SIST ISO 10051:1997
(Main)Thermal insulation -- Moisture effects on heat transfer -- Determination of thermal transmissivity of a moist material
Thermal insulation -- Moisture effects on heat transfer -- Determination of thermal transmissivity of a moist material
Specifies a method to determine the thermal transmissivity of a moist material ( lambda ) under steady-state moisture conditions, i. e. not affected by moisture movement.
Isolation thermique -- Effets de l'humidité sur les propriétés relatives au transfert de chaleur -- Détermination de la transmissivité thermique d'un matériau humide
Toplotna izolacija - Vpliv vlage na prenos toplote - Določanje toplotne prevodnosti vlažnega materiala
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INTERNATIONAL
IS0
STANDARD
10051
First edition
1996-04-o I
- Moisture effects on
Thermal insulation
heat transfer - Determination of thermal
transmissivity of a moist material
/so/a tion thermique - Effets de /‘humidit sur /es propriktbs relatives au
transfert de chaleur - Dbermina tion de la transmissivite thermique d’un
matbriau humide
Reference number
IS0 10051 :I 996(E)
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IS0 10051:1996(E)
Contents
Page
1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
4 Symbols and units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Description of heat and mass transfers . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Determination of thermal transmissivity of a moist materia
6 Test apparatus . . .
7 Test procedure . . . 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7.2 Specimen preparation and conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7.3 Selection of phase A or C . . .
6
7.4 Derivation of thermal transmissivity from measured values of heat
flow and temperatures . . . 6
7.5 Flow chart of possible test procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
7.6 Sources of error . . . 9
7.7 Calculations . . . 9
8 Test report . . . 9
Annexes
A Theoretical background
..................................... ..................... 11
B Evaluation of moisture flow and cases for which g”=h, is small
15
C Approximate solutions of A*(W) with negligible movement of
liquid . . . 17
D Derivation of ;1* from measured values of heat flow and temperatures
in phase C with movement of liquid in the test specimen . . . 18
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, Including photocopyrng and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
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0 IS0
IS0 10051:1996(E)
E Bibliography
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
. . .
III
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0 IS0
IS0 10051:1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work
of preparing International Standards is normally carried out through IS0
technical committees. Each member body interested in a subject for
which a technical committee has been established has the right to be
represented on that committee. International organizations, governmental
and non-governmental, in liaison with ISO, also take part in the work. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 10051 was prepared by Technical Committee
lSO/TC 163, Thermal insulation, Subcommittee SC 1, Test and measure-
ment methods.
Annexes A, B, C, D and E of this International Standard are for information
only.
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0 IS0
IS0 10051:1996(E)
Introduction
The thermal transmissivity of a moist material is needed for the assess-
ment of design values of thermal conductivity and thermal resistance
under service conditions as described in IS0 10456Y The thermal
transmissivity of a moist material is also necessary for any calculation of
combined heat and moisture transfer. Heat transfer within moist porous
materials involves a complex combination of
- radiation,
- conduction in the solid, liquid and gas phases,
- convection (in some operating conditions),
- mass transfer (in the moist materials),
and their interactions. While these heat and mass flow phenomena are
transitory in nature, some of them have a long term contribution that must
be recognised in the evaluation of thermal insulation performance. This
International Standard determines the long-term contribution of both ma-
terial structure and moisture on thermal transmissivity. This transmissivity,
called thermal transmissivity of a moist material, is a material property and
a function of the moisture content of the material. Normally, thermal
transmissivity of a moist material varies locally in the material and is a
function of the moisture content of each layer.
The correct operation of the apparatus used to obtain the thermal
transmissivity of a moist material and the interpretation of experimental
results are difficult tasks that require great care. It is recommended that
the operator and the user of measured data both have a thorough back-
ground knowledge of heat and moisture transfer mechanisms in the ma-
terials, products and systems being evaluated, coupled with experience
of measurements made using guarded hot plate or heat flow meter ap-
paratus.
1) To be published.
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IS0 10051:1996(E)
INTERNATIONAL STANDARD Q ISO
Thermal insulation
- Moisture effects on heat
transfer - Determination of thermal transmissivity of
a moist material
Members of IEC and IS0 maintain registers of cur-
1 Scope
rently valid International Standards.
This International Standard specifies a method to de-
IS0 7345: 1987, Thermal insulation - Physical quan-
termine the thermal transmissivity of a moist material
tities and definitions.
(A*) under steady-state moisture conditions, i.e. not
affected by moisture movement. It is measured using
IS0 9346: 1987, Thermal insulation - Mass transfer
standardized guarded hot plate and heat flow meter
- Physical quantities and definitions.
methods, at temperatures above 0 “C. This material
property is a function of the moisture content and
I SO 8301: 1991, Thermal insulation - Determination
does not represent the thermal performance of a
of steady-state thermal resistance and related prop-
material under service conditions. However, it can be
erties - Heat flow meter apparatus.
used, together with knowledge of the moisture con-
ditions in the material, to predict the practical thermal
IS0 8302: 1991, Thermal insulation - Determination
performance.
of steady-state thermal resistance and related prop-
erties - Guarded hot plate apparatus.
The use of A*, the distribution of moisture under ser-
vice conditions and consequently the prediction of
IS0 6946-l : 1986, Thermal insulation - Calculation
thermal performance under service conditions are
methods
- Part I: Steady state thermal properties
outside the scope of this International Standard.
of building components and building elements.
However, the moisture distribution under service
conditions should, where possible, be considered
IS0 9288: 1989, Thermal insulation - Heat transfer
when ;1* is determined. Furthermore, transient meth-
by radiation - Physical quantities and definitions.
ods of measurement are not included due to the dif-
ficulty involved in analysing and interpreting the
IS0 10456:-*I, Thermal insulation - Building ma-
results of these methods.
terials and products - Determination of declared and
design thermal values.
