ISO 6946

INTERNATIONAL STANDARD

IS0 6946 First edition 1996-08-I 5

Building components and building elements - Thermal resistance and thermal transmittance - Calculation method Composants et parois de bitiments - RBsistance thermique et coefficient de transmission thermique - M&hode de calcul

This material is reproduced from IS0 documents under international Grganization for Standardization (ISO) Copyright License number lHSllCC11996. Not for resale. No part of these IS0 documents may be reproduced in any form, electronic retrieval system or otherwise, except as allowed in the copyright law of the country of use, or with the prior written consent of IS0 (Case postale 56,121l Geneva 20, Switzerland, Fax +41 22 734 10 79), IHS or the IS0 Licenser’s members.

Reference number IS0 6946:1996(E)

IS0 6946:1996( E)

Contents

Page

1

Scope ................................................................................................

2

Normative references

3

Definitions

and symbols

4

Principles

..........................................................................................

5

Thermal resistances

6

Total thermal resistance

7

Thermal transmittance

1

.......................................................................

1

...................................................................

1

3

.........................................................................

4

...................................................................

9

...................................................................

12

..........................................................................

13

Annexes A

Surface resistance

B

Thermal resistance of unventilated

C

Calculation of the thermal transmittance of components with tapered 18 layers ....................................... .......................................................

D

Corrections to thermal transmittance

.............................................

21

E

Examples of corrections for air gaps ..............................................

23

airspaces

................................

15

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 photocopying 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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IS0 6946:1996(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 6946 was prepared by the European Committee for Standardization KEN) in collaboration with ISO/TC 163, Thermal insulation, Subcommittee SC 2, Calculation methods, in accordance with the Agreement on technical cooperation between IS0 and CEN (Vienna Agreement). This first edition cancels and replaces IS0 6946-l :1986. IS0 6946-2:1986 was withdrawn in 1995. Annexes A, B, C and D form an integral part of this International Annex E is for information only.

Standard.

.. III

IS0 6946:1996(E)

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Introduction The thermal transmittance calculated according to this standard is suitable for determining heat flow through building components that are within the scope of this standard. For most purposes heat flows can be calculated with the following peratures: -

internal: dry resultant temperature;

-

external: air temperature.

iv

tem-

IS0 6946:1996(E)

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1

Scope

This standard gives the method of calculation of the thermal resistance and thermal transmittance of building components and building elements, excluding doors, windows and other glazed units, components which involve heat transfer to the ground, and components through which air is designed to permeate. The calculation method is based on the appropriate design thermal conductivities resistances of the materials and products involved.

or design thermal

The method applies to components and elements consisting of thermally homogeneous include air layers). The standard also gives an approximate method that can be used for inhomogeneous cases where an insulating layer is bridged by metal.

2

Normative

layers (which can

layers, except

references

The following standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards. IS0 10456:--11, Thermal insulation and design thermal values.

Building materials and products -

IS0 7345:1987,

Physical quantities and definitions.

3

Definitions

3.1

Definitions

Thermal insulation -

Determination

of declared

and symbols

For the purposes of this standard, the following definitions and those given in IS0 7345 apply.

3.1 .l building element: Major part of a building such as a wall, floor or roof.

1)

To be

published.

IS0 6946:1996(E)

3.1.2 building component: Building element or a part of it. NOTE - In this standard the word “component”

is used to indicate both element and component.

3.1.3 design thermal value: Design thermal conductivity or design thermal resistance. NOTE - A given product can have more than one design value, for different applications environmental conditions.

or

3.1.4 design thermal conductivity:

Value of thermal conductivity of a building material or product under specific external and internal conditions which can be considered as typical of the performance of that material or product when incorporated in a building component.

3.1.5 design thermal resistance: Value of thermal resistance of a building product under specific external and internal conditions which can be considered as typical of the performance of that product when incorporated in a building component. 3.1.6 thermally homogeneous

layer: Layer of constant thickness having thermal properties which are uniform or which may be regarded as being uniform.

