(Heat transfer)
| 05.02 | THERMAL
PROPERTIES
(Heat transfer) |
|
Heat transfer processes
Heat transfer can be described as
the energy transfer from one system to another as a result of temperature
difference. It occurs by a combination of three basic heat transfer processes:
conduction, convection and radiation. Each of these may be a complex function
of component size, shape, material and orientation. Heat transfer
also occurs as a result of mass transfer when air at one temperature moves
to an area at a different temperature. Heat loss due to air leakage
is described in Section 05.03.
Conduction
Conduction is the transfer of energy
from the more energetic particles of a substance to the adjacent less energetic
ones as a result of interactions between the particles. Depending on the
form of the medium (solids, gases or liquids) the conduction is due to
collisions, diffusion, and vibration of the molecules or even energy transport
of free electrons (metals).
Thermal conductivity l [W/m.K] is a measure of the rate at which heat is conducted through a particular material under specified conditions. This coefficient is measured as the heat flow [W] across a thickness of 1 m for a temperature difference of 1 K and a surface area of 1 m².
The rate of heat conduction through a plane layer is proportional to the temperature difference T1 - T2 across the layer, the thermal conductivity l and the surface area A and is inversely proportional with the thickness of the layer t. The rate of heat conduction can than be written as
Q = l A ( T1 - T2 ) / t
and the heat transfer per unit area
is
q =
Q / A = l
( T1 - T2
) / t
More generally the process of conduction for homogeneous materials can be combined with the law of energy conservation
r c dT / dt = lxd2T / dx2 + lyd2T / dy2 + lzd2T / dz2
ris
the density of the material [kg/m3]
c
is the specific heat [J/(kg.K)]
T
is the temperature [K]
t
is the time [s]
lx
,ly
,lz
are the thermal conductivities in the x, y, z directions
The energy transport [W/m²] is then
qx = lxdT / dx , qy = lydT / dy and qz = lzdT / dz ,
In their most detailed form these equations are three-dimensional and the materials are time dependent, in some cases the properties are also moisture dependent.
Tabulated thermal conductivity
(l - values)
for some building materials are given in Section
05.06.
Convection heat transfer occurs in a fluid when the fluid moves over a surface that is at a different temperature. The mechanism for the fluid movement may be naturally induced buoyancy forces resulting from a conduction temperature gradient, in which case the terms natural or free convection are used, or the fluid movement may be caused by some external agency, such as a pressure difference or fan, in which case the term forced convection is applied.
Convection heat transfer between a surface and a body of fluid is defined by the relationship
Q = hc A DT
Q
is the heat transfer, in W
A
is the surface area, in m2
DT
is
the temperature difference between the fluid and the surface, in K
hc
is the convective heat transfer coefficient, in W/m2K
Generally the heat transfer coefficient hccan be predicted theoretically if the fluid movement is laminar, but must be determined experimentally if the fluid movement is turbulent.
The value of h depends on
hc = a nb
Free convection based on temperature differences:hc = a DTb
The value of b is determined by the nature of the boundary layer (laminar or turbulent).
hc = a + b n
Nu = C (Ra)n ( t / L )p
where
Nu = h t / l
and
Ra =
( b g a3r2
Cp ) /
(m l)
Nu
is the Nusselt number (dimensionless)
Ra
is the Rayleigh number (dimensionless)
t
is the thickness of the gas-space, in m
L
is the height of the gas-space, in m (the width of the gas-space may also
be important)
h
is the convective heat transfer coefficient, in W/m2K
l
is the thermal conductivity of the gas, in W/mK
b
is the coefficient of cubic expansion of the gas, in K-1
q
is the temperature difference across the gas-space, in
K
r
is the density of the gas, in kg/m3
Cp
is the specific heat capacity of the gas at constant pressure, in J/kgK
m
is the dynamic viscosity of the gas, in Ns/m2
C,
g,
n
and p are constants
(g = 9.806 m/s2,
C,
n, p depend on geometry)
This correlation is applicable regardless of the actual gas that is used. More importantly this correlation can be used to predict the transition from conduction to convection heat transfer - if the Nusselt number from this equation is less than unity (Nu < 1.0) then conduction heat transfer is occurring. If the orientation of the gas-space is known (coefficients C, n and p depend on the orientation of the gas-space) and a suitable gas is identified then it is straightforward to identify the thickness of the cavity for which the transition from conduction to convection occurs at a given temperature difference q.
