A comparative study on optimum insulation thickness of walls and energy savings in equatorial and tropical climate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 3[.]
Trang 15 Modeste Kameni Nematchouaa,⇑, Paola Ricciardia, Sigrid Reiterb, Andrianaharison Yvonc
6 a Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy
7 b LEMA, Faculty of Applied Sciences, University of Liege, Liege, Belgium
8 c Department of Electrical Engineering, National Higher Politechnical School of Antananarivo, Madagascar
10
11 Abstract
12 The increase outdoor temperature acts directly on the indoor climate of buildings In Cameroon, the energy consumption demand in
13 the buildings sector has been rapidly increasing in recent years; so well that energy supply does not always satisfy demand Thermal
insu-14 lation technology can be one of the leading methods for reducing energy consumption in these new buildings However, choosing the
15 thickness of the insulation material often causes high insulation costs In the present study, the optimum insulation thickness, energy
16 saving and payback period were calculated for buildings in Yaounde´ and Garoua cities, located in two climatic regions in Cameroon
17 The economic model including the cost of insulation material and the present value of energy consumption and the cost over a life time of
18 22 years of the building, were used to find the optimum insulation thickness, energy saving, and payback period Materials that extruded
19 polystyrene were chosen and used for two typical wall structures (concrete block (HCB) and compressed stabilized earth block wall
20 (CSEB)) The early cooling transmission loads, according to wall orientations and percentage of radiation blocked were calculated using
21 the explicit finite-difference method under steady periodic conditions As a result, it was found that the west- and east-facing walls are the
22 least favourite in the cooling season, whereas the south and north orientations are the most economical Although wall orientation had a
23 significant effect on the optimum insulation thickness, it had a more significant effect on energy savings In equatorial region (Yaounde´),
24 for south orientation, the optimum insulation thickness was 0.08 m for an energy savings of 51.69 $/m2 Meanwhile, in tropical region
25 (Garoua), for north orientation, the optimum insulation thickness was 0.11 m for an energy savings of 97.82 $/m2
26 Ó 2017 The Gulf Organisation for Research and Development Production and hosting by Elsevier B.V All rights reserved
27
28 Keywords: Energy savings; Optimum insulation; Equatorial and tropical climate; Buildings; Wall orientation
29
30 1 Introduction
31 One of the most efficient ways to reduce the
transmis-32 sion rate of heat and energy consumption to cool and heat
33
buildings is the use of an appropriated thermal insulation
34
in the building envelope An optimum thickness of
insula-35
tion offers minimum total cost, including the cost of
insula-36
tion and energy consumption on the building life (Daouas,
37
2011) In Cameroon, energy consumption in modern and
38
traditional buildings has considerably increased in recent
39
years, and unfortunately, no measure has been taken by
40
the Cameroon government to improve the thermal quality
http://dx.doi.org/10.1016/j.ijsbe.2017.02.001
2212-6090/ Ó 2017 The Gulf Organisation for Research and Development Production and hosting by Elsevier B.V All rights reserved.
⇑ Corresponding author.
E-mail address: kameni.modeste@yahoo.fr (M Kameni Nematchoua).
Peer review under responsibility of The Gulf Organisation for Research
and Development.
