Heat transfer

Content: 1. Introduction 
 1.1 AIMS OF STUDYING HEAT TRANSFER 
 1.2 APPLICATIONS OF HEAT TRANSFER 
 1.3 BASIC MODES OF HEAT TRANSFER 
 1.4 THERMAL CONDUCTIVITY 
 2. Steady State Conduction: One-dimensional Problems 
 2. Steady State Conduction: One-dimensional Problems 
 2.1 INTRODUCTION 
 2.2 FOURIER'S LAW OF HEAT CONDUCTION 
 2.3.1 FOURIER'S LAW IN CYLINDRICAL AND SPHERICAL COORDINATES 
 2.3 THE HEAT CONDUCTION EQUATION FOR ISOTROPIC MATERIALS 
 2.3.1 HEAT CONDUCTION EQUATION IN CYLINDRICAL COORDINATE SYSTEM 
 2.3.2 HEAT CONDUCTION EQUATION IN SPHERICAL COORDINATE SYSTEM 
 2.4 HEAT CONDUCTION EQUATION FOR ANISOTROPIC MATERIALS 
 2.5 INITIAL AND BOUNDARY CONDITIONS 
 2.5.1 INITIAL CONDITION 
 2.5.2 BOUNDARY CONDITIONS 
 2.5.3 NUMBER OF INITIAL AND BOUNDARY CONDITIONS 
 2.6 SIMPLE ONE-DIMENSIONAL STEADY CONDUCTION PROBLEMS 
 2.6.1 PLANE WALL 
 2.6.2 HOLLOW CYLINDER 
 2.6.3 THE COMPOSITE TUBE 
 2.6.4 HOLLOW SPHERE 
 2.8 OVERALL HEAT TRANSFER COEFFICIENT 
 2.9 CRITICAL THICKNESS OF INSULATION 
 2.10 HEAT GENERATION IN A BODY: PLANE WALL 
 2.11 HEAT GENERATION IN A SOLID CYLINDER 
 2.12 HEAT GENERATION IN A SOLID SPHERE 
 2.13 THE THIN ROD 
 2.14 THERMOMETER WELL ERRORS DUE TO CONDUCTION 
 2.15 EXTENDED SURFACES: FINS 
 2.15.1 EXTENDED SURFACES WITH CONSTANT CROSS SECTIONS 
 2.15.2 EVALUATION OF FIN PERFORMANCE 
 2.16 STRAIGHT FIN OF TRIANGULAR PROFILE 
 2.17 THERMAL CONTACT RESISTANCE 
 3. Steady State Conduction: Two- and Three-Dimensional Problems 
 3.1 INTRODUCTION 
 3.2 STEADY TWO-DIMENSIONAL PROBLEMS IN CARTESIAN COORDINATES 
 3.3 SUMMARY OF THE METHOD OF SEPARATION OF VARIABLES 
 3.4 ISOTHERMS AND HEAT FLUX LINES 
 3.5 THE METHOD OF SUPERPOSITION 
 3.5.1 THE RECTANGULAR PLATE WITH A SPECIFIED TEMPERATURE DISTRIBUTION ON MORE THAN ONE EDGE 
 3.5.2 2D HEAT CONDUCTION WITH UNIFORM HEAT GENERATION 
 3.6 METHOD OF IMAGING 
 3.7 STEADY 2D PROBLEMS IN CYLINDRICAL GEOMETRY 
 3.7.1 CIRCULAR CYLINDER OF FINITE LENGTH HAVING NO CIRCUMFERENTIAL VARIATION OF TEMPERATURE: T(R, Z) PROBLEM 
 3.7.2 LONG CIRCULAR CYLINDER HAVING CIRCUMFERENTIAL SURFACE TEMPERATURE VARIATION: T(R,  ) PROBLEM 
