• 1 Chapter One: Introduction (9)
  • 1.1 Literature review (11)
  • 1.2 Ice Adhesion to Material surface (19)
  • 1.3 Industrial applications (22)
• 2 Chapter Two: Theory (26)
  • 2.1 Heat transfer during pipe freezing (26)
  • 2.2 Phase-Change Problems (30)
    • 2.2.1 Mathematical formulation of phase-change problems [17] (31)
      • 2.2.1.1 Effects of Density Change (34)
    • 2.2.2 Generalization to Multidimension (35)
    • 2.2.3 Dimensionless Variables of Phase-Change Problem (38)
    • 2.2.4 Variable time step method for solving phase change problems: A numerical solution (40)
    • 2.2.5 Enthalpy method for solution of phase-change problems (41)
  • 2.3 The Properties of Nitrogen (45)
  • 2.4 The Structure of Ice (46)
  • 2.5 Regelation (48)
  • 2.6 The Production of Clear Ice (48)
  • 2.7 The effect of relative expansion between the ice and the pipe (49)
• 3 Chapter Three: Numerical Modeling (51)
  • 3.1 Problem Definition (51)
  • 3.2 Geometry (51)
  • 3.3 Problem setup (51)
  • 3.4 Governing Equations (52)
    • 3.4.1 One Dimensional Equation (54)
  • 3.5 Solution Method (57)
    • 3.5.1 Fixed-Grid Methods (57)
      • 3.5.1.1 Interface Conditions (59)
      • 3.5.1.2 Determination of Time Steps (60)
      • 3.5.1.3 Implicit enthalpy method for solidification at a single phase-change temperature (61)
  • 3.6 Three Dimensional Modeling (64)
    • 3.6.1 Energy Equation (65)
• 4 Chapter Four: Experimental Investigation (67)
  • 4.1 Experimental Setup (67)
    • 4.1.1 Test apparatus (68)
  • 4.2 Experimentation 1: Freezing of Water in 2 inch Pipe (73)
    • 4.2.1 Results and Discussion (75)
  • 4.3 Experiments 2: Freezing of Water in 4 inch Pipe (77)
  • 4.4 Experiments 3: Freezing of Diesel Fuel (78)
• 5 Chapter Five: Results and Discussion (84)
  • 5.1 Numerical Results Validation (84)
  • 5.2 Two Dimensional Modeling (86)
  • 5.3 Three Dimensional Modeling (89)
• 6 Chapter Six: Conclusion and Proposal for Future Works (96)
  • 6.1 Proposals for Future Work (98)
• 7 References (99)