H O S T E D BY
Gulf Organisation for Research and Development
International Journal of Sustainable Built Environment
ScienceDirect
www.sciencedirect.com
Trang 241 of the building envelope A comfortable environment is
42 necessary for an individual’s health and productivity in a
43 building (Kameni Nematchoua, 2014) A considerable
44 applied insulation thickness on the external walls of the
45 buildings results in significantly lower heat load
transmis-46 sion The cost of the insulation material increases linearly
47 with the thickness of the insulation material (Ozel, 2011)
48 In 2008, it has been shown that more than 50% of the
con-49 sumed total energy in the building has been dedicated to
50 heating and cooling (Kameni Nematchoua, 2015) This
51 percentage is going to rise in the coming years, as the global
52 population continues to increase (Kameni Nematchoua,
53 2015) Thermal insulation is also solicited to reduce the loss
54 of heat in buildings through the envelope
55 Meanwhile, the use of the most efficient energy to cool
56 buildings is the best measure to preserve energy and protect
57 environment (Azmi Aktacir et al., 2010) There are many
58 studies in the literature on the determination of optimum
59 insulation thickness on building walls, and most of them
60 had used the degree day (or degree hour) to calculate the
61 thickness (Ucar and Balo, 2009, 2010; Comakli and
62 Yu¨ksel, 2003; Dombayci et al., 2006; Daouas et al., 2010;
63
Bolattu¨rk, 2008; Yu et al., 2009; Ghrab-Morcos, 0000)
64
For instance, Bolattu¨rk (Bolattu¨rk, 2006) analysed the
65
use of insulation on the external walls of buildings during
66
many seasons, and found that the building inertia
influ-67
ences indoor comfort A good selection of construction
68
materials is very important at the time of conception of
69
building Tsilingiris (Tsilingiris, 2003) developed a
numeri-70
cal algorithm for the cooling load calculation, whileGranja
71
and Labaki (2003)presented a periodic solution of the heat
72
flow through a flat roof using Fourier analysis These
73
results have facilitated the calculation of architects
Fur-74
thermore,Dombayci et al (2006)found the optimum
insu-75
lation thickness of the external wall for different energy
76
sources and different insulation materials The study by
77
Mohsen et al (2001)showed that the insulation of external
78
walls and roofs can increase energy saving by up to 77%
79
Meanwhile, Naouel Daouas et al (2010) found that the
80
most profitable case for insulation is the stone/brick
sand-81
wich wall and expanded polystyrene, with an optimum
82
thickness of 5.7 cm, which achieved energy savings up to
83
58% with a payback period of 3.11 years This work, has
84
allowed to improve the results obtained in Tsilingiris
Nomenclature
As annual energy savings ($m2)
c specific heat (Jkg1K1)
C cost ($)
COP coefficient of performance of air-conditioning
system CDD degree-days (°C days)
g inflation rate (%)
h combined heat transfer coefficient (Wm2K1)
H monthly average of daily global radiation on
horizontal surface (MJ m2day1)
Ho monthly average of daily extraterrestrial
radia-tion on horizontal surface (MJ m2day1)
Hd monthly average of daily diffuse radiation on
horizontal surface (MJ m2day1)
L wall thickness (m)
Lop optimum insulation thickness (m)
I interest rate (%), order of node
Itotal solar radiations on the horizontal surface
(W m2)
Ib direct solar radiations on the horizontal surface
(W m2)
Id diffuse solar radiations on the horizontal surface
(W m2)
I0 hourly extraterrestrial radiation (W m2)
N number of nodes
n lifetime of building (years)
M number of layers of composite wall
pb payback period (years)
qi heat flux density at indoor surface of the wall
(W m2)
Qc annual cooling transmission load (MJ m2)
sd shade level
t time (s)
T temperature (C)
x coordinate direction normal to wall (m)
Greek symbols
a solar absorptivity of outside surface of wall
c surface azimuth angle (°)
d declination angle (°)
k thermal conductivity (W m1K1) / latitude (°)
w hour angle (°)
ws sunset-hour angle for a horizontal surface (°)
q density of material (kg m3)
qr ground reflectivity
Subscripts
el electricity enr energy
I inside ins insulation max maximum value min minimum value
o outside
sa solar-air
t total
2 M Kameni Nematchoua et al / International Journal of Sustainable Built Environment xxx (2017) xxx–xxx
1 March 2017
Trang 385 (2003), Granja and Labaki (2003), Dombayci et al (2006).
