Stefan-Like Problems in Series Form - p. 423 35. 12.4 Analytical-Numerical Solutions of Stefan Problems - p. 460 36. 12.5 Analytical-Numerical Solutions of Inverse Stefan Problem - p. 497 37. 12.6 Quasianalytical Solutions of Hyperbolic Stefan Problems - p. 511 38. 12.7 Solutions of Stefan Problems Using Conformal Transformation Method - p. 530 39. 12.8 Approximate Methods of Solutions of Stefan and Stefan-Like Problems - p. 550 40. 12.9 Review of Some Limited Number of Perturbation Methods and Solutions of Stefan and Stefan-Like Problems - p. 614 41. 12.10 Brief Reviews of Some Supplementary References Concerning This Chapter - p. 658 42. Appendix A: Preliminaries - p. 663 43. Appendix B: Some Function Spaces and Norms - p. 671 44. Appendix C: Fixed Point Theorems and Maximum Principles - p. 676 45. Appendix D: Sobolev Spaces - p. 678 46. Bibliography - p. 683 47. Index - p. 717
