FOOD ENGINEERING Contents About the Authors .................................................................................................................v Foreword .............................................................................................................................vii Preface .................................................................................................................................. ix CHAPTER 1 Introduction .......................................................................................................1 1.1 Dimensions .............................................................................................1 1.2 Engineering Units ...................................................................................2 1.2.1 Base Units ....................................................................................2 1.2.2 Derived Units ..............................................................................3 1.2.3 Supplementary Units ..................................................................4 1.3 System ...................................................................................................10 1.4 State of a System.................................................................................... 11 1.4.1 Extensive Properties ..................................................................12 1.4.2 Intensive Properties ..................................................................13 1.5 Density ...................................................................................................13 1.6 Concentration .......................................................................................15 1.7 Moisture Content ..................................................................................17 1.8 Temperature ...........................................................................................20 1.9 Pressure ..................................................................................................22 1.10 Enthalpy.................................................................................................26 1.11 Equation of State and Perfect Gas Law ................................................26 1.12 Phase Diagram of Water .......................................................................27 1.13 Conservation of Mass ...........................................................................29 1.13.1 Conservation of Mass for an Open System .............................30 1.13.2 Conservation of Mass for a Closed System .............................32 1.14 Material Balances ..................................................................................32 1.15 Thermodynamics ..................................................................................41 1.16 Laws of Thermodynamics .....................................................................42 1.16.1 First Law of Thermodynamics ..................................................42 1.16.2 Second Law of Thermodynamics .............................................42 1.17 Energy ...................................................................................................43 1.18 Energy Balance ......................................................................................45 1.19 Energy Balance for a Closed System ....................................................45 1.19.1 Heat ...........................................................................................45 1.19.2 Work ..........................................................................................46 1.20 Energy Balance for an Open System ....................................................55 1.20.1 Energy Balance for Steady Flow Systems .................................56 1.21 A Total Energy Balance ..........................................................................56 1.22 Power .....................................................................................................59 1.23 Area ........................................................................................................59 Problems .........................................................................................................60 List of Symbols ...............................................................................................62 Bibliography ...................................................................................................63 CHAPTER 2 Fluid Flow in Food Processing ...........................................................................65 2.1 Liquid Transport Systems ........................................................................66 2.1.1 Pipes for Processing Plants ...........................................................67 2.1.2 Types of Pumps .............................................................................68 2.2 Properties of Liquids ...............................................................................71 2.2.1 Terminology Used in Material Response to Stress ......................72 2.2.2 Density...........................................................................................72 2.2.3 Viscosity .........................................................................................73 2.3 Handling Systems for Newtonian Liquids .............................................81 2.3.1 The Continuity Equation ..............................................................81 2.3.2 Reynolds Number .........................................................................84 2.3.3 Entrance Region and Fully Developed Flow ................................88 2.3.4 Velocity Profi le in a Liquid Flowing Under Fully Developed Flow Conditions ........................................................90 2.3.5 Forces Due to Friction ...................................................................96 2.4 Force Balance on a Fluid Element Flowing in a Pipe—Derivation of Bernoulli Equation ............................................................................100 2.5 Energy Equation for Steady Flow of Fluids ..........................................107 2.5.1 Pressure Energy ........................................................................... 110 2.5.2 Kinetic Energy ............................................................................. 110 2.5.3 Potential Energy ..........................................................................112 2.5.4 Frictional Energy Loss .................................................................112 2.5.5 Power Requirements of a Pump .................................................115 2.6 Pump Selection and Performance Evaluation .....................................119 2.6.1 Centrifugal Pumps ......................................................................119 2.6.2 Head ............................................................................................121 2.6.3 Pump Performance Characteristics ............................................121 2.6.4 Pump Characteristic Diagram ................................................... 125 2.6.5 Net Positive Suction Head ......................................................... 126 2.6.6 Selecting a Pump for a Liquid Transport System ..................... 129 2.6.7 Affi nity Laws ............................................................................... 135 2.7 Flow Measurement ............................................................................... 136 2.7.1 The Pitot Tube ............................................................................ 140 2.7.2 The Orifi ce Meter ....................................................................... 142 2.7.3 The Venturi Meter....................................................................... 146 2.7.4 Variable-Area Meters .................................................................. 146 2.7.5 Other Measurement Methods ................................................... 147 2.8 Measurement of Viscosity .................................................................. 148 2.8.1 Capillary Tube Viscometer .................................................... 148 2.8.2 Rotational Viscometer ........................................................... 150 2.8.3 Infl uence of Temperature on Viscosity ................................. 153 2.9 Flow Characteristics of Non-Newtonian Fluids ............................... 155 2.9.1 Properties of Non-Newtonian Fluids ................................... 155 2.9.2 Velocity Profi le of a Power Law Fluid ....................................161 2.9.3 Volumetric Flow Rate of a Power Law Fluid ......................... 162 2.9.4 Average Velocity in a Power Law Fluid .................................. 163 2.9.5 Friction Factor and Generalized Reynolds Number for Power Law Fluids ............................................................. 163 2.9.6 Computation of Pumping Requirement of Non-newtonian Liquids ........................................................ 166 2.10 Transport of solid foods .................................................................... 169 2.10.1 Properties of Granular Materials and Powders .....................170 2.10.2 Flow of Granular Foods ......................................................... 175 Problems ...................................................................................................... 178 List of Symbols ............................................................................................ 183 Bibliography ................................................................................................ 185 CHAPTER 3 Energy and Controls in Food Processes ...........................................................187 3.1 Generation of Steam .......................................................................... 187 3.1.1 Steam Generation Systems .................................................... 188 3.1.2 Thermodynamics of Phase Change ...................................... 190 3.1.3 Steam Tables ........................................................................... 194 3.1.4 Steam Utilization ................................................................... 200 3.2 Fuel Utilization .................................................................................. 204 3.2.1 Systems ................................................................................... 206 3.2.2 Mass and Energy Balance Analysis .........................................207 3.2.3 Burner Effi ciencies ..................................................................209 3.3 Electric Power Utilization ................................................................... 