Energy Transfers by Conduction

Abdelhanine Benallou, École des mines, Morocco.

• Preface ixIntroduction xiChapter 1. Fundamental Equations of Conduction 11.1. Introduction 11.2. General equations of conduction 21.2.1. Expressing the term (I – O) 21.2.2. The term “generation” 41.2.3. The term “accumulation” 41.2.4. Energy balance equation 51.3. Equations of conduction in different coordinate systems 71.3.1. When l is not constant 81.3.2. When l is constant 91.3.3. Simplified cylindrical and spherical coordinates 91.3.4. One-dimensional conduction 101.4. Reading: metal tempering 10Chapter 2. Conduction in Steady State and Applications 132.1. Introduction 132.2. Equations of conduction in steady state 132.2.1. Expressions in the different coordinate systems 142.2.2. Simplifications in the case of one-dimensional conduction  142.3. Applying to single-layer walls 152.4. Concept of thermal resistance 162.5. Applying to composite or multi-layer walls 172.6. Applying to cylindrical walls 202.7. Applying to composite cylindrical walls 232.8. Applying to spherical walls 242.9. Case of composite spherical walls 262.10. Convective-type boundary conditions: case of a single-layer wall 282.10.1. Internal convection resistance 292.10.2. External convection resistance 292.10.3. Conduction resistance 292.10.4. Expressing the flux as a function of Ti and Te 292.11. Composite walls with convective boundary conditions 322.11.1. Illustration: calculating heat losses through the walls of an industrial furnace 332.12. Parallel resistances with convective boundary conditions 382.12.1. Illustration: composite wall with parallel thermal resistances 392.13. Composite cylindrical pipes with convective boundary conditions 472.13.1. Illustration: transfer through a composite cylindrical wall 482.14. Composite spherical installations with convective boundary conditions 51Chapter 3. Conduction Applications in Thermal Insulation 553.1. Introduction 553.2. The main insulation materials 563.2.1. Cork 563.2.2. Sawdust and wood wool 573.2.3. Hemp 573.2.4. Cellulose 583.2.5. Glass and rock wools 593.2.6. Polyurethane foam 613.2.7. Expanded polystyrene 623.3. Choosing a suitable thermal insulator 643.3.1. Optimum heat-lagging thickness for plane walls 663.3.2. Heat-lagging cylindrical jackets 753.3.3. Heat-lagging spherical containers 87Chapter 4. Conduction Applications in the Reduction of Heat Losses in Construction 994.1. Introduction 994.2. Thermal building regulations 1004.3. Calculating losses through building partitions 1054.3.1. Expressing the flux of energy losses 1054.3.2. Notations specific to building energy efficiency calculations 1064.3.3. Calculating losses through composite partitions: walls, floors and roofs 1074.4. Calculating losses through glass walls 1094.4.1. Illustration: minimum thermal resistances for the walls of a hotel to be constructed 1124.5. Optimizing energy choices for building heat insulation 1164.5.1. Illustration: energy losses through the windows of a building 1184.6. Reading: financing energy renovations, innovative schemes 123Chapter 5. Conduction with Energy Generation 1255.1. Introduction 1255.2. Plane conductor with generation 1255.2.1. Illustration: generation in a plane conductor 1275.3. Cylindrical conductor with generation 1335.3.1. Illustration: thermal technology in the core of a nuclear reactor 1355.4. Conduction in rectangular fins 1425.4.1. Illustration: gain in efficiency through use of a fin 147Chapter 6. Conduction in Transient State 1496.1. Introduction 1496.2. Methods for resolving the conduction equation 1506.3. Discretizing the heat equation 1516.4. Implementing the discrete heat equation 1546.4.1. Resolution algorithm 1546.4.2. Choosing the Δx and Δt  increments  1556.4.3. Simplifications in the case of stationary state 1556.4.4. Simplifications in the two-dimensional case 1566.4.5. Simplifications in the one-dimensional case 1606.5. Developing precise analytical solutions in the one-dimensional case 1606.6. Approximate analytical solutions 1656.6.1. For Bi = 0 1666.6.2. For 0 < Bi < 0.1 1666.6.3. For Bi = 0.1 1706.6.4. For Bi > 0.1 1716.7. Graphical method for solving the heat equation 1746.7.1. Temperature profile at center of solid 1766.7.2. Using charts to determine temperature profile at center of solid 1796.7.3. Temperature distribution inside the solid 1796.7.4. Using Figures 6.8 to 6.10 to determine the temperature distribution inside the solid 1826.7.5. Calculating the fluxes exchanged 1826.8. Case study: comparison of graphical and numerical methods 1966.8.1. Resolution using the graphical method 1976.8.2. Resolution using the numerical method 2026.8.3. Comparison of the numerical and graphical results 2056.8.4. Comparison with the analytical solution 2066.9. Reading: Jean-Baptiste Biot 212Chapter 7. Exercises and Solutions 215Appendix. Database 381Bibliography  421Index  433