# Building Heat Transfer

# Building Heat Transfer

ISBN: 978-0-470-02055-5

May 2006

524 pages

## Description

A third or more of the energy consumption of industrialized countries is expended on creating acceptable thermal and lighting conditions in buildings. As a result, building heat transfer is keenly important to the design of buildings, and the resulting analytical theory forms the basis of most design procedures. Analytical Theory of Building Heat Transfer is the first comprehensive reference of its kind, a one-volume compilation of current findings on heat transfer relating to the thermal behavior of buildings, forming a logical basis for current design procedures.**Preface.**

**Acknowledgements.**

**1 Elementary Steady-State Heat Transfer.**

1.1 Human Thermal Comfort.

1.2 Ambient Temperature.

1.2.1 Design Temperature.

1.2.2 Degree-Day Value.

1.3 The Traditional Building Heating Model.

1.3.1 Ventilation Loss.

1.3.2 Conduction Loss.

1.3.3 Loss from a Cylinder.

1.4 Seasonal Heat Need.

1.5 Plan of the Book.

**2 Physical Constants of Materials.**

2.1 Thermal Parameters for Gases: Kinetic Theory.

2.2 Representative Values for Solids.

2.3 Discussion.

2.4 Appendix: The Maxwellian Distribution.

**3 Conduction-Dominated Systems.**

3.1 Heat Flow along a Fin.

3.2 Heat Loss from a Solid Floor.

3.2.1 One-Dimensional Heat Loss.

3.2.2 Two-Dimensional Heat Loss.

3.2.3 Three-Dimensional Heat Loss.

3.2.4 Discussion of Floor Losses.

3.2.5 Placement of Insulation.

3.2.6 Heat Flow through Corners.

3.3 Solution using the Schwarz–Christoffel Transformation.

3.4 Appendix: Systems of Orthogonal Circles.

**4 Thermal Circuit Theory.**

4.1 Basic Thermal Elements.

4.1.1 Reference Temperature.

4.1.2 Temperature Node.

4.1.3 Pure Temperature Source.

4.1.4 Pure Heat Source.

4.1.5 Conductance.

4.1.6 Switch.

4.1.7 Quasi Heat Source.

4.1.8 Quasi Temperature Source.

4.2 The Heat Continuity Equation in an Enclosure.

4.2.1 The Mesh Approach.

4.2.2 The Nodal Approach.

4.3 Examples.

4.3.1 The Ventilated Cavity.

4.3.2 A Basic Circuit for Thermal Response.

4.4 Circuit Transforms.

4.4.1 Th&eeacute;venin’s and Norton’s Theorems.

4.4.2 Delta-Star Transformation.

4.4.3 Series-Parallel Transformation.

**5 Heat Transfer by Air Movement.**

5.1 Laminar and Turbulent Flow.

5.2 Natural Convection: Dimensional Approach.

5.2.1 Vertical Surface.

5.2.2 Inclined Surface.

5.2.3 Horizontal Surface.

5.3 Natural Convection at a Vertical Surface: Analytical Approach.

5.3.1 Heat Transfer through a Laminar Boundary Layer.

5.3.2 Discussion of the Laminar Flow Solution.

5.3.3 Heat Transfer through a Vertical Turbulent Boundary Layer.

5.4 Natural Convection between Parallel Surfaces.

5.5 Convective Exchange at Room Surfaces.

5.6 Convective Exchange through an Aperture between Rooms.

5.7 Heat Exchange at an External Surface.

**6 Heat Transfer by Radiation.**

6.1 The Fourth-Power Law.

6.2 Emissivity, Absorptivity and Reflectivity.

6.3 Radiation View Factors.

6.3.1 Basic Expression for View Factors.

6.3.2 Examples of View Factors.

6.3.3 View Factors by Contour Integration.

6.4 Direct Radiant Exchange between Surfaces.

6.4.1 Assumptions for Radiant Exchange.

6.4.2 The Thermal Circuit Formulation.

6.5 Radiant Exchange in an Enclosure.

6.5.1 Net Conductance *G* *Δ _{jk}*between Two Nodes.

6.5.2 Star Conductance *G* _{jk}*or Resistance

*R**jk.

