JOURNAL TTG TERMAL

Renewable Energy 29 (2004) 1877–1886

www.elsevier.com/locate/renene

Technical note

Passive cooling by evapo-reflective roof

for hot dry climates

Hamida Ben Cheikh

a,, Ammar Bouchair

De´partement d’architecture, Universite´ de Laghouat, Laghouat, Algeria

Laboratoire de Recherche Cadre Baˆ ti et Environnement (LBCE), De´partement d’ Architecture,

Faculte´ des Sciences de I’ Inge´nieur, Universite´ de Jijel, Jijel, Algeria

Received 20 November 2003; accepted 5 December 2003

Abstract

A dynamic mathematical model for an evapo-reflective roof to improve space cooling in

buildings for hot arid climates has been developed. The proposed roof design is composed of

a concrete ceiling over which lies a bed of rocks in a water pool. Over this bed is an air gap

separated from the external environment by an aluminium plate. The upper surface of this

plate is painted with a white titanium-based pigment to increase reflection of a radiation to a

maximum during the day. At night, the temperature of the aluminium sheet falls below the

temperature of the rock bed mixed with water. Water vapour inside the roof condenses and

falls by gravity. This heat pipe effect carries heat outwards and cold inwards. Heat exchange

is improved by radiation between two humid internal surfaces. The efficiency of this cooling

system is studied using finite difference method. Numerical calculations performed for different

external temperatures and solar radiation show that the cooling produced by such a system

is significant. As a result of this, the mean air temperature in the room may be kept a

few degrees above the minimum nocturnal outdoor temperature throughout the day. However,

the maximum indoor air temperature was observed at sunset. This could further be

lowered by allowing ventilation of the building in the evening. The work is continuing.

Keywords:

Evaporative cooling; Evapo-reflective roof; Hot dry climate; Night ventilation; Dynamic

model

Corresponding author. Tel.: 0021329920153; fax: 0021329932698.

E-mail address:

h.bencheikh@mail.lagh-univ.dz (H. Ben Cheikh).

0960-1481/$ – see front matter

doi:10.1016/j.renene.2003.12.021

1. Introduction

In regions with hot climates such as southern Algeria, excessive heat is the major

problem that causes human thermal discomfort. Space cooling is therefore the

most desirable factor for the inhabitants. Various examples of dwellings responsive

to climatic constraints are found in vernacular architecture throughout the world.

Compact cellular layout with minimum external surface exposure to the sun, whitewashed

surfaces to reduce absorptivity, blind external facades, courtyards, vegetation

to provide humidity and shade, and heavy buildings constructed from high

thermal capacity materials are common passive features in most regions with hot

arid climates, such as the Mzab settlements in southern Algeria, Egypt and Iran

[1–

. Wind towers for cooling ventilation are well known in Iranian and Middle East

architecture, which along with cooling of the air by earth and water evaporation

keep the building comfortable in hot periods

[5]

. Building underground to take

advantage of the large thermal storage capacity of the earth is used in Matmata in

Tunisia and Cappadocia in central Turkey

[2]

In recent years, several investigations were performed and showed that there can

be multiple solutions to the excessive heat problem. A popular method is cooling

ventilation using a solar chimney

[2,6,7]

. The results showed that cooling ventilation

using a solar chimney can reduce internal temperature of buildings. Shading

devices (overhangs and verandas) to reduce summer solar radiation were also

investigated and useful depths of these shading elements for various orientations in

continental climates were defined

[8]

Space cooling can also be achieved by improving the performance of roofs. This

is because the roofs are the surfaces most exposed to direct solar radiation and

can cause excessive heat gain in hot periods. Some efforts were made by investigators

to improve roof thermal performance. The use of low emissivity material in

Nomenclature

ai specific heat of inside air (J kg1 K1

)

ae specific heat of outside air (J kg1 K1

)

surface emissivity

total solar radiation (W m2

)

j long wave radiation (W m2

)

ci inside convection heat transfer coefficient (W m2 K1

)

r radiation heat transfer coefficient (W m2 K1

)

c,wr,al

convection heat transfer coefficient between the rock bed and aluminium

(W m

2 K1

)

saturated vapour pressure (kPa)

al aluminium outside surface temperature (v

solair temperature

wr rock bed upper surface temperature (v

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the attic of a building reduced the underside ceiling surface temperature, which

lowered the room air temperature

[9]

