Building heat transfer

Preface xv Acknowledgements xxiii 1 Elementary Steady-State Heat Transfer 1 1.1 Human Thermal Comfort 1 1.2 Ambient Temperature 8 1.2.1 Design Temperature 8 1.2.2 Degree-Day Value 8 1.3 The Traditional Building Heating Model 10 1.3.1 Ventilation Loss 10 1.3.2 Conduction Loss 11 1.3.3 Loss from a Cylinder 16 1.4 Seasonal Heat Need 17 1.5 Plan of the Book 19 2 Physical Constants of Materials 21 2.1 Thermal Parameters for Gases: Kinetic Theory 21 2.2 Representative Values for Solids 27 2.3 Discussion 29 2.4 Appendix: The Maxwellian Distribution 33 3 Conduction-Dominated Systems 37 3.1 Heat Flow along a Fin 37 3.2 Heat Loss from a Solid Floor 40 3.2.1 One-Dimensional Heat Loss 40 3.2.2 Two-Dimensional Heat Loss 44 3.2.3 Three-Dimensional Heat Loss 47 3.2.4 Discussion of Floor Losses 49 3.2.5 Placement of Insulation 49 3.2.6 Heat Flow through Corners 51 3.3 Solution using the Schwarz.Christoffel Transformation 51 3.4 Appendix: Systems of Orthogonal Circles 55 viii CONTENTS 4 Thermal Circuit Theory 57 4.1 Basic Thermal Elements 57 4.1.1 Reference Temperature 57 4.1.2 Temperature Node 57 4.1.3 Pure Temperature Source 58 4.1.4 Pure Heat Source 59 4.1.5 Conductance 60 4.1.6 Switch 60 4.1.7 Quasi Heat Source 61 4.1.8 Quasi Temperature Source 61 4.2 The Heat Continuity Equation in an Enclosure 62 4.2.1 The Mesh Approach 63 4.2.2 The Nodal Approach 64 4.3 Examples 65 4.3.1 The Ventilated Cavity 65 4.3.2 A Basic Circuit for Thermal Response 66 4.4 Circuit Transforms 67 4.4.1 Th¢¥evenin،¯s and Norton،¯s Theorems 67 4.4.2 Delta-Star Transformation 69 4.4.3 Series-Parallel Transformation 70 5 Heat Transfer by Air Movement 75 5.1 Laminar and Turbulent Flow 76 5.2 Natural Convection: Dimensional Approach 77 5.2.1 Vertical Surface 77 5.2.2 Inclined Surface 83 5.2.3 Horizontal Surface 84 5.3 Natural Convection at a Vertical Surface: Analytical Approach 85 5.3.1 Heat Transfer through a Laminar Boundary Layer 85 5.3.2 Discussion of the Laminar Flow Solution 90 5.3.3 Heat Transfer through a Vertical Turbulent Boundary Layer 92 5.4 Natural Convection between Parallel Surfaces 94 5.5 Convective Exchange at Room Surfaces 100 5.6 Convective Exchange through an Aperture between Rooms 107 5.7 Heat Exchange at an External Surface 110 6 Heat Transfer by Radiation 115 6.1 The Fourth-Power Law 115 6.2 Emissivity, Absorptivity and Reflectivity 117 6.3 Radiation View Factors 118 6.3.1 Basic Expression for View Factors 119 6.3.2 Examples of View Factors 120 6.3.3 View Factors by Contour Integration 123 6.4 Direct Radiant Exchange between Surfaces 124 6.4.1 Assumptions for Radiant Exchange 124 6.4.2 The Thermal Circuit Formulation 125 CONTENTS ix 6.5 Radiant Exchange in an Enclosure 127 6.5.1 Net Conductance G
jk between Two Nodes 128 6.5.2 Star Conductance G . jk or Resistance R . jk 129 6.5.3 Optimal Star Links 129 6.5.4 How Good is the Delta-Star Transformation? 131 6.5.5 Discussion 132 6.5.6 Linearisation of the Driving Potentials 133 6.5.7 Inclusion of the Emissivity Conductance 134 6.6 Space-Averaged Observable Radiant Temperature 135 6.6.1 Space-averaged Observable Temperature due to an Internal Radiant Source 136 6.6.2 Space-averaged Observable Radiant Temperature due to Bounding Surfaces 139 6.7 Star-Based Model for Radiant Exchange in a Room 141 6.8 Representation of Radiant Exchange by Surface-Surface Links 141 6.9 Long-Wave Radiant Exchange at Building Exterior Surfaces 142 6.10 Appendix: Conductance between Rectangles on Perpendicular and Parallel Surfaces 145 7 Design Model for Steady-State Room Heat Exchange 149 7.1 A Model Enclosure 150 7.2 The Rad-Air Model for Enclosure Heat Flows 155 7.3 Problems in Modelling Room Heat Exchange 158 7.3.1 The Environmental Temperature Model 158 7.3.2 The Invalidity of Environmental Temperature 160 7.3.3 Flaws in the Argument 161 7.4 What is Mean Radiant Temperature? 