Food Processing & Engineering Contents 1 Review of Mathematical Principles and Applications in Food Processing Graphing and Fitting Equations to Experimental Data Variables and Functions Graphs Equations Linear Equations Nonlinear Equations Linearization of Nonlinear Equations Nonlinear Curve Fitting Logarithmic and Semi-Logarithmic Graphs . Intercept of Log-Log Graphs Roots of Equations Polynomials Quadratic Equation Factoring Iteration Technique programming Using Visual BASIC for Applications in Microsoft Excel Use of Spreadsheets to Solve Engineering Problems Simultaneous Equations Substitutions Elimination Determinants Solutions to a System of Linear Equations Using the “Solver” Macro in Excel Power Functions and Exponential Functions Logarithmic Functions Differential Calculus Definition of a Derivative Differentiation Formulas Maximum and Minimum Values of Functions Integral Calculus Integration Formulas Integration Techniques Constants Integration by Parts Partial Fractions Substitution Graphical Integration Rectangular Rule Trapezoidal Rule Simpson’s Rule Differential Equations Finite Difference Approximation of Differential Equations Problems Suggested Reading 2 Units and Dimensions Definition of Terms Systems of Measurement The SI System Units in SI and Their Symbols Prefixes Recommended for Use in SI Conversion of Units Precision, Rounding-Off Rule, Significant Digits The Dimensional Equation Conversion of Units Using the Dimensional Equation The Dimensional Constant (Gc) Determination of Appropriate SI Units Dimensional Consistency of Equations Conversion of Dimensional Equations Problems Suggested Reading 3 Material Balances Basic Principles Law of Conservation of Mass Process Flow Diagrams System Boundaries Total Mass Balance Component Mass Balance Basis and “Tie Material” Material Balance Problems Involved in Dilution, Concentration, and Dehydration Steady State Volume Changes on Mixing Continuous Versus Batch Recycle Unsteady State Blending of Food Ingredients Total Mass and Component Balances Use of Specified Constraints in Equations Multistage Processes Problems Suggested Reading 4 Gases and Vapors Equations of State for Ideal and Real Gases . The Kinetic Theory of Gases Absolute Temperature and Pressure . Quantity of Gases The Ideal Gas Equation P-V-T Relationships for Ideal Gases van der Waal’s Equation of State Critical Conditions for Gases Gas Mixtures Thermodynamics Thermodynamic Variables The Relationship Between Cp and Cv for Gases P-V-T Relationships for Ideal Gases in Thermodynamic Processes Changes in Thermodynamic Properties, Work, and Heat Associated with Thermodynamic Processes Work and Enthalpy Change on Adiabatic Expansion or Compression of an Ideal Gas Work and Enthalpy Change on Isothermal Expansion or Compression of an Ideal Gas Work and Enthalpy Change on Isothermal Expansion or Compression of an Ideal Gas Vapor-Liquid Equilibrium The Clausius-Clapeyron Equation Liquid Condensation from Gas Mixtures . Problems Suggested Reading 5 Energy Balances General Principles Energy Terms Heat Heat Content, Enthalpy Specific Heat of Solids and Liquids . Enthalpy Changes in Foods During Freezing . Correlation Equations Based on Freezing Points of Food Products Unmodified from the Natural State Enthalpy Changes During the Freezing of Foods Calculated from Molality of Liquid Water Fraction of the Food Freezing Point Depression by Solutes . Amount of Liquid Water and Ice at Temperatures Below Freezing Sensible Heat of Water and Ice at Temperatures Below the Freezing Point Total Enthalpy Change Specific Heats of Gases and Vapors . Properties of Saturated and Superheated Steam . The Steam Tables The Saturated Steam Table . The Superheated Steam Tables Double Interpolation from Superheated Steam Tables Properties of Steam Having Less Than 100% Quality Heat Balances Problems Suggested Reading 6 Flow of Fluids The Concept of Viscosity Rheology Viscometry Viscometers Based on Fluid Flow Through a Cylinder Derivation