3.2

Symbols and units Symbol

Quantity

Unit

A

area

m*

R

design thermal resistance

m2WW

R9

thermal resistance of airspace

m*K/W

Rse

external surface resistance

m*K/W

Rsi

internal surface resistance

m*K/W

RT

total thermal resistance (environment

6

upper limit of total thermal resistance

m*K/W

RY

lower limit of total thermal resistance

m*K/W

R” u

thermal resistance of unheated space

m*K/W

thermal transmittance

W/(m*.K)

d

thickness

m

h

heat transfer coefficient

W/(m*.K)

a

design thermal conductivity

W/( m+K)

to environment)

m*K/W

IS0 6946:1996(E)

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4

Principles

The principle of the calculation

method is to:

a) obtain the thermal resistance of each thermally homogeneous

part of the component;

b) combine these individual resistances so as to obtain the total thermal resistance of the component, including (where appropriate) the effect of surface resistances. Thermal resistances of individual parts are obtained according to 5.1. The values of surface resistance given in 5.2 are appropriate in most cases. Annex A gives detailed procedures for low-emissivity surfaces, specific external wind speeds, and non-planar surfaces. Air layers may be regarded as thermally homogeneous for the purposes of this standard. Values of the thermal resistance of large air layers with high-emissivity surfaces are given in 5.3, and annex B gives procedures for other cases. The resistances of the layers are combined as follows: a) for components consisting of thermally homogeneous layers, obtain the total thermal resistance according to 6.1 and the thermal transmittance according to clause 7; b) for components having one or more thermally inhomogeneous layers, obtain the total thermal resistance according to 6.2 and the thermal transmittance according to clause 7; c) for components containing a tapered layer, obtain the thermal transmittance thermal resistance according to annex C.

and/or the total

Finally, corrections are applied to the thermal transmittance if appropriate according to annex D, to allow for the effects of air gaps in insulation, mechanical fasteners penetrating an insulation layer, and precipitation on inverted roofs. The thermal transmittance so calculated applies component concerned, for example internal and case of an internal partition, internal environment given in 5.4 for treating an unheated space as a

between the environments on either side of the external environments, two internal environments in the and an unheated space. Simplified procedures are thermal resistance.

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IS0 6946: 1996(E)

5

Thermal

resistances

5.1

Thermal resistance of homogeneous layers

Design thermal values can be given as either design thermal conductivity or design thermal resistance. if thermal conductivity is given, obtain the thermal resistance of the layer from:

where d

is the thickness of the material layer in the component;

a

is the design thermal conductivity of the material, either calculated according to ISO/DIS 10456.2 or obtained from tabulated values. NOTE - The thickness d may be different from the nominal thickness (e.g. when a compressible product is installed in a compressed state, d is less than the nominal thickness). If relevant, d should also make appropriate allowance for thickness tolerances (e.g. when they are negative).

Thermal resistance values used in intermediate calculations shall be calculated to at least 3 decimal places.

5.2

Surface resistances

Use the values in table 1 for plane surfaces in the absence of specific information on the boundary conditions. The values under “horizontal” apply to heat flow directions +30” from the horizontal plane. For non-planar surfaces or for specific boundary conditions use the procedures in annex A.

Table 1 - Surface resistances (in m2WW) Direction of heat flow Upwards r

Horizontal I

Downwards I

1 %i

1

0~10

(

0,13

1

OS17

(

I

I

0,04

I

0,04

I

0,04

I

Rse

NOTE - The values in table 1 are design values. For the purposes of declaration of the thermal transmittance of components and other cases where values independent of heat flow direction are required, it is recommended that the values for horizontal heat flow are used.

