Math Concepts for Food Engineering

Chapter 1 Algebra 1 1.1 Variables and constants 1 1.1.1 Variables 1 1.1.2 Constants 2 1.2 Equations 2 1.2.1 Functions 2 1.2.2 Manipulation of equations 3 1.2.3 Rules of equations applied to engineering units 6 1.3 Linear and nonlinear equations 8 1.4 Multiple linear equations 10 1.4.1 Algebraic manipulation 10 1.4.2 Substitution 13 1.4.3 Matrices (Kramer's rule) 15 1.4.3.1 Addition and subtraction 16 1.4.3.2 Multiplication 17 Chapter 2 Interpolation of data in tables and charts 27 2.1 Single interpolation 27 2.2 Double interpolation 31 2.3 Interpolation in charts 36 Chapter 3 Graphs and curve fitting 39 3.1 Coordinate systems 39 3.1.1 Cartesian coordinates 39 3.1.2 Polar coordinates and cylindrical coordinates 41 3.2 Linear graphs 44 3.3 Logarithmic transformations 49 3.3.1 Semi-log graphs 52 3.3.2 Log-log graphs 54 Chapter 4 Calculus 57 4.1 Differentiation 57 4.1.1 Derivatives 57 4.1.2 Formal differentiation 61 4.1.3 Rules of differentiation 62 4.1.4 Second derivatives 64 4.1.5 Partial derivatives 64 4.1.6 Applications 65 4.1.6.1 Time derivatives 65 4.1.6.2 Maxima and minima 65 4.2 Integration 67 4.2.1 The antiderivative 67 4.2.2 Formal integration 68 4.2.3 Rules of integration 69 4.2.4 Closed integrals 70 4.2.5 Trapezoidal rule 71 4.2.6 Areas by integration 72 4.3 Differential equations 73 Chapter 5 Problem solving 77 Chapter 6 Gases and vapors 83 6.1 Pressure 83 6.2 Gas laws 86 6.3 Gas mixtures 89 6.3.1 Partial pressure 89 6.3.2 Partial volume 90 Chapter 7 Mass balances 93 7.1 Steady-state operation, no reaction 95 7.2 Steady-state operation, with chemical reaction 105 7.3 Unsteady-state operation, no reaction 108 Chapter 8 Energy balances 111 8.1 Steam tables 113 8.1.1 Saturated steam 113 8.1.2 Superheated steam 117 8.2 Enthalpy balances 120 Chapter 9 Fluid mechanics 127 9.1 Rheology 127 9.1.1 Modeling rheological behavior of fluid foods 128 9.1.2 Measurement of rheological properties 131 9.2 Fluid flow 135 9.2.1 Continuity equation 135 9.2.2 Determination of flow regime 137 9.2.3 Flow of a Newtonian fluid in a pipe 138 9.2.4 Effects of friction on fluid flow 143 9.2.5 Mechanical energy balance equation in fluid flow 146 9.3 Non-Newtonian fluid flow 149 References 151 Chapter 10 Heat transfer 153 10.1 Steady state 154 10.1.1 Conduction heat transfer 154 10.1.2 Convection heat transfer 160 10.1.3 Convective heat-transfer coefficients 166 10.1.4 Heat exchangers 170 10.2 Unsteady-state heat transfer 174 10.3 Freezing 179 10.4 Radiation heat transfer 182 Chapter 11 Mass transfer 185 11.1 Psychrometrics 185 11.1.1 Moist-air properties using thermodynamic principles and the gas laws 186 11.1.2 Moist-air properties on psychrometric chart 187 11.1.3 Using the psychrometric chart to find the state of air during processing 189 11.2 Molecular diffusion 191 11.3 Convective mass transfer 196 11.4 Unsteady-state mass transfer 199 References 202 Appendix 1: Common conversion factors for engineering units 203 Appendix 2: Answers to practice problems 205 Appendix 3a: Quiz 209 Appendix 3b: Quiz with answers 215 Index 219