Contents Preface 1 Review of Mathematical Principles and Applications in Food Processing

Transcription

1 Preface... 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 RootsofEquations Polynomials Quadratic Equation Factoring Iteration Technique Programming Using Visual BASIC for Applications in Microsoft Excel Use of Spreadsheets to Solve Engineering Problems Simultaneous Equations Substitution Elimination Determinants Solutions to a System of Linear Equations Using the "Solver" Macro in Excel Power Functions and Exponential Functions LogarithmicFunctions Differential Calculus Definition of a Derivative Differentiation Formulas Maximum and Minimum Values of Functions IntegralCalculus Integration Formulas...

2 ... viii 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.... SuggestedReading... 2 UnitsandDimensions 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 TheDimensionalEquation Conversion of Units Using the Dimensional Equation The Dimensional Constant (G, ) Determination of Appropriate SI Units Dimensional Consistency of Equations Conversion of Dimensional Equations.... 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. anddehydration Steady State Volume Changes on Mixing Continuous Versus Batch Recycle Unsteadystate Blending of Food Ingredients Total Mass and Component Balances...

3 x 5.4 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 SuggestedReading 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 Wide Gap Viscometer with Cylindrical Spindles 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...

4 6.8.2 Factors to Be Considered in Pump Selection Performance Curves of Pumps.... Suggested Reading... 7 Heatnansfer 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 Difference Local Heat Transfer Coefficients Dimensionless Quantities Equations for Calculating Heat Transfer Coefficients Simplified Equations for Natural Convection to Airorwater Fluids in Laminar and Turbulent Flow Inside Tubes Heat Transfer to Non-Newtonian Fluids in Laminar Flow...

5 xii 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 Heatingcumes FreezingRates.... SuggestedReadings... 8 Kinetics of Chemical Reactions in Foods Theory of Reaction Rates Types of Reactions Unimolecular Reactions Bimolecular Reactions Reversible Reactions EnzymeReactions 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 Qlo Value The z Value Determination of Reaction Kinetic Parameters Use of Chemical Reaction Kinetic Data for Thermal Process Optimization.... 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...

6 f ii Processing in Glass Containers... I Flame Sterilization Systems 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 Fo 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 Fo Thermal Process Calculations for Canned Foods The General Method Heat Transfer Equations and Time-Temperature Curves forcamedfoods Plotting Heat Penetration Data Determination of fh and j 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 Process Constant Temperature Processes Process Temperature Change Broken Heating Curves Quality Factor Degradation Suggested Reading 10 Refrigeration Mechanical Refrigeration System Principle of Operation: The Heat Pump Refrigerants Xlll

7 xiv 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... Suggested Reading Evaporation Single-Effect Evaporators The Vapor Chamber Thecondenser Removal of Noncondensible Gases TheHeatExchanger Improving the Economy of Evaporators Vapor Recompression Multiple-Effect Evaporators Entrainment Essence Recovery... SuggestedReading... Dehydration Water Activity Thermodynamic Basis for Water Activity Osmotic Pressure Water Activity at High Moisture Gibbs-Duhem Equation Other Equations for Calculating Water Activity Water Activity at Low Moisture The GAB (Guggenheim-Anderson-de Boer) Equation Other Equations for Sorption Isotherms of Foods...

8 xv 12.2 Mass Transfer Mass Diffusion Mass Transfer from Surfaces to Flowing Air Psychrometry Canying Capacity of Gases for Vapors ,2 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 TheStagesofDrying 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 SprayDrying Drying Times in Spray Drying FreezeDrying Drying Times for Symmetrical Drying Vacuum Belt Dryer... SuggestedReading Physical Separation Processes Filtration Filtrate Flow Through Filter Cake Constant Pressure Filtration Filtration Rate Model Equations for Prolonged Filtration When Filter Cakes Exhibit Time-Dependent Specific Resistance Exponential Dependence of Rate on Filtrate Volume Model Equation Based on Time-Dependent Specific Cake Resistance Optimization of Filtration Cycles Pressure-Driven Membrane Separation Processes Membrane System Configurations Transmembrane Flux in Pressure-Driven Membrane Separation Processes (Polarization Concentration and Fouling) Solute Rejection Sterilizing Filtrations Ultrafiltration Reverse Osmosis Temperature Dependence of Membrane Permeation Rates Other Membrane Separation Processes Sieving Standard Sieve Sizes Gravity Separations Force Balance on Particles Suspended in a Fluid...

9 xvi Buoyant Force Drag Force Terminal Velocity The Drag Coefficient... SuggestedReading Extraction Types of Extraction Processes Single-Stage Batch Processing... A.l Multistage Cross-Flow Extraction Multistage Countercurrent Extraction Continuous Countercurrent Extractors General Principles Diffusion Solubility Equilibrium Solid-Liquid Extraction: Leaching The Extraction Battery: Number of Extraction Stages Determination of the Number of Extraction Stages Using the Ponchon-Savarit Diagram The Lever Rule in Plotting Position of a Mixture of Two Streams in anx-ydiagram Mathematical and Graphical Representation of the Point J in the Ponchon-Savarit Diagram Mathematical and Graphical Representation of the Point P Equation of the Operating Line and Representation on the X-Y Diagram Construction of the Ponchon-Savarit Diagram for the Determination of the Number of Ideal Extraction Stages Supercritical Fluid Extraction Extraction Principles Critical Points of Supercritical Fluids Used in Foods Critical Point of Mixtures Properties of Supercritical Fluids Relative to Gases Supercritical Fluid Extraction Parameters... SuggestedReading... Conversion Factors Expressed as a Ratio... A.2 Properties of Superheated Steam... A.3 Saturated Steam Tables: English Units... A.4 Saturated Steam Tables: Metric Units

10 xvii A.5 Flow Properties of Food Fluids... A.6 Psychrometric Chart: English Units... A.7 Psychrometric Chart: Metric Units... A.8 Average Composition of Foods (From USDA Handbook 8)... A.9 Thermal Conductivity of Construction and Insulating Materials... A.10 Thermal Conductivity of Foods... A.ll Spreadsheet Program for Calculating Thermophysical Properties of Foods from Their Composition... A.12 Correlation Equations for Heat Transfer Coefficients... A.13 Visual BASIC Program for Evaluating Temperature Response of a Brick-Shaped Solid... A.14 Visual BASIC Program for Evaluating Local Heat Transfer Coefficient from Temperature Response of a Brick-Shaped Solid... A.15 Thermal Conductivity of Water as a Function of Temperature... A.16 Density of Water as a Function of Temperature... A.17 Viscosity of Water as a Function of Temperature... Index...