**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

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