 3.8 STEADY THREE-DIMENSIONAL CONDUCTION IN CARTESIAN COORDINATES 
 3.9 THE GRAPHICAL METHOD AND CONDUCTION SHAPE FACTOR 
 3.9.1 BASIC PRINCIPLES 
 3.9.2 CALCULATION OF HEAT FLOW RATE 
 4. UNSTEADY STATE CONDUCTION 
 4.1 INTRODUCTION 
 4.2 LUMPED SYSTEM TRANSIENTS 
 4.3 ELECTRICAL NETWORK ANALOGY 
 4.4 ONE-DIMENSIONAL TRANSIENT PROBLEMS: DISTRIBUTED SYSTEM 
 4.5 MULTIDIMENSIONAL TRANSIENT PROBLEMS: APPLICATION OF HEISLER CHARTS 
 4.5.1 APPLICABILITY OF HEISLER CHARTS 
 4.5.2 CONCLUDING REMARKS ON HEISLER CHARTS 
 4.6 SEMI-INFINITE SOLID 
 4.6.1 OTHER SURFACE BOUNDARY CONDITIONS 
 4.6.2 PENETRATION DEPTH 
 5. FORCED CONVECTION HEAT TRANSFER 
 5.1 INTRODUCTION 
 5.2 THE CONVECTION BOUNDARY LAYERS 
 5.2.1 THE VELOCITY (OR MOMENTUM) BOUNDARY LAYER 
 5.2.2 THE THERMAL BOUNDARY LAYER 
 5.3 NUSSELT NUMBER 
 5.4 PRANDTL NUMBER 
 5.5 LAMINAR AND TURBULENT FLOWS OVER A FLAT PLATE 
 5.6 ENERGY EQUATION IN THE THERMAL BOUNDARY LAYER IN LAMINAR FLOW OVER A FLAT PLATE 
 5.6.1 IMPORTANCE OF THE VISCOUS DISSIPATION TERM 
 5.6.2 GOVERNING EQUATIONS AND BOUNDARY CONDITIONS 
 5.6.3 BASIC SOLUTION METHODOLOGY 
 5.7 SOLUTION OF THERMAL BOUNDARY LAYER ON AN ISOTHERMAL FLAT PLATE 
 5.7.1 EXACT SOLUTION: SIMILARITY ANALYSIS OF POHLHAUSEN 
 5.7.2 APPROXIMATE ANALYSIS: VON KARMAN'S INTEGRAL METHOD 
 5.8 PROCEDURE FOR USING ENERGY INTEGRAL EQUATION 
 5.9 APPLICATION OF ENERGY INTEGRAL EQUATION TO THE THERMAL BOUNDARY LAYER OVER AN ISOTHERMAL FLAT PLATE 
 5.9.1 ENERGY INTEGRAL SOLUTION FOR UNIFORM HEAT FLUX ( = CONSTANT) AT THE WALL 
 5.10 FILM TEMPERATURE 
 5.11 THE RELATION BETWEEN FLUID FRICTION AND HEAT TRANSFER 
 5.12 TURBULENT BOUNDARY LAYER OVER A FLAT PLATE 
 5.12.1 PHYSICAL ASPECTS OF TURBULENT BOUNDARY LAYER 
 5.12.2 TIME-AVERAGED EQUATIONS 
 5.12.3 EDDY DIFFUSIVITIES OF MOMENTUM AND HEAT 
 5.12.4 PRANDTL'S MIXING LENGTH HYPOTHESIS 
 5.12.5 TURBULENT PRANDTL NUMBER 
 5.12.6 WALL FRICTION 
 5.12.7 BASIC APPROACH IN SOLVING TURBULENT HEAT TRANSFER ON A FLAT PLATE 
 5.12.8 HEAT TRANSFER 
 5.13 HEAT TRANSFER IN LAMINAR TUBE FLOW 
 5.13.1 EFFECT OF AXIAL CONDUCTION IN THE FLUID IN LAMINAR TUBE FLOW 
 5.14 HYDRODYNAMIC AND THERMAL ENTRY LENGTHS 
