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Multi-criteria heatwave vulnerability assessment of residential wall systems

Authors:
  • CAS/Monash University / Swinburne University of Technology

Abstract and Figures

It is generally accepted that building external wall design affects its ability to protect occupants from weather extremes, such as heatwaves. However, there is no established methodology to assess this ability in assisting building designers to identify the most resilient design. This study aims at developing an analytical tool to examine wall heatwave vulnerability using dynamic thermal modelling and multi-criteria analysis. Optimum wall design for Melbourne was identified among eight selected residential walls based on various criteria, i.e. maximum air temperature (MAT), maximum air temperature difference (MATD), thermal discomfort proportion (TDP), statistical maximum air temperature (SMAT), and averaged night-time temperature (ANT). Using these criteria wall designs were ranked and ranking deviations among the criteria were analysed. Results showed that uninsulated brick veneer wall is the most vulnerable design, experiencing a maximum daytime room temperature of 31 °C and proportion in discomfort of 31.5% during heatwaves. While insulated cavity brick wall is found to be the most resilient design in most cases. The results indicate that using insulated cavity brick wall in Melbourne would significantly reduce summer overheating and thermal discomfort in non-air conditioned buildings in daytime period. It was found that no one criterion should be used for evaluating both daytime and night-time wall performance as ranking would be different between daytime and night-time periods. The decision procedure for design of a residential wall system may need to be reconsidered using the multi-criteria analysis, particularly under global warming.
Content may be subject to copyright.
Energy
and
Buildings
66
(2013)
373–383
Contents
lists
available
at
ScienceDirect
Energy
and
Buildings
j
ourna
l
ho
me
page:
www.elsevier.com/locate/enbuild
Multi-criteria
heatwave
vulnerability
assessment
of
residential
wall
systems
Jun
Han,
Dong
Chen,
Xiaoming
Wang
CSIRO
Climate
Adaptation
Flagship
and
CSIRO
Ecosystem
Sciences,
Commonwealth
Scientific
and
Industrial
Research
Organisation
(CSIRO),
Highett,
Victoria
3190,
Australia
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
17
March
2013
Received
in
revised
form
3
June
2013
Accepted
7
July
2013
Keywords:
Heatwave
Adaptation
Thermal
performance
Overheating
Cooling
load
Dynamic
building
simulation
model
Finite
difference
approach
a
b
s
t
r
a
c
t
It
is
generally
accepted
that
building
external
wall
design
affects
its
ability
to
protect
occupants
from
weather
extremes,
such
as
heatwaves.
However,
there
is
no
established
methodology
to
assess
this
abil-
ity
in
assisting
building
designers
to
identify
the
most
resilient
design.
This
study
aims
at
developing
an
analytical
tool
to
examine
wall
heatwave
vulnerability
using
dynamic
thermal
modelling
and
multi-
criteria
analysis.
Optimum
wall
design
for
Melbourne
was
identified
among
eight
selected
residential
walls
based
on
various
criteria,
i.e.
maximum
air
temperature
(MAT),
maximum
air
temperature
differ-
ence
(MATD),
thermal
discomfort
proportion
(TDP),
statistical
maximum
air
temperature
(SMAT),
and
averaged
night-time
temperature
(ANT).
Using
these
criteria
wall
designs
were
ranked
and
ranking
devi-
ations
among
the
criteria
were
analysed.
Results
showed
that
uninsulated
brick
veneer
wall
is
the
most
vulnerable
design,
experiencing
a
maximum
daytime
room
temperature
of
31 C
and
proportion
in
dis-
comfort
of
31.5%
during
heatwaves.
While
insulated
cavity
brick
wall
is
found
to
be
the
most
resilient
design
in
most
cases.
The
results
indicate
that
using
insulated
cavity
brick
wall
in
Melbourne
would
signif-
icantly
reduce
summer
overheating
and
thermal
discomfort
in
non-air
conditioned
buildings
in
daytime
period.
It
was
found
that
no
one
criterion
should
be
used
for
evaluating
both
daytime
and
night-time
wall
performance
as
ranking
would
be
different
between
daytime
and
night-time
periods.
The
decision
procedure
for
design
of
a
residential
wall
system
may
need
to
be
reconsidered
using
the
multi-criteria
analysis,
particularly
under
global
warming.
©
2013
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
In
the
past
decade,
the
number
of
extreme
heatwaves
has
been
on
the
rise
globally,
for
example,
the
Shanghai
in
2003
[1],
the
Euro-
pean
in
2003
[2],
the
Greece
in
2007
[3],
the
southern
Australia
in
2009
[4],
and
the
U.S.
in
2012
[5].
According
to
World
Bank
report
2012
[6],
the
global
climate
is
warming,
and
its
average
tempera-
ture
is
anticipated
to
rise
by
4C
by
the
end
of
this
century,
without
effective
interventions.
Such
increases
in
the
future
climate
are
likely
to
lead
to
more
frequent
and
longer
heatwaves
[7,8].
An
intensifying
heatwave
event
can
have
a
significant
social
and
economic
impact
on
communities,
especially
on
public
health
[9–11].
Public
health
problems,
heat-related
illness
and
deaths
for
example,
might
increase
as
a
result
of
changing
climate
and
increasing
temperature.
Research
found
that
if
outdoor
ambient
temperature
increases
beyond
a
particular
threshold,
so
do
mor-
tality/morbidity
rates
[12].
Corresponding
author.
Tel.:
+61
3
92526462;
fax:
+61
3
92526249.
