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Peter Booth Wiley
Chairman of the Board


To my wife, children and grandchildren

In remembrance of Professor A. de Grave,
who introduced Building Physics as a new discipline
at the University of Louvain, K. U. Leuven, Belgium, in 1952



Until the first energy crisis of 1973, building physics survived as a somewhat dormant field in building engineering, with seemingly limited applicability in practice. While soil mechanics, structural mechanics, building materials, building construction and HVAC were seen as essential, designers only demanded advice on room acoustics, moisture tolerance, summer comfort or lighting when really needed or when, after construction of their designs, when problems arose. Energy was even not a concern, while indoor environmental quality was presumably guaranteed thanks to the ever present infiltration, to opening windows and to the heating system. The energy crises of the seventies, persisting moisture problems, complaints about sick buildings, thermal, visual and olfactory discomfort, the move towards more sustainability, changed it all. The societal pressure to diminish energy consumptions in buildings without degrading usability acted as a trigger that activated the whole notion of performance based design and construction. As a result, building physics and its potentiality to quantify performances was suddenly pushed to the frontline of building innovation.

As all engineering sciences, building physics is oriented towards application. Hence, creativity in application demands a sound knowledge of the basics in each of the branches building physics encompasses: heat and mass, acoustics, lighting, energy and indoor environmental quality. Integrating these basics into an up to date text on heat and mass has been the main goal of this book, with mass limited to air, water vapour and moisture. The book is the result of thirty years of teaching architectural, building and civil engineers, coupled to thirty five years of experience, research and consultancy in the field. Apart of that, where and when needed, inputs and literature from over the world is used, reason why each part is followed by an extended literature list.

In an introductory chapter, building physics is presented as a discipline. Then, the first part concentrates on heat transport, with conduction, convection and radiation as main topics, followed by concepts and applications, typical for building physics. The second part treats mass transport, with air, water vapour and moisture as most important components. Again, much attention is devoted to the concepts and applications which relate to building physics. The last part finally discusses combined transport of heat and mass, who in fact act as if they were Siamese twins. The first and second part is followed by exemplary exercises, with some of them solved and the others offered to the reader as an element of training.

The book is written in SI-units. It should be especially usable for undergraduate and graduate studies in architectural and building engineering, although also mechanical engineers, studying HVAC, and practising building engineers, who want to refresh their knowledge, may benefit from it. The level of presentation anyhow assumes that the reader has a sound knowledge of calculus and differential equations along with some background in physics, thermodynamics, hydraulics, building materials and building construction.


A book of this magnitude reflects the work of many, not only the author. Therefore, first of all, we like to thank the thousands of students we had during our thirty years of teaching building physics. They gave us the opportunity to test the content of the book and helped in upgrading it by the corrections they proposed and the experience they offered in learning what parts should be better explained.

The book should not have been written the way it is, if not standing on the shoulders of those, who preceded us. Although we started our carrier as a structural engineer, our predecessor, Professor Antoine de Grave, planted the seeds that slowly fed our interest in building physics. The late Bob Vos of TNO, the Netherlands, and Helmut Künzel of the Fraunhofer Institut für Bauphysik, Germany, showed the importance of experimental work and field testing for understanding building performance, while Lars Erik Nevander of Lund University, Sweden, taught that solving problems in building physics does not always ask complex modelling, mainly because reality in building construction is ever again much more complex than any model may be.

During the four decennia at the Laboratory of Building Physics, several researchers and PhD-students got involved. I am very grateful to Gerrit Vermeir, Jan Carmeliet and Staf Roels, who became colleagues at the university, to Piet Standaert, Filip Descamps, now part-time professor at the Free University Brussels (VUB); Arnold Janssens, now associate professor at the University of Ghent (UG); Dirk Saelens, Hans Janssen, now associate professor at the Technical University Denmark (TUD); Rongjin Zheng and Bert Blocken, now associate professor at the Technical University Eindhoven (TU/e), who all contributed to this book by their work. The experiences gained by leading four Annexes of the IEA, Executive Committee on Energy Conservation in Buildings and Community Systems, further-on forced me to rethink parts of the text over time. The many ideas I exchanged and got in Canada and the USA from Kumar Kumaran, Paul Fazio, Bill Brown, William B. Rose, Joe Lstiburek and Anton Ten Wolde were also of great help in drafting the text

A number of reviewers took time to evaluate the book. Although we do not know their names, we like to thank them. Many merits also go to Miss Gerrie Doche from Montreal, Quebec, Canada, who made the first translation of the text from Dutch into English.