86 Hanan et al (2011)identified several design-related faults
87 common in Saudi Arabian house design, which contributed
88 to inefficient use of energy.Kemal and Bedri (2003)showed
89 that optimization is based on the lifecycle cost analysis, and
90 obtained an able energy saving by applying optimum
91 insulation thickness.Farshid et al (2014), showed thatthe
92 sustainability scenario could offer, approximately, 100%
93 increase in the optimum thickness of extra insulation
com-94 pared to the Business As Usual scenario (BAU) However,
95 the implication of different life spans of 40, 50 or 60 years,
96 on the optimum measure appeared to be either negligible
97 or very small, depending on the chosen scenario It must
98 be noted that the results obtained in each of these studies
99 differed according to the study places with their climate
100 zone In the Sub-Sahara Africa regions, ambient
tempera-101 tures and solar radiation levels are sufficiently high that,
102 even during winter, buildings do not need energy for
heat-103 ing The roof insulation is as important as that of wall This
104 work is the continuation ofWati and Meukam (2015) The
105 choice of Yaounde and Garoua as the main investigation
106 field cities has not been made randomly Several countries
107 in sub-Saharan Africa and Asia have a climate similar to
108 that of these two cities In this sense, the results can also
109 serve as a standard for construction and design of buildings
110 in these different regions and also improve Existing
ASH-111 RAE database In addition, Yaounde´ and Garoua are
112 two cities with a very high population density in Central
113 Africa These cities are highly threatened by the effects of
114 climate change, which explains the high energy demand
115 for cooling in new residences
116 The aim of the present study was to determine optimum
117 insulation thickness for external walls of buildings in two
118 climate areas of Cameroon Optimization was based on
119 an economic model, in which a lifecycle cost analysis was
120 conducted using one type of insulation material and two
121 typical wall structures The yearly cooling transmission
122 loads according to wall orientations were calculated using
123 explicit finite-difference method under steady periodic
con-124 ditions In addition, the thermal performance of the walls
125 under optimal conditions was also investigated
126 2 Methodology
127 2.1 Analysed cities
128 The Yaounde´ city is built on several hills and enjoys a
129 picturesque setting and a relatively ‘‘fresh” climate It is
130 the capital of the central region and also the Cameroon
131 political capital This city is located between 3°520N and
132 11°310E, then, around of 726 m of altitude Precipitation
133 ranges from 22 mm (January) to 298 mm (October) In
134 February, the average temperature is 24.9°C February is
135 therefore the hottest month of the year August is the
136 coldest month of the year The average temperature is
137 22.2°C during this period Yaounde city is approximately
138 300 km from the Atlantic coast and enjoys a temperate
139
sub-equatorial climate with four seasons, including a long
140
dry season (mid-November to late March), a short rainy
141
season (April to mid-June), a short dry season (mid-June
142
to mid-August) and a long rainy season (mid-August to
143
mid-November) Its population was about 2.5 million in
144
2011, and since the early 1990 s, the population has
145
increased with a growth rate of 7% per year
146
Located between 9°180N and 13°230E, around altitude
147
199 m; Garoua is the capital of the northern region of
148
Cameroon It has approximately 357,000 inhabitants
Gar-149
oua city is the third largest city of Cameroon In this city,
150
scorching heat can be experienced in the late dry season
151
despite the shade provided by the trees that line the main
152
streets, and the average monthly temperature is 26°C in
153
August and 40°C in March (extreme temperatures varied
154
from 17°C to 46 °C) It has Sudanian-type tropical
cli-155
mate It is characterized by a long dry season from October
156
to April and a short rainy season from May to September
157
The total monthly rainfall varies from 0 to 250 mm Its
158
monthly sunshine varies from 194 to 300 h
159
2.2 Mathematical formulation
160
The walls of the modern houses in the sub-Saharan
161
Africa, in general, and in Cameroon, in particular, are
gen-162
