EFFECT OF GLASS THICKNESS ON THE THERMAL PERFORMANCE OF EVACUATED GLAZING

Abstract

Flat evacuated glazing consists of two plane glass panes separated by a narrow internal evacuated space. Separation of the space is maintained by an array of support pillars typically 0.32mm in diameter and 0.12mm high arranged on a regular square grid with an inter-pillar separation of up to 40mm. A detailed 3-dimensional finite volume model has been employed to determine the variation of thermal performance of an evacuated glazing as a function of glass pane thickness. It was predicted that for an evacuated glazing with dimension of less than 1m by 1m, reducing glass pane thickness gave improved thermal performance. For evacuated glazings with dimensions larger than 1m by 1m, the opposite was predicted.

Full text

EFFECT OF GLASS THICKNESS ON THE THERMAL
PERFORMANCE OF EVACUATED GLAZING
Yueping Fang*, Philip C. Eames*, Brian Nortonº and Trevor J. Hyde*
* Centre for Sustainable Technologies, School of the Built Environment,
University of Ulster, Newtownabbey, BT37 0QB, N. Ireland
º Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland
Abstract
Flat evacuated glazing consists of two plane glass panes separated by a narrow internal evacuated
space. Separation of the space is maintained by an array of support pillars typically 0.32mm in
diameter and 0.12mm high arranged on a regular square grid with an inter-pillar separation of up to
40mm. A detailed 3-dimensional finite volume model has been employed to determine the variation
of thermal performance of an evacuated glazing as a function of glass pane thickness. It was
predicted that for an evacuated glazing with dimension of less than 1m by 1m, reducing glass pane
thickness gave improved thermal performance. For evacuated glazings with dimensions larger than
1m by 1m, the opposite was predicted.
Keywords: Evacuated glazing; thermal performance; glass thickness; finite volume model.
1. Introduction
Evacuated glazing as shown in Fig. 1 comprises two contiguously sealed glass panes between
which the presence of a vacuum of less than 0.1Pa effectively eliminates gaseous conduction and
convection. Transparent low-emittance coating on one or both interior surfaces of the glass panes
reduces the radiative heat transfer to a low level. Conductive heat transfer occurs through both the
support pillars and the vacuum glazing edge seal. The successful fabrication of
an evacuated glazing with low
gas conduction was first
reported by Robinson and
Collins (1989) using a solder
glass edge seal formed at a
temperature of about 400
0C
.
The drawback of a solder
glass edge seal is that its
melting temperature is too
high to be used in conjunction
with many soft low-emittance
coatings and with tempered
glass. Subsequently Griffiths
et al (1998) have fabricated
successfully an evacuated
glazing with a metal edge seal
with a melting point well below 200
0C
. Many of low-emittance coatings can tolerate this
temperature and the use of tempered glass is made possible.
2. Finite Volume Model Solution to Heat Transfer in an Evacuated Glazing
Low
emittance
coatings
Glass
panes
Metal
edge seal
Separating
pillars
Not to scale
Fig. 1 Cut-away schematic diagram of an evacuated glazing with a metal
edge seal.