In order to use this correlation it is necessary to know the value of the property
l ( b r2 Cp/ m l )n
Some values of this group are given
below (at atmospheric pressure and a mean temperature of 10°C),
based on horizontal heat transfer through a vertical gas-space for which
n
= 0.38 (BS 6993:Part 1 [1989])
| Gas | l ( b r2Cp/ m l )0.38 [W/mK] |
| Kr (krypton) |
|
| Ar (argon) |
|
| Air |
|
| SF6 (sulphur hexafluoride) |
|
Sulphur hexafluoride has been used in multiple glazing because it has a higher density and lower viscosity than other gases and so gives better sound insulation. However, it should also be noted that from a purely thermal point of view the use of a gas such as sulphur hexafluoride also allows thinner gas-spaces than with other gases (the thermal conductivity of SF6 is about half that of air) - this is often preferred as a reduction in the volume of gas means that the build-up of pressure due to gas heating is reduced.
In some simplifications convective
and radiative heat transfer are combined together into one coefficient.
Radiation
All bodies emit electro-magnetic radiation
and the amount of radiation emitted by a body is primarily a function of
its absolute temperature. In a vacuum, a body will reach a stable temperature
when there is a no nett exchange of radiant energy between itself and its
surroundings i.e. when it emits energy at the same rate as it absorbs energy
from its surroundings. If the body were to emit energy at a greater rate
than that at which it absorbs energy then the temperature of the body would
fall, and vice versa.
When considering the thermal effects of radiation it is often assumed that the spectral composition of the radiation is of minor importance because the emissivity of the surfaces is fairly constant over a wide range of wavelengths. However, the spectral composition of radiation can be important when considering energy transfer within buildings and it is of crucial importance in lighting. This section describes only the heat transfer due to long wave radiation. Section 05.04 describes the different forms of radiation and heat transfer due to solar radiation.
The amount of radiation that is emitted by a flat surface is limited by the physical law
Q = s eh A T4
A
is the area of the surface, in m2
T
is the absolute temperature of the surface, in K
eh
is the hemispherical emissivity of the surface (the average emissivity
over all viewing directions, dimensionless)
s
is the Stefan-Boltzmann constant (s
=
5.67´ 10-8W/m2K4)
However, the exchange of radiation between two flat surfaces is a more complex problem. Infrared radiation is just another part of the electromagnetic spectrum, and behaves in an identical manner to light - thus infra-red radiation may be reflected by a surface, absorbed, transmitted, scattered or prevented from reaching a surface if there is some obstruction which casts a thermal shadow. If two surfaces are in direct line of sight of one-another then there can be multiple reflections between the surfaces, and not all of the radiation leaving one surface will strike the other.
This complex interaction between surfaces means that radiation heat exchange can only be calculated in a number of special cases. Where the infra-red exchange between two surfaces can be calculated it is usually in the form
Q12 = s A1 F12 (T14 - T24)
Q12
is the net amount of energy leaving surface 1 which arrives at surface
2, in W
A1
is the area of surface 1, in m2
T1
is the absolute temperature of surface 1, in K
T2
is the absolute temperature of surface 2, in K
F12
is some combination of the surface emissivities together with a factor
for the visibility of surface 1 from surface 2
Although this relationship appears complex it can be factorised into the form
Q12 = a A1 F12 (T12 + T22) (T1 + T2) (T1 - T2)
Now, T1 and T2 must be absolute temperatures, in degrees Kelvin, and so in buildings they will have values typically in the range 263 - 313 K (-10 to +40°C). The term
(T12 + T22) (T1 + T2)
can then be replaced (simplified) with the term
4 Tm3
Tm is the mean surface absolute temperature, in K
Tm = (T1 + T2) / 2
This then gives
Q12 = 4 Tm3 s A1 F12(T1 - T2)
This substitution gives an error of
just 0.75% if T1 =
263 K and T2 = 313
K.
