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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