2 Normative references
3 Definitions
The following standards contain provisions which,
For the purposes of this International Standard, the
through reference in this text, constitute provisions
following definitions apply.
of this International Standard. At the time of publi-
cation, the editions indicated were valid. All standards
3.1 thermal transmissivity of a moist material,
are subject to revision, and parties to agreements a*: Intrinsic material property dependent upon
based on this International Standard are encouraged moisture content and temperature but not on testing
to investigate the possibility of applying the most re- conditions. It is often referred to elsewhere as ther-
cent editions of the standards indicated below. mal conductivity of a moist material. It is defined for
2) To be published.
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IS0 10051:1996(E) 0 IS0
the followi
a moist material by ng differential equation
R Thermal resistance rn*-K/W
during steady-state con ditions:
t Time S
- I’.d$
T Thermodynamic temperature K
4m =
V Humidity by volume
kg/m3
when moisture distribution within the material is in
W Moisture content mass by vol-
kg/m3
the steady-state and there is no liquid movement
ume
within the material.
Moisture content, below which
Wcr kg/m3
NOTE 1 The transmissivity, either for dry materials (see gl may be considered negligible
IS0 9288, IS0 8301 and IS0 8302) or for moist materials
Moisture content in vapour
WV kg/m3
(see this document) expresses a material property that has
phase
the dimension of a thermal conductivity but that can replace
it only in some expressions (in most cases those related to Moisture content in liquid phase
kg/m3
WI
steady-state heat and mass transfer in a slab). Usually
Moisture permeability
m*/s
4
transmissivity cannot replace conductivity in most two- and
three-dimensional flow patterns, in the expression of ther- Bulk density of material
P
kg/m3
mal diffusivity and non steady-state problems. Due to the
;1
Thermal conductivity of dry ma-
W(m=K)
of heat and mass transfer problems,
complexity
terial
transmissivity can seldom be determined through one single
experiment, rather a procedure or particular testing con-
;1’ Thermal transmissivity of a
W(m=K)
ditions are required, e.g. tests at high thicknesses for the
moist material
determination of the thermal transmissivity and equilibrium
Relative humidity
4
of moisture distribution and absence of moisture flow for
the determination of thermal transmissivity of a moist ma-
NOTE 2 In this International Standard, humidity by vol-
terial (non steady-state methods are usually excluded from
ume (v) has been used as the driving force for water vapour
the determination of transmissivity).
diffusion and moisture content mass by volume (w) as
moisture content. The use of partial water vapour pressure
3.2 hygroscopic range: Moisture content in equi-
01,) and moisture content mass by mass (u) respectively
librium with 98 % relative humidity or lower.
are equivalent provided that relevant material properties and
boundary conditions are used.
4 Symbols and units
Subscripts
For the purposes of this International Standard the b
Border between zones 1 and 2, see
following symbols and units apply. figure 2
cold Cold surface of specimen
Symbol Quantity
Unit
cr See wcr
a Material-related constant in a
Wmm*/(kg=K)
hot Hot surface of specimen
linear relationship
i
Arbitrary slice of specimen
Thickness m
Liquid
Density of moisture flow rate
m Measured
Density of total moisture flow
rate sat
Saturation
sur
Density of vapour flow rate kg/ m*=s Specimen surface
t
Density of liquid flow rate kg/ m*=s Total
i i
Specific enthalpy V Vapour
J/kg
Specific latent enthalpy of evap-
J/b
oration or condensation
5 General considerations
Specific enthalpy of vapour
t2v J/kg
Specific enthalpy of liquid
hl J/kg
5.1 Introduction
Density of heat flow rate
W/m*
4
Measured density of heat flow
W/m*
This clause describes the mechanisms by which
4m
rate at the hot and cold sides of
moisture affects heat transfer in order to give the
the specimen
theoretical background for a test method which allows
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0 IS0 IS0 10051:1996(E)
prediction of thermal performance in the presence of - evaporation and condensation within a pore or a
moisture. local area, and
Although the equations derived hereafter are as gen- radiation and natural convection in the
- thermal
eral as possible, examples of the use of these
equations are given presupposing that measurements
Each of these four heat flows is considered pro-
will be performed
portional to the gradient of temperature, so we can
write by analogy with Fourier’s law:
in standardized apparatus intended for a steady-
state method (guarded hot plate or heat flow me-
dT
. . .
q = 41 + q* + 43 + 44 = - A'mz
(4)
ter), and
above freezing point.
In the case of thermal transmissivity of a moist ma-
terial, increased conduction due to the presence of
moisture in the material must be considered.
5.2 Description of heat and mass transfers
The second and third terms of equation (3) describe
the parts of the heat flow associated with the
Moisture flow is defined here to include flows of both
enthalpies of vapour and liquid and the effects of
vapour and liquid. Physically, moisture transfer is a
evaporation and condensation. These fluxes are not
combination of vapour and liquid flows in series and
proportional to the temperature gradient.
in parallel and it is normally not possible to clearly
distinguish between the two kinds of flows. The
For the treatment of heat transfer in moist materials
specific enthalpy of vapour, however, differs con-
it is necessary to separate the mechanisms “con-
siderably from that of liquid; it is therefore essential “heat
duction heat flux” and flux by
to treat moisture transfer as the sum of a vapour flow
evaporation/diffusion/condensation”.
and a liquid flow:
In the past it has been customary to divide the total
. . .
gt = gv + &?I (1)
heat flux by the temperature gradient to obtain the
thermal conductivity of a moist material. This pro-
In a closed system (i.e. with constant moisture con-
cedure is clearly faulty, because it gives a variable
tent) steady-state moisture fl ow is reached whe n:
I
value, dependent on conditions of measurement.