E-mail
addresses:
bejunhan@gmail.com,
jun.han@csiro.au
(J.
Han).
As
the
main
shelter
of
human
beings,
buildings
play
a
vital
role
in
protecting
occupants
from
extreme
environment
and
should
be
designed
to
cope
with
the
warming
climate
and
likely
heat-
wave
impacts.
In
this
regard,
we
are
now
facing
the
challenges
not
only
in
designing
low
energy
buildings
to
reduce
greenhouse
gas
emissions
for
mitigating
global
warming,
but
also
in
maintain-
ing
required
thermal
comfort
under
changing
climate,
in
particular,
during
extreme
climate
event.
Current
building
codes,
such
as
the
Australian
National
Construction
Code
[13],
set
the
criteria
for
reg-
ulating
the
energy
efficiency
of
residential
buildings.
However,
they
consider
little
about
the
ability
of
current
wall
structures
to
buffer
against
extreme
weather
events
and
corresponding
thermal
stress
to
which
occupants
are
exposed.
Consequently,
in
recent
years,
there
is
a
growing
interest
in
investigating
the
impact
of
climate
change,
possible
adaptation
and
mitigation
measures
to
reduce
overheating
risks.
Various
mitiga-
tion
strategies
were
proposed
and
assessed,
such
as
use
of
controls
for
blinds
to
reduce
solar
heat
gain
[14],
natural
ventilation
[15–17],
better
construction
material
[18]
and
energy
efficient
building
envelope
[19],
upgrading
office
IT
equipment
and
light
[20],
double
glazing
[21].
The
selection
of
building
construction
materials
is
one
of
the
most
important
factors
in
designing
a
low
energy
and
better
0378-7788/$
see
front
matter
©
2013
Elsevier
B.V.
All
rights
reserved.
http://dx.doi.org/10.1016/j.enbuild.2013.07.015
374
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
Nomenclature
A
area
(m2)
a
constant
(–)
b
constant
(–)
Bi
Biot
number
(–)
Cp
specific
heat
capacity
(J/kg
K)
Ctturbulent
natural
convection
constant
(–)
Fo
Fourier
number
(–)
GTintensity
of
solar
radiation
on
wall
(W/m2)
g
acceleration
of
gravity
(m/s2)
H
height
of
the
air
gap
(m)
h
convective
heat
transfer
coefficient
(W/m2K)
¯
h
average
heat
transfer
coefficient
(W/m2K)
k
thermal
conductivity
(W/m
K)
L
width
of
the
air
gap
(m)
NuLaverage
Nusselt
number
(–)
n
number
of
material
or
space
surface
(–)
Pr
Prandtl
number
(–)
RaLRayleigh
number
(–)
SHGC
solar
heat
gain
coefficient
(–)
T
temperature
(C)
t
time
(s)
Uwin heat
loss
coefficient
(W/m2K)
V
volume
of
space
(m3)
V0wind
velocity
(m/s)
x
coordinate
as
defined
(–)
Greek
symbols
˛
thermal
diffusivity
(m2/s)
ˇ
volumetric
thermal
expansion
coefficient
(K1)
density
(kg/m3)
kinematic
viscosity
(m2/s)
ε
absorptivity
(–)
Subscripts
air
room
air
or
air
in
the
gap
of
wall
c
refers
to
cold
wall
D
thickness
of
solid
wall
d
thickness
of
air
cavity
e
environment
g
air
gap
h
refers
to
hot
wall
i
inner
surface
of
wall
in
inside
or
indoor
j
number
of
material
max
maximum
N
number
of
node
o
outside
r
roof
wf
wall
surface
and
fluid
in
the
air
gap
of
the
wall
win
window
w1
left
wall
surface
of
the
air
gap
in
the
cavity
wall
w2
right
wall
surface
of
the
air
gap
in
the
cavity
wall
thermal
comfort
building
in
response
to
large
diurnal
temperature
swings
[22].
Porritt
et
al.
[23]
claimed
that
external
wall
insulation
and
measures
to
reduce
solar
heat
gain
are
the
most
effective
inter-
ventions
to
reduce
overheating
as
a
result
of
heatwaves.
Internal
wall
insulation
seems
less
effective
and
could
even
increase
over-
heating
in
some
cases
[24].
In
addition,
building
form
is
another
important
factor
in
designing
a
comfort
building
to
modify
or
fil-
ter
climate
extremes.
An
integrated
design
of
building
construction
material
and
building
form
as
a
total
system
is
a
sustainable
way
to
achieve
optimum
comfort
and
energy
savings
without
heavily
depending
on
mechanical
cooling
systems.
This
passive
building
design
strategy
does
not
have
a
high
initial
cost,
while
it
provides
an
effective
solution
to
mitigate
heatwave.
In
addition
to
the
effect
of
climate
change,
the
urban
heat
island
(UHI)
phenomenon
as
another
contributing
factor
to
overheating
in
buildings
cannot
be
neglected.
Indoor
temperature
and
its
related
overheating
risk
in
urban
buildings
are
likely
to
be
exacerbated
in
the
future
as
a
result
of
the
combined
effect
of
UHI
effects
and
cli-
mate
change
[25].
According
to
Coutts
[39],
a
mean
maximum
UHI
intensity
of
3–4 C
at
2
a.m.
in
January
in
Melbourne
was
predicted
using
an
urban
canopy
model
software.
Oikonomou
et
al.
[26]
com-
pared
the
relative
importance
of
UHI
and
the
thermal
quality
of
dwellings
for
overheating
in
London.