164 8 Moisture Movement in Rooms 167 8.1 Vapour Loss by Ventilation 169 8.2 Vapour Resistivity 170 8.3 Vapour Loss by Diffusion through Porous Walls 172 8.4 Condensation on a Surface 173 8.5 Condensation in a Wall: Simple Model 176 8.6 Condensation in a Wall: More Detailed Models 178 8.6.1 Condensation in Glass Fibre 181 8.6.2 The Sorption Characteristic for Capillary-Porous Materials 185 8.6.3 Moisture Movement in Capillary-Porous Materials 188 8.7 Appendix: The Saturated Vapour Pressure Relation 191 8.8 Appendix: Saturated Vapour Pressure over a Curved Surface 193 8.9 Appendix: Measures of the Driving Potential for Water Vapour Transport 194 8.10 Appendix: Mould Growth in Antiquity 196 9 Solar Heating 197 9.1 Factors Affecting Radiation Reaching the Earth 197 9.2 Earth،¯s Orbit and Rotation 199 x CONTENTS 9.3 The Sun،¯s Altitude and Azimuth 201 9.4 Intensity of Radiation 204 9.5 Solar Incidence on Glazing 206 9.6 The Steady-State Solar Gain Factor 210 9.7 Solar Gain Contribution to Heat Need 212 10 The Wall with Lumped Elements 217 10.1 Modelling Capacity 217 10.2 Forms of Response for a Single-Capacity Circuit 219 10.2.1 The r-c Circuit 219 10.2.2 The r-c-r Circuit: Ramp Solution 220 10.2.3 The r-c-r Circuit: Periodic Solution 222 10.3 The Two-Capacity Wall 223 10.3.1 Wall Decay Times 224 10.3.2 Unit Flux Temperatures 228 10.3.3 The Orthogonality Theorem and the Transient Solution 229 10.3.4 Step and Steady-Slope Solutions 230 10.3.5 Ramp Solution 231 10.3.6 Examples 232 10.4 Finite Difference Method 234 10.4.1 Subdivision of the Wall 234 10.4.2 Computational Formulae 237 10.4.3 Discussion 239 10.4.4 Evaluation of Complex Quantities 240 10.5 The Electrical Analogue 241 10.6 Time-Varying Elements 243 10.7 Appendix 245 11 Wall Conduction Transfer Coefficients for a Discretised System 249 11.1 The Response Factors ¥ُ50,k 250 11.2 The d Coefficients 253 11.3 The Transfer Coefficients b50,k 254 11.4 The Response Factors ¥ُ00,k, ¥ُ55,k and Transfer Coefficients a, c 256 11.5 Simple Cases 256 11.6 Heat Stored in the Steady State 257 11.7 Discussion 259 11.8 Appendix 260 12 The Fourier Continuity Equation in One Dimension 263 12.1 Progressive Solutions 265 12.2 Space/Time-Independent Solutions 266 12.2.1 The Transient Solution 267 12.2.2 The Periodic Solution 271 12.3 The Source Solution and its Family 273 12.3.1 Further Source-Based Solutions 277 12.4 Solutions for the Temperature Profile and Taylor،¯s Series 279 12.5 Transform Methods 280 CONTENTS xi 12.6 Use of the Solutions 282 12.7 Appendix: Penetration of a Signal into an Infinite Slab 284 13 Analytical Transient Models for Step Excitation 287 13.1 Slab without Films 287 13.1.1 Cooling at the Surface 288 13.1.2 Cooling at the Midplane 290 13.2 The Film and Slab, Adiabatic at Rear: Groeber،¯s Model 291 13.2.1 Solution 292 13.2.2 Limiting Forms 295 13.2.3 Early and Late Stages of Cooling at the Surface 295 13.2.4 Cooling Curves: Exposed Surface 298 13.2.5 Surface Response Time 299 13.2.6 Cooling at the Midplane 299 13.2.7 Discussion 