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5.3

IS0 6946:1996(E)

Thermal resistance of air layers

The values given in this subclause apply to an air layer which: -

is bounded by two faces which are effectively parallel and perpendicular and which have emissivities not less than 0,8;

-

has a thickness (in the direction of heat flow) of less than 0,i times each one of the other two dimensions, and not greater than 0,3 m;

to the direction of heat flow

NOTE - A single thermal transmittance should not be calculated for components containing air layers thicker than 0,3 m. Rather, heat flows should be calculated by performing a heat balance (see ISO/DIS 13789, Thermal performance of buildings - Transmission heat loss coefficient Calculation method). -

has no air interchange

If the above conditions

53.1

with the internal environment.

do not apply, use the procedures in annex B.

Unventilated air layer

An unventilated air layer is one in which there is no express provision for air flow through it. Design values of thermal resistance are given in table 2. The values under “horizontal” apply to heat flow directions *30” from the horizontal plane.

Table 2 - Thermal resistance (in m2XAIV) of unventilated high emissivity surfaces Thickness of air layer mm

0 5 7 10 15 25 50 100 300

air layers:

Direction of heat flow Upwards

Horizontal

Downwards

0,oo

0,oo

0,oo

0,ll 0,13 0,15 0,16 0,16 0,16 0,16 0,16

0,ll 0,13 0,15 0,17 0,18 0,18 0,18 0,18

0,ll 0,13 0,15 0,17 0,19 0,21 0,22 0,23

NOTE - Intermediate values may be obtained by linear interpolation.

IS0 6946: 1996(E)

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An air layer having no insulation layer between it and the external environment but with small openings to the external environment shall also be considered as an unventilated air layer, if these openings are not arranged so as to permit air flow through the layer and they do not exceed: -

500 mm2 per m length for vertical air layers 500 mm2 per m2 of surface area for horizontal air layers.‘) NOTE - Drain openings (weep holes) in the form of open vertical joints in the outer leaf of a masonry cavity wall are not regarded as ventilation openings.

5.3.2

Slightly ventilated air layer

A slightly ventilated air layer is one in which there is provision for limited air flow through it from the external environment by openings within the following ranges: -

> 500 mm2 but 5 1500 mm2 per m length for vertical air layers > 500 mm2 but 5 1500 mm2 per m2 of surface area for horizontal air layers.‘)

The design thermal resistance of a slightly ventilated air layer is one half of the corresponding value in table 2. If, however, the thermal resistance between the air layer and the external environment exceeds 0,15 m2WW, it shall be replaced by the value 0,15 m2WW.

5.3.3

Well ventilated air layer

A well ventilated air layer is one for which the openings between the air layer and the external environment exceed: -

1500 mm2 per m length for vertical air layers 1500 mm2 per m2 of surface area for horizontal air layers.‘)

The total thermal resistance of a building component containing a well-ventilated air layer shall be obtained by disregarding the thermal resistance of the air layer and all other layers between the air layer and external environment, and including an external surface resistance corresponding to still air (i.e. equal to the internal surface resistance of the same component).

‘1 For vertical air layers the range is expressed the area of openings per square metre area.

as the area of openings per metre length. For horizontal air layers it is expressed

as

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5.4

IS0 6946:1996(E)

Thermal resistance of unheated spaces

When the external envelope of the unheated space is not insulated the following simplified procedures, treating the unheated space as a thermal resistance, may be applied. NOTE - ISO/DIS 13789, Thermal performance of buildings - Transmission heat loss coefficient Calculation method, gives general, and more precise, procedures for the calculation of heat transfer from a building to the external environment via unheated spaces, and should be used when a more accurate result is required. For crawl spaces below suspended floors see ISO/DIS 13370, Thermal performance of buildings - Heat transfer via the ground - Calculation method.

5.4.1

Roof spaces

For a roof structure consisting of a flat, insulated ceiling and a pitched roof, the roof space may be regarded as if it were a thermally homogeneous layer with thermal resistance as given in table 3.

