CONTENTS i Nomenclature ix Preface xiii IElementary Course xv 1 Introduction 1 2 Heat and mass transfer 3 2.1Heat transfer 4 2.2Mass transfer 4 2.3Energy and mass conservation 5 3 Heat 11 3.1Superposition principle 13 3.2Heat conduction, one-dimensional cases 15 3.2.1 Steady-state heat conduction in single and multi- layered structures . 16 3.2.2Plane radial heat flow at steady-state 20 3.2.3Response to temperature variations - Step-changes 22 3.2.4Contact temperature between two layers 24 3.2.5Response to periodic temperature variations 26 3.3Network analysis 29 3.4Heat conduction in 2D and 3D 33 3.4.1 Thermal bridges 34 3.4.2 Heat loss to the ground 37 3.5Convection 42 3.5.1 Surfaces to air 43 3.5.2Non-ventilated air gap 44 3.6Radiation46 3.6.1 Solar radiation, (Short wave) 48 3.6.2Long wave radiation 48 3.6.3Long wave radiation exchange between two isothermal surfaces in an enclosure 51 3.7Combined heat transfer 53 3.7.1Energy balances for a surface - Equivalent temperature53 3.7.2Heat transfer through a layered wall structure, U-values 57 3.7.3Non-ventilated air gap 58 3.7.4Air channel59 3.7.5Porous insulation materials60 3.7.6Convection in porous insulation materials62 3.8Energy balances for ventilated spaces 64 3.8.1 Room with well mixed air, periodical varying conditions 66 3.8.2Room with well mixed air and no heating 69 4 Air 71 4.1Driving forces 71 4.1.1 Wind pressure 71 4.1.2Stack effect75 4.1.3Mechanical ventilation 76 4.1.4Combining wind, stack and fan pressures 77 4.2Air transfer through the building envelope 77 4.2.1 Permeable materials 78 4.2.2Air gaps 78 4.2.3Holes in thin air tight layers 81 4.2.4Position of the neutral pressure plane 82 4.3Ventilation of a building 83 4.3.1 Air exchange rate 83 4.3.2Air-tightness84 4.3.3Heat losses due to transmission and ventilation 84 5 Moisture 87 5.1Moisture sources 87 5.2Moisture in air 88 5.3Moisture in porous materials 90 5.4Moisture transfer in air or by air 92 5.4.1 Diffusion 92 5.4.2 Convection 93 5.5Moisture transfer in porous material 96 5.5.1 Diffusion 96 5.5.2Capillary suction 99 5.5.3 Combined diffusion and capillary suction 102 5.6Transfer of liquid water due to pressure difference 105 5.6.1 Permeable material layer105 5.6.2A hole in a water tight layer 105 5.7Moisture to and from a surface106 5.7.1Convection106 5.7.2Surface condensation and evaporation107 5.8Drying of a layer107 5.9Moisture balance for two building components 110 5.10 Moisture balance for ventilated spaces112 5.10.1 Transient change due to a moisture source 112 5.10.2 Steady-state condition, wet surface and surface condensation113 5.11 Interstitial condensation 116 Exercises 119 Answers to exercises 139 IIAdvanced Course 143 6 Balance equations 145 6.1Conservation equations 146 6.2Heat capacity 148 6.3Moisture capacity 150 6.4Vector properties of heat and mass flow154 6.5The divergence operator 156 Heat and air transfer 159 7 Transfer equations 161 7.1Heat and mass flow in materials 161 7.1.1 Heat conduction 161 7.1.2 Air flow due to external pressure difference162 7.1.3Convective flows of heat 164 7.1.4 Combined convection and conduction 165 7.2Partial differential equations . 165 7.2.1 Heat conduction 165 7.2.2Air flow due to external pressure difference 165 7.2.3 Combined convection and conduction 166 7.3Initial conditions. 167 7.4Boundary conditions167 7.4.1 Heat conduction167 7.4.2 Air . 168 7.5Superposition principles 168 7.6Periodic complex solutions-Equations 172 7.7Numerical solution technique174 7.7.1Mesh 175 7.7.2Energy balance for a rectangular cell 176 7.7.3Algorithm for the numerical simulation 176 7.7.4Calculation of the heat flow, two-dimensional case 177 7.7.5Calculation of the heat flow, one-dimensional case 178 7.7.6Boundary conditions 178 7.7.7Stable time step 179 8Steady-state problems 181 8.1Varying thermal conductivity181 8.2Heat source 182 8.3Transverse heat loss 183 8.4Air channel with transverse heat flow 185 8.5Air and heat flow through layers 187 8.5.1 A layer with constant thermal conductivity 187 8.5.2Layer with varying thermal conductivity 189 8.6Thermally insulated slab on ground 190 8.6.1 SD-problems with a insulated rectangle190 8.6.2Long insulated