BIOLOGICAL AND BIOENVIRONMENTAL HEAT AND MASS TRANSFER
CONTENTS I ENERGY TRANSFER EQUILIBRIUM, ENERGY CONSERVATION, AND TEMPERATURE THERMAL EQUILIBRIUM AND THE LAWS OF THERMODYNAMICS LAWS OF THERMODYNAMICS THERMAL EQUILIBRIUM ENERGY CONSERVATION NON-EQUILIBRIUM THERMODYNAMICS AND THE TRANSPORT OF ENERGY TEMPERATURE IN LIVING SYSTEMS TEMPERATURE RESPONSE TO HUMAN BODY TEMPERATURE SENSATION IN HUMANS THERMAL COMFORT OF HUMAN AND ANIMALS TEMPERATURE IN THE ENVIRONMENT THE GREENHOUSE EFFECT TEMPERATURE SCALES CHAPTER SUMMARY—ENERGY CONSERVATION AND TEMPERATURE CONCEPT AND REVIEW QUESTIONS FURTHER READING MODES OF HEAT TRANSFER CONDUCTIVE HEAT TRANSFER THERMAL CONDUCTIVITY OF BIOLOGICAL AND OTHER MATERIALS THERMAL DIFFUSIVITY DENSITY AND SPECI?C HEAT CONVECTIVE HEAT TRANSFER RADIATIVE HEAT TRANSFER CHAPTER SUMMARY—MODES OF HEAT TRANSFER PROBLEMS GOVERNING EQUATION AND BOUNDARY CONDITIONS OF HEAT TRANSFER GOVERNING EQUATION FOR HEAT TRANSFER DERIVED MEANING OF EACH TERM IN THE GOVERNING EQUATION EXAMPLES OF THERMAL SOURCE (GENERATION) TERM IN BIOLOGICAL SYSTEMS UTILITY OF THE ENERGY EQUATION GENERAL BOUNDARY CONDITIONS THE BIOHEAT TRANSFER EQUATION FOR MAMMALIAN TISSUE GOVERNING EQUATION DERIVED IN CYLINDRICAL COORDINATES GOVERNING EQUATIONS IN VARIOUS COORDINATE SYSTEMS AN ALGORITHM TO SOLVE TRANSPORT PROBLEMS CHAPTER SUMMARY—GOVERNING EQUATIONS AND BOUNDARY CONDITIONS 3 10 PROBLEMS CONDUCTION HEAT TRANSFER: STEADY-STATE STEADY-STATE HEAT CONDUCTION IN A SLAB THERMAL RESISTANCE AND OVERALL HEAT TRANSFER COEF?CIENT STEADY-STATE HEAT CONDUCTION IN A CYLINDER THERMAL RESISTANCE TERM FOR THE HOLLOW CYLINDER COMPARISON WITH THE SOLUTION FOR THE SLAB THICKNESS OF FUR IN SMALL AND LARGE ANIMALS STEADY-STATE HEAT CONDUCTION IN A SLAB WITH INTERNAL HEAT GENERATION THERMOREGULATION–MAINTAINING THE CORE BODY TEMPERATURE OF HUMAN AND ANIMALS STEADY-STATE HEAT TRANSFER FROM EXTENDED SURFACES: FINS FINS AND BIO-HEAT TRANSFER CHAPTER SUMMARY—STEADY-STATE HEAT CONDUCTION CONDUCTION HEAT TRANSFER: UNSTEADY STATE TRANSIENT HEAT TRANSFER WITH NO INTERNAL RESISTANCE BIOT NUMBER: DECIDING WHEN TO IGNORE THE INTERNAL RESISTANCE TRANSIENT HEAT TRANSFER WITH INTERNAL RESISTANCE HOW TEMPERATURE CHANGES WITH TIME TEMPERATURE CHANGE WITH POSITION AND SPATIAL AVERAGE TEMPERATURE CHANGE WITH SIZE CHARTS DEVELOPED FROM THE SOLUTIONS: THEIR USES AND LIMITATIONS INTERNAL AND EXTERNAL RESISTANCE NUMERICAL METHODS AS ALTERNATIVES TO THE CHARTS TRANSIENT HEAT TRANSFER IN A FINITE GEOMETRY— MULTI-DIMENSIONAL PROBLEMS SEMI-IN?NITE REGION CHAPTER SUMMARY—TRANSIENT HEAT CONDUCTION CONVECTION HEAT TRANSFER GOVERNING EQUATION FOR CONVECTION TEMPERATURE PRO?LES AND BOUNDARY LAYERS OVER A SURFACE LAMINAR AND TURBULENT FLOWS CONVECTIVE HEAT TRANSFER COEF?CIENT DE?NED SIGNI?CANT PARAMETERS IN CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER COEF?CIENT CALCULATIONS FLAT PLATE, FORCED CONVECTION FLAT PLATE, NATURAL CONVECTION FLOW OVER CYLINDER, NATURAL CONVECTION FLOW OVER CYLINDER, FORCED CONVECTION FLOW THROUGH CYLINDER, FORCED CONVECTION FLOW OVER SPHERE, NATURAL CONVECTION FLOW OVER SPHERE, FORCED CONVECTION LAMINAR VS TURBULENT FLOW ORDERS OF MAGNITUDE FOR HEAT TRANSFER COEF?CIENT VALUES 6 6 10 COEF?CIENTS FOR AIR FLOW OVER HUMAN SUBJECTS 6 6 11 WIND CHILL FACTOR AND BOUNDARY LAYER THICKNESS CHAPTER SUMMARY—CONVECTIVE HEAT TRANSFER 6 10 PROBLEMS HEAT TRANSFER WITH CHANGE OF PHASE FREEZING AND THAWING FREEZING OF PURE WATER FREEZING PROCESS PROPERTY CHANGES DURING FREEZING FREEZING OF SOLUTIONS AND BIOMATERIALS SOLUTIONS CELLULAR TISSUES COOLING RATES AND SUCCESS OF FREEZING TEMPERATURE PRO?LES AND FREEZING TIME FREEZING TIME FOR AN IN?NITE SLAB OF PURE LIQUID FREEZING TIME FOR BIOMATERIALS EVAPORATION EVAPORATION FROM WET SURFACES EVAPORATION INSIDE A SOLID MATRIX EVAPORATION OF SOLUTIONS CHAPTER SUMMARY—HEAT TRANSFER WITH CHANGE OF PHASE RADIATIVE ENERGY TRANSFER THE ELECTROMAGNETIC SPECTRUM RE?ECTION, ABSORPTION AND TRANSMISSION OF WAVES AT A SURFACE TRANSMISSIVITY OF A LEAF AND PHOTOSYNTHESIS TRANSMISSIVITY OF THE ATMOSPHERE: GREENHOUSE EFFECT ALBEDO–RE?ECTION FROM SOIL ABSORPTION AND TRANSMISSION IN BIOMATERIALS THERMAL RADIATION FROM AN IDEAL (BLACK) BODY FRACTION OF ENERGY EMITTED THERMAL RADIATION FROM A REAL BODY: EMISSIVITY EMISSION FROM HUMAN BODIES SOLAR, ATMOSPHERIC, AND EARTH SURFACE RADIATION SOLAR RADIATION–MAGNITUDE AND SPECTRAL DISTRIBUTION EMISSION FROM EARTH’S SURFACE ATMOSPHERIC EMISSIONS GLOBAL ENERGY BALANCE RADIATIVE EXCHANGE BETWEEN BODIES RADIATIVE HEAT TRANSFER COEF?CIENT RADIATIVE EXCHANGE BETWEEN A LEAF AND SURROUNDINGS RADIATIVE EXCHANGE BETWEEN HUMAN (OR ANIMAL) AND ITS SUR- ROUNDINGS CHAPTER SUMMARY—RADIATIVE ENERGY TRANSFER 8 10 CONCEPT AND REVIEW QUESTIONS 8 11 FURTHER READING 8 12 PROBLEMS II MASS TRANSFER EQUILIBRIUM, MASS CONSERVATION, AND KINETICS CONCENTRATION CONCENTRATIONS IN A GASEOUS MIXTURE SPECIES MASS BALANCE (MASS CONSERVATION) EQUILIBRIUM EQUILIBRIUM BETWEEN A GAS AND A LIQUID EQUILIBRIUM BETWEEN A GAS AND A SOLID (WITH ADSORBED LIQUID) EQUILIBRIUM BETWEEN SOLID AND LIQUID IN ADSORPTION CHEMICAL KINETICS: GENERATION OR DEPLETION OF A MASS SPECIES RATE LAWS OF HOMOGENEOUS REACTIONS ZEROTH ORDER REACTION FIRST ORDER REACTION NTH ORDER REACTION EFFECTS OF TEMPERATURE CHAPTER SUMMARY—EQUILIBRIUM, MASS CONSERVATION, AND KINETICS 10 MODES OF MASS TRANSFER 10 1 A PRIMER ON POROUS MEDIA FLOW 10 1 1 PHYSICAL INTERPRETATION OF HYDRAULIC CONDUCTIVITY K AND PER- MEABILITY K 10 1 2 CAPILLARITY AND UNSATURATED FLOW IN A POROUS MEDIA 10 1 3 OSMOTIC FLOW IN A POROUS MEDIA 10 2 DIFFUSIVE MASS TRANSFER 10 2 1 MOLECULAR DIFFUSION 10 2 2 CAPILLARY DIFFUSION 10 3 