A three dimensional finite volume heat transfer model of an evacuated glazing has been established.
The geometry of the
system modelled is
illustrated
schematically in Fig.
2. Due to symmetry
considerations, only
a quarter section of a
full evacuated
glazing was
simulated.
The evacuated
glazing modelled
consisted of two
6mm thick glass
panes with a narrow
0.12mm internal
evacuated space. The
separation of the
panes under
atmospheric pressure
was maintained by
an array of small support pillars of diameter 0.32mm spaced at up to 40mm separation on a regular
square grid. A finite volume model was used to simulate the thermal performance of this evacuated
glazing with different glass thicknesses. The temperatures of the warm indoor and cold outdoor air
were set at 21.1
0C
and -17.8
0C
respectively. The convective heat transfer coefficients from the
cold outdoor ambient and warm indoor side external glazing surfaces were set to be
0
h
=
30
Wm K
 2 1
and
i
h
= 8.3
Wm K
 2 1
respectively to correspond to the measurement standards for
winter conditions (ASTM, 1991). The emittances of the low-emittance coatings on both interior
glass surfaces within the vacuum gap were set to be 0.2, the edge seal width was 3mm and the
height of frame insulation was 20mm.
3. Thermal Performance of an Evacuated Glazing with Different Glass Pane Thicknesses
3.1 Finite volume model
analysis
The thickness of the glass
panes is a determinant of
pillar separation for an
evacuated glazing system
(Simko, 1996). In
simulations, the glass sheet
thickness was varied but the
pillar separation was
maintained at a constant
distance. Tensile stress
within the glazing was not
considered. The predicted
thermal performance
variations with changing
Glass
panes
Illustrative
support
pillars
Vacuum
space
0.12
Outdoor
condition
Indoor
condition
Toutdoor
ho
Tindoor
hi
Not to scale
Metal edge
seal
Frame
Length unit: mm
250
250
Low emittance
coatings
Edge
seal
Fig. 2 A quarter section of a 500mm by 500mm evacuated glazing was modelled using the
finite volume model: (a) full view, and (b) cross sectional view (on a different scale). Two
glass panes joined at their edges by a metal edge seal are separated by an array of support
pillars, 0.12mm high with a diameter of 0.32mm spaced at 40mm. The emittances of the
interior vacuum surfaces were 0.2.
15
15.5
16
16.5
17
17.5
18
3 4 5 6
Thickness of glass panes (mm)
Temperature (°C)
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
C,U-value (WK
-1m-2 )
Centre glass C-value
Total system C-value
Total system U-value
Internal average
surface temperature
Fig. 3 Thermal performance variation due to changing thickness of glass
sheets. The emittances of coatings on the both interior vacuum gap surfaces
were 0.2. The dimensions of the evacuated glazing were 500mm by 500mm
with pillars of 0.32mm diameter separated at 40mm. The vacuum space was
0.12mm wide and the frame insulation height was 20mm.

thickness of glass sheet are shown in Fig. 3.
It can be seen from Fig. 3 that the U-value of the evacuated glazing increases with increasing
thickness of glass panes when using a constant pillar separation. The average internal glass surface
temperature decreases and the heat transfer rate through the full glazing system increases.
3.2 Analytic model analysis
The heat flow per unit length of edge due to edge conduction is given by (Simko, 1996):
021
0//
)(
hkthktww
TTkt
Q
i
i
edge 


(1)
The heat transfer resistance and U-value through one pillar is given by (Wilson et al., 1998):
Ah
ak
AhAk t
Ah
Rg
radgi
airtoair 0
1
11
2)
12
(
1











(2)
)/(1
,ARU airtoairpillarone 

(3)
The rate of heat transfer per unit
length of edge calculated by
equation (1) corresponding to
different glass sheet thickness t is
presented in Fig. 4. The heat
transfer rate through a single pillar
calculated using equations (2) and
(3) is also shown in Fig. 4. The heat
transfer rate through the glazing
system and the U-value of the
glazing system calculated by the
finite volume model is included.
It can be seen from Fig. 4 that with
increasing glass sheet thickness, the
air to air U-value through a single
pillar decreases, this is because the
increased glass thickness increases
the thermal resistance above the
two pillar ends. The heat transfer
per unit length of the edge due to
edge conduction increases with
increasing glass sheet thickness.
This rate of increase is larger than
the rate of decrease of heat transfer through the pillar array, which leads to the heat transfer rate
through the whole glazing increasing, thus the U-value of the whole glazing system increases. A
schematic diagram for heat transfer in an evacuated glazing is shown in Fig. 5.
1
1.2
1.4
1.6
1.8
2
2.2
2.4
3 4 5 6
Thickness of glass sheets (mm)
Heat transfer (W)
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
U-valu e (W K
-1m-2 )
Heat trans fer through total
glazing s ystem
Heat trans fer per
unit length of edge
U-value of total
glazing s ystem
U-value through
one pillar
Fig. 4. The effect of glass sheet thickness on the thermal performance
of an evacuated glazing calculated by both an analytic and a finite
volume model. In the 500mm by 500mm evacuated glazing modelled,
two glass panes with low-e coatings with emittance of 0.2 were sealed
by a 3mm wide metal edge seal, and supported by a pillar array with
diameter of 0.32mm separated at 40mm. The height of the frame
insulation was 20mm.