strip 191 9 Transient problems 195 9.1Infinite region195 9.1.1 Thermal decline, region with a higher initial temperature 196 9.1.2Thermal decline due to a plane point source 197 9.2Step response for semi-infinite slab198 9.2.1 Zero surface resistance199 9.2.2Surface resistance 200 9.2.3Constant heat flux 202 9.2.4Linearly increasing boundary temperature202 9.3Slab202 9.3.1 Temperature decline, no surface resistance203 9.3.2 Temperature decline, surface resistance 205 9.3.3 Step response from one side, no surface resistance207 9.4Step response for a cylinder 209 9.5Corner 211 9.6Step response-Slab on ground 211 9.7Periodic solutions for semi-infinite region 214 9.7.1No surface resistance 214 9.7.2With surface resistance 215 9.8Periodic solutions for homogeneous slab 216 9.9Periodic solutions - Slab on ground217 10 Lumped system analysis 221 10.1 Step change in ambient temperature 222 10.2 Arbitrary ambient temperature 225 10.3 Periodic solution226 11 Long wave radiation exchange 229 11.1 Gray and diffuse radiation 229 11.2 View factors 230 11.2.1 Definitions 230 11.2.2 Rules 232 11.2.3 Cross-string method234 11.2.4 View factors for some cases235 11.3 Blackbody radiation exchange 241 11.4 Radiation exchange in an enclosure 242 11.4.1 Balance for the surface242 11.4.2 Two-surfaces enclosure244 12 Network components 249 12.1 Heat conduction through slabs 249 12.1.1 Steady-state250 12.1.2 Periodic 250 12.2 Heat transfer to the ground 252 12.2.1 Steady-state252 12.2.2 Periodic one-dimensional heat flow 252 12.3 Convective heat transfer 254 12.3.1 Surface heat transfer 254 12.3.2 Ventilation255 12.4 Heat sources256 12.5 Lumped systems 257 12.6 Radiation exchange 258 12.6.1 Surface 258 12.6.2 Coupling between surfaces. 258 12.7 A- to -network couplings 258 12.7.1 Reduction from A- to F-network 258 12.7.2 Reduction from Y- to A-network259 13 Examples of energy balance problems 261 13.1 Steady-state attic temperature 261 13.2 Energy balance-dynamic insulation 269 13.3 Operative temperature 273 13.4 Wall 275 13.5 Garage 279 13.6 Ventilated room 281 Moisture transfer 285 14 Transfer Mechanisms 287 14.1 Conditions in the pore system . 287 14.2 Vapor transport mechanisms 292 14.3 Liquid transport mechanisms 293 14.4 Isothermal moisture transfer293 14.4.1 Pick's law 294 14.4.2 Kirchhoff potential 296 14.4.3 Combined vapor and liquid transport 297 14.5 Non-Isothermal moisture transfer299 14.5.1 General moisture flow equation299 14.5.2 Combined vapor and liquid flow 300 14.5.3 Other potentials 300 14.6 Partial differential equation 301 14.6.1 General equations, no air flow 301 14.6.2 Isothermal condition-Kirchoff potential 302 14.6.3 Isothermal - linearized, one-dimensional 302 14.7 Initial conditions 303 14.8 Boundary conditions 303 14.8.1 Surface facing the air 303 14.8.2 Interface between different material 305 15 Steady-state problems 309 15.1 Layer with surface resistance 309 15.2 Diffusion versus capillary suction 310 15.3 Roof with moisture tight top surface312 15.4 Air channel with transverse moisture flow 314 16 Transient problems 317 16.1 Periodically varying humidity at boundary 317 16.2 Drying out of a layer318 16.3 Moisture uptake from a water surface320 16.4 Vapor exchange with walls - Step response 321 16.4.1 Step response in the boundary humidity321 16.4.2 Balance for a ventilated room324 16.5 Vapor exchange with walls - Periodic case 325 16.5.1 Periodic variations in the boundary humidity 325 16.5.2 Balance for a ventilated room326 Derivations 331 Exercises 349 Answers to exercises 369 Swedish-English dictionary 373 References and literature 375 A Important functions 381 A.I Error functions 381 A.2 Bessel function 387 A.3 Hyperbolic functions 388 A.4 Transcendental equations with tangent389 A.5 Transcendental equations with Bessel functions 390 A.6 Functions for periodic problems391 B Complex analysis 397 C Vector analysis 399 C.I The gradient operator 399 C.2 Nabla operator calculation rules 400 C.3 Temperature gradient 401 C.4 Laplace operator in different coordinate systems 401 D Humidity by volume at saturation 403 E Material data 405 E.I Thermal data405 E.2 Properties of air408 E.3 Moisture properties410 Index 417