erally made with parpen, with a cement coating on each
163
side However, the development of techniques for
stabiliz-164
ing mud brick (mechanical and chemical) has led to a
165
renewed interest in it Thus, to optimize the thickness of
166
the insulation in the walls in modern homes, composite
167
walls are considered (Fig 1)
168
The outside face of the wall is subjected to variations in
169
temperature ToðtÞ and solar radiation IðtÞ The inside face
170
of wall comes in contact with the indoor air maintained
171
at a fixed temperature for Ti to have better thermal
com-172
fort Each layer, J, of the composite wall is therefore the
173
seat of a unidirectional transfer of heat in the supposed
174
case was defined as in (Kameni Nematchoua, 2015)
175
qjcj@Tj
@t ¼ kj
@2
Tj
178
where j refers to the serial number of the layer (j = 1, ., M
179
for a wall of M layer); x and t are the spatial and temporal
180
coordinates, respectively; Tjis the temperature at the
181
point of coordinates x in layer j and qj, cj and kj are the
182
density, specific heat and thermal conductivity of the
mate-183
rial of layer j, respectively The resolution of Eq (1)
184
requires the determination of the boundary conditions
185
and initial condition Thus, at the initial moment, we
186
assume that all points of the wall have the same
tempera-187
ture (25°C) The outside face conditions and indoor
condi-188
tion are given by Eqs (2) and (3), (see Daouas, 2011),
189
respectively
190
k1 @T
@x
x 1 ¼0¼ hoðTo T1Þ þ aI ð2Þ
192
Trang 4kM
@T
@x
195
196 where a is the absorption coefficient and he and hi are the
197 thermal exchange coefficient on the outside and inside
198 faces, respectively Their values (he¼ 22W :m2:K1 and
199 hi¼ 9W :m2:K1) were obtained from a previous study
200 (Ozel, 2011) I is the radiation of short wavelength received
201 by outdoor face wall (vertical), and was obtained using
202 Eq.(4) given inOzel (2011)
203
I¼ IdRbþ1
2qyIhþ1
205
206 where Id; Dh and Ih are the direct radiation, diffuse
207 radiation and global radiation on a horizontal surface,
208 respectively and qy is the albedo of the area assumed to
209 be equal to 0.2 The parameter Rbis given for a vertical
sur-210 face byOzel (2011)
211
Rb¼cos d sin / cos x þ cos d sin c sin x sin d cos / cos c
cos / cos d cos x þ sin / sin d
ð5Þ
213
214 where d, x, c and / are the solar declination, hourly angle,
215 surface of the azimuth and solar elevation, respectively c is
216 equal to 0 for an inclined surface facing south, 90 for a
217 surface turned towards east, 90 for a surface turned
218 towards west and 180 for a north surface
219 The third term of Eq.(4)designating the diffuse radiance
220 on a vertical surface was obtained from a model developed
221 in El-Sebaii et al (2010) This model uses the simplifying
222 hypothesis of a distribution isotrope of the diffuse radiation
223 that is independent of the ze´nithal and azimuthal angles
224
2.3 Method of solution
225
To solve the above-mentioned problem, a thermal
226
model of an area consisting of a wall was constructed from
227
the component library of Ham-tools developed in the
envi-228
ronment of MATLAB-Simulink simulation (Kolaitis et al.,
229
2013) The Ham-tools has been developed jointly by
230
Chalmers University of Technology (Sweden) and the
231
University of Technology in Denmark (Copenhagen,
Den-232
mark), and is solved numerically using the finite-difference
233
method and a scheme of explicit temporal resolution
234
(Eq (1)).For a stitch of thickness di inside the materials
235
(Fig 2), the thermal balance at node i mesh centre can be
236
written as follows:
237
Tniþ1 Tn
i
Dt ¼ 1
qicidi
Tni1 Tn
i
Ri1þ Ri
þTniþ1 Tn
i
Riþ1þ Ri
ð6Þ
239
240
where i denotes the number of node and n indicates the
241
time step The resistances are defined as (Ozel, 2011):
242
Ri¼ di
2ki
ð7Þ 244
245
where kiis the thermal conductivity of the node material i
246
As the studied wall is composite, a node is placed at every
247
interface between the two materials of different nature The
248
complete modelling of the heat transfer to the node of
con-249
tact is given inNielsen (2002)
250
The thermal balances are given by Eqs (8) and (9),
251
respectively
252
Tnþ11 Tn
1
Dt ¼ 1
qicidout
Tn
2 Tn 1
R2þ R1
þ hoðTo T1Þ þ aI
ð8Þ
254
Fig 1 Typical wall structures (a: hollow concrete block wall, b: CSEB wall) and proposed wall structures (c: insulated hollow concrete block wall, d: insulated CSEB wall).