6.5.3 Optimal Star Links.

6.5.4 How Good is the Delta-Star Transformation?

6.5.5 Discussion.

6.5.6 Linearisation of the Driving Potentials.

6.5.7 Inclusion of the Emissivity Conductance.

6.6 Space-Averaged Observable Radiant Temperature.

6.6.1 Space-averaged Observable Temperature due to an Internal Radiant Source.

6.6.2 Space-averaged Observable Radiant Temperature due to Bounding Surfaces.

6.7 Star-Based Model for Radiant Exchange in a Room.

6.8 Representation of Radiant Exchange by Surface-Surface Links.

6.9 Long-Wave Radiant Exchange at Building Exterior Surfaces.

6.10 Appendix: Conductance between Rectangles on Perpendicular and Parallel Surfaces.

**7 Design Model for Steady-State Room Heat Exchange.**

7.1 A Model Enclosure.

7.2 The Rad-Air Model for Enclosure Heat Flows.

7.3 Problems in Modelling Room Heat Exchange.

7.3.1 The Environmental Temperature Model.

7.3.2 The Invalidity of Environmental Temperature.

7.3.3 Flaws in the Argument.

7.4 What is Mean Radiant Temperature?

**8 Moisture Movement in Rooms.**

8.1 Vapour Loss by Ventilation.

8.2 Vapour Resistivity.

8.3 Vapour Loss by Diffusion through Porous Walls.

8.4 Condensation on a Surface.

8.5 Condensation in a Wall: Simple Model.

8.6 Condensation in a Wall: More Detailed Models.

8.6.1 Condensation in Glass Fibre.

8.6.2 The Sorption Characteristic for Capillary-Porous Materials.

8.6.3 Moisture Movement in Capillary-Porous Materials.

8.7 Appendix: The Saturated Vapour Pressure Relation.

8.8 Appendix: Saturated Vapour Pressure over a Curved Surface.

8.9 Appendix: Measures of the Driving Potential for Water Vapour Transport.

8.10 Appendix: Mould Growth in Antiquity.

**9 Solar Heating.**

9.1 Factors Affecting Radiation Reaching the Earth.

9.2 Earth’s Orbit and Rotation.

9.3 The Sun’s Altitude and Azimuth.

9.4 Intensity of Radiation.

9.5 Solar Incidence on Glazing.

9.6 The Steady-State Solar Gain Factor.

9.7 Solar Gain Contribution to Heat Need.

**10 The Wall with Lumped Elements.**

10.1 Modelling Capacity.

10.2 Forms of Response for a Single-Capacity Circuit.

10.2.1 The *r*-*c* Circuit.

10.2.2 The *r*-*c*-*r* Circuit: Ramp Solution.

10.2.3 The *r*-*c*-*r* Circuit: Periodic Solution.

10.3 The Two-Capacity Wall.

10.3.1 Wall Decay Times.

10.3.2 Unit Flux Temperatures.

10.3.3 The Orthogonality Theorem and the Transient Solution.

10.3.4 Step and Steady-Slope Solutions.

10.3.5 Ramp Solution.

10.3.6 Examples.

10.4 Finite Difference Method.

10.4.1 Subdivision of the Wall.

10.4.2 Computational Formulae.

10.4.3 Discussion.

10.4.4 Evaluation of Complex Quantities.

10.5 The Electrical Analogue.

10.6 Time-Varying Elements.

10.7 Appendix.

**11 Wall Conduction Transfer Coefficients for a Discretised System.**

11.1 The Response Factors *Φ _{50,k}*.

11.2 The *d* Coefficients.

11.3 The Transfer Coefficients *b _{50,k}*.

11.4 The Response Factors *Φ _{00,k}, Φ_{55,k}* and Transfer Coefficients

*a, c*.

