Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems

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Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Arthur T. Johnson, PhD, PE Biological Resources Engineering Department University of Maryland College Park, MD 20742 1997

This book is dedicated to all the little children in my life who made me smile even on the grayest of days.

Table of Contents Page Foreword... xii 1 SYSTEMS CONCEPTS FOR TRANSPORT PROCESSES... 1 1.1 INTRODUCTION... 1 1.2 EFFORT VARIABLES... 4 1.3 FLOW VARIABLES... 4 1.4 RELATIONSHIPS BETWEEN FLOW AND EFFORT VARIABLES... 4 1.4.1 Power... 6 1.4.2 Resistance... 7 1.4.3 Capacity... 8 1.4.4 Inertia... 13 1.4.5 Nonlinearities... 16 1.4.6 Biological Variation... 24 1.5. SOURCES... 34 1.6 COMBINATION OF ELEMENTS... 41 1.6.1 Sources... 42 1.6.2 Resistances... 45 1.6.3 Capacity... 49 1.6.4 Inertia... 51 1.6.5 Combinations Involving Time... 54 1.6.6 Alternative Representations... 64 1.7 BALANCES... 68 1.7.1 Chemical Balances... 68 1.7.2 Force Balances... 69 1.7.2.1 Law of Laplace... 70 1.7.3 General Flow Balances... 75 1.7.3.1 Mass and Materials Balance... 78 1.7.3.2 Field Equation... 81 Solutions of the General Field Equation... 86 Other Coordinate Systems... 88 One Dimensional Flow with Distributed Constant ù& Source... 93 One Dimensional Flow with Central ù& Source... 94 One Dimensional Unsteady State Solution... 98 i

1.7.3.3 Energy Balance... 105 1.7.4 Differences Between Effort and Flow Balances... 106 1.7.5 Kirchhoff's Laws... 107 1.7.6 Visualizing Boundary Conditions... 116 1.8 SYSTEM APPLICATIONS... 121 1.8.1 Flow Through Porous Media... 122 1.8.2 Conduction Heat Transfer... 133 1.8.3 Binary Diffusion Mass Transfer... 137 1.8.4 Conduction of Electricity... 144 1.8.5 Other Transport Systems... 147 1.9 SYSTEMS APPROACH... 151 Problems... 159 References... 175 2 FLUID FLOW SYSTEMS... 176 2.1 INTRODUCTION... 176 2.2 CONSERVATION OF MASS... 180 2.2.1 Continuity Equation... 182 2.2.2 Elemental Form of Continuity Equation... 184 2.3 CONSERVATION OF ENERGY... 188 2.3.1 Potential Energy... 188 2.3.2 Kinetic Energy... 194 2.3.3 Modified Bernoulli Equation... 201 2.3.4 Energy Allocation Within the Fluid... 204 2.3.5 General Form of Energy Balance Equation... 206 2.4 MOMENTUM BALANCE... 208 2.4.1 Viscosity... 210 2.4.2 Momentum Balance in a Circular Pipe... 224 2.4.3 Flow Velocity Profile... 231 2.4.4 General Form for Momentum Balance... 233 2.4.5 Navier-Stokes Equations... 235 2.4.6 Drag Coefficient and Settling Velocity... 238 ii

2.5 FRICTION LOSSES IN PIPES... 243 2.5.1 Pipe Losses... 244 2.5.2 Minor Losses... 257 2.5.2.1 Loss Coefficients... 257 2.5.2.2 Entrance Length... 260 2.5.2.3 Pipe Discharge... 262 2.5.3 Fluid System Impedance... 266 2.5.3.1 Compliance... 266 2.5.3.2 Inertance... 276 2.5.3.3 Resistance... 278 2.5.3.4 Time Relationships... 281 2.5.4 NonIsothermal Flow... 282 2.5.5 Elastic Tubes... 285 2.5.5.1 Pulsating Flow... 285 2.5.5.2 Steady Flow... 293 2.5.6 Bifurcations... 297 2.5.7 Compressible Flow... 300 2.5.7.1 Sonic Velocity... 300 2.5.7.2 Pressure Drop and Maximum Flow Rate... 303 2.5.7.3 Viscosity and Density Dependence... 310 2.5.7.4 Compression Heating... 313 2.5.8 Fluid Flow in Plants... 314 2.5.9 Deposition of Suspended Particles... 317 2.6 NON-NEWTONIAN FLUID FLOW... 329 2.6.1 Rheological Properties... 329 2.6.2 Pipe Flow... 341 2.6.2.1 Velocity Profiles... 343 2.6.2.2 Kinetic Energy... 345 2.6.2.3 Friction Losses... 347 2.7 OPEN CHANNEL FLOW... 357 2.8 DESIGN PROCEDURE FOR PUMP SPECIFICATION... 363 Problems... 391 Design Problems... 408 References... 422 iii