210 3.3.1 Electrical Terms and Units ......................................................212 3.3.2 Ohm’s Law ..............................................................................213 3.3.3 Electric Circuits .......................................................................214 3.3.4 Electric Motors ........................................................................216 3.3.5 Electrical Controls ...................................................................217 3.3.6 Electric Lighting ......................................................................218 3.4 Process Controls in Food Processing ................................................ 220 3.4.1 Processing Variables and Performance Indicators ................ 222 3.4.2 Input and Output Signals to Control Processes ................... 224 3.4.3 Design of a Control System ................................................... 224 3.5 Sensors ................................................................................................ 232 3.5.1 Temperature ............................................................................. 232 3.5.2 Liquid Level in a Tank .............................................................. 234 3.5.3 Pressure Sensors ....................................................................... 235 3.5.4 Flow Sensors ............................................................................. 236 3.5.5 Glossary of Terms Important in Data Acquisition ................. 237 3.6 Dynamic Response Characteristics of Sensors .................................... 237 Problems .......................................................................................................241 List of Symbols ............................................................................................ 244 Bibliography ................................................................................................ 245 CHAPTER 4 Heat Transfer in Food Processing ....................................................................247 4.1 Systems for Heating and Cooling Food Products ............................... 248 4.1.1 Plate Heat Exchanger ............................................................... 248 4.1.2 Tubular Heat Exchanger .......................................................... 252 4.1.3 Scraped-surface Heat Exchanger.............................................. 253 4.1.4 Steam-infusion Heat Exchanger .............................................. 255 4.1.5 Epilogue .................................................................................... 256 4.2 Thermal Properties of Foods ................................................................ 257 4.2.1 Specifi c Heat ............................................................................. 257 4.2.2 Thermal Conductivity .............................................................. 260 4.2.3 Thermal Diffusivity .................................................................. 262 4.3 Modes of Heat Transfer ........................................................................ 264 4.3.1 Conductive Heat Transfer ........................................................ 264 4.3.2 Convective Heat Transfer ......................................................... 267 4.3.3 Radiation Heat Transfer ........................................................... 269 4.4 Steady-State Heat Transfer.....................................................................270 4.4.1 Conductive Heat Transfer in a Rectangular Slab .....................271 4.4.2 Conductive Heat Transfer through a Tubular Pipe ................ 274 4.4.3 Heat Conduction in Multilayered Systems ............................. 277 4.4.4 Estimation of Convective Heat-Transfer Coeffi cient .............. 285 4.4.5 Estimation of Overall Heat-Transfer Coeffi cient .....................302 4.4.6 Fouling of Heat Transfer Surfaces ........................................... 306 4.4.7 Design of a Tubular Heat Exchanger .......................................312 4.4.8 The Effectiveness-NTU Method for Designing Heat Exchangers ................................................................................ 320 4.4.9 Design of a Plate Heat Exchanger ........................................... 325 4.4.10 Importance of Surface Characteristics in Radiative Heat Transfer ............................................................................ 332 4.4.11 Radiative Heat Transfer between Two Objects ....................... 334 4.5 Unsteady-State Heat Transfer ............................................................... 337 4.5.1 Importance of External versus Internal Resistance to Heat Transfer ..................................................................................... 339 4.5.2 Negligible Internal Resistance to Heat Transfer (NBi _ 0.1)—A Lumped System Analysis ................................ 340 4.5.3 Finite Internal and Surface Resistance to Heat Transfer (0.1 _ NBi _ 40) ....................................................................... 345 4.5.4 Negligible Surface Resistance to Heat Transfer (NBi _ 40) ..... 348 4.5.5 Finite Objects ............................................................................. 348 4.5.6 Procedures to Use Temperature–Time Charts .......................... 350 4.5.7 Use of fh and j Factors in Predicting Temperature in Transient Heat Transfer ............................................................. 358 4.6 Electrical Conductivity of Foods .......................................................... 366 4.7 Ohmic Heating ..................................................................................... 369 4.8 Microwave Heating ................................................................................371 4.8.1 Mechanisms of Microwave Heating.......................................... 372 4.8.2 Dielectric Properties .................................................................. 373 4.8.3 Conversion of Microwave Energy into Heat ............................ 374 4.8.4 Penetration Depth of Microwaves ............................................ 375 4.8.5 Microwave Oven ........................................................................ 377 4.8.6 Microwave Heating of Foods .................................................... 378 Problems ...................................................................................................... 380 List of Symbols ............................................................................................ 397 Bibliography ................................................................................................ 399 CHAPTER 5 Preservation Processes ...................................................................................403 5.1 Processing Systems ............................................................................... 403 5.1.1 Pasteurization and Blanching Systems ..................................... 404 5.1.2 Commercial Sterilization Systems ............................................ 406 5.1.3 Ultra-High Pressure Systems ...................................................... 410 5.1.4 Pulsed Electric Field Systems .....................................................412 5.1.5 Alternative Preservation Systems ...............................................413 5.2 Microbial Survivor Curves .....................................................................413 5.3 Infl uence of External Agents .................................................................418 5.4 Thermal Death Time F ......................................................................... 422 5.5 Spoilage Probability ............................................................................. 423 5.6 General Method for Process Calculation ............................................ 424 5.6.1 Applications to Pasteurization .................................................. 426 5.6.2 Commercial Sterilization .......................................................... 429 5.6.3 Aseptic Processing and Packaging ............................................ 432 5.7 Mathematical Methods ........................................................................ 440 5.7.1 Pouch Processing ....................................................................... 444 Problems ...................................................................................................... 447 List of Symbols ............................................................................................ 450 Bibliography .................................................................................................451 CHAPTER 6 Refrigeration ..................................................................................................455 6.1 Selection of a Refrigerant ..................................................................... 456 6.2 Components of a Refrigeration System ............................................... 460 6.2.1 Evaporator ...................................................................................461 6.2.2 Compressor ................................................................................ 463 6.2.3 Condenser .................................................................................. 466 6.2.4 Expansion Valve ......................................................................... 468 6.3 Pressure–Enthalpy Charts .....................................................................470 6.3.1 Pressure–Enthalpy Tables .......................................................... 474 6.3.2 Use of Computer-Aided Procedures to Determine Thermodynamic Properties of Refrigerants .............................. 475 6.4 Mathematical Expressions Useful in Analysis of Vapor-Compression Refrigeration ....................................................... 478 6.4.1 Cooling Load.............................................................................. 478 6.4.2 Compressor ................................................................................ 480 6.4.3 Condenser .................................................................................. 480 6.4.4 Evaporator ...................................................................................481 6.4.5 Coeffi cient of Performance .........................................................481 6.4.6 Refrigerant Flow Rate ..................................................................481 6.5 Use of Multistage Systems .................................................................... 490 6.5.1 Flash Gas Removal System .........................................................491 Problems .................................................................................................... 495 List of Symbols ............................................................................................ 