Table 3 - Thermal resistance of roof spaces Characteristics

of roof

RU m*XM

1

Tiled roof with no felt, boards or similar

0,06

2

Sheeted roof, or tiled roof with felt or boards or similar under the tiles

02

3

As 2 but with aluminium cladding or other low emissivity surface at underside of roof

093

4

Roof lined with boards and felt

093

NOTE - The values in table 3 include the thermal resistance of the ventilated space and the thermal resistance of the (pitched) roof construction. They do not include the external surface resistance (Rse).

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IS0 6946:1996(E)

Other spaces

5.4.2

When the building has a small unheated space attached to it, the thermal transmittance between the internal and external environments can be obtained by treating the unheated space together with its external construction components as if it were an additional homogeneous layer with thermal resistance R,, given by: R, = 0,09 + 94;

(2) U

subject to RU IO,5 m2-WW, where

4

is the total area of all components between the internal environment and the unheated space;

4

is the total area of all components between the unheated space and the external environment. NOTES 1 Examples of small unheated spaces include garages, store rooms and conservatories. 2 If there is more than one component between the internal environment and the unheated space, R, should be included in the calculation of the thermal transmittance of each such component.

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6

IS0 6946: 1996(E)

Total

thermal

resistance

If the total thermal resistance is presented as a final result, it shall be rounded to two decimal places.

6.1

Total thermal resistance of a building component consisting of homogeneous

layers

The total thermal resistance RT of a plane building component consisting of thermally homogeneous layers perpendicular to the heat flow shall be calculated by the following expression:

RT = &j + Rl + & + ........ Rn + Rse

(3)

where hii

is the internal surface resistance;

Rl, R-J . ... . Rn

are the design thermal resistances of each layer;

Rse

is the external surface resistance.

In the case of calculation of the resistance of internal building components (partitions etc.), or an component between the internal environment and an unheated space, R,i applies on both sides. NOTE - The surface resistances should be omitted in equation (3) when the resistance of a component from surface to surface is required.

6.2

Total thermal resistance of a building component consisting of homogeneous and inhomogeneous layers

This subclause gives a simplified method to calculate the thermal resistance of building components consisting of thermally homogeneous and inhomogeneous layers, except in cases where an insulation layer is bridged by metal. NOTES 1 A more precise result will be obtained by using a numerical method conforming to IS0 10211, Thermal bridges in building construction - Heat flows and surface temperatures - Part I: General calculation methods, or Part 2 (under preparation): Calculation of linear thermal bridges. 2 The procedure described in 6.2 is not suitable to compute surface temperatures purposes of evaluating the risk of condensation.

for the

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IS0 6946: 1996(E)

6.2.1

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Total thermal resistance of an component

The total thermal resistance, RT, of an component consisting of thermally homogeneous and thermally inhomogeneous layers parallel to the surface is calculated as the arithmetic mean of the upper and lower limits of the resistance: R /r+dr T

2

(4)

where Fir

is the upper limit of the total thermal resistance, calculated according to 6.2.2;

R;

is the lower limit of the total thermal resistance, calculated according to 6.2.3.

Calculation of the upper and lower limits shall be carried out by considering the component split into sections and layers, as shown in figure 1, in such a way that the component is divided into parts mj, which are themselves thermally homogeneous.

lc

lb

1CI

Figure 1 - Sections and layers of a thermally inhomogeneous

component

The component (figure la) is considered cut into sections (figure 1b) and into layers (figure lc). The section m (m = a, b, c, ... 9) perpendicular The layerj(j=

to the surfaces of the component has fractional area f,,,.

1,2, .. . n) parallel to the surfaces has thickness c$.

The part mj has thermal conductivity

hmj, thickness c$, fractional area fm and thermal resistance R,Q.

The fractional area of a section is its proportion of the total area. Thus fa + fb + ... . + f, = 1.