Their
study
indicates
that
the
thermal
characteristics
of
a
dwelling
have
a
greater
effect
on
indoor
temperatures
during
the
‘hot’
period
than
the
UHI
itself.
The
effects
of
built
form
and
other
dwelling
characteristics
appear
to
be
more
important
determinants
of
indoor
thermal
performance.
The
relationship
between
thermal
comfort
and
building
design
has
been
well
recognised
and
investigated
among
building
pro-
fessionals
in
the
past.
Various
overheating
assessment
criteria
were
adopted
and
applied
based
on
different
purposes.
A
simple
approach,
such
as
static
thresholds
of
comfort,
is
sometimes
used
to
define
when
a
building
might
be
too
warm
[27].
Another
crite-
rion,
the
adaptive
comfort
criterion,
takes
consideration
of
adaptive
approach
to
thermal
comfort.
Upper
limits
for
temperatures
in
building
with
and
without
heating
and
cooling
are
suggested
in
terms
of
running
mean
of
the
outdoor
temperature
[28].
Nicol
et
al.
[29]
suggested
that
criteria
for
building
overheating
can
be
defined
as
achieving
a
specified
Potential
Discomfort
Index
(PDI)
and
also
described
an
approach
to
predict
the
magnitude
or
frequency
of
overheating
in
buildings.
Wright
et
al.
[30]
measured
the
internal
temperatures
in
four
dwellings
in
Manchester
and
five
dwellings
in
London,
of
diverse
ages,
sizes
and
constructions
during
the
August
2003
heatwaves.
Resultant
statistics
and
various
comfort
metrics
indicated
a
high
level
of
discomfort
in
most
dwellings,
particularly
in
London.
Sakka
et
al.
[31]
investigated
indoor
thermal
characteris-
tics
in
50
free-running
low
income
houses
during
the
extremely
hot
summer
of
2007
in
Athens,
Greece.
Very
high
indoor
temperatures,
up
to
40 C,
were
observed.
The
above
literature
review
indicates
that
warming
climate
due
to
climate
change
and
UHI
will
increase
the
risk
of
over-
heating.
However,
few
studies
have
been
conducted
to
assess
the
heat
vulnerability
of
residential
walls
in
order
to
identify
optimal
building
design
which
can
result
in
reduced
energy
consumption
during
extreme
heatwave
event
while
maintaining
thermal
com-
fort
requirement
at
the
same
time.
The
current
study
is
to
examine
the
vulnerability
of
selected
Australian
residential
walls
to
heat-
wave
in
Melbourne
using
dynamic
thermal
modelling.
Numerical
simulations
of
the
periodic
heat
transfer
through
various
walls
were
carried
out
first.
Then
the
dynamic
thermal
performance
of
wall
systems
and
their
resulted
room
air
temperature
were
compared
and
analysed
in
terms
of
various
assessment
criteria
in
order
to
identify
effective
wall
designs
to
accommodate
heatwaves
in
Mel-
bourne.
2.
Dynamic
thermal
modelling
2.1.
Heat
transfer
in
solid
walls
The
purpose
of
the
study
is
to
examine
the
vulnerability
of
var-
ious
residential
walls
to
heatwaves.
Eight
different
wall
structures
selected
from
Australian
residential
wall
catalogue
were
stud-
ied.
Traditional
weatherboard
wall
is
not
included
in
the
present
study,
as
it
is
now
not
commonly
used
for
new
residential
building
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
375
Table
1
Construction
details
of
residential
walls.
Number
Wall
construction
details
Wall
name
A
Brickwork
(110
mm)–air
gap
(40
mm)–polystyrene
expanded
(39
mm)–brickwork
(110
mm)–plasterboard
(10
mm)
‘CavBrInP’
B
Aerated
autoclaved
concrete
block
(200
mm)–plasterboard
(10
mm)
‘ACC100’
C
Brickwork
(110
mm)–air
gap
(40
mm)–brickwork
(110
mm)–plasterboard
(10
mm)
‘CavBrUninP’
D
Hollow
concrete
block
work
(190
mm)–polystyrene
expanded
(39
mm)–plasterboard
(10
mm)
‘CTT190InP’
E
Concrete
(100
mm)-plasterboard
(10
mm)
‘CTT100P’
F
Concrete
(150
mm)–plasterboard
(10
mm)
‘CTT150P’
G
Brickwork
(110
mm)–air
gap
(40
mm)–plasterboard
(10
mm)
‘BrVP’
H
Timber
chardwood
(40
mm)-air
gap
(40
mm)-brickwork
(110
mm)-plasterboard
(10
mm)
‘CavWoP’
Table
2
Thermal
properties
of
building
construction
materials.
Material
Density
(kg/m3)
Thermal
conductivity
(W/m
K)
Specific
heat
capacity
(J/kg
K)
Aerated
autoclaved
concrete
block
600
0.18
1000
Brickwork
1700
0.84
800
Concrete
medium
weight
1400
0.51
1000
Polyurethane
30
0.025 1400
Plasterboard
950
0.16
840
Fig.
1.
Cross
section
schematics
of
eight
different
Australian
residential
walls.
376
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
Fig.
1.
(Continued
).
construction
in
Melbourne.
The
schematics
of
the
walls
are
shown
in
Fig.
1,
and
their
thermal
properties
are
listed
in
Tables
1
and
2.
For
the
composite
wall
system
considering
various
layer
thick-
nesses
and
thermal
properties,
a
one-dimensional
transient
heat
transfer
equation
without
internal
heat
generation
was
employed.