 5.15 HEAT TRANSFER IN TURBULENT TUBE FLOW 
 5.15.1 SALIENT FEATURES OF LIQUID METAL HEAT TRANSFER IN TURBULENT TUBE FLOW 
 5.16 EXTERNAL FLOWS OVER CYLINDERS, SPHERES, AND BANKS OF TUBES 
 5.16.1 SINGLE CYLINDER IN CROSSFLOW 
 5.16.2 SPHERE 
 5.16.3 BANK OF TUBES IN CROSSFLOW 
 6. NATURAL CONVECTION HEAT TRANSFER 
 6.1 INTRODUCTION 
 6.1.1 PHYSICAL MECHANISM OF NATURAL CONVECTION 
 6.2 FREE CONVECTION FROM A VERTICAL PLATE 
 6.2.1 ANALYSIS 
 6.2.2 GOVERNING EQUATIONS 
 6.2.3 NON-DIMENSIONALIZATION 
 6.2.4 GENESIS OF THE PHYSICAL MEANING OF GR, RE, AND GR/RE2 FROM DIMENSIONAL ANALYSIS 
 6.3 FLOW REGIMES IN FREE CONVECTION OVER A VERTICAL PLATE 
 6.4 BASIC SOLUTION METHODOLOGY 
 6.4.1 SIMILARITY SOLUTION 
 6.4.2 INTEGRAL ANALYSIS 
 6.4.3 TURBULENT PROCESSES 
 6.5 FREE CONVECTION FROM OTHER GEOMETRIES 
 6.5.1 INCLINED PLATE 
 6.5.2 HORIZONTAL SURFACES 
 6.5.3 VERTICAL CYLINDERS 
 6.5.4 HORIZONTAL CYLINDERS 
 6.5.5 ENCLOSE SPACE BETWEEN INFINITE PARALLEL PLATES 
 6.5.6 ENCLOSED SPACE BETWEEN VERTICAL PARALLEL PLATES 
 6.6 CORRELATIONS FOR FREE CONVECTION OVER A VERTICAL PLATE SUBJECTED TO UNIFORM HEAT FLUX 
 6.7 MIXED CONVECTION 
 7. BOILING AND CONDENSATION 
 7.1 BOILING 
 7.1.1 EVAPORATION 
 7.1.2 NUCLEATE BOILING 
 7.2 REVIEW OF PHASE CHANGE PROCESSES OF PURE SUBSTANCES 
 7.2.1 THE P- -T SURFACE 
 7.3 BOILING MODES 
 7.3.1 SATURATED POOL BOILING 
 7.3.2 THE BOILING CURVE 
 7.3.3 MODES OF POOL BOILING 
 7.3.4 IMPORTANCE OF CRITICAL HEAT FLUX 
 7.3.5 THE TW VERSUS QW" CURVE 
 7.4 FORMATION OF VAPOUR BUBBLES 
 7.5 BUBBLE DEPARTURE DIAMETER AND FREQUENCY OF BUBBLE RELEASE 
 7.5.1 DEPARTURE DIAMETER CORRELATIONS 
 7.5.2 FREQUENCY OF BUBBLE RELEASE CORRELATIONS 
 7.6 EMPIRICAL CORRELATIONS AND APPLICATION EQUATIONS 
 7.6.1 CORRELATION OF ROHSENOW IN THE NUCLEATE POOL BOILING REGIME 
 7.6.2 CRITICAL HEAT FLUX FOR NUCLEATE POOL BOILING 
 7.7 HEAT TRANSFER IN THE VICINITY OF AMBIENT PRESSURE 
 7.8 HEAT TRANSFER MECHANISM IN NUCLEATE BOILING: ROHSENOW'S MODEL AND ITS BASIS 
 7.9 MINIMUM-HEAT-FLUX EXPRESSION 
 7.10 FILM BOILING CORRELATIONS 
 7.11 CONDENSATION 
 7.11.1 LAMINAR FILM CONDENSATION ON A VERTICAL PLATE 