3 HEAT TRANSFER SYSTEMS... 425 3.1 INTRODUCTION... 425 3.2 CONDUCTION... 430 3.2.1 Thermal Conductivity... 431 3.2.2 Thermal Conductance... 438 3.2.2.1 Clothing... 438 3.2.2.2 Fur and Feathers... 449 3.2.3 Multidimensional Conduction... 453 3.2.4 Unsteady State Conduction... 462 3.3 CONVECTION... 462 3.3.1 Convection Coefficients... 466 3.3.1.1 Dimensionless Numbers... 468 3.3.1.2 Forced Convection Equations... 478 3.3.1.3 Natural Convection Equations... 494 3.3.1.4 Mixed Convection... 502 Cylinders... 504 Spheres... 504 Fruits... 507 3.3.1.5 Inaccuracies... 512 3.3.1.6 Convection with Viscous Dissipation... 518 3.3.1.7 Boiling and Condensation... 520 3.3.2 Convection Thermal Resistance... 521 3.3.3 Theoretical Relationships Among Parameters... 527 3.4 RADIATION... 530 3.4.1 Black Body Radiation... 533 3.4.1.1 Shape Factors... 535 3.4.1.2 Spectral Distribution... 545 3.4.2 Real Surfaces... 549 3.4.3 Radiation Exchange Among Gray Bodies... 556 3.4.4 One Body Completely Enclosed in Another... 560 3.4.5 Radiation Through Absorbing Gases... 564 3.4.6 Radiation Coefficient... 570 3.4.7 Solar Flux... 573 iv

3.5 HEAT GENERATION... 576 3.5.1 Diffuse Heat Production... 576 3.5.2 Temperature Dependence... 577 3.5.3 Biological Heat Production... 580 3.5.3.1 Microbial Systems... 581 3.5.3.2 Human and Animal Heat Production... 591 Basal Metabolic Rate... 591 Food Ingestion... 595 Muscular Activity... 598 3.5.3.3 Living Plants... 603 3.5.3.4 Stored Fruits and Vegetables... 604 3.5.3.5 Ecological Scale... 610 3.5.4 Non-Biological Heat Production... 612 3.5.4.1 Microwaves and Other Electromagnetically- Induced Heat... 613 3.5.5 Conduction with Heat Generation... 615 3.5.5.1 Constant Rate of Heat Production... 617 3.5.5.2 Temperature Dependent Heat Production... 622 3.6 HEAT STORAGE... 626 3.6.1 Specific Heats... 627 3.6.2 Flow Systems... 635 3.6.3 Convection Determination... 637 3.6.4 Heat Storage in Biological Systems... 641 3.6.5 Thermal Capacity... 643 3.7 MIXED MODE HEAT TRANSFER... 645 3.7.1 Heat Exchangers... 645 3.7.1.1 Heat Exchanger Types... 646 Change of State... 646 Parallel Flow... 649 Counter Flow... 650 Cross Flow... 653 3.7.1.2 Heat Transferred... 654 All Inlet and Outlet Temperatures Known... 654 v

All Inlet and Outlet Temperatures Not Known... 659 3.7.1.3 Fouling Factors... 670 3.7.1.4 Heat Exchanger Specification... 671 3.7.2 Transient Heat Transfer... 687 3.7.2.1 Dimensionless Numbers... 690 3.7.2.2 Heisler Charts... 691 Chart Use... 696 Composite Shapes... 699 Interior Fluid... 705 3.7.2.3 Sterilization of Food and Medical Devices... 714 3.7.3 Extended Surfaces... 727 3.8 CHANGE OF PHASE... 736 3.8.1 Change of State... 736 3.8.1.1 Freezing... 737 Freezing Point Depression... 739 Chilling... 742 Freezing Time... 747 3.8.1.2 Evaporation... 754 3.8.1.3 Sublimation... 756 3.8.2 Heat of Solution... 762 3.8.3 Phase Changes... 764 3.9 HEAT SYSTEM DESIGN... 766 Problems... 769 Design Problems... 787 References... 798 4 MASS TRANSFER... 804 4.1 INTRODUCTION... 804 4.2 MASS BALANCE... 807 vi

