# ISO 15099:2003

(Main)## Thermal performance of windows, doors and shading devices — Detailed calculations

## Thermal performance of windows, doors and shading devices — Detailed calculations

ISO 15099:2003 specifies detailed calculation procedures for determining the thermal and optical transmission properties (e.g., thermal transmittance, total solar energy transmittance) of window and door systems based on the most up-to-date algorithms and methods, and the relevant solar and thermal properties of all components. Products covered by ISO 15099:2003 include windows and doors incorporating: single and multiple glazed fenestration products with or without solar reflective, low-emissivity coatings and suspended plastic films; glazing systems with pane spacing of any width containing gases or mixtures of gases; metallic or non-metallic spacers; frames of any material and design; fenestration products tilted at any angle; shading devices; projecting products.

## Performance thermique des fenêtres, portes et stores — Calculs détaillés

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### Standards Content (Sample)

INTERNATIONAL ISO

STANDARD 15099

First edition

2003-11-15

Thermal performance of windows, doors

and shading devices — Detailed

calculations

Performance thermique des fenêtres, portes et stores — Calculs

détaillés

Reference number

ISO 15099:2003(E)

©

ISO 2003

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ISO 15099:2003(E)

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ii © ISO 2003 — All rights reserved

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ISO 15099:2003(E)

Contents

Foreword. iv

Introduction . v

1 Scope. 1

2 Normative references . 1

3 Symbols . 2

3.1 General. 2

3.2 Symbols and units . 2

3.3 Subscripts. 4

4 Determination of total window and door system properties. 5

4.1 Thermal transmittance. 5

4.2 Total solar energy transmittance . 9

4.3 Visible transmittance. 10

5 Vision area properties . 10

5.1 Glazing layer optics . 10

5.2 Glazing system optics . 11

5.3 Vision area heat transfer . 13

6 Frame effects. 20

6.1 Area and lineal thermal transmittance. 20

6.2 Governing equations for calculating thermal transmittance. 20

6.3 Geometric representation and meshing. 20

6.4 Solid materials. 23

6.5 Effective conductivity — Glazing cavities. 23

6.6 Effective conductivity — Unventilated frame cavities . 23

6.7 Ventilated air cavities and grooves. 30

7 Shading devices. 31

7.1 Definitions. 31

7.2 Optical properties . 32

7.3 Slat type of shading. 34

7.4 Ventilation. 39

7.5 Total solar energy transmittance and thermal transmittance . 50

8 Boundary conditions . 50

8.1 General. 50

8.2 Reference boundary conditions . 50

8.3 Convective heat transfer . 51

8.4 Longwave radiation heat transfer . 55

8.5 Combined convective and radiative heat transfer. 58

8.6 Prescribed density of heat flow rate . 59

Annex A (informative) Solution technique for the multi-layer solar optical model . 60

Annex B (normative) Thermophysical fill gas property values . 62

Annex C (informative) Examples of calculated values for optical properties of slat type of shading

devices . 64

Bibliography . 69

© ISO 2003 — All rights reserved iii

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ISO 15099:2003(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies

(ISO member bodies). The work of preparing International Standards is normally carried out through ISO

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. ISO collaborates closely with the

International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. 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.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

ISO 15099 was prepared by Technical Committee ISO/TC 163, Thermal performance and energy use in the

built environment.

iv © ISO 2003 — All rights reserved

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ISO 15099:2003(E)

Introduction

This International Standard describes a procedure for calculating indices of merit of many window and door

products. The method provided in this International Standard allows the user to determine total window and

door product indices of merit, viz thermal transmittance, total solar energy transmittance and visible light

transmittance.

The procedures give the actual thermal performance of fenestration products for use in building energy

analysis and for the evaluation of products in specific building applications. These procedures can also be

used to produce data to compare products by using the standardized boundary conditions given either in this

International Standard or taken from the appropriate International or National Standards (e.g., ISO 12567-1,

ISO 10292, ISO 9050). This International Standard is also intended as a reference document for the

description of models used in computer programs for detailed calculation of the thermal and optical

transmission properties of window and door systems.

