Changes in thermal
conductivity of building materials
as a consequence of
vapor condensation
Jan
Skramlik, Ondrej Fuciman, Miloslav Novotny
Brno University of Technology, Faculty of Civil Engineering, Institute
of Building Structures,
Veverí 95, 602 00 Brno,
e-mail: skramlik.j@fce.vutbr.cz, fuciman.o@fce.vutbr.cz
Abstract
In
construction work, we often deal with structures which are not allowed to
contain a great amount of moisture; however, in other structures, raising the
amount of moisture does not pose any risks to the insulation layers, nor does
it cause thermal conductivity to increase. In quite a number of cases, moisture
causes certain physical properties of the materials to deteriorate, rendering them
useless for construction work.
1.
Introduction
The Czech norm 730540 standard only deals with accumulating moisture in
building constructions. The amount of moisture that accumulates in the winter
months should ideally be equal to or less than the amount of moisture that
evaporates in the summer. The standard does not seek to monitor the thickness
of the layer of material affected by condensation, nor does it attempt to find
out whether the increased moisture levels have a negative effect on the thermal
insulation layer, rendering it, in extreme cases, utterly ineffective.
2.
The
effect of moisture on thermal conductivity
The effect of moisture on thermal conductivity of materials is vast. It
differs with different temperatures and the dampness of the respective
material. Research has shown that in the case of dry materials, temperature and
atmospheric pressure do not affect thermal
conductivity (in the common temperature range). However, in the case of damp
materials, at certain temperatures and certain pressure values, the so-called
'diffusional thermal conductivity' prevails over molecular thermal conductivity
of air in air ducts, affecting negatively the thermal conductivity of the
material as a whole. Therefore, thermal conductivity is a variable that is
subject to changes in dampness, temperature and pressure in a particular
material.
It is interesting to note that in the diffusion process, materials that
are normally waterproof absorb a great deal of moisture. Such materials do not,
under normal conditions, absorb any water; it only spreads to the cracks and
pores that are on the surface and later on evaporates into the outer space
without penetrating the material. This happens, for instance, to good quality
polystyrene with closed pores, if exposed to moisture. However, in a number of
cases, a sample of polystyrene taken from a building site was proven to contain
so much moisture that it lead to a fivefold increase in its weight. This is due
to the penetration of water vapor into the molecular structure of polystyrene.
The aforementioned standard and its
insufficient calculations allow us to focus merely on the quantity of condensed
moisture while overlooking the changes in the qualities of materials subjected
to condensed moisture in winter. These changes may not always be insignificant,
even though the ratio of condensed and evaporated moisture might, at the same
time, comply with the standard. The calculations provided by the standard may
therefore never be taken as absolute. Depending on the composition of the
peripheral structure and the construction of the roof, the increase in thermal
conductivity may be minimal for certain materials; however, if the intensity of
the diffusion flow is great, it needs to be taken into account.
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Fig.1 Thermal conductivity coefficient
in relation to moisture (functional dependence) |
The thermal conductivity of water (in all its states) depends on its
temperature. Temperature affects the thermal conductivity coefficient also in
solid materials; an increase in temperature results in an increase in the value
of the coefficient (in temperatures both below and above zero).
Knowing the relation between moisture and the thermal conductivity
coefficient allows us to use a particular moisture value to calculate the
corresponding value of the thermal conductivity coefficient. The variables
measured are visualized using the semi-graphical method. The most elementary
relationship is a linear relationship (lines 1 and 2 in Fig. 1). It is expressed
by a straight line equation [4]:
[W.m-1.K-1] (1)
or in this form:
[W.m-1.K-1] (2)
lw – thermal
conductivity coefficient for a damp material [W.m-1.K-1]
ls - thermal
conductivity coefficient for a dry material [W.m-1.K-1]
u – volumetric moisture content of the respective material [% obj.]
gl - moisture coefficient of thermal conductivity which expresses the
percentage increase in thermal conductivity of a dry material based upon the
percentage increase in the amount of moisture [-]
A – a linear constant obtained using the semi-graphical method from the
relation measured between the two variables: l = f (w).