301 13.3 Jaeger،¯s Model 302 13.4 Pratt،¯s Model 304 13.5 A One-Dimensional System cannot have Two Equal Decay Times 308 13.6 Discussion 309 14 Simple Models for Room Response 311 14.1 Wall Time Constant Models 311 14.2 Enclosure Response Time Models 316 14.2.1 Response Time by Analysis 316 14.2.2 Response Time by Computation 320 14.2.3 Response Time by Observation 320 14.2.4 Response Time and HVAC Time Delays 322 14.3 Models with Few Capacities 323 14.3.1 One-Capacity Wall Models 324 14.3.2 One-Capacity Enclosure Models 326 14.3.3 Enclosure Models with Two or More Capacities 328 14.4 Discussion 332 15 Wall Parameters for Periodic Excitation 335 15.1 The Finite-Thickness Slab 336 15.2 The Slab with Films 339 15.3 Thermal Parameters for an External Multilayer Wall 340 15.4 Admittance of an Internal Wall 343 15.5 Discussion 345 15.6 An Exact Circuit Model for a Wall 345 15.7 Optimal Three-Capacity Modelling of a Slab 347 15.8 Appendix: Complex Quantities and Vector Representation 350 16 Frequency-Domain Models for Room Response 353 16.1 Basic Principles 353 16.2 24Hour Periodicity: Admittance Model 356 xii CONTENTS 16.3 Submultiples of 24Hours 365 16.4 Further Developments 367 16.5 Periodic Response for a Floor Slab 367 17 Wall Conduction Transfer Coefficients for a Layered System 371 17.1 The Single Slab 375 17.2 Slope Response for a Multilayer Wall 379 17.3 Transient Solution for a Multilayer Wall 383 17.4 The Orthogonality Theorem 385 17.5 Heat Flows in a Multilayer Wall 387 17.5.1 Same-Side and Cross Excitation 390 17.5.2 Transfer Coefficients 391 17.6 Response Factors and Transfer Coefficients for an Example Wall 393 17.6.1 Two-Layer Wall 393 17.6.2 Wall with Resistances 395 17.6.3 Discussion 397 17.7 Derivations from Transfer Coefficients 397 17.7.1 Wall Thermal Capacity 397 17.7.2 Transfer Coefficients and Measures for Daily Sinusoidal Excitation 399 17.7.3 Transfer Coefficients, Decay Times and Time of Peak Flow 401 17.7.4 Transfer Coefficients with and without Film Coefficients 401 17.7.5 Summary of Modelling Parameters 402 17.8 The Equivalent Discretised Wall 402 17.8.1 Error and Wall Thickness 404 17.8.2 The Two-Capacity Homogeneous Wall 407 17.8.3 The Real Wall is Discretised 408 17.8.4 The Homogeneous Wall 409 17.8.5 Wall Modelling 411 17.9 Time- and Frequency-Domain Methods Compared 412 17.10 Appendix: Finding the Decay Times 414 17.11 Appendix: Inclusion of Moisture Movement 418 18 Accuracy of Temperature Estimates Using Transfer Coefficients 423 18.1 The r-c Model 423 18.2 The Single Slab Driven by a Ramp 425 18.3 The Single Slab Driven by a Flux 428 18.4 The Single Slab Driven Sinusoidally 429 18.5 Film and Slab Driven by a Ramp 430 18.5.1 Film and Slab as Separate Entities 430 18.5.2 Film and Slab as a Combined Entity 431 18.6 The General Wall 432 18.7 Discussion 433 19 Room Thermal Response Using Transfer Coefficients 435 19.1 Simplifying Assumptions 436 19.2 A Basic Enclosure 438 CONTENTS xiii 19.3 An Example Enclosure 440 19.3.1 Internal Heat Transfer 440 19.3.2 Heat Flow through the Walls 442 19.3.3 Thermal Response to Ambient Temperature and Heat Input 443 19.3.4 The Continuity Equations 444 19.3.5 Response of the Enclosure 447 19.3.6 Heating or Cooling when Comfort Temperature is Specified 451 19.4 Development of the Model 451 19.5 Infiltration between Adjacent Rooms 454 19.6 Discussion 456 19.7 Closure 458 Principal Notation 459 References 465 Bibliography 493 Index 495