The
outer
surface
of
the
wall
is
subjected
to
convection
heat
transfer,
solar
radiation,
and
long-wave
radiation
heat
exchanges,
while
the
inner
surface
is
exposed
to
the
indoor
space
of
a
sin-
gle
zone
detached
house
as
shown
in
Fig.
2.
The
governing
partial
Fig.
2.
Geometries
of
a
single
zone
detached
house.
differential
equation
(PDE)
of
the
conductive
heat
transfer
through
the
composite
wall
is
described
as:
∂Tj(x,
t)
∂t =kj
jcj
2Tj(x,
t)
∂x2,
j
=
1,
2,
.
.
.,
n
(1)
where
x
and
t
are
the
space
and
time
coordinates,
respectively;
Tjis
the
temperature
of
the
jth
layer, C;
j,
cj,
kjare
the
density,
kg/m3,
the
specific
heat,
J/kg
K,
and
the
thermal
conductivity
of
the
jth
layer
material,
W/m
K,
respectively;
and
n
is
the
total
number
of
material
layers
in
a
wall.
The
adjacent
layers
are
assumed
to
be
in
good
thermal
con-
tact,
and
hence
the
interface
resistance
is
negligible.
The
thermal
conduction
of
the
adjacent
layers
is
expressed
by:
Tj(x,
t)
=
Tj+1(x,
t),
j
=
1,
2,
.
.
.,
n
1
(2)
kj
∂Tj(x,
t)
∂x =
kj+1
∂Tj+1(x,
t)
∂x ,
j
=
1,
2,
.
.
.,
n
1
(3)
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
377
Table
3
MoWiTT
model
constants.
Wind
direction
Ct(W/m2K4/3)
a
(W/m2K(m/s)b)
b
(–)
Windward
0.84
2.38
0.89
Leeward
0.84
2.86
0.617
The
initial
temperature
distribution
across
the
wall
is
assumed
to
be
uniform
and
is
expressed
as
follows:
Tj(x,
0)
=
T0(4)
The
boundary
conditions
at
the
inner
surface
of
the
wall
are
given
as
follows:
k1
∂T(x,
t)
∂x
x=0
=
hi(Tin
Tx=0)(5)
where
hiis
the
convection
heat
transfer
coefficient,
W/m2K;
from
the
ASHRAE
handbook
of
fundamentals
[32]:
hi=
9.26W/m2K
for
upward
direction
of
heat
flow,
and
hi=
6.13
W/m2K
for
downward
direction
of
heat
flow,
Tin is
the
room
temperature, C.
The
boundary
conditions
at
the
outer
surface
are:
kn∂T(x,
t)
∂x
x=D
=
h0(Tx=D
Te)
(6)
Here,
Te,
the
sol–air
temperature
is
calculated
based
on
the
ambient
temperature,
solar
radiation
and
heat
transfer
coefficient
[33].
Te=
T0+εGT
h0
(7)
where
ε
is
the
solar
absorptivity
of
the
outer
surface
of
the
wall;
GTis
the
total
intensity
of
solar
radiation
incident
upon
the
outer
surface
of
the
wall,
which
is
calculated
according
to
sun
position
and
follows
the
procedure
in
author’s
previous
work
[34],
W/m2;
Tx=Dis
the
temperature
of
the
outer
surface
of
the
wall, C;
T0is
the
ambient
temperature, C.
The
convective
heat
transfer
coefficient
of
the
outer
surface,
h0,
is
dependent
on
the
outdoor
air
conditions,
such
as
air
velocity
and
its
direction,
and
the
temperature
differ-
ence
between
the
wall
outer
surface
and
the
ambient
air.
According
to
the
MoWiTT
model
[35],
the
coefficient
can
be
determined
as
follows:
h0=[Ct(T)1/3]2
+
[aVb
0]2(8)
where
Ctis
the
turbulent
natural
convection
constant;
T
is
the
temperature
difference
between
the
outer
surface
and
outside
air;
a
and
b
are
constants;
V0is
wind
speed
at
standard
conditions,
m/s.
The
values
of
the
coefficients
and
constants
for
the
MoWiTT
model
are
summarised
in
Table
3.
2.2.
Heat
transfer
in
the
air
cavity
of
the
wall
For
the
air
cavity
in
a
wall:
Vc dT
dt =
hwf Ag(Tw1
T)
+
hwf Ag(Tw2
T)
(9)
where
Tis
temperature
in
the
air
cavity, C;
is
the
density
of
the
air
in
the
cavity,
kg/m3;
V
is
air
volume
in
the
cavity,
m3;
c
is
specific
heat
capacity
of
air,
J/kg
K.
Agis
wall
surface
area;
hwf is
overall
heat
transfer
coefficient
which
will
be
further
discussed
in
Section
2.4,
Tw1andTw2are
left
and
right
side
wall
surface
temperatures,
respectively, C.
They
are
calculated
by
Eqs.
(1),
(10)
and
(11).
The
surface
energy
balances
at
the
two
surfaces
of
the
air
cavity
in
the
wall
are:
k∂T(x,
t)
∂x
x=D
=
hwf (Tw1
T)
(10)
k∂T(x,
t)
∂x
x=D+d
=
hwf (T
Tw2)
(11)
where
d
denotes
the
thickness
of
the
air
in
the
wall.
2.3.
Heat
balance
of
the
room
air
An
enclosed
single-zone
building
of
internal
volume
V
is
con-
sidered
with
various
external
wall
designs
as
shown
in
Fig.
2.
The
air
in
the
building
is
assumed
to
be
well-mixed
with
a
uniform
air
temperature.