It can be concluded that if the pillar separation is kept constant for the evacuated glazing system
modelled, the thicker the glass sheet, the larger the resultant U-value of the glazing system.
Consideration of the tensile stress for thinner glass sheets would indicate the pillar separation
should decrease. 4. Predicted Surface
Temperature of Evacuated
Glazing
The predicted isotherms on the
outdoor ambient surfaces of
0.5m by 0.5m evacuated glazing
with 6mm and 4mm thick glass
panes were calculated by the
finite volume model and shown
in Fig.6 (a) and (b). The
isotherms on the zoomed
corners are shown in Fig.7 (a)
and (b) respectively. The
evacuated space was sealed by
3mm wide metal edge seal and
supported by a pillar array with
diameter of 0.32mm separated
at 40mm. The emittances of
low-e coating on both interior
glass surfaces were 0.2. No
frame insulation was used.
Comparing Fig.6 (a) and Fig.6 (b), it can be seen that the centre-of-glass area with average
temperature –16.5C in Fg.6 (a) is less than that in Fig.6 (b). For the outdoor side, the average
ambient surface temperature of evacuated glazing with 6mm glass panes is higher than that of
evacuated glazing with 4mm glass panes. Similarly indoor side average surface temperature of the
evacuated glazing with 6mm glass panes is lower than that with 4mm glass panes. The heat transfer
due to edge conduction through the evacuated glazing with 4mm glass panes is less that that
through the evacuated glazing with 6mm glass panes.
This result is identical with the analytic analysis by Simko, 1996. The analytic model presented that
the temperature of each glass pane approaches the centre-of-glass value exponentially with a
characteristic distance of:
hktl/
(4)
Where h is the heat transfer coefficient being considered (i.e.
i
hh ,
0
). In the evacuated glazing
modelled under ASTM winter condition, k =1
Wm K
 1 1
, for glazing with
1
t
of 6mm, for the external
side,
o
l1
= 14.1mm; for the internal side,
i
l1
= 26.9mm. For glazing with a thickness
2
t
of 4mm, for
the cold side,
o
l2
= 11.5mm; for the warm side,
i
l2
= 22.0mm. The areas in Fig.6 (a) from the glass
edge to the centre-of-glass with a characteristic distance
o
l1
are larger than those in Fig.6 (b) with
distance
o
l2
. The average surface temperature of the full glazing in Fig.6 (a) is therefore greater
than that in Fig.6 (b). Similarly the average temperature of the indoor side surface of evacuated
glazing with 4mm thick glass panes is higher than that with 6mm thick glass panes. The heat
0.12mm
Frame insulation
w
Conductive heat transfer
through pillars
Cold air Warm air
o
h
i
h
500mm Radiative heat transfer
between surfaces
Conductive heat transfer
per unit length of edge
Metal edge
Fig. 5. Schematic diagram of heat transfer in an evacuated glazing

