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Determination and selecting the optimum thickness of insulation for buildings in hot countries by accounting for solar radiation

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Determination and selecting the optimum thicknessof insulation for buildings in hot countries by accountingfor solar radiation
Mohammed J. Al-Khawaja
*
University of Qatar, Department of Mechanical Engineering, P.O. Box 2713, Doha, Qatar
Received 17 November 2003; accepted 22 March 2004Available online 18 May 2004
Abstract
Determination and selecting the optimum thickness of insulation is the prime interest of many engi-neering applications. One of those applications is insulating buildings with an appropriate insulation.Calculations have been done for the determination of the optimum thickness of insulation for someinsulating materials used in order to reduce the rate of heat ﬂow to the buildings in hot countries. Reducingheat ﬂow rate would reduce the electricity cost for the house lifetime. The solar energy radiation is cal-culated and used to calculate the solar-air temperature which is employed for the determination of the heatﬂow rate. Some results were obtained for a typical house in Qatar which is an example of hot area. Thewallmate insulation is found to have the best performance for houses in Qatar.
2004 Elsevier Ltd. All rights reserved.
Keywords:
Optimum thickness of insulation determination; Solar radiation calculations; Air conditioners for buildings,and insulation in hot countries
1. Introduction
Insulating buildings, such as walls, roofs and ﬂoors is an important matter for reducing the rateof heat ﬂowing into (in time of summer) and from (in time of winter) the houses. To reduce theheat ﬂow eﬃciently we should select the proper insulation by accounting for the purpose, envi-ronment, ease of handling and installation, and the cost. The latter is an important factor that willalter our decision for selecting the insulation. As we know, the ﬁnal selection among insulations
*
Corresponding author. Tel.: +974-485-2109; fax: +974-467-0421.
E-mail address:
khawaja@qu.edu.qa (M.J. Al-Khawaja).1359-4311/$ - see front matter
2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2004.03.019Applied Thermal Engineering 24 (2004) 2601–2610
www.elsevier.com/locate/apthermeng
Nomenclature
E
qt
Equation of time [min]
G
0
solar constant [W/m
2
]
G
D
direct solar radiation [W/m
2
]
G
d
diﬀuse solar radiation [W/m
2
]
G
N
solar energy incident on a surface placed normal to sun’s rays [W/m
2
]
h
o
outer surface heat transfer coeﬃcient [W/m
2
C]
m
relative air masslong
local
local longitude of the location of interestlong
sm
standard longitude
q
solar
total solar radiation [W/m
2
]
T
surface tilted angle from the horizontal
T
ambient
ambient temperature [
C]
T
sky
sky temperature [
C]
T
sol-air
solar-air temperature [
C]
t
ins
insulation thickness [cm]
t
local
local standard time [h]
t
solar
solar time [h]
z
zenith angle
Greek symbols
a
s
solar absorptivity
c
surface rotated angle from the north–south axis
d
declination angle of the sun
e
surface emissivity
h
angle deﬁned in Eq. (5)
k
latitude of the location of interest
r
Stefan–Boltzmann constant
s
a
transmission coeﬃcient for unit air mass
x
hour angle [radians]
Subscripts
a airD directd diﬀuseins insulationN normalo outers solarsol-air solar airsm standard mean
2602
M.J. Al-Khawaja / Applied Thermal Engineering 24 (2004) 2601–2610
that meet the requirements is made on the basis of the lowest cost. Once the choices are narrowedto a few, an economic analysis is performed to identify the one with the minimum total cost. Thethickness of insulation is also determined on the basis of minimum cost, as discussed below.To determine the lowest cost, we need to determine, for any given insulation, the optimumthickness of insulation, which is the thickness corresponding to the minimum total cost. Here, thetotalcostconsistsofthecostoftheinsulationandthecostofelectricityforthelifetimeofthehouse.A tremendous work has been done for the determination of heating and cooling loads of buildings using the handbooks established by ASHRAE [1]. But the case of reducing the heattransfer to the buildings during summer using an adequate insulation was not analyzed consid-erably. It is clear that this insulation might make a lot of savings for the lifetime of the house.Another important factor that eﬀects the optimum thickness of insulation is the solar radiationenergy ﬂowing into the house. The solar radiation can be accounted for by introducing the solar-air temperature [2] which is deﬁned as the equivalent outdoor air temperature that gives the samerate of heat ﬂow to a surface as would the combination of the incident solar radiation, convectionwith ambient air, and radiation exchange with the sky and the surrounding surfaces.