Internal
heat
gain,
air
exchange
and
latent
heat
load
are
not
considered
for
ease
of
wall
performance
comparison.
Adia-
batic
boundary
conditions
are
applied
to
the
floor.
The
heat
balance
of
the
room
air
is
described
as:
Vc dTin
dt =
n
i=1
hwf Aw,i(Tw,i
Tin)
+
hrAr(Tr
Tin)
+
n
i=1
UwinAwin,i (Tout
Tin)
+
n
i=1
GT,iAwin,i SHGC
(12)
where
is
the
density
of
the
air
in
the
room,
kg/m3;
V
is
the
volume
of
the
room;
c
is
specific
heat
capacity
of
air
Tin is
room
air
temper-
ature, C;
hwf is
overall
heat
transfer
coefficient
between
wall
and
room
air,
W/m2K;
AW,iis
the
surface
area
of
the
ith
wall,
m2;
TW,i
is
the
surface
temperature
of
the
ith
wall, C;
hris
convective
heat
transfer
coefficient
of
the
roof,
W/m2K;
Tris
the
interior
surface
temperature
of
the
roof, C;
Uwin is
the
overall
heat
loss
coefficient
of
the
windows,
Uwin =
4.2
W/m2K,
[32];
Awin,i is
the
surface
area
of
the
ith
window,
m2;
Tout is
outdoor
ambient
temperature, C;
GT,iis
solar
radiation
striking
the
vertical
surface,
W/m2;
SHGC
is
solar
heat
gain
coefficient
of
a
double
glazed
window
assumed
at
SHGC
=
0.71
[36].
2.4.
Heat
transfer
coefficients
The
convective
heat
transfer
coefficients
in
the
air
gap
of
the
cav-
ity
wall
types,
such
as
‘wall
A,
C,
G,
H’
were
determined
through
a
set
of
existing
correlations
in
the
literature.
The
following
correlations
proposed
by
Catton
[37]
have
been
used:
NuL=
0.22Pr
0.2
+
Pr RaL0.28H
L1/4
,
for
2
<H
L<
10
Pr
<
105
RaL<
1010
(13)
NuL=
0.18Pr
0.2
+
Pr RaL0.29
,
for
1
<H
L<
2
103<
Pr
<
105
103<
(RaLPr)/(0.2
+
Pr)
(14)
The
Rayleigh
number
RaLis
determined
by
the
following
for-
mula:
RaL=(Tw1
Tw2)L3
˛ (15)
Convection
coefficients
for
the
vertical
cavity
heated
from
one
side
may
be
obtained
from
the
following
corrections.
All
properties
are
evaluated
at
the
mean
temperature,
(Tw1+
Tw2)/2.
NuL=hL
k(16)
378
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
024 48 72 96 120 144 168
0
450
900
2009
TMY
Solar radiation
SOLAR RADIATION(W/m
2
)
TIME(Hour)
024 48 72 96 120 144 168
5
10
15
20
25
30
35
40
45
2009
TMY
Heat wave
Ambient air
TEMPERATURE(
o
C)
TIME (Hour)
Fig.
3.
Ambient
air
temperature
and
global
solar
radiation
from
TMY
and
2009
(25th–31st
January
2009)
weather
data
of
Melbourne
showing
record
breaking
heatwave
by
the
red
circle.
where
NuLis
average
Nusselt
number
which
is
the
ratio
of
con-
vective
to
conductive
heat
transfer;
RaLis
Rayleigh
number;
Pr
is
Prandtl
number;
H
is
height
of
air
gap,
m;
L
is
the
thickness
of
air
gap,
m;
g
is
acceleration
of
gravity,
g
=
9.8
m/s2;
ˇ
is
volumetric
thermal
expansion
coefficient,
K1;
Tw1and
Tw2are
left
and
right
side
wall
surface
temperatures, C;
is
kinematic
viscosity,
m2/s;
˛
is
thermal
diffusivity,
m2/s;
h
is
average
heat
transfer
coefficient,
W/m2K.
3.
Numerical
solution
procedure
The
transient
heat
transfer
equations
as
shown
in
Section
2
are
solved
numerically
by
explicit
finite
difference
approach.
A
com-
puter
code
using
Fortran
90
compiler
has
been
developed
for
the
solution
of
the
above
equations.
The
following
lists
finite
difference
equations
for
various
nodes
including
the
interior
nodes,
bound-
ary
nodes,
interface
face
nodes
between
two
layers
of
different
materials.
3.1.
Finite
difference
formulations
A
dynamic
model
is
introduced
for
analysing
the
transient
heat
transfer
through
the
walls,
which
was
solved
by
the
control
volume
finite-difference
method
employing
an
explicit
scheme.
The
exterior
and
interior
boundary
nodes:
Tn+1
1=
2Fo(BiTn
e+
(1/2Fo
1
Bi)Tn
1+
Tn
2)
(17)
Tn+1
N=
2Fo(Tn
N1+
(1/2Fo
1
Bi)Tn
N+
BiTn
in)
(18)
The
interior
nodes
within
same
material:
Tn+1
i=
Fo(Tn
i1+
(1/Fo
2)Tn
i+
Tn
i+1)
(19)
The
interface
nodes
between
two
different
materials:
Tn+1
i=
2FojTn
i1+
(1
2Foj
2Foj+1)Tn
i+
2Foj+1Tn
i+1(20)
The
air
in
the
cavity
of
the
wall:
Tn+1
air =t
Vc hwf Ag(Tn
w1
Tn
air )
+
hwf Ag(Tn
w2
Tn
air )+
Tn
air (21)
The
air
in
the
room:
Tn+1
in =t
Vc n
i=1hwf Aw,i(Tn
w,i
Tn
in)
+
hrAr(Tn
r
Tn
in)
+n
i=1UwinAwin,i (Tn
out Tn
in)
+n
i=1Gn
T,iAwin,i SHGC+
Tn
in
(22)
where:
Bi
=h0x
k=
Biot
number
(23)
Foj=kjt/xj
jcjxj+
j+1cj+1xj+1
=
Fourier
number
for
material
j
(24)
Here,
the
Biot
number
is
a
ratio
of
the
heat
transfer
resistance
inside
of
and
at
the
surface
of
a
body
in
interest.