. The evaporative cooling approach for passive

cooling of buildings in hot arid climates has also become an attractive subject

of investigation for many researchers. The relative advantages of evaporative cooling

in relation to many other approaches (cavity wall, insulation, whitewash and

large exposure orientations, vegetable pergola shading, roof with removable canvas,

water film, soil humid grass and roof with white pots as cover) were demonstrated

[10,11]

The reduction of heat gain through the roofs using evaporative cooling systems

was extensively investigated with open roof ponds

[18,19]

, on water spraying over

the roof, moving water layer over the roof, thin water film and roofs with wetted

gunny bags

[12–17]. Chandra and Chandra [12]

have developed a periodic heat

transfer model to study the effects of evaporative cooling using water spray and

variable ventilation on the temperature control of a non-air-conditioned building.

The influence of evaporative cooling over the roof as compared to the bare roof

case and intermittent ventilation as compared to the continuous or no-ventilation

case have been assessed for controlling the indoor air temperature. It was found

that the effectiveness of the evaporative cooling can be improved by conscious

choice of the rate and duration, which controls the inside air temperature significantly.

It was concluded that a combination of evaporative cooling and variable

ventilation can make the internal environment of a building more comfortable.

Chandra et al.

[13]

presented a theoretical assessment of three roof cooling systems

for a non-air-conditioned building, and showed that the maximum cooling is

achieved by water spray over the roof. But the roof pond system with stationary

water is more effective in stabilizing the fluctuations of indoor temperature.

The present study suggests an improved roof design by combining the advantages

of the previously described cooling techniques (water ponds, low emissivity

surfaces) and inserted rocks of high thermal capacity. The resulting design can be

more advantageous and effective than other systems for reducing heat during daytime

and storing coolness at night. High thermal capacity materials (rock bed) will

delay the entry of daytime heat into the building by such a period that it reaches

the interior during the evening, when it is least bothersome and often welcome.

The roof is composed of a concrete ceiling and a flat aluminium plate separated by

an air space partially filled with high thermal capacity rocks placed in a small

quantity of water. The system is properly closed to prevent water vapour escaping

outside. A schematic diagram of the model design is shown in

Fig. 1

2. Mathematical model

The basic configuration of the model considered here is shown in

Fig. 1

. It is a

cubic room 3 m high 3 m wide. The south wall is provided with a window and the

north one is provided with a door. The physical properties of the materials used

for the roof are presented in

Table 1

H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–18 86

1879

The purpose of the present mathematical model is to determine the inside air

temperature at each time step as a function of outside air temperature, solar radiation

and air flow. The solution is based on the inside heat balance at each time

step; the method of lagging with zone capacitance uses information from previous

time steps to predict system response and update the zone temperature at the

current time. One hour is used as the time step (the shorter the time step the smaller

the error). The simulation was done for the described model for two highest

temperature summer days. The model was assumed situated in Algeria (Laghouat,

latitude 33.46

v N, longitude 2.56v

W and elevation 767 m). The simulated days

were the 26th and the 27th of July; the maximum and the minimum temperature

were respectively 42.7, 41, 24.5 and 22

3. Inside air heat balance equation

The heat balance for the air inside the room may be formulated as follows:

aiC

t ¼ Qint þ Qci þ Qv ð1

where

MaiCaidTai=dt

is the change in the energy stored (heat contents) of air inside

the room.

Mai is the room air weight in kg and Cai

is the specific heat capacity of

Table 1

Material properties

Element Material Thickness

(m)

Density

(kg/m

)

Specific heat

(J/kg K)

Conductivity

(W/m K)

Roof Concrete slab 0.10 2400 1080 1.8

Rocks 0.10 2600 800 2.3

Water 0.07 1000 4175 0.613

Aluminium 0.005 2750 936 204

Walls Concrete slab 0.20 2400 1080 1.8

Fig. 1. Model description: (a) room with cooling roof system; (b) room without cooling roof system.