4 M Kameni Nematchoua et al / International Journal of Sustainable Built Environment xxx (2017) xxx–xxx
1 March 2017
Trang 5Tnþ1N Tn
N
Dt ¼ 1
qicidin
Tn
N 1 Tn N
RN 1þ RN
þ hiðTi TNÞ
ð9Þ
257
258 The numeric solution gives the temporal evolution of
259 the temperature to every internal node of the wall and on
260 internal and external face of the wall The density of heat
261 flux transmitted to the zone is given by El-Sebaii et al
262 (2010)
263
qcðtÞ ¼ hiðTi TNðtÞÞ if Ti> TN
0 if Ti6 TN
ð10Þ
265
266 The maximum step size of the time adopted in our
267 model is an hour, and the hourly exterior conditions are
268 considered
269 2.4 Hourly exterior conditions
270 The monthly averages of the minimum and daily
max-271 ima of temperature of every month on a relatively long
per-272 iod (1984–2005) were first calculated from the archives of
273 the Department of Meteorology (Directorate of National
274 Meteorology) These values were used to estimate the
mid-275 dle hourly values of temperature of every month from the
276 model of cosine (Safeeq and Fares, 2011), as shown in
277 Eq.(11)
278
Tt¼Tmax Tmin
2 cos
pðt aÞ 12
þTmaxþ Tmin
280
281 where Ttis the temperature at time tðhÞ starting from
mid-282 night (in the range of 1–24); Tmaxand Tminare the minimum
283 and maximum daily temperature, respectively and a is the
284 hour of the day at which temperature is maximum In the
285 present study, the parameter a was considered as 14, as
286 reported bySafeeq and Fares (2011), De Wit (1978)
287 The daily averages of the diffuse and global radiances on
288 a horizontal surface of every month were obtained by
289 dividing the number of day of the month considered, and
290 the monthly averages of one relatively long period
291 (1985–2005) was obtained from Sola (2014) The hourly
292 averages of the diffuse and global radiances were obtained
293 from the model of decomposition of Lui and Jordan and
294 Collares-Pereira (Basunia et al., 2012), considering the
295 15th day of the month as the representative day Figs 3
296 and 4show the monthly diurnal averages of temperatures
297
and solar radiation levels in Garoua and Yaounde´,
298
respectively
299
The outdoor temperature varied from 17.6°C to 40.9 °C
300
with a standard deviation (SD) of 0.97 A peak was
301
obtained in March at around 2 pm This peak persisted till
302
April and then fell by 3.9°C in May From May, a light
303
reduction in the air temperature was observed until the
304
month of November when the temperature appeared to
305
increase The global radiation was about 1000 W/m2from
306
January to March, and the direct normal radiation
307
increased up to 825 W/m2 in January, while the diffuse
308
radiation was around 300 W/m2, except for the period
309
from November to January (Fig 3) In the equatorial zone
310
(Yaounde), the climatic conditions were more favourable;
311
the outdoor air temperature varied from 21.5°C to 31.7 °
312
C (SD = 0.74), and the horizontal global radiation was
313
rarely 800 W/m2 (Fig 4) Generally, the global radiation
314
was more important in tropical region than equatorial
315
region But, almost equal in January and February in the
316
two regions These different studied elements testified the
317
unequal variation in the energies used for the cooling of
318
the buildings in these regions The climatic conditions of
319
these cities were often very unfavourable to compare with
320
those of the city of Jeddahen (Hanan et al., 2011)
321
3 Thermal performance of the uninsulated wall
322
Hence forth, the composite walls presented in
323
Fig 1a and b will be designated as wall 1 and wall 2, whose
324
outside faces were exposed to the climatic conditions of the
325
cities of Yaounde and Garoua, respectively The solar
radi-326
ation calculations were made for the 15th day of the hottest
327
month of each of the two climates as indicated by Jeddahen
328
(Hanan et al., 2011); i.e., March for Garoua and January
329
for Yaounde The month of January was chosen for
330
Yaounde´, because of the importance of the amplitude of
331
the diurnal temperature variations The thermophysical
332
properties of the materials used are given in Table 1
333
3.1 Effect of wall orientation
334
Fig 5, shows the remarkable effect of wall orientation
335
on the heat flux density on the internal face of every wall
336
model The peak density of the flux on the internal surface
Fig 2 Numeric model.