transfer due to edge conduction effect through an evacuated glazing with 4mm thick glass panes is
less than that for an evacuated glazing with 6mm glass panes.
It can be seen from Fig.6 and Fig.7 that the surface temperatures above the first row of pillars are
higher than that of the central pillars. This is because heat transfer through the edge seal increases
the temperature of edge area on the external glass surface. In Fig.7 (a) the temperatures above the
second row of pillars are affected clearly by the heat conduction through the edge seal, as
conduction in this evacuated glazing fabricated from 6mm thick glass panes is larger than that in the
evacuated glazing fabricated with 4mm glass panes. Comparing Fig. 7 (a) and (b), it can be seen
that the heat transfer through the pillars in an evacuated glazing with 4mm thick glass panes is
larger than that with 6mm thick glass panes. This is identical with the analytic results discussed in
the above sections.
5. Effect of Frame Insulation Height on the Variation of the Thermal Performance of an
Evacuated Glazing with Different Thickness of Glass Panes
Frame insulation reduces
heat transfer through the
edge seal and so affects the
heat transfer coefficient of
an evacuated glazing system
fabricated with different
thickness glass panes. The
heat transfer within an
evacuated glazing system
with different edge
insulation heights was
simulated with the finite
volume model, and the
predicted heat transfer
coefficients are presented in
Fig. 8.
From Fig. 8 it can be seen
that the gradients of the
curves decrease with
increasing insulation height,
the gradient variation is now very small. For the glazing system of 500mm by 500mm, when no
insulation present, the heat transfer coefficient increases about 0.30
12  KWm
when the glass pane
thickness increases from 3mm to 6mm. When the insulation is 48mm, the heat transfer coefficient
increases by 0.13
12  KWm
when the glass pane thickness increases from 3mm to 6mm. The
difference in heat transfer coefficient variations between evacuated glazing systems with 48mm and
without any frame insulation is 0.17
12  KWm
. Increasing frame insulation height influences the
rate of increase of heat transfer coefficient with increasing glass sheet thickness in an evacuated
glazing unit is small. This is because the heat flow per unit length of edge due to edge conduction
mainly depends on the heat conduction within the glass sheets, although the U-value of the overall
system decreases significantly with increasing frame insulation height. This can be seen from
equation (1).
6. Variations in the Thermal Performance of an Evacuated Glazing with Different Thickness
of Glass Pane due to Different Edge Seal Widths
0.5
1
1.5
2
3 4 5 6
Thick ness of glass pane (m m)
He at tran sfer coefficien t of gla zing (WK
-1m-2 )
No insulation
Insulation
height=6mm
Insulation
height=14mm
Insulation
height=20mm
Insulation
height=48mm
Fig. 8. The variations of heat transfer coefficient of an evacuated glazing with
different thickness glass panes and frame insulation heights. The glazing size
simulated was 500mm by 500mm. The two glass panes coated with low-e
coatings on the both interior glass surfaces were sealed by a 3mm wide metal
edge seal and were supported by an array of pillars with a diameter of 0.32mm
and a separation of 40mm.

The effect of the edge seal width on the thermal performance of an evacuated glazing with different
thickness glass panes was simulated using the finite volume model. The predicted results are
presented in Fig. 9.
It can be seen that decreasing the
edge seal width has less effect on
the rate of increase of the heat
transfer coefficient with increasing
thickness of glass pane. For the
evacuated glazing with edge seal
width of 2mm, with increasing glass
pane thickness from 3mm to 6mm,
the heat transfer coefficient
increases 0.28
12  KWm
. For
evacuated glazing with edge seal
width of 12mm, the heat transfer
coefficient increases 0.36
12  KWm
.
The edge seal width affects the rate
of increasing of heat transfer
coefficient with increasing glass
pane thickness, this effect is very
small. This is because the heat flow
per unit edge mainly depends on the heat conduction within the glass sheets, which is determined
mainly by the thickness of glass sheets and edge insulation height of evacuated glazing.
7. Effect of Glazing Size on the Thermal Performance of an Evacuated Glazing with Different
Thickness of Glass Pane
The ratio of the heat transfer through
the edge seal to the heat transfer
through the whole evacuated glazing
is different for evacuated glazings of
different dimensions. When the edge
seal width and the frame insulation
height are constant, the larger the
glazing dimensions, the smaller the
ratio of the heat transfer through the
edge seal to the heat transfer through
the centre region and thus the whole
evacuated glazing. Evacuated
glazings with dimensions of 0.3m by
0.3m, 0.5m by 0.5m, 1m by 1m, 1.5m
by 1.5m and 2m by 2m were
simulated using the finite volume
model. The results are presented in
Fig. 10.
It can be seen from Fig. 10 that the rate of increase of heat transfer coefficient with increasing glass
pane thickness decreases when the dimension of the evacuated glazing increases. When the glazing
size is 2m by 2m, the variation of heat transfer coefficient is minimal. It can be concluded that if the
dimension is less than 2m by 2m, the thinner the glass panes, the smaller the heat transfer
1
1.2
1.4
1.6
1.8
2
3 4 5 6
Thick ness of glass pane (m m)
He at tra nsfer c oeffi cien t of g lazin g (WK
-1m-2 )
Edge se al: 2mm
Edge se al: 4mm
Edge se al: 3mm
Edge se al: 6mm
Edge se al: 12mm
Fig. 9. Predicted heat transfer coefficient of an evacuated glazing as a
function of the thickness of glass panes and edge seal width. The
simulated glazing size was 500mm by 500mm and comprised two
glass panes with low-e coatings of emittance 0.2 on both interior
surfaces of the glass with an array of 0.32mm diameter pillars
separated at 40mm. The frame insulation height was 6mm.
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
3 4 5 6
Thick ness of glas s pane (mm )
Heat tran sfer co ef fici ent of gl azi ng (Wm
-2K-1)
Glazin g size : 0.3m
by 0.3m
Glazin g size : 0.5m
by 0.5m
Glazin g size : 1m by
1m
Glazin g size : 1.5m
by 1.5m
Glazin g size : 2m by
2m
Fig. 10. The effect of different glass thickness on the thermal
performance of evacuated glazings with various dimensions. The
array of pillars with 0.32mm diameter and 40mm separation
supported the glass sheets with low-e coatings with 0.2 emittance.
The edge seal width was 3mm. The frame insulation height was
6mm.