The other curves represent exponential or
parabolic functions. It may also, however, take the shape of a power
polynomial:
[W.m-1.K-1] (3)
Aside from the functions expressed by (1), (2)
and (3), a number of other functional relations lu = f (u) were created [4]::
[W.m-1.K-1] (4)
[W.m-1.K-1] (5)
[W.m-1.K-1] (6)
Thermal conductivity increases with an increase in temperature. This
applies to temperatures both below and above zero. A significant increase in
thermal conductivity can be detected only at very high temperatures, which are
very uncommon in the building construction context. The temperature applied to
building materials hardly exceeds 70 or 100°C.
Temperatures below zero offer an entirely
different picture. The thermal conductivity of ice is roughly four times
greater than the thermal conductivity of water. If all the holes and bubbles in
the material are filled with ice, the thermal conductivity coefficient of the
frozen material is somewhere in between the thermal conductivity of ice (lv = 2,3 W.m-1.K-1) and the thermal conductivity of the material itself. Below
freezing point, when water (with the following value of thermal conductivity - lv = 0,59 W.m-1.K-1) inside the material turns into
ice, the thermal conductivity of the material in question rises dramatically.
The greater the moisture, the more water turns into ice and the greater is,
then, the thermal conductivity coefficient of the frozen material. Research
measurements have supported this hypothesis. In Fig.2, we can see changes in
the thermal conductivity coefficient of polystyrene.
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Fig.2 Thermal conductivity of expanded
polystyrene in relation to moisture and temperature |
The number of new materials is growing rapidly and building research,
quite naturally, lags behind with devising new technologies and creating
projections. Therefore, research results need to be generalized to such an
extent that the functional relations
sufficiently characterize the behavior of materials based on changes in
density, moisture and temperature.
A. Polansky postulated general relationships between the thermal
conductivity coefficient and volumetric moisture content for building
materials, which is expressed in the following form:
·
for uv = 0 %
(dry material)
[W.m-1.K-1] (7)
·
for uv = 5
%
[W.m-1.K-1] (8)
·
for uv = 10
%
[W.m-1.K-1] (9)
·
for uv = 15
%
[W.m-1.K-1] (10)
By means of adjusting the aforementioned relationships, we may devise
the following equation, which describes thermal conductivity in relation to
moisture and density:
[W.m-1.K-1] (11)
J. S. Cammerer expressed the relationship between the thermal
conductivity coefficient and moisture by means of the moisture coefficient of
thermal conductivity gl from the equation in (2):
[W.m-1.K-1] (12)
The values ls gl inserted into the equation are taken
from norms and regulations, or from the data provided by manufacturers.
3.
Analysis
of the moisture coefficient of thermal conductivity
Thermal transmission in damp materials occurs
in three different ways:
·
in a
solid material lc,
·
in a
liquid lv,
·
in a
mixture of air and vapor la.
The value of the moisture coefficient of thermal conductivity gl expresses the percentage increase in
unit thermal conductivity in a dry material, in relation to every one
percentage point of volumetric moisture content [5]:.
3.1 Thermal conductivity in dry
materials
Thermal transition in dry materials occurs in
its solid content as well as in the mixture of air and vapor that is found in
its pores and bubbles.
[W.m2.K-1] (13)
ls – thermal conductivity coefficient of a dry
material [W.m-1.K-1]
V – overall volume of the dry material [m3]
la – thermal conductivity coefficient of the
mixture of air and vapor [W.m-1.K-1]
Va – the volume of the mixture of
air and vapor [m3]
lc – thermal conductivity coefficient of the dry
component [W.m-1.K-1]
Vc – the volume of the dry component
[m3]
If we introduce the porosity of a material [-] p into our calculations, then:
[-] (14)
[W.m-1.K-1] (15)
3.2 Thermal conductivity in damp
materials
In contrast to what happens in dry materials, thermal transmission in a
damp material occurs not only in its solid component and the mixture of air and
vapor in its pores, but also in the water (or ice) that is present in the pores
and bubbles of the material [5]::
[W.m2.K-1] (16)
lw – thermal conductivity coefficient of the damp
material [W.m-1.K-1]
V – overall volume of the damp material [m3]
la - thermal conductivity coefficient of the
mixture of air and vapor[W.m-1.K-1]
Va – volume of the mixture of air
and vapor [m3]
lc - thermal conductivity coefficient of the
solid component[W.m-1.K-1]
Vc – volume of the solid component [m3]
lv - thermal conductivity coefficient of water
(or ice) [W.m-1.K-1]
Vv – volume of water (ice) [m3]
(Va – Vv) – volume of the
mixture of air and vapor minus volume of water [m3].