498 Bibliography ................................................................................................ 498 CHAPTER 7 Food Freezing .................................................................................................501 7.1 Freezing Systems ....................................................................................502 7.1.1 Indirect Contact Systems ............................................................502 7.1.2 Direct-Contact Systems ...............................................................507 7.2 Frozen-Food Properties ......................................................................... 510 7.2.1 Density......................................................................................... 510 7.2.2 Thermal Conductivity ................................................................. 511 7.2.3 Enthalpy ...................................................................................... 511 7.2.4 Apparent Specifi c Heat ...............................................................513 7.2.5 Apparent Thermal Diffusivity.....................................................513 7.3 Freezing Time.........................................................................................514 7.3.1 Plank’s Equation .........................................................................516 7.3.2 Other Freezing-Time Prediction Methods ................................ 520 7.3.3 Pham’s Method to Predict Freezing Time ................................. 520 7.3.4 Prediction of Freezing Time of Finite-Shaped Objects ............ 524 7.3.5 Experimental Measurement of Freezing Time .......................... 528 7.3.6 Factors Infl uencing Freezing Time ............................................ 528 7.3.7 Freezing Rate .............................................................................. 529 7.3.8 Thawing Time ............................................................................. 529 7.4 Frozen-Food Storage ............................................................................. 530 7.4.1 Quality Changes in Foods during Frozen Storage ................... 530 Problems ............................................................................................... 534 List of Symbols ............................................................................................ 538 Bibliography ............................................................................................... 539 CHAPTER 8 Evaporation ....................................................................................................543 8.1 Boiling-Point Elevation ........................................................................ 545 8.2 Types of Evaporators ............................................................................ 547 8.2.1 Batch-Type Pan Evaporator ....................................................... 547 8.2.2 Natural Circulation Evaporators ............................................... 548 8.2.3 Rising-Film Evaporator .............................................................. 548 8.2.4 Falling-Film Evaporator ............................................................. 549 8.2.5 Rising/Falling-Film Evaporator ................................................. 550 8.2.6 Forced-Circulation Evaporator ...................................................551 8.2.7 Agitated Thin-Film Evaporator ...................................................551 8.3 Design of a Single-Effect Evaporator ................................................... 554 8.4 Design of a Multiple-Effect Evaporator ............................................... 559 8.5 Vapor Recompression Systems ............................................................. 565 8.5.1 Thermal Recompression ............................................................ 565 8.5.2 Mechanical Vapor Recompression ............................................ 566 Problems ............................................................................................... 566 List of Symbols ............................................................................................ 569 Bibliography ............................................................................................... 569 CHAPTER 9 Psychrometrics ................................................................................................571 9.1 Properties of Dry Air..............................................................................571 9.1.1 Composition of Air .....................................................................571 9.1.2 Specifi c Volume of Dry Air ........................................................ 572 9.1.3 Specifi c Heat of Dry Air ............................................................. 572 9.1.4 Enthalpy of Dry Air .................................................................... 572 9.1.5 Dry Bulb Temperature ............................................................... 573 9.2 Properties of Water Vapor .................................................................... 573 9.2.1 Specifi c Volume of Water Vapor ................................................ 573 9.2.2 Specifi c Heat of Water Vapor ..................................................... 573 9.2.3 Enthalpy of Water Vapor ............................................................ 574 9.3 Properties of Air–Vapor Mixtures ........................................................ 574 9.3.1 Gibbs–Dalton Law ..................................................................... 574 9.3.2 Dew-Point Temperature ............................................................. 574 9.3.3 Humidity Ratio (or Moisture Content) .............................. 575 9.3.4 Relative Humidity ................................................................ 576 9.3.5 Humid Heat of an Air–Water Vapor Mixture ...................... 576 9.3.6 Specifi c Volume .................................................................... 577 9.3.7 Adiabatic Saturation of Air .................................................. 577 9.3.8 Wet Bulb Temperature.......................................................... 579 9.4 The Psychrometric Chart .................................................................. 582 9.4.1. Construction of the Chart .................................................... 582 9.4.2 Use of Psychrometric Chart to Evaluate Complex Air-Conditioning Processes ................................................. 584 Problems ...................................................................................................... 589 List of Symbols ............................................................................................ 592 Bibliography ............................................................................................... 593 CHAPTER 10 Mass Transfer ................................................................................................595 10.1 The Diffusion Process....................................................................... 596 10.1.1 Steady-State Diffusion of Gases (and Liquids) through Solids ...................................................................... 599 10.1.2 Convective Mass Transfer ..................................................... 600 10.1.3 Laminar Flow over a Flat Plate ............................................ 604 10.1.4 Turbulent Flow Past a Flat Plate .......................................... 608 10.1.5 Laminar Flow in a Pipe ........................................................ 608 10.1.6 Turbulent Flow in a Pipe ..................................................... 609 10.1.7 Mass Transfer for Flow over Spherical Objects ................... 609 10.2 Unsteady-State Mass Transfer ........................................................... 610 10.2.1 Transient-State Diffusion ...................................................... 611 10.2.2 Diffusion of Gases .................................................................616 Problems ....................................................................................................619 List of Symbols ..........................................................................................621 Bibliography ............................................................................................. 622 CHAPTER 11 Membrane Separation .................................................................................623 11.1 Electrodialysis Systems ..................................................................... 625 11.2 Reverse Osmosis Membrane Systems .............................................. 629 11.3 Membrane Performance ................................................................... 636 11.4 Ultrafi ltration Membrane Systems .................................................. 637 11.5 Concentration Polarization ............................................................. 639 11.6 Types of Reverse-Osmosis and Ultrafi ltration Systems .................. 645 11.6.1 Plate and Frame .................................................................... 646 11.6.2 Tubular .................................................................................. 646 11.6.3 Spiral-Wound ....................................................................... 646 11.6.4 Hollow-Fiber ........................................................................ 649 Problems ................................................................................................... 649 List of Symbols ......................................................................................... 650 Bibliography ..............................................................................................651 CHAPTER 12 Dehydration .................................................................................................653 12.1 Basic Drying Processes ..................................................................... 653 12.1.1 Water Activity ....................................................................... 654 12.1.2 Moisture Diffusion .............................................................. 657 12.1.3 Drying-Rate Curves .............................................................. 658 12.1.4 Heat and Mass Transfer ....................................................... 658 12.2 Dehydration systems ........................................................................ 660 12.2.1 Tray or Cabinet Dryers ........................................................ 660 12.2.2 Tunnel Dryers .......................................................................661 12.2.3 Puff-Drying .......................................................................... 662 12.2.4 Fluidized-Bed Drying .......................................................... 