3.2.
Stability
requirements
For
stability
consideration
of
the
explicit
scheme,
the
stability
requirements
for
the
internal,
boundary
and
interface
nodes
are
listed
as
follows:
For
the
internal
node:
(2
1/Fo)0
or
Fo
1
2(25)
For
the
boundary
nodes:
(1
+
Bi
1/2Fo)0
or
Fo
1
2(1
+
Bi)(26)
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
379
Fig.
4.
Room
air
temperature
comparisons
of
various
residential
walls
for
three
consecutive
days
(28th–30th
January
2009).
For
the
interface
nodes
between
the
composite
layers
of
differ-
ent
materials:
(2Foj+
2Foj+1
1)0
or
(Foj+
Foj+1)
1
2(27)
4.
Results
and
analysis
4.1.
Weather
data
The
recorded
weather
data
of
Melbourne
in
2009
were
used
as
the
model
input
to
assess
and
predict
the
resilience
capability
of
dif-
ferent
residential
walls
to
the
heatwave.
For
comparison
purposes,
Typical
Meteorological
Year
(TMY)
data
file
of
Melbourne,
which
is
commonly
used
for
building
energy
simulation,
was
also
employed
for
model
input.
The
model
output
includes
the
internal
wall
sur-
face
temperatures
and
hourly
indoor
temperature
in
response
to
the
outdoor
weather
conditions.
Fig.
3
shows
the
ambient
air
temperature
and
global
solar
radi-
ation
on
25th–31st
January
2009.
During
the
extremely
hot
period,
Melbourne
has
experienced
a
record
prolonged
heatwave,
with
three
days
over
43 C
and
its
CBD
area
reached
44.2 C,
when
the
latest
heatwave
and
‘Black
Saturday’
hit
Victoria
on
7th
February
2009.
The
circle
in
Fig.
3
illustrates
this
record
breaking
heatwave
period.
4.2.
Averaged
maximum
air
temperature
during
heatwave
The
room
air
temperatures
in
the
building
with
different
wall
systems
in
the
heatwave
period
were
predicted
using
the
dynamic
model
described
in
Sections
2
and
3.
Fig.
4
compares
the
room
air
temperatures
for
the
eight
wall
systems.
The
aver-
aged
maximum
air
temperatures,
which
are
defined
as
the
means
of
the
daily
maximum
air
temperatures
during
the
heatwave
period
for
the
eight
wall
systems
are
compared
in
Table
4.
It
also
lists
wall
relative
heatwave
vulnerability
rankings
in
terms
of
the
Averaged
Maximum
Air
Temperature
(AMAT)
index,
the
higher
the
vulnerability
ranking,
the
more
vulnerable
the
wall
system.
It
was
found
that
‘wall
A’
shows
a
better
thermal
per-
formance
with
the
lowest
AMAT
for
three
consecutive
days
from
28th
to
30th
January
2009.
‘Wall
G’
is
more
sensitive
to
exter-
nal
weather
conditions
especially
the
ambient
temperature
fluc-
tuation.
Different
from
previous
work
in
the
literature
using
maximum
air
temperature
in
an
office
building
as
an
indicator
for
over-
heating
assessment
[28],
AMAT
index
uses
the
mean
peak
daily
temperature
during
the
heatwave
period.
AMAT
provides
a
straightforward
way
of
comparing
the
peak
daytime
tempera-
tures
inside
a
building
by
using
different
wall
systems.
However,
it
doesn’t
consider
the
night-time
temperature
at
sleeping
time.
This
weakness
makes
it
difficult
to
assess
thermal
environment
in
particular
when
walls
with
high
thermal
mass
release
heat
dur-
ing
night-time
period.
The
released
heat
intends
to
increase
the
internal
air
temperature
at
night.
4.3.
Maximum
air
temperature
difference
during
heatwave
Maximum
Air
Temperature
Difference
(MATD)
index
is
defined
as
the
maximum
difference
in
the
room
air
temperatures
pre-
dicted
for
the
same
period
with
TMY
weather
data
and
those
during
the
heatwave
period.
Table
4
lists
the
MATD
for
the
eight
wall
systems
and
their
relative
heatwave
vulnerability
rankings.
In
terms
of
MATD,
‘wall
A’
performs
the
best
with
MATD
at
1.58 C.
‘wall
G’
is
more
vulnerable
to
the
outdoor
climate
change
with
MATD
reaching
about
4.29 C
as
shown
in
Fig.
5.
The
maximum
room
air
temperature
during
the
heatwave
period
for
‘wall
A’
is
found
to
be
27.72 C,
while
30.65 C
for
‘wall
G’.
MATD
ser-
vices
as
an
indicator
of
internal
temperature
difference
between
two
weather
conditions,
i.e.,
normal
and
extremes.
Vulnerable
design
thus
could
be
clearly
identified
by
using
this
index.