4.3 MOLECULAR DIFFUSION... 808 4.3.1 Fick's Laws... 810 4.3.2 Mass Diffusivity... 820 4.3.2.1 Gas Diffusivities... 821 4.3.2.2 Liquid Diffusivities... 829 4.3.2.3 Solid Diffusivities... 840 4.3.2.4 Porous Solids... 843 4.3.2.5 Knudsen Diffusion... 847 4.3.2.6 Food and Biological Materials... 857 4.3.3 Diffusion Through Membranes and Films... 860 4.3.3.1 Nonporous Membranes... 861 Partition Coefficient... 863 Diffusion... 867 Permeability... 868 4.3.3.2 Porous Membranes... 877 Ultrafiltration Membranes... 881 4.3.3.3 Osmotic Pressure... 886 Reverse Osmosis Mass Transfer... 894 4.3.3.4 Ionic Equilibria... 911 4.3.3.5 Skin Permeability... 917 4.3.3.6 Drug Delivery... 919 4.3.4 Diffusion Resistance... 929 4.4 CONVECTION... 933 4.4.1 Analogies with Heat Transfer... 934 4.4.2 Packed Beds... 942 4.5 MASS GENERATION... 952 4.5.1 Enzymatic Reactions... 953 4.5.1.1 Enzyme-Substrate Kinetics... 955 4.5.1.2 Immunoassays... 959 4.5.1.3 Biosensors... 961 4.5.2 Plant Root Nutrient Uptake... 968 vii

4.5.3 Bacterial Growth Rate... 969 4.6 MASS STORAGE... 970 4.6.1 Mass Storage in Solution... 970 4.6.2 Mass Capacitance 980 4.7 MIXED-MODE MASS TRANSFER... 981 4.7.1 Extended Surfaces... 981 4.7.2 Simultaneous Diffusion and Convection... 986 4.7.3 Dispersion... 991 4.7.3.1 Static Dispersion... 994 4.7.3.2 Dispersion in Flowing Fluid... 996 4.7.3.3 Taylor Dispersion... 997 4.7.3.4 Turbulent Dispersion in Pipes... 1000 4.7.3.5 Atmospheric Dispersion... 1002 Odor... 1012 4.7.3.6 Dispersion Within Soil... 1015 4.7.3.7 Dispersion Impedances... 1017 4.7.4 Unsteady-State Mass Transfer... 1021 4.7.5 Mass Exchangers... 1026 4.8 SIMULTANEOUS HEAT AND MASS TRANSFER... 1030 4.8.1 Psychrometrics... 1031 4.8.1.1 Ideal Atmosphere... 1031 4.8.1.2 Saturated Water Vapor Pressure... 1036 4.8.1.3 Measurements of the Amount of Water in the Air... 1039 4.8.1.4 Temperature Measures... 1041 4.8.1.5 Enthalpy... 1044 4.8.1.6 Psychrometric Charts... 1050 Sensible Heating or Cooling... 1053 Adiabatic Saturation... 1056 Mixing... 1057 Dehumidification... 1061 Ventilation... 1061 4.8.2 Drying... 1077 4.8.2.1 Moisture Content... 1083 4.8.2.2 Equilibrium Moisture Content... 1085 viii

4.8.2.3 Drying Rate... 1091 Constant Rate Drying... 1091 Sweating... 1094 Falling Rate Drying... 1096 Thick Layer Drying... 1097 Thin Layer Drying... 1100 4.8.2.4 Shrinkage... 1102 4.9 DESIGN OF MASS TRANSFER SYSTEMS... 1113 Problems... 1117 Design Problems... 1141 References... 1141 5 LIFE SYSTEMS... 1156 References... 1158 ix

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