This International Standard gives detailed models for thermal and optical transmission in windows. These

detailed models are necessary in many types of window to get agreement between calculations and tests.

Traditionally, windows have been characterized by separately calculating the “dark” or “night-time” thermal

transmittance and the solar energy transmittance through the fenestration system. The thermal transmittance

without the effect of solar radiation is calculated using the procedures given in ISO 10292 (for the vision

portion) and the total solar energy transmittance, without taking into account the actual temperatures of the

various panes, is obtained using ISO 9050. These calculations require the use of reference conditions that are

not representative of actual conditions. In this International Standard the energy balance equations are set up

for every glazing layer taking into account the solar absorption and actual temperatures. From these energy

balance equations, the temperatures of the individual layers and gaps are determined. This is the only

standard that takes into account these complex interactions. This more detailed analysis provides results that

can then be expressed as thermal transmittance and τ -values and these values can differ from the results of

S

simpler models.

Individual indices of merit obtained using fixed reference boundary conditions are useful for comparing

products. However, the approach taken is the only way of calculating the energy performance of window

systems for other environmental conditions including those conditions that may be encountered during hot box

measurements.

Finally it must be emphasized that this International Standard is intended for use in computer programs. It was

never intended as a “simplified calculation” procedure. Simplified methods are provided in other International

Standards. It is essential that these programs produce consistent values and that they are based on a sound

standard methodology. Although more complicated than the formulae used in the simplified standards, the

formulae used in this International Standard are entirely appropriate for their intended use.

© ISO 2003 — All rights reserved v

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INTERNATIONAL STANDARD ISO 15099:2003(E)

Thermal performance of windows, doors and shading

devices — Detailed calculations

1 Scope

This International Standard specifies detailed calculation procedures for determining the thermal and optical

transmission properties (e.g., thermal transmittance, total solar energy transmittance) of window and door

systems based on the most up-to-date algorithms and methods, and the relevant solar and thermal properties

of all components.

Products covered by this International Standard include windows and doors incorporating:

a) single and multiple glazed fenestration products with or without solar reflective, low-emissivity coatings

and suspended plastic films;

b) glazing systems with pane spacing of any width containing gases or mixtures of gases;

c) metallic or non-metallic spacers;

d) frames of any material and design;

e) fenestration products tilted at any angle;

f) shading devices;

g) projecting products.

2 Normative references

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.

ISO 7345, Thermal insulation — Physical quantities and definitions

ISO 8301, Thermal insulation — Determination of steady-state thermal resistance and related properties —

Heat flow meter apparatus

ISO 8302, Thermal insulation — Determination of steady-state thermal resistance and related properties —

Guarded hot plate apparatus

ISO 9050, Glass in building — Determination of light transmittance, solar direct transmittance, total solar

energy transmittance, ultraviolet transmittance and related glazing factors

ISO 9288, Thermal insulation — Heat transfer by radiation — Physical quantities and definitions

ISO 9845-1, Solar energy — Reference solar spectral irradiance at the ground at different receiving

conditions — Part 1: Direct normal and hemispherical solar irradiance for air mass 1,5

© ISO 2003 — All rights reserved 1

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ISO 15099:2003(E)

ISO 10077-2:2003, Thermal performance of windows, doors and shutters — Calculation of thermal

transmittance — Part 2: Numerical method for frames

ISO 10211-1, Thermal bridges in building construction — Heat flows and surface temperatures, Part 1:

General calculation methods

ISO/CIE 10526:1999, CIE standard Illuminants for colorimetry

ISO/CIE 10527, CIE standard colorimetric observers

ISO 12567-1, Thermal performance of windows and doors — Determination of thermal transmittance by hot

box method — Part 1: Complete windows and doors

EN 12898, Glass in building — Determination of the emissivity

3 Symbols

3.1 General

Symbols and units used are in accordance with ISO 7345 and ISO 9288. The terms, which are specific to this

International Standard, are listed in Table 1.