The relationship for radiation heat
transfer can now be expressed in the form
Q12 = hr A1(T1 - T2)
hr is the radiative heat transfer coefficient, in W/m2K
hr = 4 Tm3 sF12
In principle the external long wave radiation is the same as the internal long wave radiation. The surface between which radiation exchange occurs are the building external envelop on one side and the sky, the ground and the surrounding buildings on the other side. The assumptions made for the external long wave radiation can be different:
The long wave heat exchange is described by a heat transfer coefficient and heat sink to the clear sky
fse = hr ( Ta - T1 ) + fsink
fse
is the specific heat flow rate [W/m²]
hr
is the radiative surface heat transfer coefficient [W/m².K]
Ta
is the temperature of the air [K]
T1
is the temperature of the surface [K]
fsink
is the heat flow rate to clear sink [W/m²]
If there is no heat sink to clear
sky the factor fsink
= 0 in the formula above.
Combined heat transfer relationships
(series and parallel)
The relationships for the individual
forms of heat transfer can often be combined to determine an overall relationship
for the heat transfer through a component. The heat transfer through the
combined structure can be determined using the principle of thermal resistance.
The overall resistance to heat transfer through a component is a complex
function (combination of resistances in series and parallel) of the resistance
to heat transfer through each individual part of the component.
This image
gives an example of a simplified resistance diagram for a thermally broken
metal window frame.
The thermal resistance of an object is defined as
= DT
/ Q
is the resistance, in K/W
DT
is the overall temperature difference across the object, in K
Q
is the resulting heat transfer through the object, in W
Generally there is
The resistances between the environments and the surfaces of the component (surface resistances) depend on the location of the component on the facade and on the prevailing weather conditions. The surface resistance represents the combined effects of radiation and convection heat transfer at surfaces. In practice the surface resistances vary according to the internal and external conditions, but fixed values are used for the purposes of assessment, and these are defined in national or international standards. The surface resistance may also be given in the form of a surface heat transfer coefficient, which is simply the reciprocal of the surface resistance.
The convection heat transfer at a surface of the component depends on the air temperature adjacent to the surface, but the radiation heat transfer depends on the temperature of all of the surfaces facing the component. An environmental temperature is used in assessments, which is an appropriately weighted function of the air and surface temperatures within the environment. The environmental temperature is also defined in national standards.
The thermal performance of a facade or facade element is normally expressed in terms of the thermal transmittance or U-value which is the reciprocal of the resistance per unit area. Heat flow through the facade and U-value are related by the following formula;
U = Q / A DT
U
is the thermal transmittance in W/m2K
Q
is the heat flow in W
A
is the area of the facade or component in m2
DT
is the difference in environmental temperature across the facade in K
Cold-bridging / Thermal-bridging
Cold- or thermal-bridges are sections
through the fabric of significantly lower thermal resistance than the rest
of the construction. These happen particularly around openings and at junction
of walls/floors and walls/roofs. Concrete and metal framed buildings or
facades are particularly prone to cold-bridging unless these elements are
individually insulated. Cold-bridging is the result of localised areas
of low thermal resistance caused by the presence of elements with a high
thermal conductivity.
Typical examples are non-thermally broken metal frames, concrete frames, openings etc.
The result of thermal-bridging is localised
areas of increased heat loss/gain and possible increased condensation risk,
mould growth (which can also cause respiratory and other allergies in sensitive
people), pattern staining and corrosion.