Trang 6Fig 3 Monthly diurnal averages of temperatures and solar radiation levels in Garoua.
Fig 4 Monthly diurnal averages of temperatures and solar radiation levels in Yaounde´.
6 M Kameni Nematchoua et al / International Journal of Sustainable Built Environment xxx (2017) xxx–xxx
1 March 2017
Trang 7337 of walls (1) and (2) was higher when they were oriented
338 towards east in the tropical climate (Garoua) during the
339 representative day of the month of March
340 (Fig 5a and b) This is due to the fact that this facing is
341 the one that receives more radiance of short wavelength
342 when the outside temperature reaches its maximal value
343 (around 14 h) These heat fluxes of the density peaks on
344 the interior wall faces were observed at around 20 h in
345 the case of wall 1 and at about 24 h in the case of wall 2
346 The thermal inertia difference between the two types of
347 walls could be the origin of this shift Indeed, in March,
ini-348 tially, the heat flux density was 30 W/m2, it has decreased
349 up to 5 W/m2 around of 10 h, then begin to increase till
350 20 h, where it reaches 40 W/m2 In January, at the same
351 time, the heat flux density was near to 25 W/m2 (South
352 facing)
353 During the representative day of the month of January,
354 in Yaounde´, the peak density of heat flux on the internal
355
face of each type of wall was observed when the wall was
356
oriented southwards (Fig 5c and d) This is due to the fact
357
that south face receives more solar energy than east, west
358
and north faces at that moment or when the outdoor
tem-359
perature exhibits maximum variation As stated previously,
360
the difference between the hours when peaks appear and
361
their values are due to the thermal inertia difference
362
between the two types of walls In the equatorial region
363
(yaounde), the heat flow density flux was less important
364
than tropical region (Garoua) In March (Yaounde´), at
365
first time, the heat flux density was 25 W/m2, then, it has
366
decreased up to 15 W/m2, around of 13 h, till 23 h, then
367
it increased and reaches 25 W/m2 In January it increased
368
linearily However, the heat flow density flux on the
inte-369
rior layer of the wall when it was oriented towards north
370
was weaker than that noted when it was oriented towards
371
other directions (south, east and/or west) This could be
372
due to the fact that the north wall received very little solar
373
energy during the representative days of the months
con-374
sidered in the two climates (Fig 5) The wall orientation
375
influences the heat flux density on its internal face
How-376
ever,Fig 5shows that for the compressed stabilized earth
377
brick (CSEB) (wall 2), fluctuations within the surface
con-378
ditions were significantly reduced, when compared with
379
those shown by the concrete block wall (wall 1) This is
380
due to the good capacity of the earth bricks to store heat,
Fig 5 Effect of wall orientation on the hourly variation of the inside surface heat flux density in Garoua [(a) and (b)] and Yaounde´ [(c) and (d)] for the two wall structures.
Table 1
Material properties ( Meukam et al., 2004; Sisman et al., 2007 ).