coefficient will be; if the glazing size is greater than 2m by 2m, the thicker the glass pane, the
smaller the heat transfer coefficient will be. In this section when the glass thickness changes, the
pillar separation and pillar radius are kept constant, i.e. the stress is not considered.
8. Optimal Glass Thickness for an Evacuated Glazing
In practical evacuated glazing design, the stress within the glazing must be considered. The pillar
separation, pillar radius and glass thickness should be determined from the following four
restrictions (Collins and Simko, 1998):
 that conical indentation fractures do not occur;
 compressive stresses in pillars are less than a set given value, which is determined by the pillar
material; for pillars of stainless steel material this value is 1.3GPa;
 maximum external tensile stress above pillars is less than 4MPa;
 thermal conductance of the pillar array is less than a given value. The minimal value of
conductance can be determined by equation (5) (Collins and Robinson, 1991) with the greatest
pillar separation and smallest pillar radius that satisfies the three stress related design criteria
above.
C k a p
pillar array glass,/22
(5)
The design process for pillar
separation, pillar radius and minimal
conductance of pillar array is
illustrated in Fig. 11.
Evacuated glazings with different
dimensions of 0.3m by 0.3m, 0.5m by
0.5m and 1m by 1m were simulated.
Using the four restrictions (Collins
and Simko, 1998) (i.e. the stress in
the evacuated glazing being
considered), for 3mm, 4mm, 5mm
and 6mm thick glass panes, the values
of pillar separation, pillar radius and
minimal conductance of pillar array
were determined and are listed in
Table 1. By the finite volume model,
the thermal performances of these
glazing systems were analysed and
the results are illustrated in Fig. 12.
It can be seen that for the three
systems selected, the 3mm thick glass pane is the optimal thickness for the 0.3m by 0.3m and 0.5m
by 0.5m systems. For systems of these dimensions, increasing the glass thickness leads to the heat
transfer coefficient of the evacuated glazing system increasing. When the evacuated glazing size is
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2.5
3 4 5 6
Glass thickness (m m)
Heat tra nsfer coeffi cient (Wm
-2K-1)
0.3m by 0.3m pane
0.5m by 0.5m pane
1m by 1m pane
Fig. 12 The predicted thermal performance of an evacuated glazing
with the values of pillar separation and pillar radius specified in
Table 1. For all of the systems in this diagram, the emittances of
low-e glass coatings on both interior surfaces were 0.16, the frame
insulation width is 6mm and the edge seal width was 12mm.
Glass pane thickness
(mm)
Pillar radius
(mm)
Pillar separation
(mm)
Minimal conductance of pillar
array (
Wm K
 2 1
)
3
0.10
20
0.50
4
0.13
25
0.40
5
0.15
30
0.34
6
0.16
35
0.30
Table 1. Pillar radius, pillar separation and minimal conductance of pillar array commensurate to different glass pane
thickness. The above values were determined using the four restrictions specified by Collins and Simko, 1998.

