ENERGY MODELING
and COMPUTATIONS
in THE BUILDING
ENVELOPE
2016
مطالب
1. Introduction: The Buildings’ Envelope—A Component of the
Building Energy System.................................................................................1
1.1 Systematic Approach Applied to Buildings.......................................1
1.2 Envelope System (Envelope) and Energy Functions Design...........3
1.3 Summary Analysis of the Building–Surrounding Energy
Interactions........................................................................................... 11
2. Physics of Energy Conversions in the Building Envelope at
Microscopic Level.......................................................................................... 13
2.1 Idealized Physical Model of the Building Envelope as an
Energy-Exchanging Medium (Review of the Literature from
Microscopic Point of View)................................................................. 16
2.2 Conclusions and Generalizations Based on the Survey of
Literature Published in the Field.......................................................30
2.3 Design of a Hypothetical Physical Model of Phonon
Generation in Solids: Scatter of Solar Radiation within
the Solid.............................................................................................. 32
2.3.1 Internal Ionization and Polarization Running in
Solids (Formation of Temporary Electrodynamic
Dipoles)..................................................................................... 32
2.3.2 Hypothetical Mechanism of Energy Transfer in the
Building Envelope Components...........................................36
2.3.2.1 Physical Pattern of Energy Transfer within
the Envelope Components.....................................36
2.3.3 Hypothetical Model of Energy Transfer through
Solid Building Components: A Model of Lagging
Temperature Gradient............................................................ 41
2.3.3.1 Model of Lagging Temperature Gradient............48
2.4 Micro–Macroscopic Assessment of the State of the Building
Envelope................................................................................................ 51
2.4.1 Microscopic Canonical Ensemble: Collective
Macroscopic State.................................................................... 51
2.4.2 Introduced Macroscopic State Parameters of
the Building Envelope Considered as a Physical
Medium of the Electrothermodynamic System.................53
2.4.2.1 Temperature Field and Gradient of the
Lagrange Multiplier................................................53
2.4.2.2 Pressure Field...........................................................58
2.4.2.3 Field of the Electric Potential: Potential
Function and Gradient of the Electric
Potential................................................................. 61
2.4.2.4 Entropy: A Characteristic of Degeneration
of the Heat Charges (Phonons) within the
Envelope Control Volume......................................66
2.4.3 Conclusions on the General Methodological
Approaches to the Study of an
Electrothermomechanical System........................................73
3. Design of a Model of Energy Exchange Running between
the Building Envelope and the Surroundings: Free Energy
Potential........................................................................................................ 75
3.1 Energy-Exchange Models of the Building Envelope......................75
3.2 Work Done in the Building Envelope and Energy-Exchange
Models................................................................................................... 81
3.2.1 Law of Conservation of the Energy Interactions
between the Envelope Components and the Building
Surroundings...........................................................................82
3.2.2 Special Cases of Energy Interactions...................................86
3.2.2.1 Energy Model of Transfer of Entropy and
Electric Charges.......................................................86
3.2.2.2 Energy Model of Entropy Transfer with or
without Mass Transfer............................................88
3.3 Specification of the Structure of the Free Energy
in the Components of the Building Envelope
(Electrothermodynamic Potential of the System)............................89
3.3.1 Finding the Structure of the Free Energy Function...........92
3.3.1.1 Links between Entropy and the System
Basic Parameters......................................................95
3.4 Distribution of the Free Energy within the Building
Envelope........................................................................................ 97
3.4.1 State Parameters Subject to Determination via the
Free Energy Function.............................................................99
4. Definition of the Macroscopic Characteristics of Transfer................. 101
4.1 General Law of Transfer.................................................................... 106
4.2 Physical Picture of the Transmission Phenomena........................ 108
4.3 Conclusions......................................................................................... 111
5. Numerical Study of Transfer in Building Envelope
Components..........................................................................................113
5.1 Method of the Differential Relations.............................................. 113
5.2 Method of the Integral Forms.......................................................... 119
5.3 Weighted Residuals Methodology Employed to Assess the
ETS Free Energy Function................................................................122
5.3.1 Basic Stages of the Application of WRM in
Evaluating Transport within the Envelope....................... 125
5.3.1.1 One-Dimensional Simple Finite Element.......... 140
5.3.1.2 Two-Dimensional Simple Finite Element in
Cartesian Coordinates.......................................... 140
5.3.1.3 Two-Dimensional Simple Finite Element in
Cylindrical Coordinates....................................... 141
5.3.1.4 Three-Dimensional Simple Finite Element....... 141