663 12.2.5 Spray Drying ........................................................................ 663 12.2.6 Freeze-Drying ....................................................................... 664 12.3 Dehydration System Design............................................................. 665 12.3.1 Mass and Energy Balance .................................................... 665 12.3.2 Drying-Time Prediction .......................................................670 Problems ................................................................................................... 680 List of Symbols ......................................................................................... 685 Bibliography .............................................................................................. 686 CHAPTER 13 Supplemental Processes ...............................................................................689 13.1 Filtration ........................................................................................... 689 13.1.1 Operating Equations ........................................................... 689 13.1.2 Mechanisms of Filtration .................................................... 695 13.1.3 Design of a Filtration System .............................................. 696 13.2 Sedimentation .................................................................................. 699 13.2.1 Sedimentation Velocities for Low-Concentration Suspensions ......................................................................... 699 13.2.2 Sedimentation in High-Concentration Suspensions..........702 13.3 Centrifugation ...................................................................................705 13.3.1 Basic Equations .....................................................................705 13.3.2 Rate of Separation ................................................................705 13.3.3. Liquid-Liquid Separation .....................................................707 13.3.4 Particle-Gas Separation ........................................................709 13.4 Mixing ...............................................................................................709 13.4.1 Agitation Equipment ............................................................ 711 13.4.2 Power Requirements of Impellers ........................................714 Problems ....................................................................................................718 List of Symbols ..........................................................................................719 Bibliography ............................................................................................. 720 CHAPTER 14 Extrusion Processes for Foods .......................................................................721 14.1 Introduction and Background ..........................................................721 14.2 Basic Principles of Extrusion ............................................................ 722 14.3 Extrusion Systems ............................................................................. 729 14.3.1 Cold Extrusion ...................................................................... 730 14.3.2 Extrusion Cooking ................................................................731 14.3.3 Single Screw Extruders ......................................................... 732 14.3.4 Twin-Screw Extruders ........................................................... 734 14.4 Extrusion System Design .................................................................. 735 14.5 Design of More Complex Systems ................................................... 740 Problems ....................................................................................................741 List of Symbols ......................................................................................... 742 Bibliography .............................................................................................. 742 CHAPTER 15 Packaging Concepts .....................................................................................745 15.1 Introduction...................................................................................... 745 15.2 Food Protection ................................................................................ 746 15.3 Product Containment ...................................................................... 747 15.4 Product Communication ................................................................. 748 15.5 Product Convenience ....................................................................... 748 15.6 Mass Transfer in Packaging Materials .............................................. 748 15.6.1 Permeability of Packaging Material to “Fixed” Gases .........751 15.7 Innovations in Food Packaging ....................................................... 754 15.7.1 Passive Packaging ................................................................. 755 15.7.2 Active Packaging ................................................................... 755 15.7.3 Intelligent Packaging ............................................................ 756 15.8 Food Packaging and Product Shelf-life ........................................... 758 15.8.1 Scientifi c Basis for Evaluating Shelf Life.............................. 758 15.9 Summary ........................................................................................... 766 Problems ................................................................................................... 766 List of Symbols ......................................................................................... 767 Bibliography ............................................................................................. 768 Appendices ........................................................................................................................771 A.1 SI System of Units and Conversion Factors .......................................771 A.1.1 Rules for Using SI Units ...........................................................771 Table A.1.1: SI Prefi xes ........................................................................771 Table A.1.2: Useful Conversion Factors ............................................ 774 Table A.1.3: Conversion Factors for Pressure .................................... 776 A.2 Physical Properties of Foods .............................................................. 777 Table A.2.1: Specifi c Heat of Foods ................................................... 777 Table A.2.2: Thermal Conductivity of Selected Food Products ......................................................................... 778 Table A.2.3: Thermal Diffusivity of Some Foodstuffs ...................... 780 Table A.2.4: Viscosity of Liquid Foods ...............................................781 Table A.2.5: Properties of Ice as a Function of Temperature ................................................................... 782 Table A.2.6: Approximate Heat Evolution Rates of Fresh Fruits and Vegetables When Stored at Temperatures Shown ................................................. 782 Table A.2.7: Enthalpy of Frozen Foods ............................................. 784 Table A.2.8: Composition Values of Selected Foods ........................ 785 Table A.2.9: Coeffi cients to Estimate Food Properties ..................... 786 A.3 Physical Properties of Nonfood Materials ........................................ 787 Table A.3.1: Physical Properties of Metals ........................................ 787 Table A.3.2: Physical Properties of Nonmetals ................................. 788 Table A.3.3: Emissivity of Various Surfaces ....................................... 790 A.4 Physical Properties of Water and Air ................................................. 792 Table A.4.1: Physical Properties of Water at the Saturation Pressure ........................................................ 792 Table A.4.2: Properties of Saturated Steam ....................................... 793 Table A.4.3: Properties of Superheated Steam .................................. 795 Table A.4.4: Physical Properties of Dry Air at Atmospheric Pressure .......................................................................... 796 A.5 Psychrometric Charts ......................................................................... 797 Figure A.5.1: Psychrometric chart for high temperatures ................. 797 Figure A.5.2: Psychrometric chart for low temperatures .................. 798 A.6 Pressure-Enthalpy Data ...................................................................... 799 Figure A.6.1: Pressure–enthalpy diagram for Refi gerant 12 ............. 799 Table A.6.1: Properties of Saturated Liquid andVapor R-12 ............ 800 Figure A.6.2: Pressure–enthalpy diagram of superheated R-12 vapor .................................................................... 803 Table A.6.2: Properties of Saturated Liquid and Vapor R-717 (Ammonia) .......................................................... 804 Figure A.6.3: Pressure-enthalpy diagram of superheated R-717 (ammonia) vapor ..........................807 Table A.6.3: Properties of Saturated Liquid and Vapor R-134a ...................808 Figure A.6.4: Pressure–enthalpy diagram of R-134a ......................... 811 Figure A.6.5: Pressure–enthalpy diagram of R-134a (expanded scale) ...........................................................812 A.7 Symbols for Use in Drawing Food Engineering Process Equipment ...........................................................................................813 A.8 Miscellaneous ......................................................................................818 Table A.8.1: Numerical Data, and Area/Volume of Objects ..................................................................818 Figure A.8.1: Temperature at geometric center of a sphere (expanded scale) .............................819 Figure A.8.2: Temperature at the axis of an infi nitely long cylinder (expanded scale) ........................ 820 Figure A.8.3: Temperature at the midplane of an infi nite slab (expanded scale) ............................821 A.9 Dimensional Analysis ........................................................................ 822 Table A.9.1: Dimensions of selected experimental variables .............................................................. 823 Bibliography .............................................................................................. 826 Index .......................................................................................................... 829 Food Science and Technology: International Series ............................. 839
FOOD ENGINEERING
Contents