. . .
g, = (2)
O * g, = - gl
It is also important to distinguish carefully between
moisture effects in service and those in laboratory
In other words, steady-state moisture flow is reached
test conditions.
when vapour and liquid transfers are equal and op-
posite, i.e. when movement of liquid by capillarity is
Simulation of all the complex moisture effects, which
balanced by movement of vapour by diffusion.
occur under service conditions and during a test, is
not considered within the framework of this docu-
As vapour and liquid migrate, they carry their re-
ment. Effects of moisture flow and phase changes
spective enthalpies, a condition which leads to an in-
depend entirely on the occurrence and magnitude of
crease of heat transfer.
moisture transfer in the material. If these effects are
allowed during the test, it is difficult to assess a ma-
This heat transport caused by moisture flow is added
terial or component property. There will also be a
to the conduction heat transfer described by Fourier’s
great risk that these types of effects are estimated
law, thus giving the following expression for the total
inaccurately. The main purpose of the test is therefore
density of heat flow rate, q:
to determine ;1* which is a necessary basis for the
dT
prediction of the thermal performance in service con-
=-
. . .
q ;1**
(3)
dx + &-h, + &hl
ditions. The prediction itself is, however, outside the
scope of this International Standard.
The first term in the right-hand part of equation (3)
describes the heat flow caused by a temperature
5.3 Determination of thermal transmissivity
gradient. It consists essentially of
of a moist material
- conduction in the solid material and in the air in the
Determination of thermal transmissivity of a moist
pores of the material,
material requires a temperature gradient. Normally, a
- conduction in water bound to the pore walls
temperature gradient causes a redistribution of the
3
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0 IS0
IS0 10051:1996(E)
moisture in the material, which leads to two types of midity in the pores is approximately 100 %) and con-
sequently the distribution of humidity by volume (or
problems:
vapour pressure) is unaffected by changes in distri-
- The test is carried out on material with changing
bution of moisture content.
and unknown moisture distribution.
Phase A is deemed to occur if
- Redistribution of the moisture may simultaneously
- the moisture content at the hot face of the speci-
induce phase changes and heat transfer by
men is above the hygroscopic range, and
moisture flow. Thus, heat is transported from the
hot to the cold face by latent heat effects. How-
- the heat flow at the hot face of the specimen is
ever, by definition of the thermal transmissivity of
constant for at least 2 h after thermal equilibrium
a moist material according to this International
has been reached.
Standard, such latent heat effects are not included.
Therefore it is necessary to apply a correction to
During phase A there is evaporation of moisture at the
the measured heat flow (unless it is established
hot face and vapour passes through the specimen.
that such a correction is zero or very small) before
There is not an equal (counterbalancing) mass flow in
dividing by the temperature gradient.
the opposite direction in the liquid phase. Thus, there
is net mass transfer and no moisture equilibrium.
During testing of a moist material the heat flow
measured at the hot or cold surface will vary essen-
In phase C, moisture evaporates at the hot face of the
tially as shown in figure 1: an initial phase A, with
specimen, passes through the specimen in the vapour
more or less constant heat flow due to the combined
phase and condenses at the cold side. At the same
effect of conduction, effects of moisture flow and
time, water could be transferred in the liquid phase
phase changes; a transition phase B, and finally
from the cold side to the hot side. In terms of mass,
phase C with moisture equilibrium.
these two flows are equal and opposite, and there is
equilibrium.
Phase A is the period during the test, when the rate
of evaporation at the hot face of the specimen is
NOTE 3 Substantial moisture transfer in the liquid phase
constant. This is only possible as long as the moisture
is very rare in thermal insulating materials and furthermore
content is above the hygroscopic range (relative hu- requires a moisture content above a critical level (wCJ.
2 I
35
Phase A Phase C
c
m
i+!
u
aJ
L
z (
fu
i!
Moisture
equilibrium
Time
Figure 1 - Heat flow during a test to determine thermal transmissivity of a moist material
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0 IS0 IS0 10051:1996(E)
It can be derived [see annex A, equation (A.711 that
7.2 Specimen preparation and conditioning
the measured heat flow at the hot and cold surfaces
The specimen shall be conditioned to the desired
may be expressed as
moisture content and moisture distribution.
. . .
(5)
Where possible, the moisture distribution under ser-
vice conditions should be considered when 1’ is de-
To determine A*(W), the following must be known: the
termined.
moisture content, the temperature gradient, the den-
Conditioning may be by water immersion, with or
sities of heat flow and the moisture flow rates in the
without vacuum, absorption in humid air, spraying of
vapour phase at the surface.
water on the specimen or by subjecting the specimen
to a temperature gradient. Combinations of these
methods are also possible.
6 Test apparatus
Note that, due to hysteresis effects, the moisture
Heat flow meter apparatus according to IS0 8301
pre-history of the test specimen may influence the
with two heat flux transducers (configuration b) is
moisture content. The equilibrium moisture content
preferred. Heat flow meter apparatus (HFM) with one
at identical ambient conditions may depend on, for
heat flux transducer at the hot side, or a guarded hot
example, whether the equilibrium is reached by ab-
plate (GHP) according to IS0 8302 may also be used.
sorption or desorption.
Downward vertical heat flow is recommended. If
Specimens having been conditioned under service
downward vertical heat flow is not used the risk of
conditions may also be tested.
moisture redistribution by gravity air movements
(convection) shall be considered. The following guidance for conditioning in 7.2.1 and
7.2.2 covers most combinations of materials and
Provision to record surface temperatures and heat
moisture content levels.
flow(s) at the specimen’s surface(s) as functions of
time shall be made.
7.2.1 Materials for which the effects of moisture
movements may be neglected within the
In some cases (see clause 7), additional temperature
hygroscopic range
sensors to determine the temperature distribution
within the test specimen shall be provided.
Condition the material at the desired relative humidity
to constant mass. The moisture content may be con-
The test specimen shall be enclosed in a vapour-tight
sidered uniform. Measure according to 7.4.1 .I.
envelope, see 7.2 for details.