Heat transfer directions through
the building elements
The heat transfer through building
elements can happen in one, two or three dimensions. The following table
categorises some examples of building elements into these three groups.
| 1-DIM | 2-DIM | 3-DIM |
| Plane, uniform elements such as walls and the centre of glazing units | Framing members
for curtain wall and windows
Interfaces between walls and windows |
Junctions between
framing members of curtain walls and windows
Corners of buildings Local imperfections |
Depending on the thermal behaviour,
the elements can then be assessed by one, two or three- dimensional heat
transfer assessment.
One-dimensional heat transfer assessment
One dimensional heat transfer assumes
that heat flows in a straight line, from the warm side of a component to
the cold side, and perpendicular to the plane of the component. This is
typical of heat flow through a pane of single glazing.
One-dimensional heat transfer is usually
calculated by hand (using analytical formulae) or assessed by measurement.
However, although based on the assumption that heat transfer is one-dimensional
few people are actually experienced enough to look at a component and state
whether it will truly experience one-dimensional heat flow. Unfortunately
this approach has been inherited from the glazing and traditional wall
(i.e. masonry/blockwork) industries where the majority of the heat flow
is one-dimensional. Even so, even in those traditional applications the
limitations of the one-dimensional method are now being realised, as the
effect of the edge spacer on glazing unit performance, and of mortar joints
and wall ties on masonry wall performance, are being quantified.
Two-dimensional heat transfer assessment
Two-dimensional heat transfer assumes
that some lateral heat flow occurs across the plane, but that there is
a set of parallel cross-sections along the component that have identical
performance. This might apply to an extruded glazing frame profile, for
example, away from corners and intersections.
Two-dimensional heat transfer calculation
may be performed in two ways - either by using a slightly more detailed
form of the hand calculation procedure identified above, by using computer
simulation or measurement equipment.
Three-dimensional heat transfer
assessment
Three-dimensional heat transfer assumes
that heat flow may occur in any direction. An example would be at an intersection
between two or more framing components.
Three-dimensional heat transfer assessment can be performed by a very detailed form of a hand calculation procedure, by simulation or by measurement.
The following table gives an overview
of what assessment type to choose for the direction of the heat flow.
| Direction of heat flow | |||
| Method of assessment |
|
|
|
| Analytical calculation by hand or spreadsheet |
|
|
|
| Computer simulation by FEM or FDM |
|
|
|
| Measurement by testing |
|
|
|
The different methods of assessing
the heat loss are described in the following section.
Methods for predicting heat loss
(U-value)
Analytical calculation method
Simplified calculation methods are
generally based on the principle of thermal resistance, which is directly
analogous to electrical resistance and uses the same basic equations, but
with temperature difference in place of potential difference, and heat
transfer in place of electrical current.
A basic requirement for the calculation of a thermal resistance is that the heat transfer through the element being considered is one-dimensional. This is usually assumed to be the case for layered, plane, components such as cavity walls, glazing units and insulated panels. However, the presence of a metal layer in such components can invalidate the thermal resistance model (such as often occurs in insulated or glazing panels), and in these components the edge detail must be taken into account. Note also that resistance models for layered components are invariably based on a ‘unit area’, and the formulae are modified accordingly.
A typical resistance-based method is described in the CIBSE Guide Part A3. In this method parallel heat paths (such as might exist through the edge detail of an insulated panel) can be allowed for using a proportional area calculation. This is the methodology currently adopted in the Building Regulations Approved Document L.
The calculation of two- and three-dimensional heat transfer is described in the CIBSE Guide Part A3 [1986] and also in BS EN ISO 6946 [1997]; the Standard has the advantage that it includes formulae for dealing with non-rectangular elements and small cavities. However, in both methods the procedure is to break a component down into a network of elements for which one-dimensional heat flow is occurring.