of the Poiseuille Equation Velocity Profile and Shear Rate for a Power Law Fluid Glass Capillary Viscometers Forced Flow Tube or Capillary Viscometry Evaluation of Wall Effects in Tube Viscometry Glass Capillary Viscometer Used as a Forced Flow Viscometer Effect of Temperature on Rheological Properties Back Extrusion Determination of Rheological Properties of Fluids Using Rotational Viscometers Wide Gap Rotational Viscometer Continuous Viscosity Monitoring and Control . . Capillary Viscometer Rotational Viscometer Viscosity Sensitive Rotameter Flow of Falling Films Films of Constant Thickness Time-Dependent Film Thickness Processes Dependent on Fluid Film Thicknesses Transportation of Fluids Momentum Balance The Continuity Principle Fluid Flow Regimes The Reynolds Number Pipes and Tubes Frictional Resistance to Flow of Newtonian Fluids Frictional Resistance to Flow of Non-Newtonian Fluids Frictional Resistance Offered by Pipe Fittings to Fluid Flow Mechanical Energy Balance: The Bernoulli Equation Pumps Types of Pumps and Their Characteristics Factors to Be Considered in Pump Selection Performance Curves of Pumps Problems Suggested Reading 7 Heat Transfer Mechanisms of Heat Transfer Heat Transfer by Conduction Fourier’s First Law of Heat Transfer Estimation of Thermal Conductivity of Food Products Fourier’s Second Law of Heat Transfer Temperature Profile for Unidirectional Heat Transfer Through a Slab . Conduction Heat Transfer Through Walls of a Cylinder The Temperature Profile in the Walls of a Cylinder in Steady-State Heat Transfer Heat Transfer by Convection Natural Convection Forced Convection Heat Transfer by Radiation Types of Surfaces Effect of Distance Between Objects on Heat Transfer Radiant Energy Exchange . Microwave and Dielectric Heating . Energy Absorption by Foods in a Microwave Field Relative Heating Rates of Food Components Temperature Measuring Devices Liquid-in-Glass Thermometers Fluid-Filled Thermometers Bimetallic Strip Thermometers Resistance Temperature Devices (RTDs) Thermocouples Radiation Pyrometers Accurate Temperature Measurements . . Steady-State Heat Transfer The Concept of Resistance to Heat Transfer Combined Convection and Conduction: The Overall Heat Transfer Coefficient Heat Exchange Equipment Heat Transfer in Heat Exchangers . The Logarithmic Mean Temperature Differences Local Heat Transfer Coefficients Dimensionless Quantities Equations for Calculating Heat Transfer Coefficients Simplified Equations for Natural Convection to Air or Water Fluids in Laminar and Turbulent Flow Inside Tubes Heat Transfer to Non-Newtonian Fluids in Laminar Flow Adapting Equations for Heat Transfer Coefficients to Non-Newtonian Fluids Unsteady-State Heat Transfer Heating of Solids Having Infinite Thermal Conductivity Solids with Finite Thermal Conductivity . The Semi-Infinite Slab with Constant Surface Temperature The Infinite Slab Temperature Distribution for a Brick-Shaped Solid Use of Heissler and Gurney-Lurie Charts . Calculating Surface Heat Transfer Coefficients from Experimental Heating Curves Freezing Rates Problems Suggested Readings 8 Kinetics of Chemical Reactions in Foods Theory of Reaction Rates Types of Reactions Unimolecular Reactions Bimolecular Reactions Reversible Reactions Enzyme Reactions Reaction Order Zero-Order Reactions First-Order Reactions Second-Order Reactions nth-Order Reactions Reactions Where Product Concentration Is Rate Limiting The Reaction Rate Constant Temperature Dependence of Reaction Rates The Arrhenius Equation The Q10Value The z Value Determination of Reaction Kinetic Parameters . Use of Chemical Reaction Kinetic Data for Thermal Process Optimization Problems Suggested Reading 9 Thermal Process Calculations Processes and Systems for Stabilization of Foods for Shelf-Stable Storage: Systems Requirements In-Can Processing Stationary Retorts Hydrostatic Cooker Continuous Agitating Retorts . Crateless Retorts Processing Products Packaged in Flexible Plastic Containers Processing