7.2.2 Materials for which the effects of moisture
movements may be neglected above the
7 Test procedure
hygroscopic range
Condition the specimen by subjectin g it to a tem-
7.1 General perature g radient. Measure according to 7.4.1.
When carrying out tests on moist materials, the di-
7.2.3 Other materials
rections regarding test procedures for dry materials in
the relevant International Standard for the apparatus
Phase C is normally preferred. Condition the material
shall be complied with.
under the same temperature gradient which is going
to be used in the guarded hot plate or heat flow meter
Test temperatures shall not be high enough to dam-
apparatus. Measure according to 7.4.2.
age the material. High temperatures may cause va-
pour pressures high enough to destroy the cell walls
After conditioning the specimen it shall be enclosed
in closed-cell materials.
in a vapour-tight envelope. The envelope shall prevent
moisture content greater than
Further requirements for moist materials are given in
7.2. In case of discrepancies between this lnter-
national Standard and the relevant International Stan- If the presence of the envelope introduces significant
dard for the apparatus, this International Standard
thermal resistances between the specimen and the
takes precedence.
apparatus, the thermal resistance of the envelope
5
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0 IS0
IS0 10051:1996(E)
7.3.4 Thermal conductivity of dry material
must be considered as described in the relevant
International Standard for the apparatus.
In materials with a high value of thermal conductivity,
;1, the relative importance of the effects of moisture
movement are small and may be neglected. Compare
7.3 Selection of phase A or C
this to the relation B/L (see 7.4.1).
In theory either phase A or phase C can be selected
for determining ;1*. In practice, however, only one of
7.3.5 Heat flow meter apparatus with two heat
the phases is recommended, depending on material
flux transducers
properties and moisture content and distribution.
It is easier to judge moisture equilibrium when a heat
Guidan ce on the choice of phase is given in 7.3.1 to
flow apparatus with two heat flux transducers is used.
7.3.5.
This allows more information about the heat transfer
and the mass transfer in the specimen to be deter-
mined and therefore improves the quality of the re-
7.3.1 Moisture permeability
sults.
For materials with a low moisture permeability it takes
a very long time to reach moisture equilibrium
7.4 Derivation of thermal transmissivity
(phase C) and at the same time the effects of
from measured values of heat flow and
moisture movements are small during phase A. For
temperatures
these materials phase A is recommended. An alter-
native is to condition the specimen to the equilibrium
of phase C (see 7.2) and measure during phase C. 7.4.1 Phase A
Two cases are possible:
7.3.2 Moisture distribution
- uniform or almost uniform distribution of moisture;
A uniform or almost uniform moisture distribution may
be maintained only during phase A. In phase C the
- non-uniform distribution of moisture.
moisture content is always non-uniform. The rate of
redistribution is smaller and the equilibrium moisture
7.4.1 .I Uniform or almost uniform distribution
content is more uniform when working at low tem-
of moisture
perature gradients. If the moisture distribution during
the test cannot be monitored simultaneously, it shall
The temperature distribution is considered linear in
be estimated by either
the specimen, and the temperature gradient is ap-
proximated by
- measurements of moisture distribution before and
T
after the test, or;
dT hot - Tcold
--
-
. . .
(6)
d
dx
- measurement of the moisture distribution before
To derive thermal transmissivity ;1*, from the
or after the test and calculation of the rate of re-
measured heat flow, it is necessary to either
distribution.
If there is a risk of moisture redistribution by gravity,
- evaluate (gJsUT or,
the evaluation of the results should be carried out
extremely carefully. - have conditions for which the term (gv-hJsur is
negligible.
7.3.3 Hygroscopicity and moisture content level
Evaluation of g, is dealt with in B.l .
Cases which g,=h, may be neglected are dealt with
Phase A requires a moisture content above the for
in B.2.
hygroscopic range, where changes in moisture con-
tent do not affect the distribution of the humidity by
volume. For materials with negligible effects of
7.4.1.2 Non-uniform distribution of moisture
moisture transfer (see 7.4.1) phase A may be used for
any moisture content level. In phase C the major part
To derive i*(wsur) it is necessary to either
of the material has a moisture content in the
hygroscopic range. - evaluate (gJ,,, or,
6
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0 IS0
IS0 10051:1996(E)
- have conditions for which the term (gVJ&Ur is
negligible, see B.2.
w* WC,
-7-_
If g, is evaluated, the left-hand side of equation (7) is
I
Zone1 Zone2
known
I
I
. . .
(7)
4m - (Iq”mh,),,, = - a** $ I
( 1
sur
I
I
and consequently dT/dx at the surface has to be de-
I
I
termined to evaluate L*(w~J.
I
If g& is negligible equation (5) may be written
. . .
(8)
sur
Note that this relationship is valid at the surface of the
specimen.
Figure 2 Phase C, zone 1 and zone 2, with and
In the specimen, equation (3) may be applied. If gV4z,
without liquid flow
is negligible, gV=h, may be neglected since h, > Iz, and
h, = h - h,
In many cases g,=h, may also be neglected (for exam-
ple when gl is negligible) and then equation (8) may In theory, zone 2 is the portion of the material where
be applied through the whole specimen. the moisture content is above the critical moisture
content, wcr, which is defined as the moisture content
To derive a* as a function of w it is necessary to
below which negligible transfer of moisture in the
measure the moisture and temperature distributions.
liquid phase takes place. Two cases are possible:
Note the possibility of determining temperature
and/or moisture distribution in parallel specimens
a) moisture content never exceeds Q;
subjected to boundary conditions equal to those in the
guarded hot plate or heat flow meter apparatus. An
b) moisture content exceeds We,. in a zone of thick-
approximate solution, which requires measurement ness x2.
of the moisture distribution only, is given in C.I.
Case a) with liquid movement (W > wcr in zone 2) is
treated in annex D.