It
provides
useful
reference
for
building
energy
budget
planning
considering
the
effect
of
weather
extremes.
However,
similar
to
AMAT,
MATD
is
an
index
closely
related
to
the
maximum
daytime
room
air
temperature
and
it
does
not
include
night-time
perfor-
mance.
4.4.
Thermal
discomfort
proportion
during
heatwave
Proportion
in
thermal
discomfort
(TDP)
in
the
building
using
the
eight
residential
walls
during
the
heatwave
period
was
assessed.
TDP
is
defined
as
the
ratio
of
number
of
hours
with
temperatures
exceeding
a
thermal
discomfort
threshold
to
the
total
hours
in
a
day.
The
thermal
discomfort
threshold
is
chosen
as
28 C
according
to
Chartered
Institution
of
Building
Services
(CIBSE)
Guide
A
[38].
Table
4
lists
the
TDP
for
the
eight
wall
systems
and
their
relative
heatwave
vulnerability
rankings
in
terms
of
the
TDP
index.
Achiev-
ing
the
worst
comfort
level
from
25th
to
31st
January,
‘wall
G’
has
a
mean
proportion
in
discomfort
of
31.5%
through
the
above
men-
tioned
7
day
period,
which
is
the
highest
value
observed
among
other
walls.
During
the
extreme
hot
four
days
starting
from
28th
to
31st
January
2009,
‘wall
G’
experienced
percentages
of
tempera-
ture
exceeding
the
threshold
as
50%,
50%,
41.6%,
29.2%,
respectively.
TDP
is
capable
of
evaluating
the
duration
of
possible
overheating
problems
in
a
building,
during
a
period
of
weather
extreme
event,
by
counting
number
of
hours
exceeding
a
specific
temperature
threshold.
TDP
provides
an
indicator
for
assessing
thermal
com-
fort
among
various
building
wall
designs
under
weather
extreme
conditions.
It
is
noted
that
TDP
is
an
index
related
to
high
indoor
temperatures
which
are
mainly
related
to
daytime
thermal
performance.
4.5.
Statistical
maximum
air
temperature
The
entire
data
set
of
predicted
hourly
room
temperatures,
cal-
culated
during
the
summer
period
(i.e.
90
days)
with
heatwave
(TMY
weather)
and
non-heatwave
periods
(2009
weather),
was
analysed.
The
histogram
frequency
distribution
of
the
hourly
room
temperature
data
is
presented
in
Figs.
6
and
7.
From
Figs.
6
and
7,
it
was
found
that
during
non-heatwave
period
(i.e.
entire
summer
period
in
TMY),
the
frequency
for
temperature
exceeding
28 C
for
‘walls
A,
B,
D,
H’
is
nearly
zero,
but
frequency
of
5%
is
observed
for
‘wall
G’.
During
the
hot
summer
in
2009
where
heatwave
was
380
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
Table
4
Summary
of
the
vulnerability
index
and
relative
rankings.
Wall
type
A
B
C
D
E
F
G
H
TMAX (C)
27.72
27.96
29.74
27.78
30.65
30.33
30.65
28.67
Ranking
1
3
5
2
7
6
8
4
AMAT
(C) 27.36
27.54
28.42
27.40
29.30
29.09
29.47
27.93
Ranking
1
3
5
2
7
6
8
4
TDP
(>28 C)
0%
0%
20.2%
0%
29.8%
28.6%
31.5%
13.1%
Ranking
1
1*5
1*7
6
8
4
SMAT
(5%)(C)
27.72
27.95
29.73
27.78
30.62
30.31
30.58
28.66
Ranking
1
3
5
2
8
6
7
4
MATD
(C) 1.58 2.05 3.89 1.29 4.09 3.78 4.29
2.24
Ranking
2
3
5
1
7
6
8
4
R20.9031
0.9259
0.9628
0.8968
0.9757
0.9738
0.9595
0.9557
Ranking
2
3
5
1
8
6
7
4
ANT
(C)
26.08
26.04
24.86
26.07
25.68
25.72
25.70
25.85
Ranking
8
6
1
7
2
4
3
5
recorded,
‘wall
A’
and
‘wall
D’
show
better
heat
resilience
capabil-
ity
compared
with
other
types
of
walls
with
less
frequencies
at
the
high
temperature
range.
This
statistical
difference
in
heat
resilient
capability
may
be
identified
by
the
average
of
the
top
5%
hourly
air
temperature
defined
as
Statistical
Maximum
Air
Temperature
(SMAT)
(5%).
Table
4
lists
the
SMAT
(5%)
for
the
eight
wall
systems
and
their
relative
heatwave
performance
rankings
in
terms
of
the
SMAT
(5%).
It
is
obtained
from
the
data
set
of
predicted
hourly
room
temperature
throughout
the
summer
of
2009.
It
is
seen
that
‘walls
A
and
D’
rank
the
top
two
walling
systems,
while
‘walls
E
and
G’
rank
as
the
worst
performers
in
terms
of
SMAT
(5%).
4.6.
Correlation
of
temperature
response
Fig.
8
shows
the
relationship
between
the
mean
daily
room
temperatures
and
mean
outside
temperatures
throughout
the
entire
summer
in
2009.
Fig.
9
shows
the
mean
daily
tempera-
ture
variation
for
‘wall
A’
and
‘wall
G’
for
the
entire
2009
summer
including
the
heat
wave
period.
As
shown
in
Fig.
8,
the
mean
daily
room
temperatures
of
the
buildings
correlate
well
with
the
mean
ambient
air
temperature.