DISPERSIVE MASS TRANSFER 10 4 CONVECTIVE MASS TRANSFER 10 4 1 CONVECTION-DIFFUSION MASS TRANSFER OVER A SURFACE 10 4 2 CONVECTION-DISPERSION MASS TRANSFER 10 5 COMPARISON OF THE MODES OF MASS TRANSFER 10 6 CHAPTER SUMMARY—MODES OF MASS TRANSFER 10 7 CONCEPT AND REVIEW QUESTIONS 10 8 FURTHER READING 10 9 PROBLEMS 11 GOVERNING EQUATIONS AND BOUNDARY CONDITIONS OF MASS TRANSFER 11 1 MODI?ED FICK’S LAW FOR BULK FLOW OR CONVECTION 11 1 1 VELOCITY AND MASS AVERAGE VELOCITY 11 1 2 FLUX EQUATION FOR A CONVECTIVE SITUATION 11 2 GOVERNING EQUATION FOR MASS TRANSFER 11 2 1 MEANINGS OF EACH TERM IN THE GOVERNING EQUATION 11 3 GENERAL BOUNDARY CONDITIONS 11 4 GOVERNING EQUATIONS FOR MASS DIFFUSION IN VARIOUS COORDINATE SYSTEMS 11 5 CHAPTER SUMMARY—G E & B C OF MASS TRANSFER 11 6 CONCEPT AND REVIEW QUESTIONS 11 7 FURTHER READING 11 8 PROBLEMS 12 DIFFUSION MASS TRANSFER: STEADY STATE 12 1 STEADY-STATE MASS DIFFUSION IN A SLAB 12 1 1 ONE-DIMENSIONAL MASS DIFFUSION THROUGH A COMPOSITE SLAB—OVERALL MASS TRANSFER COEF?CIENT 12 2 STEADY-STATE DIFFUSION IN A SLAB WITH CHEMICAL REACTION 12 2 1 PHOTOSYNTHESIS AND THE TRANSPORT OF WATER VAPOR AND CO2 IN A LEAF 12 3 CHAPTER SUMMARY—STEADY-STATE MASS DIFFUSION WITH AND WITHOUT CHEM- ICAL REACTION 12 4 CONCEPT AND REVIEW QUESTIONS 12 5 FURTHER READING 12 6 PROBLEMS 13 DIFFUSION MASS TRANSFER: UNSTEADY-STATE 13 1 TRANSIENT MASS TRANSFER WITH NO INTERNAL DIFFUSIVE RESISTANCE 13 2 TRANSIENT MASS TRANSFER WITH INTERNAL DIFFUSIVE RESISTANCE 13 2 1 HOW CONCENTRATION CHANGES WITH TIME 13 2 2 CONCENTRATION CHANGE WITH POSITION AND SPATIAL AVERAGE 13 2 3 CONCENTRATION CHANGE WITH SIZE 13 2 4 CHARTS DEVELOPED FROM THE SOLUTIONS: THEIR USES AND LIMITATIONS 13 2 5 WHEN BOTH INTERNAL AND EXTERNAL RESISTANCES ARE PRESENT: CON- VECTIVE BOUNDARY CONDITION 13 3 TRANSIENT DIFFUSION IN A FINITE GEOMETRY—MULTI-DIMENSIONAL PROBLEMS 13 4 TRANSIENT DIFFUSION IN A SEMI-IN?NITE REGION 13 5 CHAPTER SUMMARY—TRANSIENT DIFFUSIVE MASS TRANSFER 13 6 CONCEPT AND REVIEW QUESTIONS 13 7 FURTHER READING 13 8 PROBLEMS 14 CONVECTION MASS TRANSFER 14 1 CONVECTION-DISPERSION IN AN IN?NITE FLUID 14 2 CONVECTION-DISPERSION IN A SEMI-IN?NITE POROUS SOLID 14 3 CONVECTION-DISPERSION IN A SEMI-IN?NITE POROUS SOLID: INCLUSION OF SORPTION 14 4 CONVECTION-DIFFUSION IN A STAGNANT GAS 14 5 CONVECTION-DIFFUSION OVER A SURFACE 14 5 1 CONCENTRATION PRO?LES AND BOUNDARY LAYERS OVER A SURFACE 14 5 2 CONVECTIVE MASS TRANSFER COEF?CIENT DE?NED 14 5 3 SIGNI?CANT PARAMETERS IN CONVECTIVE MASS TRANSFER 14 5 4 CALCULATION AND PHYSICAL IMPLICATIONS OF CONVECTIVE MASS TRANS- FER COEF?CIENT VALUES 14 5 5 CONVECTION-DIFFUSION OF HEAT AND MASS (SIMULTANEOUS) OVER A SURFACE: EXAMPLE OF A WET BULB THERMOMETER 14 6 CHAPTER SUMMARY—CONVECTIVE MASS TRANSFER 14 7 CONCEPT AND REVIEW QUESTIONS 14 8 FURTHER READING 14 9 PROBLEMS