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.
Separating pillars
The successful fabrication of an evacuated glazing with low gas conduction was first reported by Robinson and
Low emittance coatings
Collins (1989) using a solder glass edge seal formed at a
Glass panes temperature of about 400
0
C .
The drawback of a solder
Metal edge seal glass edge seal is that its melting temperature is too high to be used in conjunction
Not to scale with many soft low-emittance coatings and with tempered
Fig. 1 Cut-away schematic diagram of an evacuated glazing with a metal edge seal. glass. Subsequently Griffiths et al (1998) have fabricated successfully an evacuated glazing with a metal edge seal with a melting point well below 200
0 C . 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

A three dimensional finite volume heat transfer model of an evacuated glazing has been established.
The geometry of the system modelled is illustrated
Glass
Length unit: mm panes
Outdoor condition
Indoor condition schematically in Fig.
2. Due to symmetry
Illustrative support pillars
250 T outdoor h o
T indoor h i considerations, only a quarter section of a full evacuated glazing simulated.
was
Low emittance
Vacuum coatings space
Metal edge Frame
250
Edge seal seal
0.12
Not to scale
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.
The glazing consisted
6mm thick glass panes with a narrow
0.12mm internal evacuated space. The separation panes evacuated modelled of of two the 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
0
C and -17.8
0
C respectively. The convective heat transfer coefficients from the cold outdoor ambient and warm indoor side external glazing surfaces were set to be
30

2
Wm K

1 and h =
0 h i
= 8.3

2
Wm K

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
18
17.5
17
16.5
Centre glass C-value
Internal average surf ace temperature
Total system C-value
1.4
1.3
1.2
1.1
1
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
16
15.5
15
3 4
Total system U-value
5 6
0.9
0.8
0.7
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
Thickness of glass panes (mm)
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):
Q edge
 w
1
 w
2 kt ( T i
 kt

/
T h i
0
)
 kt / h
0
(1)
The heat transfer resistance and U-value through one pillar is given by (Wilson et al., 1998):
R air
 to
 air
 h i
1
A
 



(
2 k g t
A

1 h rad
A
)

1 
2 k g a




1
 h
0
1
A
(2)
U one , pillar

1 /( R air
 to
 air
A ) (3)
2.4
2.2
2
1.8
1.6
1.4
1.2
1
3
Heat transf er through total glazing system
4
Heat transf er per unit length of edge
U-value of total glazing system
U-value through one pillar
5
Thickness of glass sheets (mm)
6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
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
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 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.

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.
0.12mm
Frame insulation
4. Predicted Surface
Temperature of Evacuated
Glazing
w
Conductive heat transfer
The predicted isotherms on the outdoor ambient surfaces of
through pillars
0.5m by 0.5m evacuated glazing with 6mm and 4mm thick glass panes were calculated by the
Cold air Warm air finite volume model and shown h o h i in Fig.6 (a) and (b). The isotherms on the zoomed
500mm Radiative heat transfer corners are shown in Fig.7 (a) and (b) respectively. The evacuated space was sealed by
Conductive heat transfer
3mm wide metal edge seal and
per unit length of edge supported by a pillar array with diameter of 0.32mm separated
Metal edge at 40mm. The emittances of low-e coating on both interior
Fig. 5.
Schematic diagram of heat transfer in an evacuated glazing 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: l
 kt / h (4)
Where h is the heat transfer coefficient being considered (i.e. h
0
, h i
). In the evacuated glazing modelled under ASTM winter condition, k = 1

1
Wm K

1
, for glazing with t
1 of 6mm, for the external side, l
1 o
= 14.1mm; for the internal side, l
1 i
= 26.9mm. For glazing with a thickness t of 4mm, for
2 the cold side, l
2 o
= 11.5mm; for the warm side, l
2 i
= 22.0mm. The areas in Fig.6 (a) from the glass edge to the centre-of-glass with a characteristic distance l
1 o
are larger than those in Fig.6 (b) with distance l
2 o
. 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

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
2 Frame insulation reduces
1.5
No insulation heat transfer through the edge seal and so affects the heat transfer coefficient of an evacuated glazing system
1
Insulation height=6mm
Insulation height=14mm
Insulation height=20mm
Insulation height=48mm fabricated with different thickness glass panes. The heat transfer within an evacuated glazing system with different edge insulation heights was simulated with the finite
0.5
3 4 5 6 volume model, and the predicted heat transfer
Thickness of glass pane (m m )
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. 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 Wm

2
K

1
when the glass pane thickness increases from 3mm to 6mm. When the insulation is 48mm, the heat transfer coefficient increases by 0.13
Wm