Finally, I like to thank my family. My loving mother who died too early. My father, who at a respectable age, still shows interest in our work. My wife, Lieve, who managed living together with a professor who was so busy, my three children who had to live with that busy father, and my many grandchildren who do not know their grandfather is still busy.

Leuven, February 2007

Hugo S. L. C. Hens

0 Introduction

0.1 Subject of the Book

This is the first of a series of books on a Building Physics and Applied Building Physics:

For the Anglo-Saxon notion, the phrase ‘Building Physics’ is somewhat unusual. ‘Building Science’ is the more usual expression. However the two do not cover the same field of knowledge. Building science in fact is broader in its approach. It encompasses all subjects related to buildings that claim to be ‘scientific’. This is especially clear when looking at journals that publish on ‘Building Science’. The range of subjects treated is remarkably wide, ranging from control issues in HVAC, to city planning and organizational issues.

In this book on ‘Building Physics: Heat, Air and Moisture Transport’, the subject is the physics behind heat, air and moisture transfer in materials and building parts. Applied Building Physics deals with climate and the usability conditions confronting building physics. Furthermore, the performance concept and some performance requirements are discussed, and tables with material properties are given. Applied Building Physics and Performance Based Design 1 and 2 then use the performance concept as a tool in the design and construction of buildings. As such, both integrate the fields of building construction, building materials, building physics and structural mechanics.

0.2 Building Physics

0.2.1 Definition

Building Physics is an applied science that studies the hygrothermal, acoustical and light-related properties of building components (roofs, façades, windows, partition walls, etc.), rooms, buildings and building assemblies. The basic considerations are the user requirements for thermal, acoustic and visual comfort, the user’s health requisites and the more-or-less compelling demands and limitations imposed by architectural, material-related, economical and ecological considerations.

The term ‘applied’ indicates that Building Physics is directed towards problem solving: the theory as a tool, not as a purpose. From the definition, the field covered contains three sub-sectors. The first, hygrothermal, stands for heat, air and moisture, and deals with heat, air and moisture transport in materials, building components and buildings, and between buildings and the outside environment. Specific topics are: thermal insulation and thermal inertia, moisture and temperature induced movements, strains and stresses; the moisture balance (rain, initial moisture, rising damp, sorption, surface condensation, interstitial condensation); salt transport; air-tightness and wind resistance; energy demand and energy consumption; ventilation of buildings, indoor air quality, wind comfort, etc. The second sub-sector, building acoustics, studies noise problems in and between buildings and their environment. The main topics are: air and impact noise transmission by walls, floors, façades and roofs; room acoustics and the abatement of installation and environmental noises. Finally, the third sub-sector, lighting, addresses issues with respect to day-lighting, as well as artificial lighting and the impact of both on energy consumption.

0.2.2 Criteria

Building Physics has to deal with a variety of criteria: on the one hand requirements related to human comfort and health, on the other hand, architectural, material-related, economical and ecological facts and restrictions. Comfort

Comfort means a state of mental and physical well-being. Attaining such a condition depends on a number of environmental and human factors. By thermal, acoustic and visual comfort we understand those qualities human beings unconsciously request from their environment in order to feel thermally, acoustically and visually comfortable when performing a given activity (not too cold, not too warm, not too noisy, no large contrasts in luminance, etc.).

Thermal comfort is connected to global human physiology. As an exothermal creature maintaining a constant body temperature of about 37 °C (310 K), a human being should be able, under any circumstance, to release heat to the environment, be it through conduction, convection, radiation, perspiration, transpiration and breathing. The heat exchanges by means of these six mechanisms are determined by air temperature, air temperature gradient, radiant temperature, radiant asymmetry, contact temperature, relative air velocity, air turbulence and relative humidity in the direct environment. For a certain activity and clothing, some combinations of these parameters are experienced as being comfortable, others are not.

Acoustic comfort is strongly connected to our mental awareness. Physically, young adults perceive sound frequencies between 20 and 16 000 Hz. Humans experience sound intensity logarithmically, with better hearing for higher than for lower frequencies. Consequently, acoustics works with logarithmical units: the decibel (dB). 0 dB stands for the audibility threshold, while 140 dB corresponds to the pain threshold. Human are easily disturbed by undesired noises, as the one the neighbour makes or the noise caused by traffic, industry and aircraft.