It is always possible, with the two-and three-dimensional calculation, to determine two extreme thermal resistance values for a component. The lower limit for the overall resistance is found by assuming that the component comprises a series of layers, often with each layer comprising a set of parallel heat paths; this is equivalent to assuming that lateral heat flow occurs freely within each layer. The upper limit for the overall resistance is found by assuming that the component comprises a set of parallel heat paths, with each parallel path made up of a series of smaller layers; this is equivalent to assuming that no lateral heat flow occurs. The ‘true’ thermal resistance is generally taken as the mean of the upper and lower values.
The two-and three-dimensional calculation method would normally be difficult to perform for components such as infill panels, which interact with the framing system.
The skill of the analyst in breaking a component down into realistic heat transfer paths is an important part of the process, and limits the accuracy of the analysis.
There are other simplified calculation procedures based on resistance methods. Typical of these are the Guide for assessment of the thermal performance of Aluminium curtain wall framing (CAB, 1996) and The assessment of thermally improved aluminium extrusions for use in windows and doors (AWA, 1992). Any method which is intended for calculating the U-value of a particular component or type of component may be used providing clear guidance is given as to what factors are taken into consideration; the method of calculation should always be clearly identified. Note that the Standards prEN 10077-1 and BS EN ISO 6946 are both relevant to resistance methods. The values given in the annexes of prEN 10077-1 should only be used informatively and not normatively.
Many published resistance-based simplified
calculation procedures do not give guidance on how to obtain point temperatures
from the results of the analysis. However, an assessor with a reasonable
understanding of heat transfer can usually extract this information.
Computer simulations methods
With a detailed calculation method
(sometimes termed a computer simulation method) a component is visualised
as a large number of small elements, the heat-transfer relationships between
which can be identified and solved using a computer. The distinction between
this approach and that of a simple hand-based calculation procedure is
that the mathematical formulae that are used are based on two- and three-dimensional
heat flow, and therefore give more realistic results. A spread-sheet calculation
procedure is not a detailed calculation method - it just uses a computer
to solve one-dimensional heat transfer problems more rapidly.
The limitation of detailed calculation methods is that to assess three-dimensional heat transfer requires considerable time and computing power. These methods are usually applied to a two-dimensional cross-section through a component, where it is assumed that the component is uniform in the third dimension; this assumption is sensible for many components, and is only violated when there is a three-dimensional joint between components.
There are two main types of computer-based calculation - finite difference methods and finite element analysis - which differ in the way that the component is broken down and represented mathematically:
Finite difference methods divide a component into rectangular elements (curved surfaces are therefore approximated as stepped surfaces). Each element is then assumed to be at a uniform temperature and the heat transfer between each pair of adjacent elements can be determined as a function of the element size, shape, properties and temperature. The large number of equations that result from this definition process are then solved automatically to determine the steady-state temperature distribution and the net heat transfer, which is readily converted into a U-value.
Finite element analysis divides the component into elements which may be rectangular, triangular or irregular in shape. Curved surfaces may be represented more realistically, depending upon the number of elements into which the curve is divided. The temperature within each element is assumed to have a simple distribution, and the relevant heat transfer relationships are solved automatically to determine the temperature distribution and the net heat transfer.
New forms of detailed calculation method are being developed, and may be encountered. It should be noted that the general measure of the suitability of a detailed calculation method to a particular type of analysis is the use of a ‘benchmark’, which is a defined component with a clearly established measured performance. Suitable published benchmarks, such as those in BS EN ISO 10211-1, may be used to check the accuracy of the calculation method. Note also that several analyses may be required to assess the performance of a composite system such as a curtain wall (one for each particular frame-profile/infill combination used in the curtain wall), although the time involved will be far less than for measurements and the effects of design changes can be examined. European guidelines are being prepared to standardise assessment by detailed calculation methods, and these will include values for the thermal conductivity of many materials, for example in prEN 10077-2.