Materials q(kg=m 3 ) c(J =kg=K) kðW =m=KÞ
Hollow concrete block 1250 880 0.67
Trang 8381 when compared with that of the concrete block These
382 results showed that CSEB, similar to stone wall (Daouas
383 et al., 2010), improves the indoor climate
384 3.2 Effect of shading
385 Fig 6, shows the shade effect on the heat flux density on
386 the internal layer of wall 1 and wall 2 This effect was noted
387 for the orientations of the wall where the heat flux density
388 on the internal layer presented the most elevated peaks
389 either on the ‘‘East face” in Garoua or ‘‘South face” in
390 Yaounde In the case of wall 1, there was a strong
reduc-391 tion in the peaks, whereas wall 2 showed a practically
uni-392 form reduction during 24 h It seen that the heat flux
393 density decreases with increasing shade level Under the
394 same climatic conditions and same orientation, the heat
395 flux density on the inside of wall 1 and wall 2 was different
396 (Figs 5 and 6) Meanwhile, the daily thermal gains through
397 these two types of walls, obtained by integrating those
mea-398 sured for 24 h as the function given in Eq (9), were very
399 close Thus, at the time of determination of the optimum
400 insulation thickness, only wall 1 was used and these results
401 were valid for wall 2
402
4 Optimum insulation thickness
403
The insulated wall reduces yearly transmission load,
404
which is the main input parameter of any optimum
insula-405
tion thickness model
406
4.1 Yearly cooling load calculation
407
The cooling period in the climatic zones under field
408
spread throughout the year or nearly the yearly quantity
409
of energy Qc received by indoor wall was determined by
410
integrating the values obtained for 1 year as the function
411
qcðtÞ given by Eq (9) Fig 7 shows the variation in the
412
yearly cooling load with insulation thickness in Yaounde´
413
and Garoua In the two climates, the thermal gains through
414
the east and west faces were practically equal and higher
415
than those of the south or north faces The thermal gains
416
through the south face were higher than those through
417
the north face because the zones of survey were in the
418
northern hemisphere, where the northward-oriented walls
419
received less solar energy than the southward-oriented
420
ones Nevertheless, irrespective of the orientation of the
421
wall, the yearly thermal gains decreased with the thickness
Fig 6 Effect of solar shading on the inside surface heat flux in Garoua [(a) and (b)] and Yaounde´ [(c) and (d)].
8 M Kameni Nematchoua et al / International Journal of Sustainable Built Environment xxx (2017) xxx–xxx
1 March 2017
Trang 9422 of the insulator These results are similar to those found in
423 the literature (Daouas, 2011; Kameni Nematchoua, 2014;
424 Ozel, 2011; Azmi Aktacir et al., 2010) On the whole, the
425 yearly thermal gains were found to be more important
426 for the climate of Garoua than for the climate of Yaounde´,
427 because the heat degree is more important in Garoua than
428 in Yaounde´ (Kemajou, 2011)
429 Fig 8a and b shows the influence of the obstruction of
430 radiations of short wavelengths on the yearly thermal gains
431 through east or west face in the two considered climatic
432 zones This effect was particularly remarkable when the
433 thickness of the insulator was weak In general, the yearly
434 thermal gains decreased with the percentage of radiation
435 blocked The last result is similar to those obtained in the
436 literature (Ozel, 2013)
437 4.2 Economic analysis
438 The installation of the insulator contributes to the
439 reduction in the air-conditioning load and thus reduction
440
in the electricity invoice This reduction is especially
441
important when the thickness of the insulator is large
442
However, to install an insulator, an initial investment is
443
required, which increases with the thickness of the
insula-444
tor The total expense bound to the wall considered during
445
the lifecycle of a building is a function of the thickness of
446
the thermal insulator installed, price of kilowatt-hour of
447
the electric energy, interest rates and inflation of the
cur-448
rency considered It is important to determine the insulator
449
thickness that minimizes this total amount (Ct), which is
450
equal to the sum of the present cost of the energy
con-451
sumed during the time of existence of the building and
452
the insulation cost (Daouas et al., 2010)
453
Ct¼ CenrPWF þ Ci¼ CenrPWF þ CinsLins ð12Þ 455
456
where Cenr ($=m2year) is the yearly cost of the electric
457
energy consumed bound to the thermal gains through
458
one square metre of wall; PWF is the ‘‘present worth
459
facto”; Cið$=m3Þ is the cost of one cubic metre of insulator
460
and LiðmÞ is the insulation thickness Cenrdepends on the
Fig 7 Cooling transmission load vs insulation thickness for the climate of Garoua (a) and Yaounde´ (b).