3.2 Symbols and units

Table 1 — Terms with their symbols and units

Symbol Term Unit

2

A

area m

A portion of absorbed solar energy by the ith glazing layer

1

i

A aspect ratio 1

R

b width (breadth) of a groove or slit mm

c specific heat capacity at constant pressure

J/(kg⋅K)

p

d thickness m

d thickness of glazing cavity m

g

2

E

irradiance

W/m

E (λ) solar spectral irradiance function (see ISO 9845-1) 1

s

colorimetric illuminance (CIE D65 function in ISO/CIE 10526:1999) lx

E (λ)

v

2

g acceleration due to gravity

m/s

G

parameter used in the calculation of convective heat transfer coefficients; see Equation (48) 1

2.

h surface coefficient of heat transfer

W/(m K)

H height of glazing cavity m

2

I total density of heat flow rate of incident solar radiation

W/m

+

I λ

()

i

spectral heat flow rate of radiant solar energy between ith and i + 1th glazing layers

W

+ −

travelling in the external ( ) or internal ( ) direction

−

I λ

()

i

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ISO 15099:2003(E)

Table 1 (continued)

Symbol Term Unit

2

J radiosity

W/m

l length m

molecular mass mole

ˆ

M

N 1

number of glazings + 2

Nu Nusselt number 1

P pressure Pa

2

q density of heat flow rate

W/m

r

reflectance: portion of incident radiation reflected such that the angle of reflection is equal 1

to the angle of incidence

2

R thermal resistance

m ⋅K/W

R(λ) photopic response of the eye (see ISO/CIE 10527)

universal gas constant

ℜ J/(kmol⋅K)

Ra Rayleigh number 1

Ra Rayleigh number based on length dimension x 1

x

2

S density of heat flow rate of absorbed solar radiation at ith glazing laver

W/m

i

t largest dimension of frame cavity perpendicular to heat flow m

perp

T thermodynamic temperature K

∆T temperature drop across ith glazing cavity, ∆T = |T − T | K

i i f,i b,i+1

u air velocity near a surface m/s

2

U thermal transmittance

W/(m ⋅K)

v free-stream air speed near window, mean air velocity in a gap m/s

x, y

dimensions in a Cartesian co-ordinate system 1

Z pressure loss factor 1

absorption 1

α

−1

β thermal expansion coefficient of fill gas

K

ε total hemispherical emissivity 1

angle °

γ

temperature

θ °C

−8 2 4

σ

Stefan-Boltzmann constant, 5,669 3 × 10 W/(m ⋅K )

λ thermal conductivity W/(m⋅K)

wavelength m

λ

w

µ dynamic viscosity Pa⋅s

3

density

ρ kg/m

τ transmittance 1

1

τ total solar energy transmittance: the portion of radiant solar energy incident on the

S

projected area of a fenestration product or component that becomes heat gain in the

internal conditioned space

φ parameter used in the calculation of viscosity and of thermal conductivity; 1

see Equations (62) and (67)

function used in the calculation of heat transfer; see Equation (112) 1

ϕ

heat flow rate W

Φ

Ψ linear thermal transmittance W/(m⋅K)

© ISO 2003 — All rights reserved 3

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ISO 15099:2003(E)

3.3 Subscripts

The subscripts given in Table 2 shall be applied.

Table 2 — Subscripts and meanings

Subscript Meaning

ai air

av average

b backward

bo bottom of a gap

cc condition on the cold side

cdv conduction/convection (unvented)

cg centre of glass

ch condition on the hot (warm) side

cr critical

cv convection

de divider edge glass

dif diffuse

dir direct

div divider

eff effective

eg edge of glass

eq equivalent

ex external

f frame

fr frame (using the alternative approach)

ft front

gv glass or vision portion

ht hot

hz horizontal

i counter

int internal

inl inlet of a gap

j counter

m mean

mix mixture

n counter

ne environmental (external)

ni environmental (internal)

out outlet of a gap

p panel

r radiation or radiant

red reduced radiation

s surface

sc source

sk sink

sl solar

t total

tp top of a gap

v number of gases in a gas mixture

v vertical

z at distance z

Ψ perimeter

2D coupling

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ISO 15099:2003(E)

4 Determination of total window and door system properties

4.1 Thermal transmittance

4.1.1 General

This International Standard presents procedures by which detailed computations can be used to determine

the thermal transmission properties of various product components, which are then used to determine the

thermal transmission properties of the total product. Where national standards allow, test procedures may be

used to determine component and total product properties.