The validity of any detailed calculation method is best checked against measured data. Measured U-values should always be sought as a means of checking the accuracy of a calculation. In the USA a rating system is used for windows and doors (NFRC 100-91) in which analyses are carried out using a detailed calculation method to assess the performance of a complete range of products, and the two products showing the extremes of performance are then measured as a check against the validity of the analysis - this approach combines the speed of calculation with the certainty of measurement.
Guide to good practice for assessing
heat transfer and condensation risk for a curtain wall (CWCT, 1998)
describes a detailed calculation of the U-value of a curtain wall.
Visualisation of temperature distribution
and heat loss (2D-3D) by computer simulation
Images showing temperature distribution
and heat flow are available here as follows;
Two dimensional simulation
Measurement methods
Measurement is generally considered
the only way in which the 3-dimensional heat transfer processes are fully
and accurately recreated. However, a test cannot be performed prior to
manufacture of a prototype or sample, which may leave too little time to
revise the design should it not perform as expected, and temperatures are
rarely measured within the component, although surface temperatures will
be recorded as part of the measurement procedure.
Measurement devices must be calibrated, and there are well-established and proven measurement standards which allow data to be adjusted to reference conditions. Measurement cannot usually be used to identify the U-values of the various parts of the sample (for example each of the different frame profiles and infill types in a large curtain wall specimen) but it does allow for the interactions between the components of the sample. Standards are available for the particular type of measurement apparatus (for example BS 874: Part 3 or prEN 12412-1 for hot-boxes) and can give guidance on suitable sample sizes and arrangements.
The hot-box is the principal laboratory-based apparatus, and is to be preferred for measurements. The sample is mounted in an insulated surround, between two thermally-controlled environments, and the heat transfer through the sample is measured.
The calorimeter is a device which encloses one side of the sample. It therefore controls only one of the thermal environments (usually on the cold-side of the sample). The calorimeter allows the warm-side of the sample to be observed, which gives the assessor the opportunity to gain more data regarding surface temperatures, and may allow condensation to be observed.
The hot-plate places the sample between, and in good thermal contact with, two surfaces at known temperatures. This is only suitable for use with plane components of uniform thickness - if the component has an edge detail of a different thickness to the remainder of the component then a different form of measurement must be used. Note that removing the edge detail to assess such a component may not give a realistic result.
Infra-red thermography uses a thermal imaging camera to ‘observe’ the surface temperatures of a structure. Useful in connection with in situ measurements, this technique usually requires additional temperature measurements from a reference surface for calibration. However, although infra-red thermography may be used in combination with a calorimeter it should not be considered as suitable for measuring U-values until further work has been undertaken on standardisation.
In situ temperature measurement may be used to assess thermal performance by measuring surface temperatures and comparing them with predicted values. Such a method is readily calibrated by using a component with a known performance, for example a double glazing unit, as a reference. As with infra-red thermography this technique should not be used to assess performance other than as a diagnostic tool, where it is useful for checking that a facade has been properly designed and constructed.
The only significant issue with measurement
of a component is to decide the size and arrangement of the test specimen;
the test specimen should be a realistic representation of a component or
system as it will be used.
The thermal transmittance (U) and
the additional heat loss (Y)
The overall thermal transmittance
(U-value)
In general a U-value assessment will
result in a predicted or measured heat transfer Q through the component,
for some overall environmental temperature difference DT.
This may have been converted to an overall U-value using the relationship
=
Q / Ap DT
The area AP is the projected area of the component. Obviously the U-value is dependent on the value taken for this area. In many cases it is possible to define a solid edge for the component, and the projected area is readily calculated. In some cases however the limits of the component may be uncertain or variable in practice; a typical example is a glazing frame with a glazing unit, where the glazing gasket, which is part of the frame, partly covers the edge of the glazing. The actual coverage of the gasket is variable in practice and in this case the solid edge of the frame is a better limit to the projected area of the frame.