7.4.2 Phase C
For case b) with no liquid movement (W < +vcr in the
In phase C both heat and mass flows are steady-state.
whole specimen) equation (5) and equation (10) be-
. . .
g, + gl = 0 (9) come
dT
Equation (5) is still valid at the surface
. . .
(11)
4m
= q = - a*m dx
qm = (
...
SLOVENSKI STANDARD
SIST ISO 10051:1997
01-december-1997
7RSORWQDL]RODFLMD9SOLYYODJHQDSUHQRVWRSORWH'RORþDQMHWRSORWQHSUHYRGQRVWL
YODåQHJDPDWHULDOD
Thermal insulation -- Moisture effects on heat transfer -- Determination of thermal
transmissivity of a moist material
Isolation thermique -- Effets de l'humidité sur les propriétés relatives au transfert de
chaleur -- Détermination de la transmissivité thermique d'un matériau humide
Ta slovenski standard je istoveten z: ISO 10051:1996
ICS:
27.220 Rekuperacija toplote. Heat recovery. Thermal
Toplotna izolacija insulation
SIST ISO 10051:1997 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST ISO 10051:1997
---------------------- Page: 2 ----------------------
SIST ISO 10051:1997
INTERNATIONAL
IS0
STANDARD
10051
First edition
1996-04-o I
- Moisture effects on
Thermal insulation
heat transfer - Determination of thermal
transmissivity of a moist material
/so/a tion thermique - Effets de /‘humidit sur /es propriktbs relatives au
transfert de chaleur - Dbermina tion de la transmissivite thermique d’un
matbriau humide
Reference number
IS0 10051 :I 996(E)
---------------------- Page: 3 ----------------------
SIST ISO 10051:1997
IS0 10051:1996(E)
Contents
Page
1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
4 Symbols and units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Description of heat and mass transfers . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Determination of thermal transmissivity of a moist materia
6 Test apparatus . . .
7 Test procedure . . . 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7.2 Specimen preparation and conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7.3 Selection of phase A or C . . .
6
7.4 Derivation of thermal transmissivity from measured values of heat
flow and temperatures . . . 6
7.5 Flow chart of possible test procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
7.6 Sources of error . . . 9
7.7 Calculations . . . 9
8 Test report . . . 9
Annexes
A Theoretical background
..................................... ..................... 11
B Evaluation of moisture flow and cases for which g”=h, is small
15
C Approximate solutions of A*(W) with negligible movement of
liquid . . . 17
D Derivation of ;1* from measured values of heat flow and temperatures
in phase C with movement of liquid in the test specimen . . . 18
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, Including photocopyrng and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
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SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
E Bibliography
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
. . .
III
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SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work
of preparing International Standards is normally carried out through IS0
technical committees. Each member body interested in a subject for
which a technical committee has been established has the right to be
represented on that committee. International organizations, governmental
and non-governmental, in liaison with ISO, also take part in the work. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 10051 was prepared by Technical Committee
lSO/TC 163, Thermal insulation, Subcommittee SC 1, Test and measure-
ment methods.
Annexes A, B, C, D and E of this International Standard are for information
only.
---------------------- Page: 6 ----------------------
SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
Introduction
The thermal transmissivity of a moist material is needed for the assess-
ment of design values of thermal conductivity and thermal resistance
under service conditions as described in IS0 10456Y The thermal
transmissivity of a moist material is also necessary for any calculation of
combined heat and moisture transfer. Heat transfer within moist porous
materials involves a complex combination of
- radiation,
- conduction in the solid, liquid and gas phases,
- convection (in some operating conditions),
- mass transfer (in the moist materials),
and their interactions. While these heat and mass flow phenomena are
transitory in nature, some of them have a long term contribution that must
be recognised in the evaluation of thermal insulation performance. This
International Standard determines the long-term contribution of both ma-
terial structure and moisture on thermal transmissivity. This transmissivity,
called thermal transmissivity of a moist material, is a material property and
a function of the moisture content of the material. Normally, thermal
transmissivity of a moist material varies locally in the material and is a
function of the moisture content of each layer.
The correct operation of the apparatus used to obtain the thermal
transmissivity of a moist material and the interpretation of experimental
results are difficult tasks that require great care. It is recommended that
the operator and the user of measured data both have a thorough back-
ground knowledge of heat and moisture transfer mechanisms in the ma-
terials, products and systems being evaluated, coupled with experience
of measurements made using guarded hot plate or heat flow meter ap-
paratus.
1) To be published.
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SIST ISO 10051:1997
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SIST ISO 10051:1997
IS0 10051:1996(E)
INTERNATIONAL STANDARD Q ISO
Thermal insulation
- Moisture effects on heat
transfer - Determination of thermal transmissivity of
a moist material
Members of IEC and IS0 maintain registers of cur-
1 Scope
rently valid International Standards.
This International Standard specifies a method to de-
IS0 7345: 1987, Thermal insulation - Physical quan-
termine the thermal transmissivity of a moist material
tities and definitions.
(A*) under steady-state moisture conditions, i.e. not
affected by moisture movement. It is measured using
IS0 9346: 1987, Thermal insulation - Mass transfer
standardized guarded hot plate and heat flow meter
- Physical quantities and definitions.
methods, at temperatures above 0 “C. This material
property is a function of the moisture content and
I SO 8301: 1991, Thermal insulation - Determination
does not represent the thermal performance of a
of steady-state thermal resistance and related prop-
material under service conditions. However, it can be
erties - Heat flow meter apparatus.
used, together with knowledge of the moisture con-
ditions in the material, to predict the practical thermal
IS0 8302: 1991, Thermal insulation - Determination
performance.
of steady-state thermal resistance and related prop-
erties - Guarded hot plate apparatus.
The use of A*, the distribution of moisture under ser-
vice conditions and consequently the prediction of
IS0 6946-l : 1986, Thermal insulation - Calculation
thermal performance under service conditions are
methods
- Part I: Steady state thermal properties
outside the scope of this International Standard.
of building components and building elements.