10

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6.2.2

IS0 6946:1996( E)

Upper limit of the total thermal resistance (R; )

The upper limit of the total thermal resistance, is determined by assuming one-dimensional perpendicular to the surfaces of the component. It is given by the following expression:

heat flow

rs -= l6 fa+fa+...+ RTa

RTb

(5)

RT9

where are the total thermal resistances from environment section, calculated using equation (3); &a,

&by

.-., &9

to environment

for each

fa fb, . ... f9 are the fractional areas of each section.

6.2.3

Lower limit of the total thermal resistance (RT )

The lower limit is determined isothermal surfaces.*)

by assuming that all planes parallel to the surfaces of the component

Calculate an equivalent thermal resistance Rj, for each thermally inhomogeneous expression:3) f La+-+...+Rj Raj

fb

6

Rbj

Rqj

layer using the following

(6)

*) If there is a non-planar surface adjacent to an air layer, the calculation should be undertaken the narrower sections extended (but without alteration to thermal resistance):

or projecting

are

as if it were planar, by considering

parts removed (so reducing the thermal resistance):

3, An alternative

method is by means of an equivalent

where the equivalent

thermal conductivity

hi

thermal conductivity

of the layer:

of layer j is:

hi = haj fa + hbj fb+e. a+hQi4 If an air layer is part of an inhomogeneous dj /F$ where F$ is the thermal resistance

layer, it may be treated as a material with an equivalent of the air layer determined

in accordance

thermal conductivity

hi

=

with annex B.

11

IS0 6946: 1996(E)

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The lower limit is then determined using equation (3) i.e. RF = Rsi + RI + R2+eam+Rn+ Rse

6.2.4

(7)

Estimation of error

This method of estimating the maximum relative error may be used when the calculated thermal transmittance is required to meet specified accuracy criteria. The maximum relative error, e, as a percentage when using this approximation

is:

eJ~-R;xlOO

(8)

2RT

EXAMPLE - If the ratio of the upper limit to the lower limit is 1,5, the maximum possible error is 20%. The actual error is usually much less than the maximum. This error may be evaluated to decide whether the accuracy obtained through the procedure described in 6.2 is acceptable, having regard to

7

-

the purpose of the calculation;

-

the proportion of the total heat flow through the building fabric that is transmitted through the components the thermal resistance of which is evaluated through the procedure described in 6.2;

-

the accuracy of the input data.

Thermal

transmittance

The thermal transmittance

is given by:

(9) Corrections shall be applied to the thermal transmittance, as appropriate, according to annex D. If, however, the total correction is less than 3% of U, the corrections need not be applied. If the thermal transmittance is presented as a final result, it shall be rounded to two significant figures, and information shall be provided on the input data used for the calculation.

12

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IS0 6946:1996(E)

Annex

A (normative)

Surface A.1

resistance

Plane surfaces

The surface resistance is given by4)

R,=L hc+hr

61)

where hc

is the convective

coefficient;

hr

is the radiative coefficient;

and h, = Ehro

(A-2)

h,=4oT;

(A.3)

where &

is the emissivity of the surface;

h ro

is the radiative coefficient for a black-body surface (see table A.l);

0

is the Stefan-Boltzmann

T?l

is the mean thermodynamic

constant (567 x 10-s W/(m2.K4)); temperature

of the surface and of its surroundings.

Table A.1 - Values of the black-body radiative coefficient I?,,

I

Temperature

I

h ro

“C

W/(mz.K)

-10 0 10 20 30

491 496 571 597 63

I

4, This is an approximate treatment of surface heat transfer. Precise calculations of heat flow can be based on the internal and external environmental temperatures (in which the radiant and air temperatures are weighted according to the respective radiative and convective coefficients, and which can also take account of room geometry effects and air temperature gradients). If, however, the internal radiant and air temperatures are not markedly different, the internal dry resultant temperature (equal weighting of air and radiant temperatures) may be used. At external surfaces it is conventional to use the external air temperature, based on an assumption of overcast sky conditions so that external air and radiant temperatures are effectively equal. This also ignores any effect of short-wave solar radiation on external surfaces.