The basis of selecting the dimensions of the projected area AP should always be stated. Note that for the purposes of the Building Regulations the projected area of the facade is defined looking from the inside of the building.
In the case of a component which overlaps another, such as a glazing frame and the glazing unit, the measured or predicted total heat transfer will combine the effects of two or more components. In this case it is only possible to separate the U-value of one component if the U-value of all other components is known. The U-values of the known components can be used to calculate an expected heat transfer through each component, using the relationship
Qc = Uc ApcDT
These ‘other-component’ heat transfers can then be subtracted from the predicted total heat transfer for the assembly. The remainder is then converted to a U-value for the final component, using equation
=
Q / Ap DT
The procedure for calculating a total facade heat transfer is to add each of the component heat transfers
Qtotal = S ( Uc ApcDT )
Note that the component U-values will have been assessed using a common reference environmental temperature difference DT, but in determining the total facade heat loss each component may be used in an area which has some different local temperature difference DTc.
The overall U-value of the facade is a projected-area-weighted average of the component U-values
Uoverall = S ( Uc Apc ) / S Apc
The total projected area of the facade must be the sum of the component projected areas, by definition.
The detailed calculation is worked
out in the following documents: Guide to good practice for assessing
glazing frame U-values and Guide to good practice for assessing
heat transfer and condensation risk for a curtain wall (both CWCT,
1998).
The edge effect of heat transfer
through insulated panels and glazing
The heat flow through glazing units
and insulated panels can be greater around the edge due to the cold bridging
effect of the edge detail, image.
The thermal performance of a part of a wall can be described in two ways;
=
Q / A DT
[W/m2K]
Q
is the total heat flow through the component, in W
A
is the projected area of the component, in m2
DT
is the overall temperature difference across the component, in K
The additional heat transfer (Y-
value)
A Y
-
value represents the additional heat transfer through an otherwise uniform
component that is caused by some linear feature of the component, such
as for instance the extra heat flow through a plane layered component caused
by a non-plane edge. As shown in this image.
The total heat transfer through the component is then expressed in terms
of the theoretical centre-panel U-value, which assumes that the whole of
the component performs as the plane layered part (i.e. according to the
simple one-dimensional calculation plus a linear transmittance (Y-
value), which relates the additional heat loss to the length of the linear
feature (in this case the perimeter of the panel).
The total heat flow through the panel is then:
Q = ( U A + Y L ) DT
Q
is the total heat flow through the panel, in W
U
is the theoretical centre-panel U-value of the panel, in W/m2K
A
is the projected area of the panel, in m2
Y
is the linear edge transmittance of the panel, in W/mK
L
is the perimeter of the panel, in m
DT
is the overall temperature difference across the panel, in K
These formulae indicate that the linear edge transmittance must be related to the average and theoretical centre-panel U-values by:
Y = A
( - U ) / L
Interactions of a panel with its
framing system
In a real application the insulated
panel/glazing would be mounted in a framing system, which would clamp or
otherwise support (and thus interact with) the edge of the panel. The Y
- value could therefore be seen as comprising two parts:
a component Y - value, which is an intrinsic property of the panel/glazing itself, plus
an interaction Y - value, which is an extrinsic property of the system.
These two Y
- values are then added together to form the total Y
- value. The component Y
- value may be minimised by the panel manufacturer by good edge detailling
but the interaction Y
- value depends on the design of both the frame and panel.
Example: the U-value of a total
window (frame and glazing)
As an example more information is
given for the calculation of the thermal transmission of a window.
The thermal transmittance of a window can be calculated using the following equation:
Uw = ( Ag Ug + Af Uf + lg Y ) / ( Ag + Af )
where
Uw
is the thermal transmittance of the window
Ug
is the thermal transmittance of the centre glazing (without edge effect;
spacer effect)
Uf
is the thermal transmittance of the frame
Y
is the linear thermal transmittance due to the combined thermal effects
of glazing, spacer and frame
Ag
is the projected glazing area
Af
is the projected frame area (i.e. the area of the projection of the frame
on a plane parallel to the glazing panel).
lg
is the total perimeter of the glazing
PrEN ISO 10077 part 1 gives more detailed information about the use of the formula given above. Note that the annexes in prEN 10077 part 1 are only informative and shouldn't be applied on curtain walling systems.