[W.m-1.K-1] (17)
If we insert (14) into (17) and reduce the
equation, we arrive at the following equation:
[W.m-1.K-1] (18)
From the definitions of mass and volumetric
moisture content:
[-] (19)
[-] (20)
w – moisture content by weight [%]
u – volumetric moisture content [%]
rs – density of the dry material [W.m-1.K-1]
rv – density of water (ice) [W.m-1.K-1]
Inserting (19) and (20) into (18), we arrive at
the following equation [5]:
[W.m-1.K-1] (21)
[W.m-1.K-1] (22)
Inserting (15) into (21) and (22), we arrive at
the following equations:
[W.m-1.K-1] (23)
[W.m-1.K-1] (24)
3.3 A comparison with the moisture
coefficient of thermal conductivity
J. S. Cammerer expressed the relationship between the thermal
conductivity coefficient and moisture by means of the moisture coefficient of
thermal conductivity gl. A comparison can be made using either moisture content by weight or
volumetric moisture content, using the equation in (2) [1]:
[W.m-1.K-1] 
[W.m-1.K-1] (25)
Inserting (23) and (24) into the calculation,
we arrive at the following:
(26)
[-] 
[-] (27)
[-] 
[-] (28)
4.
The
effect of water vapor condensation on thermal conductivity
There are a number of different opinions regarding the condensation of
moisture in building constructions. However, the prevailing opinion states that
there is no reason to prevent condensation; nevertheless, it needs to be kept
within certain boundaries.
In the case of a single-ply flat roof, with the typical layout of
layers, preventing moisture from leaking through the construction in the form
of water vapor and condensing inside is next to impossible. The high vapor
resistance of the roof cover causes moisture to condense right below it, where,
in most cases, thermal insulation can be found. Water vapor has the ability to
pervade the molecular structure of materials that otherwise have a low
absorption rate. This vapor can then condense in the pores of the material and
the moisture content of the material rises, quite contrary to our expectations.
The calculations based on the CSN 730540 standard are only concerned
with the quantitative evaluation of moisture content. However, the qualitative
influence, as it has an effect on the insulation properties of materials, may
cause an undirected increase in moisture content, because changes in insulation
properties over time bring about changes in the thermal and diffusion layout of
the construction, reducing thermal transmission resistance.
In a test sample of fibrous insulation material with a thickness of 100
mm and a thermal gradient of 35 °C in temperatures above zero, the results
of calculations that took into account the influence of the moisture coefficient
of thermal conductivity gl differ from the results of the
calculations mentioned in the standard by as much as 7 %, in terms of the
increase in the amount of condensed moisture, for a mere period of seven days.
The thermal resistance of the sample decreased, in the same period of time, by
8 %.
Temperatures below zero offer space for much more significant
differences. This is due to the fact that the thermal coefficient value (l) depends, amongst other factors, on
temperature. Temperature does not play a major part; however, if a phase change
occurs within the material, thermal conductivity of the material increases
dramatically, often by hundreds of percentage points [3]:.
In construction practice, water vapor condenses in single-ply flat roofs
with a typical layer layout right under the roof cover. In winter months, the
temperature there is nearly always below zero. Therefore, the condensate is not
water but ice.
Acknowledgements
This paper has been written while
working on partial tasks entailed in the research proposal MSM0021630511
“Progressive building materials using secondary raw materials and their impact
on service life of structures”, with a particular material support by Faculty of Civil Engineering, Department of
Building Structures,University of Technology by Brno.
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Crank,J., The
Matematics of Diffusion, Oxford UniversityPress 1975, ISBN 0 19 853344 6
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Flüssigkeitsbewegung in porösen Körpern, 1963
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Gertis,K., Kiessl,K., Feuchtetransport in Baustoffen,Forschungsberichte aus
dem Fachbereich
Bauwesen, 1980
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Kutilek M. Dampness porous material, Czech Republic Prague SNTL, 1992
5.
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F. Building materials and construction
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