13

IS0 6946:1996(E)

At internal surfaces h, = hci, where -

hci = 5,0 W/(m2.K) hci = 2,5 W/(mz.K) hci = 0,7 W/(m2.K)

for heat flow upwards: for heat flow horizontal: for heat flow downwards:

At external surfaces hc = hce, where hce=4 +4 v

(A-4)

and v is the wind speed adjacent to the surface in m/s. Values of the external surface resistance, f&e, for various wind speeds are given in table A.2. NOTE - The values given in 5.2 for internal surface resistance were calculated for E = 0,9 and with h, evaluated at 20°C. The value given in 5.2 for external surface resistance was calculated for E = 0,9, hro evaluated at O”C, and for v = 4 m/s.

Table A.2 : Values of R,, at various wind speeds Wind speed

A.2

m/s

Rse m2K/W

1 2 3 4 5 7 10

0,08 0,06 0,05 0‘04 0,04 0,03 0,02

Components with non-planar surfaces

Parts which protrude from otherwise plane surfaces, such as structural columns, shall be disregarded in the calculation of the total thermal resistance if composed of material having thermal conductivity not more than 2 W/(m.K). If the part that protrudes is composed of material having thermal conductivity greater than 2 W/(m.K) and is not insulated, the surface resistance shall be modified by the ratio of the projected area to the actual surface area of the protruding part (see figure A.1):

where:

14

Rs

is the surface resistance of a plane component according to A.1 ;

AP

is the projected area of the protruding part;

A

is the actual surface area of the protruding part.

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IS0 6946:1996(E)

Equation (A.5) applies to both internal and external surface resistance.

Figure A.1 - Actual and projected areas

Annex

B (normative)

Thermal B.l

resistance

of unventilated

airspaces

General

This annex applies to airspaces in building components necessary for glazing and window frames.

other than glazing. A more precise treatment is

The term airspace includes both air layers (which have a width and length both 10 times the thickness, with thickness measured in the heat flow direction) and air voids (which have width or length comparable to thickness). If the thickness of the air layer varies, its average value should be used to calculate the thermal resistance. NOTE - Airspaces can be treated as media with thermal resistance because the radiation and convection heat transfer across them is approximately proportional to the temperature difference between the bounding surfaces.

15

IS0 6946:1996(E)

B.2

Unventilated airspaces with length and width both more than 10 times thickness

The thermal resistance of an airspace is given by: 1 Rg= ha.+/+

(B-1)

where 44

is the thermal resistance of the airspace;

ha

is the conduction/convection

hr

is the radiative coefficient.

coefficient;

ha is calculated as follows: - for heat flow horizontal:

ha is the larger of I,25 W/(m2+K) and 0,025/d W/(m2+K);

- for heat flow upwards:

ha is the larger of I,95 W/(m’.K) and 0,025/d W/(m2.K);

- for heat flow downwards:

ha is the larger of 0,12~f-~j~~ W/(m2.K) and 0,025/dW/(m2.K);

where d is the thickness of the airspace (in heat flow direction). hr is given by hr = E hro

03.2)

where E

is the intersurface

h ro

is the radiative coefficient for a black-body surface (see table A.2);

emittance;

and E=

I 1/&,+1/&p-1

where ~1, ~2 are the hemispherical

(B.3) emissivities

of the surfaces bounding the airspace.

The design value of emissivity should allow for any effects of tarnishing with time. NOTE - The values in table 2 were calculated using equation (B.l) with ~1 = 0,9, r2 = 0,9, and hro evaluated to 10°C.