2 K

1 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
Wm

2
K

1
. 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

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.
2
1.8
It can be seen that decreasing the edge seal width has less effect on the rate of increase of the heat
1.6
1.4
1.2
Edge seal: 2mm
Edge seal: 4mm
Edge seal: 3mm
Edge seal: 6mm
Edge seal: 12mm 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
Wm

2
K

1
. For
1
3 4 5 6
Thickness of glass pane (m m )
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. evacuated glazing with edge seal width of 12mm, the heat transfer coefficient increases 0.36
Wm

2
K

1
.
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
2.6
2.4
2.2
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
2
1.8
1.6
1.4
Glaz ing s iz e: 0.3m
by 0.3m
Glaz ing s iz e: 0.5m
by 0.5m
Glaz ing s iz e: 1m by
1m
Glaz ing s iz e: 1.5m
by 1.5m
different dimensions. When the edge seal width and the frame insulation height are constant, the larger the glazing dimensions, the smaller the
1.2
1
0.8
0.6
3 4 5
Thickness of glass pane (m m )
6
Glaz ing s iz e: 2m by
2m 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
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. 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

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

2 k glass
/
2
(5)
2.5
2.3
2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
0.5
3 4
0.3m by 0.3m pane
0.5m by 0.5m pane
1m by 1m pane
5 6
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,
Gla s s thic k ne s s (m m )
Fig. 12 The predicted thermal performance of an evacuated glazing with the values of pillar separation and pillar radius specified in the thermal performances of these glazing systems were analysed and
Table 1. For all of the systems in this diagram, the emittances of the results are illustrated in Fig. 12. low-e glass coatings on both interior surfaces were 0.16, the frame insulation width is 6mm and the edge seal width was 12mm.
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
Glass pane thickness
(mm)
3
4
5
6
(mm)
0.10
0.13
0.15
0.16
(mm)
20
25
30
35
Minimal conductance of pillar array (

2
Wm K

1
)
0.50
0.40
0.34
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 Uvalue 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 a
A
Pillar radius,
Area of model, or of unit cell, over which heat transfer
Unit m h process occurs,
Heat transfer coefficient at the external surface of m
2
U the glass sheets,
Thermal transfer coefficient,

2
Wm K

2
Wm K

1

1

k
Q
R t
T w
Thermal conductivity,
Heat flow,
Thickness of glass sheet,
Temperature,
Thermal resistance,
Height of frame insulation,
C p l
Subscripts i,o Refer to internal and external glass surfaces

1
Wm K

1
W
KW

1 m
K m

1 Thermal conductance,
Pillar separation, m
Characteristic distance from the glass edge to the central m glass area whose temperature is approximately uniform.
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
vacuum glazing. Solar Energy 62 , 189-213.
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.

0.2
0.15
0.1
0.05
0.05
0.1
y (m)
0.15
( a )
0.2
0.25
temperature
-8.0
o
C
-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
0.2
0.15
0.1
0.05
temperature
-8.0
o
C
-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
0.05
0.1
0.15
y (m)
0.2
0.25
( 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.

0.15
0.1
0.05
temperature
-16.0
o
C
-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
0.05
0.1
y (m)
(a)
0.15
0.2
0.15
0.1
0.05
temperature
-16.0
-16.1
o
C
-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
0.05
0.1
y (m)
0.15
0.2
(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.

70 70
4mm glass
3mm glass
60 60
50
Conductance of pillar array<0.5Wm
-2
K
-1
40
Conical indentation fractures do not occur
50
40
Conductance of pillar array<0.4Wm
-2
K
-1
Conical indentation fractures do not occur
30 30
20
10
Design point
Compressive stress in pillars < 1.3GPa
Max external tensile stress above pillars<4MPa
0
0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pillar radius (m m )
20
10
Design point
Compressive stress in pillars<1.3GPa
Max.external tensile stress above pillars<4MPa
0
0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pillar radius (mm)
( a ) ( b )
70 70
6mm glass
60
5mm glass
60
50
40
Conductance of pillar array<0.34Wm
-2
K
-1
Conical indentation fractures do not occur
50
Conductance of pillar array<0.3Wm
-2
K
-1
40
Conical indentation fractures do not occur
30
30
20 Design point
Max.external tensile stress above pillars<4MPa
10
Compressive stress in pillar<1.3GPa
0
0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pillar radius (m m )
20
10
Design point
Max.external tensile stress above pillars<4MPa
Compressive stress in pillar<1.3GPa
0
0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pillar radius (m m )
( 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.