in Glass Containers Flame Sterilization Systems s Continuous Flow Sterilization: Aseptic or Cold Fill Steam-Air Mixtures for Thermal Processing Microbiological Inactivation Rates at Constant Temperature Rate of Microbial Inactivation Shape of Microbial Inactivation Curves Sterilizing Value or Lethality of a Process Acceptable Sterilizing Value for Processes Selection of Inoculation Levels in Inoculated Packs Determination of D Values Using the Partial Sterilization Technique . . The Heat Resistance of Spoilage Microorganisms F 0 Values Used in Commercial Sterilization of Canned Foods Surface Sterilization Effect of Temperature on Thermal Inactivation of Microorganisms Inactivation of Microorganisms and Enzymes in Continuously Flowing Fluids . Time and Temperature Used in the Pasteurization of Fluid Foods Microbial Inactivation in Continuously Flowing Fluids Nutrient Degradation High-Pressure Pasteurization High-Pressure Systems High-Pressure Pasteurization High-Pressure Sterilization . Sterilization of Fluids Containing Discreet Particulates Sterilizing Value of Processes Expressed as F0 Thermal Process Calculations for Canned Foods The General Method Heat Transfer Equations and Time-Temperature Curves for Canned Foods Plotting Heat Penetration Data Determination of fh and Determination of fc and jc. Formula Methods for Thermal Process Evaluation Stumbo’s Procedure Hayakawa’s Procedure Evaluation of Probability of Spoilage from a Given Processes Constant Temperature Processes Process Temperature Change . Broken Heating Curves Quality Factor Degradation Problems Suggested Reading 10 Refrigeration Mechanical Refrigeration System Principle of Operation: The Heat Pump Refrigerants The Refrigeration Cycle The Refrigeration Cycle as a Series of Thermodynamic Processes The Refrigeration Cycle on the Pressure/Enthalpy Diagram for a Given Refrigerant Example Problems on the Use of Refrigerant Charts The Condenser and Evaporator Problems with Heat Exchange in Systems Using Zeotropic Refrigerants . The Compressor Refrigeration Load Heat Incursion Through Enclosures . . Heat Incursion Through Cracks and Crevices Heat Incursion Through Open Doors . Heat Generation The Unsteady-State Refrigeration Load Commodity Storage Requirements Controlled Atmosphere Storage Respiration CA Gas Composition Modified Atmosphere Packaging Problems Suggested Reading 11 Evaporation . Single-Effect Evaporators The Vapor Chamber The Condenser Removal of Noncondensible Gases The Heat Exchanger Improving the Economy of Evaporators . Vapor Recompression Multiple-Effect Evaporators Entrainment Essence Recovery Problems Suggested Reading 12 Dehydration Water Activity Thermodynamic Basis for Water Activity Osmotic Pressure Water Activity at High Moisture Contents Gibbs-Duhem Equation . Other Equations for Calculating Water Activity Water Activity at Low Moisture Contents The GAB (Guggenheim-Anderson-de Boer) Equation Other Equations for Sorption Isotherms of Foods Mass Transfer Mass Diffusion Mass Transfer from Surfaces to Flowing Air Psychrometry Carrying Capacity of Gases for Vapors The Psychrometric Chart Use of Psychrometric Chart to Follow Changes in the Properties of Air-Water Mixtures Through a Process Simultaneous Heat and Mass Transfer in Dehydration The Stages of Drying Prediction of Drying Times from Drying Rate Data Materials with One Falling Rate Stage Where the Rate of Drying Curve Goes Through the Origin Materials with More Than One Falling Rate Stage The Constant Drying Rate Spray Drying Drying Times in Spray Drying . Freeze Drying Drying Times for Symmetrical Drying Vacuum Belt Dryer Problems Suggested Reading
Food Processing & Engineering
Contents
1 Review of Mathematical Principles and Applications in Food Processing
Graphing and Fitting Equations to Experimental Data
Variables and Functions
Graphs
Equations
Linear Equations
Nonlinear Equations
Linearization of Nonlinear Equations
Nonlinear Curve Fitting
Logarithmic and Semi-Logarithmic Graphs .