16

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B.3

IS0 6946:1996(E)

Small or divided unventilated

airspaces (air voids)

-70 I ;; heat0

, flow

Figure B.l - Dimensions of small airspace Figure B.l illustrates a small airspace with width less than 10 times its thickness. Its thermal resistance is given by: 1 Rg = ha + % Eh,(l

+ ,/m-

U3.4)

d ! b)

where 63

is the thermal resistance of the airspace;

d

is the thickness of the airspace;

b

is the width of the airspace;

E, ha and hro are calculated as in B.2.5) NOTE - Equation(B.4) is appropriate for the calculation of heat flow through building components for any thickness of air void, and for the calculation of temperature distributions in building components having air voids whose thickness d less than or equal to 50 mm. For thicker air voids, the equation gives an approximate temperature distribution. For an air void that is not rectangular in shape, take its thermal resistance as equal to that of a rectangular void which has the same area and aspect ratio as the actual void.

5, h, depends on d but is independent

0; b. Obtain E using the emissivities

of the hot and cold faces in equation (6.3)

17

Annex

C (normative)

Calculation C.l

of the thermal

transmittance

of components

with tapered

layers

General

When a component has a tapered layer (e.g. in external roof insulation layers to establish fall) the total thermal resistance varies over the area of the component. Such components

are built up as shown in figure C.l.

NOTE - For tapered air layers see annex B.

Figure C.l - Principle of build-up of component

The thermal transmittance

is defined by an integral over the area of the relevant component.

The calculation shall be carried out separately for each part (e.g. of a roof) with different pitch and/or shape as shown in figure C.2. In addition to those in clause 3, the following symbols are used in this annex:

Quantity

Xl

design thermal conductivity thickness at one end)

RO

design thermal resistance of the remaining part, including surface resistances on both sides of the component

m24VW

RI

maximum thermal resistance of the tapered layer

m%/W

4

maximum thickness of the tapered layer

m

and In denotes natural logarithm.

18

Unit

Symbol

of the tapered part (having zero

W/( m-K)

IS0 6946:1996(E)

+

indicates direction of pitch (which can be in either direction)

---

indicates alternative

(supplementary)

subdivision

to enable use of equations (C.l) to (C.3)

Figure C.2 - Examples of how to subdivide roofs into individual parts

C.2

Calculation for common shapes

The thermal transmittance not exceeding 5%.

of common shapes shall be calculated by equations (C.l) to (C.3) for pitches

NOTE - Numerical methods can be used for greater pitches.

C.2.1

Rectangular area

(C-1)

C.2.2

Triangular area, thickest at apex

A r’

HIL\ dl- 1

I

,’

,’

-=?

i.)ln(I+?)-I]

(C.2)

IS0 6946:1996(E)

C.2.3

Triangular area, thinnest at apex

(C.3)

C.3

Calculation procedure

The calculation

shall be carried out as follows:

1) Calculate Ro as the total thermal resistance of the component excluding the tapered layer, using equation (3) if all layers are thermally homogeneous, or the procedure in 6.2 if there are inhomogeneous layers. 2) Subdivide the area with tapered layers into individual parts as necessary (see figure C.2). 3) Calculate RI for each tapered layer using

4) Calculate the thermal transmittance in C.2.

of each individual part (UJ according to the relevant equation

5) Calculate the overall thermal transmittance

for the whole area A using (C.5)

If total thermal resistance of a component with tapered layers is required then RT = l/U

20

(C.6)

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IS0 6946:1996(E)

Annex D (normative) Corrections D.l

to thermal

transmittance

General

The thermal transmittance obtained by the procedures given in this standard shall be corrected where relevant to allow for the effects of: -

air gaps in insulation;

-

mechanical fasteners penetrating an insulation layer;

-

precipitation

on inverted roofs6).

The corrected thermal transmittance

UC is obtained by adding a correction term AU:

“,=“+A”

(D-1)

AU is given by A” = A”,

-I-A”f + A”,

(D-2)

where

D.2

AUg

is the correction for air gaps;

AlJf

is the correction for mechanical fasteners;

A”,

is the correction for inverted roof@).

Correction for air gaps

There are three levels of correction, depending on the extent and position of the gaps, as given in table D.1.