 7.11.2 LAMINAR FILM CONDENSATION ON INCLINED PLATES 
 7.11.3 LAMINAR FILM CONDENSATION ON THE INNER OR OUTER SURFACE OF A VERTICAL TUBE 
 7.12 TURBULENT FILM CONDENSATION 
 7.13 SUB-COOLING OF THE CONDENSATE 
 7.14 SUPERHEATING OF THE VAPOUR 
 7.15 LAMINAR FILM CONDENSATION ON HORIZONTAL TUBES (NUSSELT'S APPROACH) 
 7.16 VERTICAL TIER OF N HORIZONTAL TUBES 
 7.16.1 CHEN'S MODIFICATION OF NUSSELT'S CORRELATION 
 7.17 STAGGERED TUBE ARRANGEMENT 
 7.18 FLOW BOILING 
 7.18.1 INTRODUCTION 
 7.18.2 DEFINITIONS OF SOME BASIC TERMS 
 7.19 CALCULATION OF X* IN A HEATED CHANNEL 
 7.19.1 CASES OF FAILURE OF EQN (7.70) 
 7.19.2 APPLICABILITY OF EQN (7.70) 
 7.20 PRESSURE DROP IN A TWO-PHASE FLOW 
 7.21 DETERMINATION OF FRICTIONAL PRESSURE DROP: THE LOCKHART AND MARTINELLI APPROACH 
 7.21.1 THE HOMOGENOUS MODEL 
 7.21.2 THE HETEROGENEOUS MODEL 
 7.23 THE VARIOUS HEAT TRANSFER REGIMES IN A TWO-PHASE FLOW 
 7.24 METHODOLOGY OF CALCULATION OF THE HEAT TRANSFER COEFFICIENT IN A TWO-PHASE FLOW: THE CHEN APPROACH 
 7.25 CRITICAL BOILING STATES 
 7.26 CONDENSATION OF FLOWING VAPOUR IN TUBES 
 7.27 HEAT PIPE 
 8. RADIATION HEAT TRANSFER 
 8.1 INTRODUCTION 
 8.2 PHYSICAL MECHANISM OF ENERGY TRANSPORT IN THERMAL RADIATION 
 8.3 LAWS OF RADIATION AND BASIC DEFINITIONS 
 8.3.1 PLANCK'S LAW 
 8.3.2 WIEN'S DISPLACEMENT LAW 
 8.3.3 STEFAN-BOLTZMANN LAW 
 8.3.4 CHANGE IN COLOUR OF A BODY WITH HEAT 
 8.4 INTENSITY OF RADIATION 
 8.4.1 RELATION TO IRRADIATION 
 8.4.2 RELATION TO RADIOSITY 
 8.4.3 RELATION BETWEEN RADIOSITY AND IRRADIATION 
 8.5 DIFFUSE SURFACE AND SPECULAR SURFACE 
 8.6 ABSORPTIVITY, REFLECTIVITY, AND TRANSMISSIVITY 
 8.7 BLACK BODY RADIATION 
 8.8 RADIATION CHARACTERISTICS OF NON-BLACK SURFACES: MONOCHROMATIC AND TOTAL EMISSIVITY 
 8.8.1 MONOCHROMATIC AND TOTAL ABSORPTIVITIES 
 8.9 KIRCHHOFF'S LAW 
 8.9.1 RESTRICTIONS OF KIRCHHOFF'S LAW 
 8.9.2 NOTE ON A GRAY BODY 
 8.10 VIEW FACTOR 
 8.10.1 THE VIEW FACTOR INTEGRAL 
 8.10.2 VIEW FACTOR RELATIONS 
 8.10.3 VIEW FACTOR ALGEBRA 
 8.10.4 HOTTEL'S CROSSED-STRINGS METHOD 
 8.11 RADIATION EXCHANGE IN A BLACK ENCLOSURE 
 8.12 RADIATION EXCHANGE IN A GRAY ENCLOSURE 