2. Solar radiation calculations
We have used the astronomical calculations to determine the hourly solar radiation ﬂux overthe year. Solar radiation calculations have more advantages over the measured ones using solarcollector. This is because the measured solar radiation depends mainly on the weather conditions,but the calculated one which does not depend on the climate would be more reliable over theyears.The solar radiation incident outside the earth’s atmosphere is called extraterrestrial radiation.On average the extraterrestrial irradiance is 1353 W/m
2
[3] which is called solar constant
G
0
. Thissolar energy is considerably weakened due to absorption, scattering, and reﬂection by theatmosphere. The solar energy that reaches the earth’s surface is attenuated to about 950 W/m
2
ona clear sky and much less on cloudy or smoggy days.It should be mentioned that the solar energy incident on a surface on earth is considered toconsist of direct and diﬀuse parts [3]. The part of solar radiation that reaches the earth’s surfacewithout being scattered or absorbed by the atmosphere is called direct solar radiation
G
D
. Thescattered radiation is assumed to reach the earth’s surface uniformly from all directions and iscalled diﬀuse solar radiation
G
d
. Then the total solar energy incident on the unit area of a surfaceon a ground is
q
solar
¼
G
D
þ
G
d
. The calculations of the direct solar energy would be proposedbelow. However, the diﬀuse radiation can be approximated as 10% of the total radiation on aclear day to nearly 100% on a totally cloudy day [4].The direct solar radiation depends on the sun’s position and surface orientation. If the surfaceon earth is placed normal to the rays of sun, then the radiant energy incident
G
N
upon the surfaceis given as [5]
G
N
¼
G
0
s
m
a
ð
1
Þ
The value of transmission coeﬃcient for unit air mass
s
a
is slightly less in the summer than in thewinter because the atmosphere contains more water vapor during the summer. It also varies with
M.J. Al-Khawaja / Applied Thermal Engineering 24 (2004) 2601–2610
2603
the conditions of the sky, ranging from 0.81 on a clear day to 0.62 on a cloudy one. A mean valueof 0.7 is generally considered acceptable for most purposes. The value of relative air mass
m
depends on the position of the sun given by the zenith distance
z
, the angle between the zenith (linevertical to horizontal plane) and the direction of the sun. Assuming that the thickness of theatmosphere is negligible compared to the radius of the earth,
m
is equal to secant
z
. This relation issuﬃciently accurate for
z
between 0
and 80
, and beyond this angle solar radiation is almostnegligible.For a horizontal surface (such as roof), the incident solar radiation is calculated from the sun’szenith equation
z
[6]
Fig. 1. Comparison between the calculated and measured solar radiations. All data were taken at Doha, Qatar on May5, 2003.Fig. 2. Direct solar radiations for diﬀerent directions for Doha, Qatar on July 15.2604
M.J. Al-Khawaja / Applied Thermal Engineering 24 (2004) 2601–2610
cos
z
¼
sin
k
sin
d
þ
cos
k
cos
d
cos
x
ð
2
Þ
where the hour angle is determined from
x
¼
p
ð
12
t
solar
Þ
12
ð
3
Þ
and the solar time
t
solar
is found from
t
solar
¼
t
local
þ
E
qt
60
þð
long
local
long
sm
Þ
15
ð
4
Þ
Values are in hours. There is an approximate formula for equation of time
E
qt
. Since it is lengthyformula, the reader should consult reference [7]. Also, the declination of the sun
d
is determinedfrom an approximate formula given in Ref. [6].The amount of direct radiation on a horizontal surface can be calculated by multiplying thedirect normal irradiance
G
N
times the cosine of the zenith angle
z
. On a surface tilted
T
from thehorizontal and rotated
c
counterclockwise from the south, the direct component on the tiltedsurface is determined by multiplying the direct normal irradiance
G
N
by [6]cos
ð
h
Þ ¼
sin
d
sin
k
cos
T
sin
d
cos
k
sin
T
cos
c
þ
cos
d
cos
k
cos
T
cos
x
þ
cos
d
sin
k
sin
T
cos
c
cos
x
þ
cos
d
sin
T
sin
c
sin
x
ð
5
Þ
It is obvious that for vertical wall, the tilted angle
T
would have a value of 90
.Fig. 1 shows the solar radiation for clear sky versus local time for May 5, 2003 at Doha, Stateof Qatar. The calculated solar radiation agrees well with the measured one (using solar collector)particularly in the morning. Fig. 2 shows the clear sky direct-solar radiation for diﬀerent surfaceorientations for the same location but for July 15. It is obvious that the horizontal surface has thehighest solar radiation near noon time.
3. Calculation of solar-air temperature
For opaque surfaces such as the walls and the roofs, the eﬀect of solar radiation is convenientlyaccounted for by considering the outside temperature to be higher by an amount equivalent to theeﬀect of solar radiation. This is done by replacing the ambient temperature in the heat transferrelation through the walls and the roof by the solar-air temperature deﬁned as [2]
T
sol-air
¼
T
ambient
þ
a
s
q
solar
h
o
er
ð
T
4ambient
T
4sky
Þ
h
o
ð
6
Þ
The last term is introduced as a correction when
T
sky
6¼
T
ambient
. This diﬀerence is due to the loweﬀective sky temperature
T
sky
. Its value depends on atmospheric conditions, ranging from a low of 230 K under a cold, clear sky to a high of approximately 285 K under warm, cloudy conditions[4]. For the sake of calculations, we will take
T
sky
as 275 K for hot, clear sky.
M.J. Al-Khawaja / Applied Thermal Engineering 24 (2004) 2601–2610
2605

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