Visual comfort is both mentally and physically related. Physically, the eye is sensitive to electromagnetic waves with wavelengths between 0.38 and 0.78 μm. The maximum sensitivity lies near a wavelength of ≈ 0.58 μm, the yellow-green light. Besides that, eye sensitivity adapts to the average luminance. For example, in the dark, sensitivity increases 10,000 times compared to daytime sensitivity. This adaptability lets the eye, just like the ear, react logarithmically. Too large differences in brightness are disturbing. Psychologically, lighting helps to create atmosphere. Health

Health does not only mean the absence of illness but also the absence of neuro-vegetative complaints, of psychological stress and of physical unease. Human wellbeing may be menaced by dust, fibres, VOC’s, radon, CO, bacteria in the air, molds and mites on surfaces, too much noise in the immeadiate environment, local thermal discomfort, etc. Architectural and Material Facts

Building physics has to operate in an architectural and material framework. Floor, façade and roof form, aesthetics and the choice of materials are all elements which shape the building and whose design among others should be based on the performance requirements building physics imposes. Conflicting structural and physical requirements may make it difficult to find an ideal solution in every case.

The need for a thermal cut, for example, may interfere with the strength and the need for stiffness-based interconnection. Waterproof-ness and vapour permeability are not always compatible. Acoustical absorption is opposed to vapour tightness. Certain materials may not remain wet for a long time, etc. Economy

Not only must the investment in the building remain within the budget limits, also the total present value of all annual expenses should be as low as possible. In that respect, energy consumption, maintenance and building life expectancy play a role. A building which has been designed and constructed in accordance with the performance requirements of building physics, could generate a much lower total present value than buildings built without much consideration for usability. Environment

Societal concern about environmental impact has increased substantially over the past years. Buildings have such impact locally, country-wide as well as globally. Locally their use produces solid, liquid and gaseous waste. Countrywide, building construction and occupancy accounts for 35–40% of the yearly primary energy use. A major part of that use is fossil fuel related, which means that the CO2-emissions by buildings closely follow that percentage. Globally, CO2-release is the most important of all gas emissions which are responsible for a global warming.

That striving for more sustainability in building construction and usage is also reflected in the increasing importance of life cycle analysis. In such analysis, buildings are evaluated in terms of environmental impact from ‘cradle to grave’, i.e. from the preliminary stage, through the construction and occupancy stage until demolition. For each stage, all material, energy and water inflows as well as the polluting solid, liquid and gaseous outflows are quantified and their impact on human wellbeing and environment assessed.

0.3 Importance of Building Physics

Building physics is bound by the necessities of building, which means the creation of a comfortable indoor environment which protects human beings against the vagaries of the outside climate. As a consequence, the separation between the inside and the outside, i.e. the envelope of the building (floors, façades, roofs) is submitted to numerous climatologic loads and climate differences (sun, rain, wind and outside noise; differences in temperatures, partial water vapour pressure and air pressure). An appropriate envelope design along with an appropriate detailing must care of these loads, attenuate them where possible or use them if possible in order to maintain the desired indoor climate with a minimum of technical means, with the least possible energy consumption and with a minimum of discomfort.

In earlier days, experience was the main guide. Former generations had only a limited range of construction materials (wood, straw, loam, natural stone, lead, copper and cast iron, blown glass), for which the know-how to use them had increased over the centuries. Standard details for attics, eaves and walls were used. From the size and orientation of the windows to the overall lay-out, buildings were constructed as to limit heating during winter and overheating during summer. Because noise sources were scarce, sound annoyance outside urban centres was unknown, and our ancestors saved on expensive energy (wood) by a lifestyle adapted to the seasons.

The industrial revolution of the 19th century brought an end to this era. New materials inundated the marketplace: steel, reinforced and later pre-stressed concrete, nonferrous metals, synthetics, bitumen, insulation materials, etc. New technologies created new possibilities for existing materials: cast and float glass, rolled metal products, pressed bricks, etc. Better knowledge of structural mechanics and the related calculation methods allowed the construction of any form and span. Energy became cheap, first coal, then petroleum and finally natural gas. Construction volume increased drastically, and buildings turned into a supply-demand market. The consequence was mass-building with a minimum of quality and, in the early 20th century, a ‘modern school’ of architects, who experimented with new structural solutions and new materials. These experiments had nothing to do with former knowledge and experience. Architects designed buildings without any concern either for energy consumption or comfort, nor any understanding of the physical parameters of the new fagade and roof solutions they proposed. Typical for these buildings was the profuse application of steel, concrete and glass, which are all difficult materials from a hygrothermal point of view. The results were, and are, obvious cases of failure which could have been avoided through a better knowledge of building physics but instead led to severe damage as well as premature restoration of many twentieth century landmark buildings.

Building physics is essential if we want to achieve high quality buildings that fit our purposes. The field should replace the time consuming practice of learning by experience, for which the evolution in technology and the subsequent changes in architectural fashion have become too rapid.

0.4 History of Building Physics

Building physics originates from a merger of three application-oriented disciplines: applied physics, building services and building construction.