About the Authors .................................................................................................................v
Foreword .............................................................................................................................vii
Preface .................................................................................................................................. ix
CHAPTER 1 Introduction .......................................................................................................1
1.1 Dimensions .............................................................................................1
1.2 Engineering Units ...................................................................................2
1.2.1 Base Units ....................................................................................2
1.2.2 Derived Units ..............................................................................3
1.2.3 Supplementary Units ..................................................................4
1.3 System ...................................................................................................10
1.4 State of a System.................................................................................... 11
1.4.1 Extensive Properties ..................................................................12
1.4.2 Intensive Properties ..................................................................13
1.5 Density ...................................................................................................13
1.6 Concentration .......................................................................................15
1.7 Moisture Content ..................................................................................17
1.8 Temperature ...........................................................................................20
1.9 Pressure ..................................................................................................22
1.10 Enthalpy.................................................................................................26
1.11 Equation of State and Perfect Gas Law ................................................26
1.12 Phase Diagram of Water .......................................................................27
1.13 Conservation of Mass ...........................................................................29
1.13.1 Conservation of Mass for an Open System .............................30
1.13.2 Conservation of Mass for a Closed System .............................32
1.14 Material Balances ..................................................................................32
1.15 Thermodynamics ..................................................................................41
1.16 Laws of Thermodynamics .....................................................................42
1.16.1 First Law of Thermodynamics ..................................................42
1.16.2 Second Law of Thermodynamics .............................................42
1.17 Energy ...................................................................................................43
1.18 Energy Balance ......................................................................................45
1.19 Energy Balance for a Closed System ....................................................45
1.19.1 Heat ...........................................................................................45
1.19.2 Work ..........................................................................................46
1.20 Energy Balance for an Open System ....................................................55
1.20.1 Energy Balance for Steady Flow Systems .................................56
1.21 A Total Energy Balance ..........................................................................56
1.22 Power .....................................................................................................59
1.23 Area ........................................................................................................59
Problems .........................................................................................................60
List of Symbols ...............................................................................................62
Bibliography ...................................................................................................63
CHAPTER 2 Fluid Flow in Food Processing ...........................................................................65
2.1 Liquid Transport Systems ........................................................................66
2.1.1 Pipes for Processing Plants ...........................................................67
2.1.2 Types of Pumps .............................................................................68
2.2 Properties of Liquids ...............................................................................71
2.2.1 Terminology Used in Material Response to Stress ......................72
2.2.2 Density...........................................................................................72
2.2.3 Viscosity .........................................................................................73
2.3 Handling Systems for Newtonian Liquids .............................................81
2.3.1 The Continuity Equation ..............................................................81
2.3.2 Reynolds Number .........................................................................84
2.3.3 Entrance Region and Fully Developed Flow ................................88
2.3.4 Velocity Profi le in a Liquid Flowing Under Fully
Developed Flow Conditions ........................................................90
2.3.5 Forces Due to Friction ...................................................................96
2.4 Force Balance on a Fluid Element Flowing in a Pipe—Derivation
of Bernoulli Equation ............................................................................100
2.5 Energy Equation for Steady Flow of Fluids ..........................................107
2.5.1 Pressure Energy ........................................................................... 110
2.5.2 Kinetic Energy ............................................................................. 110
2.5.3 Potential Energy ..........................................................................112
2.5.4 Frictional Energy Loss .................................................................112
2.5.5 Power Requirements of a Pump .................................................115
2.6 Pump Selection and Performance Evaluation .....................................119
2.6.1 Centrifugal Pumps ......................................................................119
2.6.2 Head ............................................................................................121
2.6.3 Pump Performance Characteristics ............................................121
2.6.4 Pump Characteristic Diagram ................................................... 125
2.6.5 Net Positive Suction Head ......................................................... 126
2.6.6 Selecting a Pump for a Liquid Transport System ..................... 129
2.6.7 Affi nity Laws ............................................................................... 135
2.7 Flow Measurement ............................................................................... 136
2.7.1 The Pitot Tube ............................................................................ 140
2.7.2 The Orifi ce Meter ....................................................................... 142
2.7.3 The Venturi Meter....................................................................... 146
2.7.4 Variable-Area Meters .................................................................. 146
2.7.5 Other Measurement Methods ................................................... 147
2.8 Measurement of Viscosity .................................................................. 148
2.8.1 Capillary Tube Viscometer .................................................... 148
2.8.2 Rotational Viscometer ........................................................... 150
2.8.3 Infl uence of Temperature on Viscosity ................................. 153
2.9 Flow Characteristics of Non-Newtonian Fluids ............................... 155
2.9.1 Properties of Non-Newtonian Fluids ................................... 155
2.9.2 Velocity Profi le of a Power Law Fluid ....................................161
2.9.3 Volumetric Flow Rate of a Power Law Fluid ......................... 162
2.9.4 Average Velocity in a Power Law Fluid .................................. 163
2.9.5 Friction Factor and Generalized Reynolds Number
for Power Law Fluids ............................................................. 163
2.9.6 Computation of Pumping Requirement of
Non-newtonian Liquids ........................................................ 166
2.10 Transport of solid foods .................................................................... 169
2.10.1 Properties of Granular Materials and Powders .....................170
2.10.2 Flow of Granular Foods ......................................................... 175
Problems ...................................................................................................... 178
List of Symbols ............................................................................................ 183
Bibliography ................................................................................................ 185
CHAPTER 3 Energy and Controls in Food Processes ...........................................................187
3.1 Generation of Steam .......................................................................... 187
3.1.1 Steam Generation Systems .................................................... 188
3.1.2 Thermodynamics of Phase Change ...................................... 190
3.1.3 Steam Tables ........................................................................... 194
3.1.4 Steam Utilization ................................................................... 200
3.2 Fuel Utilization .................................................................................. 204
3.2.1 Systems ................................................................................... 206
3.2.2 Mass and Energy Balance Analysis .........................................207
3.2.3 Burner Effi ciencies ..................................................................209
3.3 Electric Power Utilization ................................................................... 210
3.3.1 Electrical Terms and Units ......................................................212