5.3.2 Modeling of Transfer in a Finite Element Using a
Matrix Equation (Galerkin Method).................................. 142
5.3.3 Steady Transfer in One-Dimensional Finite Element...... 146
5.3.3.1 Integral Form of the Balance of Energy
Transfer through One-Dimensional Finite
Element................................................................... 147
5.3.3.2 Modified Matrix Equation of 1D Transfer......... 150
5.3.3.3 Transfer through 1D Simple Finite Element
Presented in Cylindrical Coordinates................ 155
5.3.4 Steady Transfer in a 2D Finite Element............................. 160
5.3.4.1 Equation of a 2D Simple Finite Element in
Cartesian Coordinates.......................................... 161
5.3.4.2 Design of Transfer Equation in Cylindrical
Coordinates regarding a Three-Noded 2D
Finite Element........................................................ 166
5.3.5 Transfer through a 3D Simple Finite Element.................. 170
5.3.5.1 Design of the Matrix Equation of Transfer
in Cartesian Coordinates..................................... 170
6. Initial and Boundary Conditions of a Solid Wall Element................. 175
6.1 Effects of the Environmental Air on the Building Envelope....... 175
6.1.1 Mass Transfer from the Building Envelope (Wall
Dehumidification, Drying)...................................................... 176
6.1.1.1 Processes Running at a Cold Wall (TA Twi ³ ).......177
6.1.1.2 Processes Running at a Cold Wall (Tw < TA ).......178
6.2 Various Initial and Boundary Conditions of Solid Structural
Elements.............................................................................................. 179
6.3 Design of Boundary Conditions of Solid Structural Elements.......182
6.3.1 Boundary Conditions of Convective Transfer
Directed to the Wall Internal Surface................................ 183
6.3.2 Boundary Conditions at the Wall External Surface......... 185
7. Engineering Methods of Estimating the Effect of the
Surroundings on the Building Envelope: Control of the
Heat Transfer through the Building Envelope (Arrangement
of the Thermal Resistances within a Structure Consisting of
Solid Wall Elements)................................................................................... 191
7.1 Calculation of the Thermal Resistance of Solid Structural
Elements.............................................................................................. 194
7.2 Solar Shading Devices (Shield) Calculation...................................203
7.3 Modeling of Heat Exchange between a Solar Shading
Device, a Window, and the Surroundings.....................................208
7.3.1 Mathematical Model............................................................. 212
7.4 Design of Minimal-Admissible Light-Transmitting Envelope
Apertures Using the Coefficient of Daylight (CDL)...................... 213
7.4.1 Energy and Visual Comfort................................................ 213
7.4.2 Calculation of the Coefficient of Daylight (CDL)............. 218
7.5 Method of Reducing the Tribute of the Construction and the
Thermal Bridges to the Energy Inefficiency..................................223
7.5.1 Characteristics of Heat Transfer through Solid
Inhomogeneous Multilayer Walls...................................... 224
7.5.2 Method Described Step by Step.........................................227
7.5.3 Description of the Energy Standard of the
Construction (EEConst)............................................................227
7.5.4 Employment of the Energy Standard to Assess How
the Building Structure Affects the Energy Efficiency......229
7.6 Assessment of Leaks in the Building Envelope and the
Air-Conditioning Systems................................................................233
7.6.1 Measuring Equipment of the Method “Delta-Q”............234
7.6.2 Modified Balance Equation of Leaks in Air Ducts,
Air-Conditioning Station, and Envelope...........................236
7.6.3 Delta-Q Procedure: Data Collection and
Manipulation......................................................................238
7.6.4 Normalization of the Collected Data................................. 241
7.7 Mathematical Model of the Environmental Sustainability of
Buildings............................................................................................. 244
7.7.1 General Structure of the Model.......................................... 244
7.7.2 Selection of an Ecological Standard: Table of
Correspondence.................................................................... 248
7.7.3 Comparison of Systems Rating the Ecological
Sustainability in Conformity with the General
Criteria................................................................................. 255
7.8 Conclusion...........................................................................................258
Acknowledgments........................................................................................ 262
8. Applications (Solved Tasks and Tables).................................................263
8.1 Matrix of Conductivity [K(1)].............................................................263
8.2 Matrix of Surface Properties [F(1)]....................................................264
8.3 Generalized Matrix of the Element Conductivity
[G(1)] = [K(1)] + [F(1)]...............................................................................265
8.4 Vector of a Load due to Recuperation Sources { fC(1)}....................265
8.5 Vector of a Load due to Convection to the Surrounding
Matter { fC(1)}.........................................................................................266
8.6 Vector of a Load due to a Direct Flux { fDr }
e .................................... 266
8.6.1 Design and Solution of the Matrix Equation.................... 267
References............................................................................................................ 293
Index......................................................................................................................305
ENERGY MODELING and COMPUTATIONS in THE BUILDING ENVELOPE, 2016