 8.13 ELECTRIC CIRCUIT ANALOGY 
 8.14 THREE-SURFACE ENCLOSURE 
 8.15 GEBHART'S ABSORPTION FACTOR METHOD 
 8.16 TWO-SURFACE ENCLOSURE 
 8.17 INFINITE PARALLEL PLANES 
 8.18 RADIATION SHIELDS 
 8.19 THE RADIATION HEAT TRANSFER COEFFICIENT 
 8.20 GAS RADIATION 
 8.20.1 PARTICIPATING MEDIUM 
 8.20.2 BEER'S LAW 
 8.20.3 MEAN BEAM LENGTH 
 8.20.4 HEAT EXCHANGE BETWEEN GAS VOLUME AND BLACK ENCLOSURE 
 8.20.5 HEAT EXCHANGE BETWEEN TWO BLACK PARALLEL PLATES 
 8.20.6 HEAT EXCHANGE BETWEEN SURFACES IN A BLACK N-SIDED ENCLOSURE 
 8.20.7 HEAT EXCHANGE BETWEEN GAS VOLUME AND GRAY ENCLOSURE 
 8.21 SOLAR RADIATION 
 8.22 THE GREENHOUSE EFFECT 
 9. HEAT EXCHANGERS 
 9.1 INTRODUCTION 
 9.2 CLASSIFICATION OF HEAT EXCHANGERS 
 9.2.1 FLUID FLOW ARRANGEMENT 
 9.2.2 TYPES OF APPLICATION 
 9.3 THE OVERALL HEAT TRANSFER COEFFICIENT 
 9.4 FOULING FACTOR 
 9.5 TYPICAL TEMPERATURE DISTRIBUTIONS 
 9.6 TEMPERATURE DISTRIBUTION IN COUNTER-FLOW HEAT EXCHANGERS 
 9.7 LOG-MEAN TEMPERATURE DIFFERENCE 
 9.8 HEAT TRANSFER AS A FUNCTION OF LMTD 
 9.9 MULTI-PASS AND CROSSFLOW HEAT EXCHANGERS: CORRECTION FACTOR APPROACH 
 9.10 EFFECTIVENESS-NTU METHOD 
 9.10.1 DERIVATION OF AN EXPRESSION FOR THE EFFECTIVENESS IN PARALLEL FLOW 
 9.10.2 PHYSICAL SIGNIFICANCE OF NTU 
 9.10.3 EFFECTIVENESS-NTU RELATIONS FOR SOME HEAT EXCHANGERS 
 9.10.4 ?-NTU CHARTS 
 9.10.5 THE ADVANTAGES OF ?-NTU METHOD 
 9.11 DESIGN CONSIDERATIONS OF HEAT EXCHANGERS 
 9.12 COMPACT HEAT EXCHANGERS 
 10. FINITE DIFFERENCE METHODS IN HEAT TRANSFER 
 10.1 INTRODUCTION 
 10.2 INTRODUCTION TO FINITE DIFFERENCE, NUMERICAL ERRORS, AND ACCURACY 
 10.2.1 CENTRAL-, FORWARD-, AND BACKWARD-DIFFERENCE EXPRESSIONS FOR A UNIFORM GRID 
 10.2.2 NUMERICAL ERRORS 
 10.2.3 ACCURACY OF A SOLUTION: OPTIMUM STEP SIZE 
 10.2.4 METHOD OF CHOOSING OPTIMUM STEP SIZE: GRID INDEPENDENCE TEST 
 10.3 NUMERICAL METHODS FOR CONDUCTION HEAT TRANSFER 
 10.3.1 NUMERICAL METHODS FOR A 1D STEADY-STATE PROBLEM 
 10.3.2 NUMERICAL METHODS FOR 2D STEADY-STATE PROBLEMS 
 10.4 TRANSIENT 1D PROBLEMS 
 10.4.1 METHODS OF SOLUTION 
 10.4.2 STABILITY: NUMERICALLY INDUCED OSCILLATIONS 