1m by 1m or greater, increasing glass thickness leads to a decrease in the heat transfer coefficient.
The ratio of the heat transfer through the edge seal to the heat transfer through the whole glazing
system determines the optimal glass thickness for each glazing size. The optimal glass thickness of
those systems simulated with dimension equal to or larger than 1m by 1m is 6mm.
Comparing Fig. 10 and Fig. 12, it can be seen that after considering the stress, i.e. when glass pane
thickness changes, the pillar separation and radius change according to the four design restrictions,
the critical dimension of evacuated glazing reduces from 2m by 2m to 1m by 1m. When dimension
of evacuated glazing is less than this critical dimension, with increasing the glass pane thickness,
the U-value of an evacuated glazing increases; when the dimensions of an evacuated glazing is
larger than this critical value, with increasing glass pane thickness, the U-value of an evacuated
glazing decreases.
9. Conclusions
In general, for a standard glazing system, the thicker the glass sheets are, the smaller the U-value of
the system will be, i.e. the thermal performance of the glazing will be better. For evacuated glazing
with dimensions of less than about 1m by 1m, the opposite effect was observed if the pillar size and
pillar separation were designed according to the four restrictions detailed by Collins and Simko,
1998. Increasing the glass sheet thickness leads to a decrease in the heat transfer through a single
pillar, this is due to the thermal resistance of the glass sheet above the two pillar ends increasing.
However increasing the glass sheet thickness leads to an increase in the heat transfer per unit length
of the edge due to edge conduction. The rate of this increase is larger than the rate of decrease of
heat transfer through the pillar array. This leads to an increase in the total heat transfer and thus U-
value through the whole glazing system.
When the glazing dimension equals to or is greater than 1m by 1m, the ratio of the heat transfer
through the edge seal to the heat transfer through the overall glazing reduces. The rate of increase in
the heat transfer per unit length of edge is less than the rate of decrease in heat transfer through the
glass central area with increasing glass pane thickness. If the evacuated glazing size equals to or is
greater than 1m by 1m, the thicker the glass pane, the better the thermal performance of the
evacuated glazing will be.
An optimal glass thickness exists for evacuated glazing systems of a given size. For the simulation
undertaken it was found that if the glazing dimension is less than 1m by 1m, the thinner the glass
thickness, the better the thermal performance will be. If the glazing size equals to or is greater than
1m by 1m, the thicker the glass sheets, the better the thermal performance will be. Increasing the
frame insulation height or decreasing the edge seal width decreases the magnitude of the variation
of heat transfer coefficient resulting from changing thickness of glass panes. This is due to the heat
flow resulting from edge seal conduction decreasing.
Nomenclature
Symbol Definition Unit
a
Pillar radius, m
A Area of model, or of unit cell, over which heat transfer
process occurs,
m2
h Heat transfer coefficient at the external surface of
the glass sheets,
Wm K
 2 1
U Thermal transfer coefficient,
Wm K
 2 1

k Thermal conductivity,
Wm K
 1 1
Q Heat flow, W
R Thermal resistance, KW
1
t Thickness of glass sheet, m
T Temperature, K
w Height of frame insulation, m
C Thermal conductance,
Wm K
 2 1
p Pillar separation, m
l Characteristic distance from the glass edge to the central m
glass area whose temperature is approximately uniform.
Subscripts
i,o Refer to internal and external glass surfaces
References
ASTM (1991) Standard procedures for determining the steady state thermal
transmittance of fenestration systems, ASTM Standard E 1423-91. In 1994
Annual Book of ASTM Standard 04.07. American Society of Testing and
Materials, pp.1160-1165.
Collins R.E. and Simko T.M. (1998) Current status of the science and technology of
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Collins R.E. and Robinson S.J. (1991) Evacuated glazing. Solar Energy 47, 27-38.
Griffiths P.W., Norton B., Eames P.C., and Lo S.N.G. (1996) Detailed Simulation of
Heat Transfer Across Evacuated Glazing, Building Research Information 24,
141-147.
Griffiths P.W., Leo M.Di, Cartwright P., Eames P.C. , Yianoulis P., Leftheriotis G
and Norton B. (1998) Fabrication of Evacuated Glazing at Low Temperature,
Solar Energy 63, 243-249.
Robinson S.J. and Collins R.E. (1989) Evacuated window  theory and practice. In
ISES Solar World Congress, Internal Solar Energy Society, Kobe, Japan.
Simko T.M., (1996) Heat transfer process and stresses in vacuum glazing. Ph.D.
thesis, University of Sydney.
Wilson C.F., Simko T.M., and Collins R.E., (1998) Heat Conduction Through The
Support Pillars in Vacuum Glazing, Solar Energy 63, 393-406.