The total properties for window and door products are calculated by combining the various component

properties weighted by either their respective projected areas or visible perimeter. The total properties are

each based on total projected area occupied by the product, A . The projected component areas and the

t

visible perimeter are shown in Figure 1.

Key

1 perimeter length at sight line - - - - -

Figure 1 — Schematic diagram showing the window projected areas and vision perimeter

Clause 4 describes the procedure for calculating thermal transmittance, total solar transmittance and visible

transmittance for the complete product. 4.1 describes the procedure for calculating thermal transmittance. The

effect of three-dimensional heat transfer in frames and glazing units is not considered. 4.1.4 describes an

alternative procedure for calculating edge of glass and frame thermal indices U , U , U and U , which are

de eg t fr

used in area-based calculations. Clause 5 describes the procedure for calculating the required centre-glass

properties τ and τ . Clause 6 describes the procedure for calculating the linear thermal transmittance, Ψ,

sgv gv

which accounts for the interaction between frame and glazing or opaque panel. Clause 7 contains the

procedure for dealing with shading devices and ventilated windows. Clause 8 describes the procedure for

determining and applying boundary conditions. The thermal transmittance of the fenestration product is given

by:

∑+AU ∑AU+∑l Ψ

gv gv f f Ψ

U = (1)

t

A

t

where A and A are the projected vision area and frame area, respectively. The length of the vision area

gv f

perimeter is l , and Ψ is a linear thermal transmittance that accounts for the interaction between frame and

Ψ

glazing or the interaction between frame and opaque panel (e.g., a spandrel panel).

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ISO 15099:2003(E)

The summations included in Equation (1) are used to account for the various sections of one particular

component type; e.g. several values of A are needed to sum the contributions of different values of U

f f

corresponding to sill, head, dividers and side jambs.

Figure 2 illustrates the division into components for the alternative approach described in 4.1.4, in which the

edge-of-glass and divider-edge areas are 63,5 mm (2,5 in) wide. The sum of all component areas equals the

total projected fenestration product area.

Key

C Centre-of-glass 1 installation clearance

E Edge-of-glass 2 projected area

F Frame 3 rough opening

D Divider 4 interior

DE Divider-edge 5 exterior

Figure 2 — Centre-of-glass, edge-of-glass, divider, divider-edge,

and frame areas for a typical fenestration product

4.1.2 Glazed area thermal transmittance

The thermal transmittance can be found by simulating a single environmental condition involving

internal/external temperature difference, with or without incident solar radiation. Without solar radiation, the

thermal transmittance is the reciprocal of the total thermal resistance.

1

U = (2)

gv

R

t

and when solar radiation is considered, then:

q

int I = 0

()

s

U = (3)

gv

TT−

ni ne

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ISO 15099:2003(E)

where q (I = 0) is the net density of heat flow rate through the window or door system to the internal

int s

2

environment for the specified conditions, but without incident solar radiation, in W/m . The condition “without

solar radiation” is used because all effects on the thermal resistances due to incident solar radiation are

incorporated in the total solar energy transmittance or τ -value [see Equation (14)], and T and T are the

S ni ne

environmental temperatures, as defined in Equation (7).

R is found by summing the thermal resistances at the external and internal boundaries, and thermal the

t

resistances of glazing cavities and glazing layers. See Figure 3.

nn

11

RR=+ +R + (4)

tg∑∑iiv,

hh

ex int

ii=2 =1

where the thermal resistance of the ith glazing is:

t

gv,i

R = (5)

gv,i

λ

gv,i

and the thermal resistance of the ith space, where the first space is external environment, the last space is

internal environment and the spaces in between are glazing cavities, (see Figure 3):

TT−

f,ib,i−1

R = (6)

i

q

i

where T , and T are the external and internal facing surface temperature of the ith glazing layer.

f,i b,i−1

The environmental temperature [as defined in Equation (7)] is a weighted average of the ambient air

temperature and the mean radiant temperature, T , which is determined for external and internal

rm

environment boundary conditions (see boundary conditions in 8.4.1).