The thermal transmittance of the glazing Ug is applicable to the central area of the glazing and does not include the effect of the glass spacers at the edge of the glazing. On the other hand the thermal transmittance of the frame Uf is applicable in the absence of the glazing. The linear thermal transmittance Y describes the additional heat conduction due to the interaction between frame, glazing and spacer. The linear transmittance Y is mainly affected by the conductivity of the spacer material.
Note that is possible to consider the linear thermal transmittance Y consisting of two components:
Y = Yg + Yf
Y
is the total linear thermal transmittance
Yg
is the additional heat flow per unit length through the glazing, which
depends on the type of the glass and the spacer
Yf
is the additional heat flow per unit length through the frame, which depends
on the type of the frame and the spacer
PrEN ISO 10077 part 2 gives more detailed
information about how to assess both values by computer simulations.
Difference between the German k-value
and the European U-value
The German and European methods for
the assessment of heat transfer through windows are different and failure
to appreciate these differences can lead to confusion. Currently
there is a German deviation for the use of the prEN 10077 (parts 1 &
2) as the calculation of the thermal transmittance of windows forms part
of the national German regulations. These German regulations specify
that the design thermal transmittance for glazing and windows and window
doors shall be in accordance with table 3 of DIN 4108-4 'Wärmeschutz
im Hochbau'. The values k (kDIN
in this text) given in those tables are obtained by the German standard
DIN 52619 'Bestimmung des Wärmedurchlaßwiderstandes und Wärmedurchgangskoeffizienten
von Fenstern - Teil 3: Messung an Rahmen'.
The standard DIN 52619 concerns measurement, however kDIN - values can also be calculated, based on numerical simulations. The method of measurement in DIN 52 619 Part 3 is a similar method to the prEN 12412-2 'Thermal performance of windows, doors and shutters - Calculation of thermal transmittance by hot box method - frames' where the frame and the glazing are assessed separately
A comparison of both standards is set
out in the following table:
| U-value from EN 10077 | kDIN - value from DIN 52619 part 3 |
| The thermal transmittance (U-value) is based on logic equations | kDIN is not a physical thermal transmittance. The 'thermal transmittance' is based on measurement method (hot box / cold box). |
| The assessment is done with the glass in the frame ('real situation). | The glazing is substituted with a flat slab of insulating material (thermal conductivity < 0.04 W/mK) |
| U-value from EN 10077 gives a 'close to reality' result. | kDIN gives in a lot of situations (especially for curtain wall and large aluminium profiles) a lower value. |
| The cooling effect of large profiles is taken in to account. | The cooling effect is almost not visible with this method. |
| Can be used for the assessment of temperature distribution and condensation risk of the real situation | This method can not be used to obtain accurate temperature distribution and condensation risk assessment. The lowest temperature at the inside of the profile is much higher than obtained from prEN 10077. |
Although the kDIN - values resulting from the DIN 52619 should only be used to classify the window frame according to DIN 4108 (and not to compare the values with the prEN 10077), k values are frequently quoted in the UK and are wrongly believed by specifiers to give a realistic assessment of the heat transfer through a curtain wall frame.
A good example of the difference and misleading use of comparing results from two different standards is worked out in the CWCT Document: 'Guide to good practice for assessing glazing frame U-values'.
In the example of a curtain walling
mullion, the calculated U-value by the CEN standards is almost twice the
one obtained from the DIN method. The minimum temperatures obtained on
the warm side with the DIN method are much higher (more than 6oC).
Section 05.02:Version
1.00.aa
© Centre for Window
and Cladding Technology - 2000, 2001