Table D.l - Correction for air gaps Level

AU” W/(m*.K)

0,oo

0,Ol

0,04

Description of air gap Insulation installed in such a way that no air circulation is possible on the warm side of the insulation. No air gaps penetrating the entire insulation layer. Insulation installed in such a way that no air circulation is possible on the warm side of the insulation. Air gaps may penetrate the insulation layer. Air circulation possible on the warm side of the insulation. Air gaps may penetrate the insulation.

6, An inverted roof is one having an insulation layer above the waterproof membrane. Correction procedures for inverted roofs are not included in the present edition of the standard, but are under preparation for incorporation by revision or amendment.

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IS0 6946:1996(E)

This correction is adjusted according to equation (D.3): 2

-4

A",=A""

(D-3)

( RT 1 where RI

is the thermal resistance of the layer containing gaps, as obtained in 5.1;

RT

is the total thermal resistance of the component, as obtained in clause 6.

NOTE - Examples of corrections for air gaps are given in annex E.

D.3

Correction for mechanical fasteners

When an insulation layer is penetrated by mechanical fasteners the correction to the thermal transmittance is given by: AUf=cxhfnfAf

P-4)

where a

is a coefficient

(see table D.2);

h

is the thermal conductivity

nf

is the number of fasteners per square metre;

4

is the cross-sectional

of the fastener;

area of one fastener.

Table D.2 - Values of the coefficient a Type of fastener

a m-l

Wall tie between masonry leaves

6

Roof fixing

5

No correction shall be applied in the following cases:

22

-

wall ties across an empty cavity;

-

wall ties between a masonry leaf and timber studs;

-

when the thermal conductivity

of the fastener, or par-t of it, is less than 1 W/(m.K).

@ IS0

IS0 6946:1996(E)

This procedure does not apply when both ends of the fastener are in contact with metal sheets. NOTE - The methods in IS0 1021 l-1, Thermal bridges in building construction - Heat flows and surface temperatures - Part 7: General calculation methods, can be used to obtain correction factors for cases where both ends of the fastener are in contact with metal sheets.

Annex

E (informative)

Examples

of corrections

A non-exhaustive

for air gaps

list of possible configurations

is shown in a) to h).

Correction level 0

4

Continuous insulation in multiple layers with staggered joints

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IS0 6946:1996(E)

b)

Continuous insulation, single layer, with shiplap, tongue-and-groove or sealed joints

cl

Continuous insulation, single layer with butt joints, provided that the length, width and squareness tolerances and the dimensional stability of the insulation are such that any gaps do not exceed 5 mm. This requirement is deemed to be satisfied if the sum of either length or width tolerances and dimensional changes is less than 5 mm, and the deviation from rectangularity for boards is less than 5 mm.

d)

Two layers of insulation, one between rafters, studs, joists or similar constructional components, the other as a continuous layer covering the first layer

6

Single layer of insulation in a construction, where the thermal resistance of the construction excluding that of the insulation layer is at least 50% of the total thermal resistance (ie RI I 0,5 /+)

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0 IS0

IS0 6946:1996(E)

Correction level 1

f)

Insulation entirely between rafters, joists, studs or similar constructional components

9)

Continuous insulation, single layer with butt joints, where the length, width and squareness tolerances plus the dimensional stability of the insulation are such that gaps exceed 5 mm. This condition is assumed if the sum of either length or width tolerances and dimensional changes is more than 5 mm, or if the deviation from rectangularity for boards is more than 5 mm.

Correction level 2

t-4

Construction with the possibility for air circulation on the warm side of the insulation due to insufficient fastening or sealing at top or bottom

25

IS0 6946:1996(E)

ICS 91.120.10 Descriptors: thermal insulation, buildings, components, resistance, thermal transmittance, rules of calculation. Price based on 25 pages

building elements,

thermal properties,

heat transfer,

determination,

thermal