However, the moisture distribution under service
conditions should, where possible, be considered
IS0 9288: 1989, Thermal insulation - Heat transfer
when ;1* is determined. Furthermore, transient meth-
by radiation - Physical quantities and definitions.
ods of measurement are not included due to the dif-
ficulty involved in analysing and interpreting the
IS0 10456:-*I, Thermal insulation - Building ma-
results of these methods.
terials and products - Determination of declared and
design thermal values.
2 Normative references
3 Definitions
The following standards contain provisions which,
For the purposes of this International Standard, the
through reference in this text, constitute provisions
following definitions apply.
of this International Standard. At the time of publi-
cation, the editions indicated were valid. All standards
3.1 thermal transmissivity of a moist material,
are subject to revision, and parties to agreements a*: Intrinsic material property dependent upon
based on this International Standard are encouraged moisture content and temperature but not on testing
to investigate the possibility of applying the most re- conditions. It is often referred to elsewhere as ther-
cent editions of the standards indicated below. mal conductivity of a moist material. It is defined for
2) To be published.
---------------------- Page: 9 ----------------------
SIST ISO 10051:1997
IS0 10051:1996(E) 0 IS0
the followi
a moist material by ng differential equation
R Thermal resistance rn*-K/W
during steady-state con ditions:
t Time S
- I’.d$
T Thermodynamic temperature K
4m =
V Humidity by volume
kg/m3
when moisture distribution within the material is in
W Moisture content mass by vol-
kg/m3
the steady-state and there is no liquid movement
ume
within the material.
Moisture content, below which
Wcr kg/m3
NOTE 1 The transmissivity, either for dry materials (see gl may be considered negligible
IS0 9288, IS0 8301 and IS0 8302) or for moist materials
Moisture content in vapour
WV kg/m3
(see this document) expresses a material property that has
phase
the dimension of a thermal conductivity but that can replace
it only in some expressions (in most cases those related to Moisture content in liquid phase
kg/m3
WI
steady-state heat and mass transfer in a slab). Usually
Moisture permeability
m*/s
4
transmissivity cannot replace conductivity in most two- and
three-dimensional flow patterns, in the expression of ther- Bulk density of material
P
kg/m3
mal diffusivity and non steady-state problems. Due to the
;1
Thermal conductivity of dry ma-
W(m=K)
of heat and mass transfer problems,
complexity
terial
transmissivity can seldom be determined through one single
experiment, rather a procedure or particular testing con-
;1’ Thermal transmissivity of a
W(m=K)
ditions are required, e.g. tests at high thicknesses for the
moist material
determination of the thermal transmissivity and equilibrium
Relative humidity
4
of moisture distribution and absence of moisture flow for
the determination of thermal transmissivity of a moist ma-
NOTE 2 In this International Standard, humidity by vol-
terial (non steady-state methods are usually excluded from
ume (v) has been used as the driving force for water vapour
the determination of transmissivity).
diffusion and moisture content mass by volume (w) as
moisture content. The use of partial water vapour pressure
3.2 hygroscopic range: Moisture content in equi-
01,) and moisture content mass by mass (u) respectively
librium with 98 % relative humidity or lower.
are equivalent provided that relevant material properties and
boundary conditions are used.
4 Symbols and units
Subscripts
For the purposes of this International Standard the b
Border between zones 1 and 2, see
following symbols and units apply. figure 2
cold Cold surface of specimen
Symbol Quantity
Unit
cr See wcr
a Material-related constant in a
Wmm*/(kg=K)
hot Hot surface of specimen
linear relationship
i
Arbitrary slice of specimen
Thickness m
Liquid
Density of moisture flow rate
m Measured
Density of total moisture flow
rate sat
Saturation
sur
Density of vapour flow rate kg/ m*=s Specimen surface
t
Density of liquid flow rate kg/ m*=s Total
i i
Specific enthalpy V Vapour
J/kg
Specific latent enthalpy of evap-
J/b
oration or condensation
5 General considerations
Specific enthalpy of vapour
t2v J/kg
Specific enthalpy of liquid
hl J/kg
5.1 Introduction
Density of heat flow rate
W/m*
4
Measured density of heat flow
W/m*
This clause describes the mechanisms by which
4m
rate at the hot and cold sides of
moisture affects heat transfer in order to give the
the specimen
theoretical background for a test method which allows
---------------------- Page: 10 ----------------------
SIST ISO 10051:1997
0 IS0 IS0 10051:1996(E)
prediction of thermal performance in the presence of - evaporation and condensation within a pore or a
moisture. local area, and
Although the equations derived hereafter are as gen- radiation and natural convection in the
- thermal
eral as possible, examples of the use of these
equations are given presupposing that measurements
Each of these four heat flows is considered pro-
will be performed
portional to the gradient of temperature, so we can
write by analogy with Fourier’s law:
in standardized apparatus intended for a steady-
state method (guarded hot plate or heat flow me-
dT
. . .
q = 41 + q* + 43 + 44 = - A'mz
(4)
ter), and
above freezing point.
In the case of thermal transmissivity of a moist ma-
terial, increased conduction due to the presence of
moisture in the material must be considered.
5.2 Description of heat and mass transfers
The second and third terms of equation (3) describe
the parts of the heat flow associated with the
Moisture flow is defined here to include flows of both
enthalpies of vapour and liquid and the effects of
vapour and liquid. Physically, moisture transfer is a
evaporation and condensation. These fluxes are not
combination of vapour and liquid flows in series and
proportional to the temperature gradient.
in parallel and it is normally not possible to clearly
distinguish between the two kinds of flows. The
For the treatment of heat transfer in moist materials
specific enthalpy of vapour, however, differs con-
it is necessary to separate the mechanisms “con-
siderably from that of liquid; it is therefore essential “heat
duction heat flux” and flux by
to treat moisture transfer as the sum of a vapour flow
evaporation/diffusion/condensation”.
and a liquid flow:
In the past it has been customary to divide the total
. . .
gt = gv + &?I (1)
heat flux by the temperature gradient to obtain the
thermal conductivity of a moist material. This pro-
In a closed system (i.e. with constant moisture con-
cedure is clearly faulty, because it gives a variable
tent) steady-state moisture fl ow is reached whe n:
I
value, dependent on conditions of measurement.
