Food Freezing and Thawing Calculations (eBook)

Preface 5
Contents 7
Nomenclature 10
Chapter-1 15
Introduction to the Freezing Process 15
Chapter-2 19
Heat Transfer Coefficient and Physical Properties 19
2.1 Introduction 19
2.2 Heat Transfer Coefficient 19
2.3 Density 20
2.4 Calorimetric Properties 22
2.4.1 Freezing Point 22
2.4.2 Bound Water 24
2.4.3 Frozen Fraction 25
2.4.4 Enthalpy 27
2.4.5 Sensible Specific Heat 29
2.4.6 Apparent Specific Heat 30
2.4.7 Calorimetric Properties at High Pressure 31
2.4.7.1 Freezing Point at High Pressure 31
2.4.7.2 Enthalpy–Temperature Curve 32
2.5 Thermal Conductivity 32
2.6 Thermal Properties of Tylose Gel 36
2.7 Summary and Recommendations 37
CAUTION 38
Chapter-3 39
Analytical Solutions 39
3.1 The Heat Conduction Equation 39
3.2 Analytical Solutions for Freezing Time 40
3.2.1 Solution for Zero Internal Resistance 41
3.2.2 Solution for Zero Sensible Heat: Plank’s Equation 41
3.2.3 The Biot Number 43
3.2.4 Shape Factors for Zero Sensible Heat in Two and Three Dimensions 44
3.2.5 Exact Analytical Solutions for Freezing with Sensible Heat 46
3.2.6 Perturbation Solutions for Freezing with Sensible Heat 49
3.3 Summary and Recommendations 49
CAUTION 50
Chapter-4 51
Approximate and Empirical Methods 51
4.1 Introduction 51
4.2 Freezing Time of 1-D Shapes 51
4.2.1 Cleland & Earle’s Empirical Method
4.2.2 Mascheroni & Calvelo’s Approximate Method
4.2.3 Pham’s Method 1 (1984) 53
4.2.4 Pham’s Method 2 (1986) 54
4.2.5 Salvadori & Mascheroni’s Method
4.2.6 Improved Shape Factors for Basic Geometries 56
4.2.7 Comparison of Approximate and Empirical Freezing Time Prediction Methods in 1-D 57
4.2.8 Freezing Time Prediction for Extended Parameter Range 59
4.3 Freezing Time of Multidimensional Shapes 62
4.3.1 Equivalent Shape Approach 62
4.3.2 EHTD Shape Factor Approach 62
4.3.2.1 Infinite Rectangular Rods, Bricks, Finite Cylinders 62
4.3.2.2 Elliptical Cylinders (2-D) 63
4.3.2.3 Three-Dimensional Ellipsoids 64
4.3.2.4 Irregular Shapes 65
4.3.3 Mean Conducting Path (MCP) Approach 66
4.3.3.1 MCP for Rectangular Rods and Bricks 67
4.3.3.2 MCP for Ellipses and Ellipsoids 67
4.3.4 Arroyo & Mascheroni’s Method
4.3.5 Comparison of Shape Factor and Mean Conducting Path Approaches 68
4.4 Thawing Time Prediction 69
4.4.1 Cleland et al.’s method 70
4.4.2 Salvadori and Masheroni’s Method 70
4.4.3 Thawing Time Prediction for Multi-Dimensional Shapes 71
4.5 Freezing Heat Load 71
4.5.1 Total and Average Heat Load 71
4.5.2 Heat Load During the Phase Change-Subcooling Period 73
4.5.3 Dynamic Heat Load During the Precooling Period 75
4.5.3.1 Analytical Solutions 75
4.5.3.2 Lovatt et al.’s Method 75
4.5.3.3 Pham’s Method 76
4.5.4 Summary of Method 77
4.6 Summary and Recommendations 77
CAUTION 78
Chapter-5 79
Numerical Methods 79
5.1 Introduction 79
5.2 Discretization of the Space Domain 80
5.2.1 Finite Difference Method (FDM) 81
5.2.2 Finite Volume Method (FVM) 84
5.2.3 Finite Element Method (FEM) 85
5.2.4 Discretization of the Space Domain in 2-D and 3-D 89
5.3 Time-Stepping 90
5.3.1 Two-Level Stepping Schemes 90
5.3.2 Lee’s Three-Level Scheme 92
5.3.3 Use of Generic ODE Solvers 93
5.3.4 Time Stepping in Structured Grid FDM and FVM 93
5.4 Dealing with Changes in Physical Properties 95
5.4.1 Latent Heat of Freezing 95
5.4.1.1 Classification of Methods 95
5.4.1.2 Fictitious Heat Source Methods 96
5.4.1.3 Apparent Specific Heat Methods 97
5.4.1.4 Enthalpy Methods 98
5.4.1.5 Pham’s Temperature Correction Method (Quasi-enthalpy Method) 100
5.4.2 Variable Thermal Conductivity 102
5.4.3 Variable Density due to Thermal Expansion 104
5.5 Convergence and Accuracy of Numerical Methods 105
5.6 Summary and Recommendations 106
CAUTION 107
Chapter-6 108
Modelling Coupled Phenomena 108
6.1 Introduction 108
6.2 Combined Heat and Mass Transfer 108
6.2.1 Mass Transfer During the Freezing of Dense Foods 109
6.2.2 Mass Transfer During Air Freezing of Porous Foods 111
6.2.3 Mass Transfer During Immersion Freezing 117
6.2.4 Mass Transfer Between Intra- and Extracellular Spaces 117
6.3 Supercooling and Nucleation Effects 118
6.3.1 Instantaneous Nucleation Followed by Dendritic Crystal Growth 118
6.3.2 Gradual Nucleation in an Emulsion 119
6.3.3 Gradual Nucleation in Cellular Tissues 120
6.4 Microscale Modelling of Crystal Growth 123
6.4.1 Enthalpy Method 124
6.4.2 Cellular Automata 125
6.4.3 Front Tracking or Sharp Interface Methods 125
6.4.4 Level Set Method 125
6.4.5 Phase Field Method 126
6.5 High Pressure Freezing and Thawing 129
6.6 Freeze Concentration 131
6.6.1 General Principles 131
6.6.2 Suspension Freeze Concentration Model 133
6.6.3 Layer Freeze Concentration Models 133
6.7 Freezing of Liquid Foods 135
6.7.1 CFD Model of Liquid Food Freezing 135
6.7.2 Freezing of a Well-Stirred Liquid 137
6.8 Microwave and Radio Frequency Thawing 138
6.8.1 General Principles 138
6.8.1.1 Lambert’s Law 138
6.8.1.2 Maxwell’s Equations 139
6.8.2 Analytical Solutions 140
6.8.3 Numerical Solutions 140
6.9 Thermomechanical Effects During Freezing 141
Chapter-7 145
Conclusions 145
Erratum 148
References 149
Index 161