Intercept of Log-Log Graphs
Roots of Equations
Polynomials
Quadratic Equation
Factoring
Iteration Technique
programming Using Visual BASIC for Applications in Microsoft Excel
Use of Spreadsheets to Solve Engineering Problems
Simultaneous Equations
Substitutions
Elimination
Determinants
Solutions to a System of Linear Equations Using the “Solver” Macro in Excel
Power Functions and Exponential Functions
Logarithmic Functions
Differential Calculus
Definition of a Derivative
Differentiation Formulas
Maximum and Minimum Values of Functions
Integral Calculus
Integration Formulas
Integration Techniques
Constants
Integration by Parts
Partial Fractions
Substitution
Graphical Integration
Rectangular Rule
Trapezoidal Rule
Simpson’s Rule
Differential Equations
Finite Difference Approximation of Differential Equations
Problems
Suggested Reading
2 Units and Dimensions
Definition of Terms
Systems of Measurement
The SI System
Units in SI and Their Symbols
Prefixes Recommended for Use in SI
Conversion of Units
Precision, Rounding-Off Rule, Significant Digits
The Dimensional Equation
Conversion of Units Using the Dimensional Equation
The Dimensional Constant (Gc)
Determination of Appropriate SI Units
Dimensional Consistency of Equations
Conversion of Dimensional Equations
3 Material Balances
Basic Principles
Law of Conservation of Mass
Process Flow Diagrams
System Boundaries
Total Mass Balance
Component Mass Balance
Basis and “Tie Material”
Material Balance Problems Involved in Dilution, Concentration,
and Dehydration
Steady State
Volume Changes on Mixing
Continuous Versus Batch
Recycle
Unsteady State
Blending of Food Ingredients
Total Mass and Component Balances
Use of Specified Constraints in Equations
Multistage Processes
4 Gases and Vapors
Equations of State for Ideal and Real Gases .
The Kinetic Theory of Gases
Absolute Temperature and Pressure .
Quantity of Gases
The Ideal Gas Equation
P-V-T Relationships for Ideal Gases
van der Waal’s Equation of State
Critical Conditions for Gases
Gas Mixtures
Thermodynamics
Thermodynamic Variables
The Relationship Between Cp and Cv for Gases
P-V-T Relationships for Ideal Gases in Thermodynamic Processes
Changes in Thermodynamic Properties, Work, and Heat Associated
with Thermodynamic Processes
Work and Enthalpy Change on Adiabatic Expansion or Compression
of an Ideal Gas
Work and Enthalpy Change on Isothermal Expansion or Compression
Vapor-Liquid Equilibrium
The Clausius-Clapeyron Equation
Liquid Condensation from Gas Mixtures .
5 Energy Balances
General Principles
Energy Terms
Heat
Heat Content, Enthalpy
Specific Heat of Solids and Liquids .
Enthalpy Changes in Foods During Freezing .
Correlation Equations Based on Freezing Points of Food Products
Unmodified from the Natural State
Enthalpy Changes During the Freezing of Foods Calculated
from Molality of Liquid Water Fraction of the Food
Freezing Point Depression by Solutes .
Amount of Liquid Water and Ice at Temperatures Below Freezing
Sensible Heat of Water and Ice at Temperatures Below the
Freezing Point
Total Enthalpy Change
Specific Heats of Gases and Vapors .
Properties of Saturated and Superheated Steam .
The Steam Tables
The Saturated Steam Table .
The Superheated Steam Tables
Double Interpolation from Superheated Steam Tables
Properties of Steam Having Less Than 100% Quality
Heat Balances
6 Flow of Fluids
The Concept of Viscosity
Rheology
Viscometry
Viscometers Based on Fluid Flow Through a Cylinder
Derivation of the Poiseuille Equation
Velocity Profile and Shear Rate for a Power Law Fluid
Glass Capillary Viscometers
Forced Flow Tube or Capillary Viscometry
Evaluation of Wall Effects in Tube Viscometry
Glass Capillary Viscometer Used as a Forced Flow Viscometer
Effect of Temperature on Rheological Properties
Back Extrusion
Determination of Rheological Properties of Fluids Using
Rotational Viscometers
Wide Gap Rotational Viscometer
Continuous Viscosity Monitoring and Control . .