. . .
g, = (2)
O * g, = - gl
It is also important to distinguish carefully between
moisture effects in service and those in laboratory
In other words, steady-state moisture flow is reached
test conditions.
when vapour and liquid transfers are equal and op-
posite, i.e. when movement of liquid by capillarity is
Simulation of all the complex moisture effects, which
balanced by movement of vapour by diffusion.
occur under service conditions and during a test, is
not considered within the framework of this docu-
As vapour and liquid migrate, they carry their re-
ment. Effects of moisture flow and phase changes
spective enthalpies, a condition which leads to an in-
depend entirely on the occurrence and magnitude of
crease of heat transfer.
moisture transfer in the material. If these effects are
allowed during the test, it is difficult to assess a ma-
This heat transport caused by moisture flow is added
terial or component property. There will also be a
to the conduction heat transfer described by Fourier’s
great risk that these types of effects are estimated
law, thus giving the following expression for the total
inaccurately. The main purpose of the test is therefore
density of heat flow rate, q:
to determine ;1* which is a necessary basis for the
dT
prediction of the thermal performance in service con-
=-
. . .
q ;1**
(3)
dx + &-h, + &hl
ditions. The prediction itself is, however, outside the
scope of this International Standard.
The first term in the right-hand part of equation (3)
describes the heat flow caused by a temperature
5.3 Determination of thermal transmissivity
gradient. It consists essentially of
of a moist material
- conduction in the solid material and in the air in the
Determination of thermal transmissivity of a moist
pores of the material,
material requires a temperature gradient. Normally, a
- conduction in water bound to the pore walls
temperature gradient causes a redistribution of the
3
---------------------- Page: 11 ----------------------
SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
moisture in the material, which leads to two types of midity in the pores is approximately 100 %) and con-
sequently the distribution of humidity by volume (or
problems:
vapour pressure) is unaffected by changes in distri-
- The test is carried out on material with changing
bution of moisture content.
and unknown moisture distribution.
Phase A is deemed to occur if
- Redistribution of the moisture may simultaneously
- the moisture content at the hot face of the speci-
induce phase changes and heat transfer by
men is above the hygroscopic range, and
moisture flow. Thus, heat is transported from the
hot to the cold face by latent heat effects. How-
- the heat flow at the hot face of the specimen is
ever, by definition of the thermal transmissivity of
constant for at least 2 h after thermal equilibrium
a moist material according to this International
has been reached.
Standard, such latent heat effects are not included.
Therefore it is necessary to apply a correction to
During phase A there is evaporation of moisture at the
the measured heat flow (unless it is established
hot face and vapour passes through the specimen.
that such a correction is zero or very small) before
There is not an equal (counterbalancing) mass flow in
dividing by the temperature gradient.
the opposite direction in the liquid phase. Thus, there
is net mass transfer and no moisture equilibrium.
During testing of a moist material the heat flow
measured at the hot or cold surface will vary essen-
In phase C, moisture evaporates at the hot face of the
tially as shown in figure 1: an initial phase A, with
specimen, passes through the specimen in the vapour
more or less constant heat flow due to the combined
phase and condenses at the cold side. At the same
effect of conduction, effects of moisture flow and
time, water could be transferred in the liquid phase
phase changes; a transition phase B, and finally
from the cold side to the hot side. In terms of mass,
phase C with moisture equilibrium.
these two flows are equal and opposite, and there is
equilibrium.
Phase A is the period during the test, when the rate
of evaporation at the hot face of the specimen is
NOTE 3 Substantial moisture transfer in the liquid phase
constant. This is only possible as long as the moisture
is very rare in thermal insulating materials and furthermore
content is above the hygroscopic range (relative hu- requires a moisture content above a critical level (wCJ.
2 I
35
Phase A Phase C
c
m
i+!
u
aJ
L
z (
fu
i!
Moisture
equilibrium
Time
Figure 1 - Heat flow during a test to determine thermal transmissivity of a moist material
---------------------- Page: 12 ----------------------
SIST ISO 10051:1997
0 IS0 IS0 10051:1996(E)
It can be derived [see annex A, equation (A.711 that
7.2 Specimen preparation and conditioning
the measured heat flow at the hot and cold surfaces
The specimen shall be conditioned to the desired
may be expressed as
moisture content and moisture distribution.
. . .
(5)
Where possible, the moisture distribution under ser-
vice conditions should be considered when 1’ is de-
To determine A*(W), the following must be known: the
termined.
moisture content, the temperature gradient, the den-
Conditioning may be by water immersion, with or
sities of heat flow and the moisture flow rates in the
without vacuum, absorption in humid air, spraying of
vapour phase at the surface.
water on the specimen or by subjecting the specimen
to a temperature gradient. Combinations of these
methods are also possible.
6 Test apparatus
Note that, due to hysteresis effects, the moisture
Heat flow meter apparatus according to IS0 8301
pre-history of the test specimen may influence the
with two heat flux transducers (configuration b) is
moisture content. The equilibrium moisture content
preferred. Heat flow meter apparatus (HFM) with one
at identical ambient conditions may depend on, for
heat flux transducer at the hot side, or a guarded hot
example, whether the equilibrium is reached by ab-
plate (GHP) according to IS0 8302 may also be used.
sorption or desorption.