11.5 Simple Cases.

11.6 Heat Stored in the Steady State.

11.7 Discussion.

11.8 Appendix.

**12 The Fourier Continuity Equation in One Dimension.**

12.1 Progressive Solutions.

12.2 Space/Time-Independent Solutions.

12.2.1 The Transient Solution.

12.2.2 The Periodic Solution.

12.3 The Source Solution and its Family.

12.3.1 Further Source-Based Solutions.

12.4 Solutions for the Temperature Profile and Taylor’s Series.

12.5 Transform Methods.

12.6 Use of the Solutions.

12.7 Appendix: Penetration of a Signal into an Infinite Slab.

**13 Analytical Transient Models for Step Excitation.**

13.1 Slab without Films.

13.1.1 Cooling at the Surface.

13.1.2 Cooling at the Midplane.

13.2 The Film and Slab, Adiabatic at Rear: Groeber’s Model.

13.2.1 Solution.

13.2.2 Limiting Forms.

13.2.3 Early and Late Stages of Cooling at the Surface.

13.2.4 Cooling Curves: Exposed Surface.

13.2.5 Surface Response Time.

13.2.6 Cooling at the Midplane.

13.2.7 Discussion.

13.3 Jaeger’s Model.

13.4 Pratt’s Model.

13.5 A One-Dimensional System cannot have Two Equal Decay Times.

13.6 Discussion.

**14 Simple Models for Room Response.**

14.1 Wall Time Constant Models.

14.2 Enclosure Response Time Models.

14.2.1 Response Time by Analysis.

14.2.2 Response Time by Computation.

14.2.3 Response Time by Observation.

14.2.4 Response Time and HVAC Time Delays.

14.3 Models with Few Capacities.

14.3.1 One-Capacity Wall Models.

14.3.2 One-Capacity Enclosure Models.

14.3.3 Enclosure Models with Two or More Capacities.

14.4 Discussion.

**15 Wall Parameters for Periodic Excitation.**

15.1 The Finite-Thickness Slab.

15.2 The Slab with Films.

15.3 Thermal Parameters for an External Multilayer Wall.

15.4 Admittance of an Internal Wall.

15.5 Discussion.

15.6 An Exact Circuit Model for a Wall.

15.7 Optimal Three-Capacity Modelling of a Slab.

15.8 Appendix: Complex Quantities and Vector Representation.

**16 Frequency-Domain Models for Room Response.**

16.1 Basic Principles.

16.2 24Hour Periodicity: Admittance Model.

16.3 Submultiples of 24Hours.

16.4 Further Developments.

16.5 Periodic Response for a Floor Slab.

**17 Wall Conduction Transfer Coefficients for a Layered System.**

17.1 The Single Slab.

17.2 Slope Response for a Multilayer Wall.

17.3 Transient Solution for a Multilayer Wall.

17.4 The Orthogonality Theorem.

17.5 Heat Flows in a Multilayer Wall.

17.5.1 Same-Side and Cross Excitation.

17.5.2 Transfer Coefficients.

17.6 Response Factors and Transfer Coefficients for an Example Wall.

17.6.1 Two-Layer Wall.

17.6.2 Wall with Resistances.

17.6.3 Discussion.

17.7 Derivations from Transfer Coefficients.

17.7.1 Wall Thermal Capacity.

17.7.2 Transfer Coefficients and Measures for Daily Sinusoidal Excitation.

17.7.3 Transfer Coefficients, Decay Times and Time of Peak Flow.

17.7.4 Transfer Coefficients with and without Film Coefficients.

17.7.5 Summary of Modelling Parameters.

17.8 The Equivalent Discretised Wall.

17.8.1 Error and Wall Thickness.

17.8.2 The Two-Capacity Homogeneous Wall.

17.8.3 The Real Wall is Discretised.

17.8.4 The Homogeneous Wall.

17.8.5 Wall Modelling.

17.9 Time- and Frequency-Domain Methods Compared.

17.10 Appendix: Finding the Decay Times.

17.11 Appendix: Inclusion of Moisture Movement.

**18 Accuracy of Temperature Estimates Using Transfer Coefficients.**

18.1 The *r*-*c* Model.

18.2 The Single Slab Driven by a Ramp.

18.3 The Single Slab Driven by a Flux.

18.4 The Single Slab Driven Sinusoidally.

18.5 Film and Slab Driven by a Ramp.

18.5.1 Film and Slab as Separate Entities.

18.5.2 Film and Slab as a Combined Entity.

18.6 The General Wall.

18.7 Discussion.

**19 Room Thermal Response Using Transfer Coefficients.**

19.1 Simplifying Assumptions.

19.2 A Basic Enclosure.

19.3 An Example Enclosure.

19.3.1 Internal Heat Transfer.

19.3.2 Heat Flow through the Walls.

19.3.3 Thermal Response to Ambient Temperature and Heat Input.

19.3.4 The Continuity Equations.

19.3.5 Response of the Enclosure.

19.3.6 Heating or Cooling when Comfort Temperature is Specified.

19.4 Development of the Model.

19.5 Infiltration between Adjacent Rooms.

19.6 Discussion.

19.7 Closure.

**Principal Notation.**

**References.**

**Bibliography.**

**Index.**