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

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