Downward vertical heat flow is recommended. If
Specimens having been conditioned under service
downward vertical heat flow is not used the risk of
conditions may also be tested.
moisture redistribution by gravity air movements
(convection) shall be considered. The following guidance for conditioning in 7.2.1 and
7.2.2 covers most combinations of materials and
Provision to record surface temperatures and heat
moisture content levels.
flow(s) at the specimen’s surface(s) as functions of
time shall be made.
7.2.1 Materials for which the effects of moisture
movements may be neglected within the
In some cases (see clause 7), additional temperature
hygroscopic range
sensors to determine the temperature distribution
within the test specimen shall be provided.
Condition the material at the desired relative humidity
to constant mass. The moisture content may be con-
The test specimen shall be enclosed in a vapour-tight
sidered uniform. Measure according to 7.4.1 .I.
envelope, see 7.2 for details.
7.2.2 Materials for which the effects of moisture
movements may be neglected above the
7 Test procedure
hygroscopic range
Condition the specimen by subjectin g it to a tem-
7.1 General perature g radient. Measure according to 7.4.1.
When carrying out tests on moist materials, the di-
7.2.3 Other materials
rections regarding test procedures for dry materials in
the relevant International Standard for the apparatus
Phase C is normally preferred. Condition the material
shall be complied with.
under the same temperature gradient which is going
to be used in the guarded hot plate or heat flow meter
Test temperatures shall not be high enough to dam-
apparatus. Measure according to 7.4.2.
age the material. High temperatures may cause va-
pour pressures high enough to destroy the cell walls
After conditioning the specimen it shall be enclosed
in closed-cell materials.
in a vapour-tight envelope. The envelope shall prevent
moisture content greater than
Further requirements for moist materials are given in
7.2. In case of discrepancies between this lnter-
national Standard and the relevant International Stan- If the presence of the envelope introduces significant
dard for the apparatus, this International Standard
thermal resistances between the specimen and the
takes precedence.
apparatus, the thermal resistance of the envelope
5
---------------------- Page: 13 ----------------------
SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
7.3.4 Thermal conductivity of dry material
must be considered as described in the relevant
International Standard for the apparatus.
In materials with a high value of thermal conductivity,
;1, the relative importance of the effects of moisture
movement are small and may be neglected. Compare
7.3 Selection of phase A or C
this to the relation B/L (see 7.4.1).
In theory either phase A or phase C can be selected
for determining ;1*. In practice, however, only one of
7.3.5 Heat flow meter apparatus with two heat
the phases is recommended, depending on material
flux transducers
properties and moisture content and distribution.
It is easier to judge moisture equilibrium when a heat
Guidan ce on the choice of phase is given in 7.3.1 to
flow apparatus with two heat flux transducers is used.
7.3.5.
This allows more information about the heat transfer
and the mass transfer in the specimen to be deter-
mined and therefore improves the quality of the re-
7.3.1 Moisture permeability
sults.
For materials with a low moisture permeability it takes
a very long time to reach moisture equilibrium
7.4 Derivation of thermal transmissivity
(phase C) and at the same time the effects of
from measured values of heat flow and
moisture movements are small during phase A. For
temperatures
these materials phase A is recommended. An alter-
native is to condition the specimen to the equilibrium
of phase C (see 7.2) and measure during phase C. 7.4.1 Phase A
Two cases are possible:
7.3.2 Moisture distribution
- uniform or almost uniform distribution of moisture;
A uniform or almost uniform moisture distribution may
be maintained only during phase A. In phase C the
- non-uniform distribution of moisture.
moisture content is always non-uniform. The rate of
redistribution is smaller and the equilibrium moisture
7.4.1 .I Uniform or almost uniform distribution
content is more uniform when working at low tem-
of moisture
perature gradients. If the moisture distribution during
the test cannot be monitored simultaneously, it shall
The temperature distribution is considered linear in
be estimated by either
the specimen, and the temperature gradient is ap-
proximated by
- measurements of moisture distribution before and
T
after the test, or;
dT hot - Tcold
--
-
. . .
(6)
d
dx
- measurement of the moisture distribution before
To derive thermal transmissivity ;1*, from the
or after the test and calculation of the rate of re-
measured heat flow, it is necessary to either
distribution.
If there is a risk of moisture redistribution by gravity,
- evaluate (gJsUT or,
the evaluation of the results should be carried out
extremely carefully. - have conditions for which the term (gv-hJsur is
negligible.
7.3.3 Hygroscopicity and moisture content level
Evaluation of g, is dealt with in B.l .
Cases which g,=h, may be neglected are dealt with
Phase A requires a moisture content above the for
in B.2.
hygroscopic range, where changes in moisture con-
tent do not affect the distribution of the humidity by
volume. For materials with negligible effects of
7.4.1.2 Non-uniform distribution of moisture
moisture transfer (see 7.4.1) phase A may be used for
any moisture content level. In phase C the major part
To derive i*(wsur) it is necessary to either
of the material has a moisture content in the
hygroscopic range. - evaluate (gJ,,, or,
6
---------------------- Page: 14 ----------------------
SIST ISO 10051:1997
0 IS0
IS0 10051:1996(E)
- have conditions for which the term (gVJ&Ur is
negligible, see B.2.
w* WC,
-7-_
If g, is evaluated, the left-hand side of equation (7) is
I
Zone1 Zone2
known
I
I
. . .
(7)
4m - (Iq”mh,),,, = - a** $ I
( 1
sur
I
I
and consequently dT/dx at the surface has to be de-
I
I
termined to evaluate L*(w~J.
I
If g& is negligible equation (5) may be written
. . .
(8)
sur
Note that this relationship is valid at the surface of the
specimen.
Figure 2 Phase C, zone 1 and zone 2, with and
In the specimen, equation (3) may be applied. If gV4z,
without liquid flow
is negligible, gV=h, may be neglected since h, > Iz, and
h, = h - h,
In many cases g,=h, may also be neglected (for exam-
ple when gl is negligible) and then equation (8) may In theory, zone 2 is the portion of the materia
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