Already in the early 20th century, some circles of physicists showed a lot of interest in the application of noise control to building construction. In 1912, Berger submitted a Ph.D. thesis to the Technische Hochschule München entitled ‘Über die Schalldurchlässigkeit’ (about sound transmission). In the thirties and forties, Lothar Cremer was responsible for a break-through in understanding sound transmission. He recognized that the coincidence effect between sound waves in the air and bending waves on a wall played a major role in sound transmission and studied impact noise in detail. In 1920, Sabine published his well-known formula regarding the reverberation time in rooms.

The application of lighting to buildings and civil engineering constructions came later. In 1931 a study was completed at the Universität Stuttgart. It dealt with ‘Der Einfluß der Besonnung auf Lage und Breite von Wohnstraßen’ (The influence of solar irradiation on the location and width of residential streets).

In the case of heat and mass transport, during the first half of the past century attention was mainly focused on thermal conductivity. In the thirties, measuring the diffusion resistance was added. In the U.S.A. Teesdale of the Forest Products Laboratory published a study in 1937 on ‘Condensation in Walls and Attics’. In 1952 an article appeared in the German journal, Der Gesundheitsingenieur’ from J. S. Cammerer on, Die Berechnung der Wasserdampfdiffusion in der Wänden’ (Calculation of Water Vapor Diffusion in Walls). Towards the end of the fifties, H. Glaser described in a series of articles in ‘Der Gesundheitsingenieur’ a calculation method for vapour transport by diffusion and interstitial condensation in cold storage walls. Others applied the method to building parts. In the sixties, more researchers got engaged in the study of combined heat and moisture transport. Some well-known names are O. Krischer, J. S. Cammerer and Helmut Künzel in Germany, A. De Vries and B. H. Vos in the Netherlands, L. E. Nevander in Sweden and A. Tveit in Norway.

In the 19 th century, engineers were especially concerned with housing and urban hygiene. Max von Pettenkofer (1818–1901) was the first to perform research on the relationship between ventilation, CO2-concentration inside and indoor air quality. Later, the notion of “breathing materials” was derived from his work, the result of an erroneous explanation of the link between the air permeability of wall materials and the healthiness of the indoor environment. In the same period, building service technicians were searching for methods to calculate the heating and cooling load of buildings. For that purpose they took advantage of the knowledge developed by physicists who provided concepts such as the ‘thermal transmittance or U-value of a wall’. Organizations such as ASHVE, later ASHRAE, and VDI created technical committees, which dealt with the topics of heat loss and heat gain. An active member of ASHVE was W. H. Carrier (1876–1950), recognized in the U.S.A. as the ‘father’ of air conditioning, who was the first to publish a usable psychometric chart. In Germany, Herrmann Rietschel, Professor at the Technische Universtat Berlin and the author of a comprehensive book on ‘Heizungs und Lüftungstechnik’ (Heating and Ventilation Techniques), was also a pioneer in the field. Heat loss and heat gain through ventilation was one of his concerns. He and others learned by experience that well-designed ventilation systems did not function properly because of a lack of air-tightness of the building envelope. This sharpened the interest in the overall subject of air transport.

The interest in moisture by HVAC-engineers arose around the period that air conditioning (HVAC) became popular. But the subject was already one of concern, mainly because moisture appeared to be very damaging to the insulation quality of some materials and could cause health problems. They also included sound insulation in their work mainly because the HVAC installations could be quite noisy. Lighting was added because more and more HVAC engineers received contracts for lighting designs and lighting advice. From 1973 on, energy consumption became a concern. The fact that HVAC and building physics are tightly linked can still be observed in the U.S.A where ‘building science’ is often seen as a branch of mechanical engineering.

Finally, building physics helped construction to understand and avoid failures that arose when using solutions which were designed and built according to the existing “state-of-the art” rules. In the thirties, peeling and blistering of paints on insulated walls was an example (insulation materials were rather new at that time). This was precisely the problem which motivated Teesdale to make his study on condensation. Later, ventilated constructions became a research topic. Towards the end of the thirties, the first experimental work of its kind on roofs was performed by F. Rowley, Professor in Mechanical Engineering at the University of Minnesota, U.S.A. In Germany, the Freiland Versuchsstelle Holzkirchen, which was created in 1951, did similar work. When, after 1973, insulation became a necessity, the accrued knowledge was very useful for the development of high quality, well insulated building parts. The demand for global quality and durability became part of the performance approach which is so widespread today.