Key

1 gap

2 glazing

Figure 3 — Numbering system for glazing system layers

The environmental temperature, T , is:

n

hT +hT

cv ai r rm

T = (7)

n

hh+

cv r

where h and h are determined according to the procedure given in Clause 8.

cv r

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ISO 15099:2003(E)

4.1.3 Frame area/edge-glass thermal indices

In order to convert the results of a two-dimensional numerical analysis to thermal transmittances, it is

necessary to record the rate of heat transfer from the internal environment to the frame and edge-glass

surfaces (in the absence of solar radiation). The linear thermal transmittance, Ψ, values and frame thermal

transmittances shall be calculated according to the following equations.

2D

Ψ=−L Ul−U l (8)

f f gv gv

2D

where L is thermal coupling coefficient determined from the actual fenestration system.

2D

L −Ul

ppp

U = (9)

f

l

f

where

2D

L is thermal coupling coefficient determined from the frame/panel insert system;

p

U is the thermal transmittance of foam insert;

p

l is the internal side exposed length of foam insert (minimum 100 mm);

p

l is the internal side projected length of the frame section;

f

l is the internal side projected length of the glass section (see Figures C.1 and C.2 of

gv

ISO 10077-2:2003, for further details on the definition of l and l ).

fr p

2D

The detailed procedure for determining L is also given in ISO 10211-1.

4.1.4 Alternative approach (see Figure 2)

An alternative method is available for calculating frame thermal transmittance, U . Using this method it is

fr

unnecessary to determine the linear thermal transmittance, Ψ. Instead, the glass area, A , is divided into

gv

centre-glass area, A , plus edge-glass area, A , and one additional thermal transmittance, U , is used to

c e eg

characterize the edge-glass area. If dividers are present then divider area, A and divider thermal

div

transmittance, U are calculated, as well as corresponding divider edge area, A and thermal transmittance,

div de

U . The following equation shall be used to calculate the total thermal transmittance:

de

UA++U A U A+ U A+ U A

∑∑cg c fr f∑ eg e∑ div div∑ de de

U = (10)

t

A

t

where U , and U can be determined from the following equations:

fr eg

Φ

fr

U = (11)

fr

lT −T

()

fni ne

Φ

eg

U = (12)

eg

lT −T

()

eg ni ne

and where l is projected length of frame area and l is the length of edge of glass area and is equal to

f eg

63,5 mm. These lengths are measured on the internal side. The quantities Φ and Φ are heat flow rates

fr eg

through frame and edge-glass areas (internal surfaces), respectively, including the effect of glass and spacer,

and both are expressed per length of frame or edge-glass. The calculations shall be performed for each

combination of frame and glazing with different spacer bars.

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ISO 15099:2003(E)

The summations included in Equation (10) are used to account for the various sections of one particular

component type; e.g., several values of A must be used to sum the contributions of different values of U

f fr

corresponding to sill, head and side jambs.

It should be noted that the two different approaches entail different definitions of frame thermal transmittance,

denoted U and U . The primary difference is that the U includes the some of the heat transfer caused by the

f fr fr

edge seal, whereas U does not. The comparison of frame properties for two different products is only

f

meaningful if the same calculation procedure has been used in both cases.

The U values for windows calculated by the two methods may differ because of differences in the way frame

t

and edge heat transfer is treated at the corners, particularly because the three dimensional effects are

neglected. This difference is more pronounced for smaller windows. The choice of l = 63,5 mm is made to

eg

reduce the discrepancy between the two alternative approaches.

4.2 Total solar energy transmittance

4.2.1 General

The total solar energy transmittance of the total fenestration product is:

ττA + A

∑∑gg f f

τ = (13)

s

A

t

where τ and τ are the individual total solar energy transmittance values of the vision area and frame area,

g f

respectively. The summations are included for the same reason that they appear in Equation (1) and shall be

applied in the same manner to account for differing sections of one particular component type.

NOTE Equation (13) includes an assumption that the solar transmittance of the edge of glass is the same as that of

the centre of glass area.

4.2.2 Vision area total solar energy transmittance

The total solar energy transmittance can be dete

**...**

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