y (m)
z (m)
0.05 0.1 0.15 0.2 0.25
0.05
0.1
0.15
0.2 temperature
-8.0
-8.5
-9.0
-9.5
-10.0
-10.5
-11.0
-11.5
-12.0
-12.5
-13.0
-13.5
-14.0
-14.5
-15.0
-15.5
-16.0
-16.5
oC
( a )
y (m)
z (m)
0.05 0.1 0.15 0.2 0.25
0.05
0.1
0.15
0.2 temperature
-8.0
-8.5
-9.0
-9.5
-10.0
-10.5
-11.0
-11.5
-12.0
-12.5
-13.0
-13.5
-14.0
-14.5
-15.0
-15.5
-16.0
-16.5
oC
( b )
Fig. 6 The predicted isotherms on the glass surface of a 0.5m by 0.5m evacuated glazing fabricated
from 6mm (a) and 4mm (b) thick glass panes with low-e coatings of 0.2 emittance on the two
interior surfaces. The evacuated space was sealed by 3mm wide metal edge seal and supported by a
pillar array with a diameter of 0.32mm separated at 40mm.

y (m)
z (m)
0.05 0.1 0.15 0.2
0.05
0.1
0.15 temperature
-16.0
-16.1
-16.1
-16.2
-16.3
-16.4
-16.4
-16.5
-16.6
-16.6
-16.7
-16.8
-16.9
-16.9
-17.0
oC
(a)
y (m)
z (m)
0.05 0.1 0.15 0.2
0.05
0.1
0.15
temperature
-16.0
-16.1
-16.1
-16.2
-16.3
-16.4
-16.4
-16.5
-16.6
-16.6
-16.7
-16.8
-16.9
-16.9
-17.0
oC
(b)
Fig. 7 The predicted isotherms on the enlarged corner region of the 0.5m by 0.5m evacuated glazing
with 6mm (a) and 4mm (b) thick glass panes. Other parameters are the same as those in Fig.6.

( a ) ( b )
( c ) ( b )
Fig. 11 The design process for the pillar array in evacuated glazing according to the four restrictions
discussed in the section 11. The diagram (a) for evacuated glazing with 3mm glass panes, (b) with
4mm glass panes, (c) with 5mm glass panes and (d) with 6mm glass panes.
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Pillar radius (mm)
Pillar separation (mm)
3mm glass
Compressive stress
in pillars < 1.3GPa
Max external
tensile stress
above
pillars<4MPa
Conductance of pillar
array<0.5Wm-2K-1
Conical
indentation
fractures
do not
occur
Design
point
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Pillar radius (mm)
Pillar separation (mm)
Conical
indentation
fractures do
not occur
Compressive
stress in
pillars<1.3GPa
Max.external
tensile stress
above
pillars<4MPa
Conductance of pillar
array<0.4Wm-2K-1
Design
point
4mm glass
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Pillar radius (m m)
Pillar separation (mm)
Max.external tensile
stress above
pillars<4MPa
Compressive stress
in pillar<1.3GPa
Conical
indentation
fractures do
not occur
Conductance of pillar
array<0.34Wm-2K-1
Design
point
5mm glass
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Pillar radius (mm)
Pillar separation (mm)
Max.external
tensile stress
above pillars<4MPa
Compressive
stress in
pillar<1.3GPa
Conductance of pillar
array<0.3Wm-2K-1
Conical
indentation
fractures do
not occur
6mm glass
Design
point