Capillary Viscometer
Rotational Viscometer
Viscosity Sensitive Rotameter
Flow of Falling Films
Films of Constant Thickness
Time-Dependent Film Thickness
Processes Dependent on Fluid Film Thicknesses
Transportation of Fluids
Momentum Balance
The Continuity Principle
Fluid Flow Regimes
The Reynolds Number
Pipes and Tubes
Frictional Resistance to Flow of Newtonian Fluids
Frictional Resistance to Flow of Non-Newtonian Fluids
Frictional Resistance Offered by Pipe Fittings to Fluid Flow
Mechanical Energy Balance: The Bernoulli Equation
Pumps
Types of Pumps and Their Characteristics
Factors to Be Considered in Pump Selection
Performance Curves of Pumps
7 Heat Transfer
Mechanisms of Heat Transfer
Heat Transfer by Conduction
Fourier’s First Law of Heat Transfer
Estimation of Thermal Conductivity of Food Products
Fourier’s Second Law of Heat Transfer
Temperature Profile for Unidirectional Heat Transfer Through a Slab .
Conduction Heat Transfer Through Walls of a Cylinder
The Temperature Profile in the Walls of a Cylinder in Steady-State
Heat Transfer
Heat Transfer by Convection
Natural Convection
Forced Convection
Heat Transfer by Radiation
Types of Surfaces
Effect of Distance Between Objects on Heat Transfer
Radiant Energy Exchange .
Microwave and Dielectric Heating .
Energy Absorption by Foods in a Microwave Field
Relative Heating Rates of Food Components
Temperature Measuring Devices
Liquid-in-Glass Thermometers
Fluid-Filled Thermometers
Bimetallic Strip Thermometers
Resistance Temperature Devices (RTDs)
Thermocouples
Radiation Pyrometers
Accurate Temperature Measurements . .
Steady-State Heat Transfer
The Concept of Resistance to Heat Transfer
Combined Convection and Conduction: The Overall Heat
Transfer Coefficient
Heat Exchange Equipment
Heat Transfer in Heat Exchangers .
The Logarithmic Mean Temperature Differences
Local Heat Transfer Coefficients
Dimensionless Quantities
Equations for Calculating Heat Transfer Coefficients
Simplified Equations for Natural Convection to Air or Water
Fluids in Laminar and Turbulent Flow Inside Tubes
Heat Transfer to Non-Newtonian Fluids in Laminar Flow
Adapting Equations for Heat Transfer Coefficients to Non-Newtonian Fluids
Unsteady-State Heat Transfer
Heating of Solids Having Infinite Thermal Conductivity
Solids with Finite Thermal Conductivity .
The Semi-Infinite Slab with Constant Surface Temperature
The Infinite Slab
Temperature Distribution for a Brick-Shaped Solid
Use of Heissler and Gurney-Lurie Charts .
Calculating Surface Heat Transfer Coefficients from Experimental
Heating Curves
Freezing Rates
Suggested Readings
8 Kinetics of Chemical Reactions in Foods
Theory of Reaction Rates
Types of Reactions
Unimolecular Reactions
Bimolecular Reactions
Reversible Reactions
Enzyme Reactions
Reaction Order
Zero-Order Reactions
First-Order Reactions
Second-Order Reactions
nth-Order Reactions
Reactions Where Product Concentration Is Rate Limiting
The Reaction Rate Constant
Temperature Dependence of Reaction Rates
The Arrhenius Equation
The Q10Value
The z Value
Determination of Reaction Kinetic Parameters .
Use of Chemical Reaction Kinetic Data for Thermal Process Optimization
9 Thermal Process Calculations
Processes and Systems for Stabilization of Foods for Shelf-Stable Storage:
Systems Requirements
In-Can Processing
Stationary Retorts
Hydrostatic Cooker
Continuous Agitating Retorts .