Trang 10461 yearly thermal gains through the unit wall surfaceðQcÞ, the
462 price of energy kilowatt-hour (Cel) and the coefficient
463 of performance of the air-conditioning unit, as given in
464 Eq.(13)
465
Cenr¼QcCel
467
468 PWF is a function of the interest rates and inflation, and
469 is expressed as (Daouas et al., 2010)
470
PWF ¼Xn
u¼1
1þ i
1þ d
u
¼1þ i
d i 1
1þ i
1þ d
n
sii–d ð14Þ
472
473
PWF ¼ n
1þ i if i¼ g ð15Þ
475
476 where n is the yearly lifecycle of the building, i is the
477 currency inflation rate and d is the interest rate The
478 pay-back period b is calculated by solving the following
479 equation for b:
480
Ci
482
483 where Ci=AS is the simple pay-back period that does not
484 take interest rate into account and AS is the amount of
485 the annual savings obtained by insulation
486 The energy savings ($/m2) obtained during the lifetime
487 of the insulation material can be calculated as (Kameni
488 Nematchoua, 2015):
489
ES¼ Cto Ctins ð17Þ 491
492
where Ctoand Ctinsare the total cost of cooling without and
493
with insulation, respectively The energy saving can be
494
expressed as% by the following equation (Kameni
495
Nematchoua, 2015):
496
ES
Cto100¼ 1 Ctins
Cto
498 499
The results obtained from the above-mentioned method
500
can be compared with those of the degree-day method In
501
fact, the degree-day method has been used by several
502
authors to estimate the optimal insulation thickness In this
503
method, the yearly transmission load per unit of wall area
504
is estimated (in J=m2) by the following equation (Kameni
505
Nematchoua, 2015):
506
Qc ¼ 86400:U:CDD ð19Þ 508
509
where CDD is the annual cooling degree-day (in°C days)
510
whose values for the climate of Garoua and Yaounde´ are
511
1315 and 361, respectively These values are calculated from
512
the meteorological data (from Directorate of National
513
Meteorology) for a long period (20 years) The annual
cool-514
ing degree-day can be obtained by the summation of the
515
positive difference between the mean daily temperature
516
and the fixed indoor base temperature (25°C) over the
517
whole year The mean daily temperature can be calculated
518
by adding the maximum and minimum temperatures for
519
the day, and then dividing it by 2ASHRAE (2009)
520
The overall heat transfer coefficient of the wall can be
521
expressed by Eq.(20)
522
Roþ Rinsþ Rwþ Ri
ð20Þ 524
525
where Ro and Ri are the heat resistance due to convective
526
transfer on the outside and inside surface of the wall,
527
respectively and Rins and Rw are the heat resistance of the
528
insulation layer and rest of the wall, respectively
529
The total cost (cost of energy and insulation) is given as
530
(Kameni Nematchoua, 2015):
531
Ct¼0:024CDD
COP
1
RtþL ins
k ins
!
CelPWF þ CinsLins ð21Þ
533 534
where Linsand kinsare the thickness and thermal
conductiv-535
ity of the insulating material, respectively
Fig 8 Effect of solar radiation blocked on yearly cooling load in Garoua
(a) and Yaounde´ (b).
Table 2 The parameters used in the calculations ( Sisman et al., 2007; Institut de l’e´nergie et de l’environnement de la Francophonie, 0000 ).
Electricity for cooling
Expanded polystyrene Cost ($/m 3 ) 164.32
10 M Kameni Nematchoua et al / International Journal of Sustainable Built Environment xxx (2017) xxx–xxx
1 March 2017