 10.4.3 STABILITY LIMIT OF THE EULER METHOD FROM PHYSICAL STANDPOINT 
 10.5 2D TRANSIENT HEAT CONDUCTION PROBLEMS 
 10.5.1 ALTERNATING DIRECTION IMPLICIT METHOD 
 10.6 PROBLEMS IN CYLINDRICAL GEOMETRY: HANDLING OF THE CONDITION AT THE CENTER 
 10.6.1 AXISYMMETRIC PROBLEMS 
 10.6.2 NON-AXISYMMETRIC PROBLEMS 
 10.7 1D TRANSIENT HEAT CONDUCTION IN COMPOSITE MEDIA 
 10.8 TREATMENT OF NON-LINEARITIES IN HEAT CONDUCTION 
 10.8.1 NON-LINEAR GOVERNING DIFFERENTIAL EQUATION: VARIABLE THERMAL CONDUCTIVITY 
 10.8.2 NON-LINEAR BOUNDARY CONDITIONS 
 10.9 HANDLING OF IRREGULAR GEOMETRY IN HEAT CONDUCTION 
 10.10 APPLICATION OF COMPUTATIONAL HEAT TRANSFER TO CRYOSURGERY 
 10.10.1 MATHEMATICAL MODEL 
 10.10.2 FINITE-DIFFERENCE FORMULATION 
 10.10.3 SOLUTION ALGORITHM 
 10.10.4 EXPERIMENTAL VERIFICATION OF THE TECHNIQUE 
 10.10.5 CONCLUDING REMARKS 
 11. MASS TRANSFER 
 11.1 INTRODUCTION 
 11.2 DEFINITIONS OF CONCENTRATIONS, VELOCITIES, AND MASS FLUXES 
 11.3 FICK'S LAW OF DIFFUSION 
 11.4 ANALOGY BETWEEN HEAT TRANSFER AND MASS TRANSFER 
 11.5 DERIVATION OF VARIOUS FORMS OF THE EQUATION OF CONTINUITY FOR A BINARY MIXTURE 
 11.6 ANALOGY BETWEEN SPECIAL FORMS OF THE HEAT CONDUCTION AND MASS DIFFUSION EQUATIONS 
 11.7 BOUNDARY CONDITIONS IN MASS TRANSFER 
 11.8 ONE-DIMENSIONAL STEADY DIFFUSION THROUGH A STATIONARY MEDIUM 
 11.9 FORCED CONVECTION WITH MASS TRANSFER OVER A FLAT PLATE LAMINAR BOUNDARY LAYER 
 11.9.1 EXACT SOLUTION 
 11.9.2 CONCENTRATION BOUNDARY LAYER AND MASS TRANSFER COEFFICIENT 
 11.10 EVAPORATIVE COOLING 
 11.11 RELATIVE HUMIDITY 
 11.11.1 EFFECTS OF RELATIVE HUMIDITY IN NATURE 
 12. SOLIDIFICATION AND MELTING 
 12.1 INTRODUCTION 
 12.2 EXACT SOLUTIONS OF SOLIDIFICATION: ONE-DIMENSIONAL ANALYSIS 
 12.2.1 PROBLEM OF STEFAN (1891) 
 12.2.2 NEUMANN PROBLEM 
 12.3 MELTING OF A SOLID: ONE-DIMENSIONAL ANALYSIS 
 APPENDICES 
 A1 THERMOPHYSICAL PROPERTIES OF MATTER 
 A2 NUMERICAL VALUES OF BESSEL FUNCTIONS 
 A3 TABLE OF LAPLACE TRANSFORMS 
 A4 NUMERICAL VALUES OF ERROR FUNCTIONS 
 A5 RADIATION VIEW FACTOR CHARTS 
 A6 BINARY DIFFUSIVITIES OF VARIOUS SUBSTANCES AT 1 ATM 
 A7 THERMOPHYSICAL PROPERTIES OF WATER AT ATMOSPHERIC PRESSURE