3.3.2 Ohm’s Law ..............................................................................213
3.3.3 Electric Circuits .......................................................................214
3.3.4 Electric Motors ........................................................................216
3.3.5 Electrical Controls ...................................................................217
3.3.6 Electric Lighting ......................................................................218
3.4 Process Controls in Food Processing ................................................ 220
3.4.1 Processing Variables and Performance Indicators ................ 222
3.4.2 Input and Output Signals to Control Processes ................... 224
3.4.3 Design of a Control System ................................................... 224
3.5 Sensors ................................................................................................ 232
3.5.1 Temperature ............................................................................. 232
3.5.2 Liquid Level in a Tank .............................................................. 234
3.5.3 Pressure Sensors ....................................................................... 235
3.5.4 Flow Sensors ............................................................................. 236
3.5.5 Glossary of Terms Important in Data Acquisition ................. 237
3.6 Dynamic Response Characteristics of Sensors .................................... 237
Problems .......................................................................................................241
List of Symbols ............................................................................................ 244
Bibliography ................................................................................................ 245
CHAPTER 4 Heat Transfer in Food Processing ....................................................................247
4.1 Systems for Heating and Cooling Food Products ............................... 248
4.1.1 Plate Heat Exchanger ............................................................... 248
4.1.2 Tubular Heat Exchanger .......................................................... 252
4.1.3 Scraped-surface Heat Exchanger.............................................. 253
4.1.4 Steam-infusion Heat Exchanger .............................................. 255
4.1.5 Epilogue .................................................................................... 256
4.2 Thermal Properties of Foods ................................................................ 257
4.2.1 Specifi c Heat ............................................................................. 257
4.2.2 Thermal Conductivity .............................................................. 260
4.2.3 Thermal Diffusivity .................................................................. 262
4.3 Modes of Heat Transfer ........................................................................ 264
4.3.1 Conductive Heat Transfer ........................................................ 264
4.3.2 Convective Heat Transfer ......................................................... 267
4.3.3 Radiation Heat Transfer ........................................................... 269
4.4 Steady-State Heat Transfer.....................................................................270
4.4.1 Conductive Heat Transfer in a Rectangular Slab .....................271
4.4.2 Conductive Heat Transfer through a Tubular Pipe ................ 274
4.4.3 Heat Conduction in Multilayered Systems ............................. 277
4.4.4 Estimation of Convective Heat-Transfer Coeffi cient .............. 285
4.4.5 Estimation of Overall Heat-Transfer Coeffi cient .....................302
4.4.6 Fouling of Heat Transfer Surfaces ........................................... 306
4.4.7 Design of a Tubular Heat Exchanger .......................................312
4.4.8 The Effectiveness-NTU Method for Designing Heat
Exchangers ................................................................................ 320
4.4.9 Design of a Plate Heat Exchanger ........................................... 325
4.4.10 Importance of Surface Characteristics in Radiative
Heat Transfer ............................................................................ 332
4.4.11 Radiative Heat Transfer between Two Objects ....................... 334
4.5 Unsteady-State Heat Transfer ............................................................... 337
4.5.1 Importance of External versus Internal Resistance to Heat
Transfer ..................................................................................... 339
4.5.2 Negligible Internal Resistance to Heat Transfer
(NBi _ 0.1)—A Lumped System Analysis ................................ 340
4.5.3 Finite Internal and Surface Resistance to Heat Transfer
(0.1 _ NBi _ 40) ....................................................................... 345
4.5.4 Negligible Surface Resistance to Heat Transfer (NBi _ 40) ..... 348
4.5.5 Finite Objects ............................................................................. 348
4.5.6 Procedures to Use Temperature–Time Charts .......................... 350
4.5.7 Use of fh and j Factors in Predicting Temperature in
Transient Heat Transfer ............................................................. 358
4.6 Electrical Conductivity of Foods .......................................................... 366
4.7 Ohmic Heating ..................................................................................... 369
4.8 Microwave Heating ................................................................................371
4.8.1 Mechanisms of Microwave Heating.......................................... 372
4.8.2 Dielectric Properties .................................................................. 373
4.8.3 Conversion of Microwave Energy into Heat ............................ 374
4.8.4 Penetration Depth of Microwaves ............................................ 375
4.8.5 Microwave Oven ........................................................................ 377
4.8.6 Microwave Heating of Foods .................................................... 378
Problems ...................................................................................................... 380
List of Symbols ............................................................................................ 397
Bibliography ................................................................................................ 399
CHAPTER 5 Preservation Processes ...................................................................................403
5.1 Processing Systems ............................................................................... 403
5.1.1 Pasteurization and Blanching Systems ..................................... 404
5.1.2 Commercial Sterilization Systems ............................................ 406
5.1.3 Ultra-High Pressure Systems ...................................................... 410
5.1.4 Pulsed Electric Field Systems .....................................................412
5.1.5 Alternative Preservation Systems ...............................................413
5.2 Microbial Survivor Curves .....................................................................413
5.3 Infl uence of External Agents .................................................................418
5.4 Thermal Death Time F ......................................................................... 422
5.5 Spoilage Probability ............................................................................. 423
5.6 General Method for Process Calculation ............................................ 424
5.6.1 Applications to Pasteurization .................................................. 426
5.6.2 Commercial Sterilization .......................................................... 429
5.6.3 Aseptic Processing and Packaging ............................................ 432
5.7 Mathematical Methods ........................................................................ 440
5.7.1 Pouch Processing ....................................................................... 444
Problems ...................................................................................................... 447
List of Symbols ............................................................................................ 450
Bibliography .................................................................................................451
CHAPTER 6 Refrigeration ..................................................................................................455
6.1 Selection of a Refrigerant ..................................................................... 456
6.2 Components of a Refrigeration System ............................................... 460
6.2.1 Evaporator ...................................................................................461
6.2.2 Compressor ................................................................................ 463
6.2.3 Condenser .................................................................................. 466
6.2.4 Expansion Valve ......................................................................... 468
6.3 Pressure–Enthalpy Charts .....................................................................470
6.3.1 Pressure–Enthalpy Tables .......................................................... 474
6.3.2 Use of Computer-Aided Procedures to Determine
Thermodynamic Properties of Refrigerants .............................. 475
6.4 Mathematical Expressions Useful in Analysis of
Vapor-Compression Refrigeration ....................................................... 478
6.4.1 Cooling Load.............................................................................. 478
6.4.2 Compressor ................................................................................ 480
6.4.3 Condenser .................................................................................. 480
6.4.4 Evaporator ...................................................................................481
6.4.5 Coeffi cient of Performance .........................................................481
6.4.6 Refrigerant Flow Rate ..................................................................481
6.5 Use of Multistage Systems .................................................................... 490
6.5.1 Flash Gas Removal System .........................................................491
Problems .................................................................................................... 495
List of Symbols ............................................................................................ 498