At the University of Louvain, Belgium, lectures in building physics were first given in 1952. This made it a pioneering establishment in Belgium. In those early years the courses were compulsory for architectural engineers and optional for civil engineers. A. de Grave, a civil engineer and head of the building department at the Ministry of Public Works, became the first professor. He taught until 1975, the year of his death. In 1957 he published the book ‘Building Physics’ (in Dutch), followed by ‘Oil Heating in the House’ (in Dutch) in the early seventies. Professor de Grave was a practical man, not a researcher. Former students still remember his enthusiastic way of teaching.

0.5 References

[0.1] CIB-W40 (1975). Quantities, Symbols and Units for the description of heat and moisture transfer in Buildings: Conversion factors, IBBC-TNP, Report No. BI-75-59/03.8.12, Rijswijk.

[0.2] Winkler Prins Technische Encyclopedie, deel 2 (1976). Article on Building Physics. Uitgeverij Elsevier, Amsterdam, pp. 157–159 (in Dutch).

[0.3] ISO-BIN (1985). Standards series X02-101 – X023-113.

[0.4] Donaldson, B., Nagengast, B. (1994). Heat and Cold: Mastering the Great Indoors. ASHRAE Publication, Atlanta.

[0.5] Kumaran, K. (1996). Task 3: Material Properties. Final Report IEA EXCO ECBCS Annex 24. ACCO, Louvain.

[0.6] Künzel, H. (2001). Bauphysik. Geschichte und Geschichten. Fraunhofer IRB-Verlag (in German).

0.6 Units and Symbols

Symbols and Units

Symbol Meaning Units
a Acceleration m/s2
a Thermal diffusivity m2/s
b Thermal effusivity W/(m2 · K · s0.5)
c Specific heat capacity J/(kg · K)
c Concentration kg/m3, g/m3
e Emissivity
f Specific free energy J/kg
Temperature ratio
g Specific free enthalpy J/kg
g Acceleration by gravity m/s2
g Mass flow rate, mass flux kg/(m2 · s)
h Height m
h Specific enthalpy J/kg
h Surface film coefficient for heat transfer W/(m2 · K)
k Mass related permeability s
l Length J/kg
l Specific enthalpy of evaporation or melting kg
m Mass s–1, h–1
n Ventilation rate Pa
p Partial pressure W/m2
q Heat flow rate, heat flux m
r Radius J/(kg · K)
s Specific entropy s
t Time J/kg
u Specific latent energy m/s
v Velocity kg/m3
w Moisture content m
x, y, z Cartesian co-ordinates
A Water sorption coefficient kg/(m2 · s0.5)
A Area m2
B Water penetration coefficient m/s0.5
D Diffusion coefficient m2/s
D Moisture diffusivity m2/s
E Irradiation W/m2
F Free energy J
G Free enthalpy J
G Mass flow (mass = vapour, water, air, salt) kg/s
H Enthalpy J
I Radiation intensity J/rad
K Thermal moisture diffusion coefficient kg/(m · s · K)
K Mass permeance (mass may be air, water ...) s/m
K Force N
L Luminosity W/m2
M Emittance W/m2
P Power W
P Thermal permeance W/(m2 · K)
P Total pressure Pa
Q Heat J
R Thermal resistance m2 · K/W
R Gas constant J/(kg · K)
S Entropy, saturation degree J/K, –
T Absolute temperature K
T Period (of a vibration or a wave) s, days, etc.
U Latent energy J
U Thermal transmittance W/(m2 · K)
V Volume m3
W Mass resistance (mass may be air, water ...) m/s
X Moisture ratio kg/kg
Z Diffusion resistance m/s
α Thermal expansion coefficient K–1
α Absorptivity
β Surface film coefficient for diffusion s/m
β Volumetric thermal expansion coefficient K–1
η Dynamic viscosity N · s/m2
θ Temperature °C
λ Thermal conductivity W/(m · K)
μ Vapour resistance factor
ν Kinematic viscosity m2/s
ρ Density kg/m3
ρ Reflectivity
σ Surface tension N/m
τ Transmissivity
ϕ Relative humidity
α, ϕ, Θ Angle rad
ξ Specific moisture capacity kg/kg per unit of moisture potential
Ψ Porosity
Ψ Volumetric moisture ratio m3/m3
Φ Heat flow W

Currently Used Suffixes

Indices Meaning
a Air
c Capillary, convection
e Outside, outdoors
h Hygroscopic
i Inside, indoors
cr Critical
CO2, SO2 Chemical symbol for gasses
m Moisture, maximal
r Radiant, radiation
sat Saturation
s Surface, area, suction
rs Resulting
v Water vapour
w Water
ϕ Relative humidity


[ ], bold Matrix, array, value of a complex number

dash Vector, e.g: image