Crateless Retorts
Processing Products Packaged in Flexible Plastic Containers
Processing in Glass Containers
Flame Sterilization Systems s
Continuous Flow Sterilization: Aseptic or Cold Fill
Steam-Air Mixtures for Thermal Processing
Microbiological Inactivation Rates at Constant Temperature
Rate of Microbial Inactivation
Shape of Microbial Inactivation Curves
Sterilizing Value or Lethality of a Process
Acceptable Sterilizing Value for Processes
Selection of Inoculation Levels in Inoculated Packs
Determination of D Values Using the Partial Sterilization Technique . .
The Heat Resistance of Spoilage Microorganisms
F
0
Values Used in Commercial Sterilization of Canned Foods
Surface Sterilization
Effect of Temperature on Thermal Inactivation of Microorganisms
Inactivation of Microorganisms and Enzymes in Continuously Flowing Fluids .
Time and Temperature Used in the Pasteurization of Fluid Foods
Microbial Inactivation in Continuously Flowing Fluids
Nutrient Degradation
High-Pressure Pasteurization
High-Pressure Systems
High-Pressure Sterilization .
Sterilization of Fluids Containing Discreet Particulates
Sterilizing Value of Processes Expressed as F0
Thermal Process Calculations for Canned Foods
The General Method
Heat Transfer Equations and Time-Temperature Curves for Canned Foods
Plotting Heat Penetration Data
Determination of fh and
Determination of fc and jc.
Formula Methods for Thermal Process Evaluation
Stumbo’s Procedure
Hayakawa’s Procedure
Evaluation of Probability of Spoilage from a Given Processes
Constant Temperature Processes
Process Temperature Change .
Broken Heating Curves
Quality Factor Degradation
10 Refrigeration
Mechanical Refrigeration System
Principle of Operation: The Heat Pump
Refrigerants
The Refrigeration Cycle
The Refrigeration Cycle as a Series of Thermodynamic Processes
The Refrigeration Cycle on the Pressure/Enthalpy Diagram
for a Given Refrigerant
Example Problems on the Use of Refrigerant Charts
The Condenser and Evaporator
Problems with Heat Exchange in Systems Using
Zeotropic Refrigerants .
The Compressor
Refrigeration Load
Heat Incursion Through Enclosures . .
Heat Incursion Through Cracks and Crevices
Heat Incursion Through Open Doors .
Heat Generation
The Unsteady-State Refrigeration Load
Commodity Storage Requirements
Controlled Atmosphere Storage
Respiration
CA Gas Composition
Modified Atmosphere Packaging
11 Evaporation .
Single-Effect Evaporators
The Vapor Chamber
The Condenser
Removal of Noncondensible Gases
The Heat Exchanger
Improving the Economy of Evaporators .
Vapor Recompression
Multiple-Effect Evaporators
Entrainment
Essence Recovery
12 Dehydration
Water Activity
Thermodynamic Basis for Water Activity
Osmotic Pressure
Water Activity at High Moisture Contents
Gibbs-Duhem Equation .
Other Equations for Calculating Water Activity
Water Activity at Low Moisture Contents
The GAB (Guggenheim-Anderson-de Boer) Equation
Other Equations for Sorption Isotherms of Foods
Mass Transfer
Mass Diffusion
Mass Transfer from Surfaces to Flowing Air
Psychrometry
Carrying Capacity of Gases for Vapors
The Psychrometric Chart
Use of Psychrometric Chart to Follow Changes in the Properties
of Air-Water Mixtures Through a Process
Simultaneous Heat and Mass Transfer in Dehydration
The Stages of Drying
Prediction of Drying Times from Drying Rate Data
Materials with One Falling Rate Stage Where the Rate
of Drying Curve Goes Through the Origin
Materials with More Than One Falling Rate Stage
The Constant Drying Rate
Spray Drying
Drying Times in Spray Drying .
Freeze Drying
Drying Times for Symmetrical Drying
Vacuum Belt Dryer
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