The
response
of
a
specific
wall
system
to
extreme
hot
weather
could
be
predicted
through
the
corresponding
correlations
obtained
under
non-heatwave
periods.
Table
4
also
compares
the
coefficient
of
determination,
R2,
for
all
wall
structures,
which
is
a
measure
of
the
goodness
of
fit
between
the
internal
temperature
response
to
the
ambient
air
temperature
and
the
regression
line.
It
was
found
that
differ-
ent
wall
systems
have
different
goodness
of
fit.
Small
R2values
indicate
that
the
indoor
temperature
does
not
closely
follow
the
movement
of
ambient
temperature.
On
the
other
hand,
large
R2
values
reflect
that
indoor
temperature
closely
follows
the
change
0
24
48
72
96 12
014
416
8
23
24
25
26
27
28
29
30
31
30.36
o
C
3.46oC
28.70
o
C
30.57
o
C
4.29oC
4.15oC
30.53
o
C
WALL
G
TIME (
Hrs)
0
24
48
72
96 12
014
416
8
25
26
27
28
TMY
200
9
1.58oC
1.51oC
1.45oC
27.09oC
27.71oC
27.67oC
27.65oC
WALL A
TEMPERATURE(
o
C) TEMPERATURE(
o
C)
TIME(Hrs)
Fig.
5.
Room
air
temperatures
for
‘wall
A’
and
‘wall
G’
under
TMY
and
2009
showing
daily
maximum
air
temperature
differences
(MATD)
under
two
weather
conditions
for
each
wall
(25th–31st
January
2009).
J.
Han
et
al.
/
Energy
and
Buildings
66
(2013)
373–383
381
22
24
26
28
30
0.00
0.09
0.18
Frequency
TEMPERATURE (Deg C)
H
22
24
26
28
30
0.00
0.09
0.18
Frequency
G
22
24
26
28
30
0.00
0.09
0.18
Frequency
F
22
24
26
28
30
0.00
0.09
0.18
Frequency
E
22
24
26
28
30
0.00
0.09
0.18
Frequency
D
22
24
26
28
30
0.00
0.09
0.18
Frequency
C
22 24 26 28 30
0.00
0.09
0.18
Frequency
B
22
24
26
28
30
0.00
0.09
0.18 Non Heatwave Period
Frequency
A
Fig.
6.
Histogram
of
the
indoor
temperatures
for
eight
typical
wall
designs
in
non-
heatwave
period.
of
ambient
temperature,
and
suggest
that
wall
system
has
less
buffering
ability
to
the
changes
in
the
ambient
weather
condi-
tions.
As
shown
in
Table
4,
‘wall
D’
is
the
most
resilient
design
with
the
lowest
R2value,
R2=
0.90,
while
‘wall
E’
(R2=
0.98)
is
most
vulnerable
to
heatwave.
We
use
coefficient
of
deter-
mination,
R2as
the
correlation
of
temperature
response
(CTR)
index.
CTR
provides
an
indication
of
the
dynamic
relationship
between
the
internal
temperatures
with
outside
ambient
temper-
ature
fluctuations.
Using
the
corresponding
correlation,
internal
temperature
could
be
predicted
under
given
weather
conditions,
while
CTR
may
provide
an
index
for
wall
vulnerability
assess-
ment.
4.7.
Average
night-time
temperature
Massively
constructed
wall
absorbs
heat
from
sun
during
day-
time
and
releases
it
at
night,
and
consequently
may
result
in
high
room
air
temperatures
during
the
night
in
summer
period.
Because
high
night
temperature
constitutes
a
major
factor
for
health
issues
and
mortality,
it
is
extremely
important
to
consider
the
thermal
comfort
at
night
as
well.
In
order
to
achieve
this
goal,
an
average
night-time
temperature
(ANT)
was
introduced
to
compare
the
night-time
thermal
performance
of
each
wall
from
sun
set
to
sun
rise.
It
was
found
that
‘wall
C’
has
a
lower
ANT
22
24
26
28
30
0.00
0.05
Frequency
TEMPE
RATUR
E (
Deg
C)
H
22
24
26
28
30
0.00
0.05
0.10
Frequency
G
22
24
26
28
30
0.00
0.05
0.10
Frequency
F
22
24
26
28
30
0.00
0.05
0.10
Frequency
E
22
24
26
28
30
0.00
0.05
0.10
Frequency
D
22
24
26
28
30
0.00
0.05
0.10
Frequency
C
22
24
26
28
30
0.00
0.05
0.10
Frequency
B
22
24
26
28
30
0.00
0.05
0.10
Heatwave Period
Frequency
A
Fig.
7.
Histogram
of
indoor
temperatures
for
eight
typical
wall
designs
in
heatwave
period.
of
24.86 C,
while
26.08 C
for
‘wall
A’.
This
indicates
that
addi-
tional
measures,
such
as
night-time
ventilation
for
removal
of
absorbed
heat,
are
required
to
avoid
thermal
discomfort
at
night
for
those
walls
with
better
performance
at
daytime,
‘wall
A’
for
example.
4.8.
Deviation
arising
in
the
above
multi-criteria
Moderate
or
small
deviations
in
the
above
multi-criteria
analysis
were
observed
for
daytime
thermal
performance
ranking,
as
shown
in
Table
4.
According
to
AMAT,
TDP,
SMAT,
‘wall
A’
performs
better
at
daytime,
while
‘wall
D’
might
be
a
resilient
wall
system
accord-
ing
to
MATD.
These
deviations
are
due
to
the
different
emphasis
among
these
different
c