Bibliography ................................................................................................ 498
CHAPTER 7 Food Freezing .................................................................................................501
7.1 Freezing Systems ....................................................................................502
7.1.1 Indirect Contact Systems ............................................................502
7.1.2 Direct-Contact Systems ...............................................................507
7.2 Frozen-Food Properties ......................................................................... 510
7.2.1 Density......................................................................................... 510
7.2.2 Thermal Conductivity ................................................................. 511
7.2.3 Enthalpy ...................................................................................... 511
7.2.4 Apparent Specifi c Heat ...............................................................513
7.2.5 Apparent Thermal Diffusivity.....................................................513
7.3 Freezing Time.........................................................................................514
7.3.1 Plank’s Equation .........................................................................516
7.3.2 Other Freezing-Time Prediction Methods ................................ 520
7.3.3 Pham’s Method to Predict Freezing Time ................................. 520
7.3.4 Prediction of Freezing Time of Finite-Shaped Objects ............ 524
7.3.5 Experimental Measurement of Freezing Time .......................... 528
7.3.6 Factors Infl uencing Freezing Time ............................................ 528
7.3.7 Freezing Rate .............................................................................. 529
7.3.8 Thawing Time ............................................................................. 529
7.4 Frozen-Food Storage ............................................................................. 530
7.4.1 Quality Changes in Foods during Frozen Storage ................... 530
Problems ............................................................................................... 534
List of Symbols ............................................................................................ 538
Bibliography ............................................................................................... 539
CHAPTER 8 Evaporation ....................................................................................................543
8.1 Boiling-Point Elevation ........................................................................ 545
8.2 Types of Evaporators ............................................................................ 547
8.2.1 Batch-Type Pan Evaporator ....................................................... 547
8.2.2 Natural Circulation Evaporators ............................................... 548
8.2.3 Rising-Film Evaporator .............................................................. 548
8.2.4 Falling-Film Evaporator ............................................................. 549
8.2.5 Rising/Falling-Film Evaporator ................................................. 550
8.2.6 Forced-Circulation Evaporator ...................................................551
8.2.7 Agitated Thin-Film Evaporator ...................................................551
8.3 Design of a Single-Effect Evaporator ................................................... 554
8.4 Design of a Multiple-Effect Evaporator ............................................... 559
8.5 Vapor Recompression Systems ............................................................. 565
8.5.1 Thermal Recompression ............................................................ 565
8.5.2 Mechanical Vapor Recompression ............................................ 566
Problems ............................................................................................... 566
List of Symbols ............................................................................................ 569
Bibliography ............................................................................................... 569
CHAPTER 9 Psychrometrics ................................................................................................571
9.1 Properties of Dry Air..............................................................................571
9.1.1 Composition of Air .....................................................................571
9.1.2 Specifi c Volume of Dry Air ........................................................ 572
9.1.3 Specifi c Heat of Dry Air ............................................................. 572
9.1.4 Enthalpy of Dry Air .................................................................... 572
9.1.5 Dry Bulb Temperature ............................................................... 573
9.2 Properties of Water Vapor .................................................................... 573
9.2.1 Specifi c Volume of Water Vapor ................................................ 573
9.2.2 Specifi c Heat of Water Vapor ..................................................... 573
9.2.3 Enthalpy of Water Vapor ............................................................ 574
9.3 Properties of Air–Vapor Mixtures ........................................................ 574
9.3.1 Gibbs–Dalton Law ..................................................................... 574
9.3.2 Dew-Point Temperature ............................................................. 574
9.3.3 Humidity Ratio (or Moisture Content) .............................. 575
9.3.4 Relative Humidity ................................................................ 576
9.3.5 Humid Heat of an Air–Water Vapor Mixture ...................... 576
9.3.6 Specifi c Volume .................................................................... 577
9.3.7 Adiabatic Saturation of Air .................................................. 577
9.3.8 Wet Bulb Temperature.......................................................... 579
9.4 The Psychrometric Chart .................................................................. 582
9.4.1. Construction of the Chart .................................................... 582
9.4.2 Use of Psychrometric Chart to Evaluate Complex
Air-Conditioning Processes ................................................. 584
Problems ...................................................................................................... 589
List of Symbols ............................................................................................ 592
Bibliography ............................................................................................... 593
CHAPTER 10 Mass Transfer ................................................................................................595
10.1 The Diffusion Process....................................................................... 596
10.1.1 Steady-State Diffusion of Gases (and Liquids)
through Solids ...................................................................... 599
10.1.2 Convective Mass Transfer ..................................................... 600
10.1.3 Laminar Flow over a Flat Plate ............................................ 604
10.1.4 Turbulent Flow Past a Flat Plate .......................................... 608
10.1.5 Laminar Flow in a Pipe ........................................................ 608
10.1.6 Turbulent Flow in a Pipe ..................................................... 609
10.1.7 Mass Transfer for Flow over Spherical Objects ................... 609
10.2 Unsteady-State Mass Transfer ........................................................... 610
10.2.1 Transient-State Diffusion ...................................................... 611
10.2.2 Diffusion of Gases .................................................................616
Problems ....................................................................................................619
List of Symbols ..........................................................................................621
Bibliography ............................................................................................. 622
CHAPTER 11 Membrane Separation .................................................................................623
11.1 Electrodialysis Systems ..................................................................... 625
11.2 Reverse Osmosis Membrane Systems .............................................. 629
11.3 Membrane Performance ................................................................... 636
11.4 Ultrafi ltration Membrane Systems .................................................. 637
11.5 Concentration Polarization ............................................................. 639
11.6 Types of Reverse-Osmosis and Ultrafi ltration Systems .................. 645
11.6.1 Plate and Frame .................................................................... 646
11.6.2 Tubular .................................................................................. 646
11.6.3 Spiral-Wound ....................................................................... 646
11.6.4 Hollow-Fiber ........................................................................ 649
Problems ................................................................................................... 649
List of Symbols ......................................................................................... 650
Bibliography ..............................................................................................651
CHAPTER 12 Dehydration .................................................................................................653
12.1 Basic Drying Processes ..................................................................... 653
12.1.1 Water Activity ....................................................................... 654
12.1.2 Moisture Diffusion .............................................................. 657
12.1.3 Drying-Rate Curves .............................................................. 658
12.1.4 Heat and Mass Transfer ....................................................... 658
12.2 Dehydration systems ........................................................................ 660
12.2.1 Tray or Cabinet Dryers ........................................................ 660
12.2.2 Tunnel Dryers .......................................................................661
12.2.3 Puff-Drying .......................................................................... 662
12.2.4 Fluidized-Bed Drying .......................................................... 663
12.2.5 Spray Drying ........................................................................ 663
12.2.6 Freeze-Drying ....................................................................... 664
12.3 Dehydration System Design............................................................. 665
12.3.1 Mass and Energy Balance .................................................... 665
12.3.2 Drying-Time Prediction .......................................................670
Problems ................................................................................................... 680
List of Symbols ......................................................................................... 685
Bibliography .............................................................................................. 686
CHAPTER 13 Supplemental Processes ...............................................................................689
13.1 Filtration ........................................................................................... 689
13.1.1 Operating Equations ........................................................... 689
13.1.2 Mechanisms of Filtration .................................................... 695
13.1.3 Design of a Filtration System .............................................. 696
13.2 Sedimentation .................................................................................. 699
13.2.1 Sedimentation Velocities for Low-Concentration
Suspensions ......................................................................... 699
13.2.2 Sedimentation in High-Concentration Suspensions..........702
13.3 Centrifugation ...................................................................................705
13.3.1 Basic Equations .....................................................................705
13.3.2 Rate of Separation ................................................................705
13.3.3. Liquid-Liquid Separation .....................................................707
13.3.4 Particle-Gas Separation ........................................................709
13.4 Mixing ...............................................................................................709
13.4.1 Agitation Equipment ............................................................ 711
13.4.2 Power Requirements of Impellers ........................................714
Problems ....................................................................................................718
List of Symbols ..........................................................................................719
Bibliography ............................................................................................. 720
CHAPTER 14 Extrusion Processes for Foods .......................................................................721
14.1 Introduction and Background ..........................................................721
14.2 Basic Principles of Extrusion ............................................................ 722
14.3 Extrusion Systems ............................................................................. 729
14.3.1 Cold Extrusion ...................................................................... 730
14.3.2 Extrusion Cooking ................................................................731
14.3.3 Single Screw Extruders ......................................................... 732
14.3.4 Twin-Screw Extruders ........................................................... 734
14.4 Extrusion System Design .................................................................. 735
14.5 Design of More Complex Systems ................................................... 740
Problems ....................................................................................................741
List of Symbols ......................................................................................... 742
Bibliography .............................................................................................. 742
CHAPTER 15 Packaging Concepts .....................................................................................745
15.1 Introduction...................................................................................... 745
15.2 Food Protection ................................................................................ 746
15.3 Product Containment ...................................................................... 747
15.4 Product Communication ................................................................. 748
15.5 Product Convenience ....................................................................... 748
15.6 Mass Transfer in Packaging Materials .............................................. 748
15.6.1 Permeability of Packaging Material to “Fixed” Gases .........751
15.7 Innovations in Food Packaging ....................................................... 754
15.7.1 Passive Packaging ................................................................. 755
15.7.2 Active Packaging ................................................................... 755
15.7.3 Intelligent Packaging ............................................................ 756
15.8 Food Packaging and Product Shelf-life ........................................... 758
15.8.1 Scientifi c Basis for Evaluating Shelf Life.............................. 758
15.9 Summary ........................................................................................... 766
Problems ................................................................................................... 766
List of Symbols ......................................................................................... 767
Bibliography ............................................................................................. 768
Appendices ........................................................................................................................771
A.1 SI System of Units and Conversion Factors .......................................771
A.1.1 Rules for Using SI Units ...........................................................771
Table A.1.1: SI Prefi xes ........................................................................771
Table A.1.2: Useful Conversion Factors ............................................ 774
Table A.1.3: Conversion Factors for Pressure .................................... 776
A.2 Physical Properties of Foods .............................................................. 777
Table A.2.1: Specifi c Heat of Foods ................................................... 777
Table A.2.2: Thermal Conductivity of Selected Food
Products ......................................................................... 778
Table A.2.3: Thermal Diffusivity of Some Foodstuffs ...................... 780
Table A.2.4: Viscosity of Liquid Foods ...............................................781
Table A.2.5: Properties of Ice as a Function of
Temperature ................................................................... 782
Table A.2.6: Approximate Heat Evolution Rates of
Fresh Fruits and Vegetables When Stored
at Temperatures Shown ................................................. 782
Table A.2.7: Enthalpy of Frozen Foods ............................................. 784
Table A.2.8: Composition Values of Selected Foods ........................ 785
Table A.2.9: Coeffi cients to Estimate Food Properties ..................... 786
A.3 Physical Properties of Nonfood Materials ........................................ 787
Table A.3.1: Physical Properties of Metals ........................................ 787
Table A.3.2: Physical Properties of Nonmetals ................................. 788
Table A.3.3: Emissivity of Various Surfaces ....................................... 790
A.4 Physical Properties of Water and Air ................................................. 792
Table A.4.1: Physical Properties of Water at the
Saturation Pressure ........................................................ 792
Table A.4.2: Properties of Saturated Steam ....................................... 793
Table A.4.3: Properties of Superheated Steam .................................. 795
Table A.4.4: Physical Properties of Dry Air at Atmospheric
Pressure .......................................................................... 796
A.5 Psychrometric Charts ......................................................................... 797
Figure A.5.1: Psychrometric chart for high temperatures ................. 797
Figure A.5.2: Psychrometric chart for low temperatures .................. 798
A.6 Pressure-Enthalpy Data ...................................................................... 799
Figure A.6.1: Pressure–enthalpy diagram for Refi gerant 12 ............. 799
Table A.6.1: Properties of Saturated Liquid andVapor R-12 ............ 800
Figure A.6.2: Pressure–enthalpy diagram of superheated
R-12 vapor .................................................................... 803
Table A.6.2: Properties of Saturated Liquid and Vapor
R-717 (Ammonia) .......................................................... 804
Figure A.6.3: Pressure-enthalpy diagram of
superheated R-717 (ammonia) vapor ..........................807
Table A.6.3: Properties of Saturated Liquid and Vapor R-134a ...................808
Figure A.6.4: Pressure–enthalpy diagram of R-134a ......................... 811
Figure A.6.5: Pressure–enthalpy diagram of R-134a
(expanded scale) ...........................................................812
A.7 Symbols for Use in Drawing Food Engineering Process
Equipment ...........................................................................................813
A.8 Miscellaneous ......................................................................................818
Table A.8.1: Numerical Data, and Area/Volume of
Objects ..................................................................818
Figure A.8.1: Temperature at geometric center
of a sphere (expanded scale) .............................819
Figure A.8.2: Temperature at the axis of an infi nitely
long cylinder (expanded scale) ........................ 820
Figure A.8.3: Temperature at the midplane of an
infi nite slab (expanded scale) ............................821
A.9 Dimensional Analysis ........................................................................ 822
Table A.9.1: Dimensions of selected experimental
variables .............................................................. 823
Bibliography .............................................................................................. 826
Index .......................................................................................................... 829
Food Science and Technology: International Series ............................. 839
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