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the room air (1005 J/kg

vC); Qint

is the total internal convective load from light

and occupants in the present model this load is neglected;

Qci

is the total convective

heat gain term from the inside room surfaces (walls, ground and roof) and

may be expressed as:

ci ¼

iAiðTst TaiÞ ð2

is the heat transfer due to air ventilation term which can be expressed as:

v ¼ maeCaeðTae TaiÞ ð3

The derivative term of

MaiCaidTai=dt

can be expressed by a finite difference

approximation as follows:

t ¼ T

Tt@

t ð4

By replacing Eqs. (2), (3) and (4) in Eq. (1) we can obtain the inside air temperature

as follows:

¼ PQt

maiC

@t þXAihiTsi þ maeCaeTaet@

t þnXAihi þ maeCae

The unknown mean inside air temperature,

, is expressed as a function of

inside surface temperatures and external air temperature at each time step

4. Surface temperatures

To calculate the internal surface temperatures,

, at each time step, t

, as a

function of outside conditions, finite difference equations based on heat balance at

each node were used, which allows for temperature determination at any point of

interest. The first step is to select these points, by subdividing the medium into a

number of small regions represented by reference points called nodes. In our case,

we considered the heat flow in one direction in plan elements (walls, roof and

floor) composed of different materials, so each layer of these material is divided

into small regions and represented by nodes. Clarke suggested that three nodes

per homogeneous element and a 1 h time step, in building applications are consistent

with acceptable accuracy

[20]

. The temperature for each single node at

time

is evaluated using heat balance equations. The heat exchange between

internal slab nodes is modelled using Fourier’s one dimensional heat conduction

equation

[21]

t ¼

cdx2 ð6

H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–18 86

1881

This equation can be solved numerically

[21]

by dividing the element into layers

of thickness

called nodes, making a heat balance for each. The heat balance for

node

in the middle of plan element (wall, roof), composed of non-homogeneous

materials is given by:

2 ¼ ðkjþ1 kj1

Dx2qjcj ðT

þ1 T

Þ þ

jðT

þ1 2T

þ T

x2qjc

The boundary condition for the inside surface nodes in contact with room air

may be given by:

x ¼ hiðTsi TaiÞ ð7

The boundary condition for the outside surface nodes in contact with outside air

may be formulated using the following equation:

x ¼ heðTse TaoÞ ð8

where

hi and he

are combined convection and radiation coefficients whose values

according to

[22] are hi ¼ Ehr þ hci and he ¼ Ehr þ hce and hce ¼ 0:76V þ 2:

The upper roof surface exchanges heat with the outside air by convection and by

radiation to the sky. According to

[23], a horizontal surface with emissivity er

and

absolute temperature

Tr, produces a net radiative cooling rate Qr

, where

r ¼ Arer T

sky ð9

where

Tsky ¼ e1=

sky

Tae, esky ¼ 0:741 þ 0:0062Tdp and r

is the Stefan–Boltzman constant

:67 108W=m2 K4

dp is the surface dew point temperature in v

C. It was computed as a function of

the ambient temperature (

Tae

) and the relative humidity (RH), using the expression

by Murray

[24]

dp ¼ 237:

lnRH

þ a

a lnRHÞ þ a b ð10

where 0

RH 1, a ¼ 17:2693882 and b ¼ Tae=ðTae þ 273Þ

The heat exchange by convection for outside horizontal surface is given by:

c ¼ AhceðTr TaeÞ ð11

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H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–1886

The heat exchange between the lower aluminium surface and the upper rock bed

surface is by radiation, convection and evaporation. Following equations reported

[25]

, we may write the following.

Heat exchange by radiation is given by:

r ¼ AhrEwr;alðTwr TalÞ ð12

where

Ewr;al

is the surface emissivity between the rock bed and the aluminium and

is given by

Ewr;al ¼ 1=ð1=ð1=ealÞ þ ð1=ewrÞÞ and hr ¼ 4rT

and A is the area (m2

)

Heat exchange by convection is given by:

c ¼ Ahc;wr;alðTwr TalÞ ð13

where

c;wr;al ¼ 0:9 ðTwr Tal

Þ þ

vsðTwrÞ PvsðTal

267 PvsðTwrÞ Twr1=

Heat exchange by evaporation and condensation is given by:

evp ¼ 6:3 103½PvsðTwrÞ PvsðTalÞ
L hc;wr;al ð15

where

is the latent heat of evaporation at an average temperature, which is

equal to 2350 kJ/kg and

Pvs

is the saturated vapour pressure in kPa at temperature

Tin

For the temperature range 20

T 80 v

C, the following polynomial gives

acceptable results

[25]

vsðTÞ¼16:037þ1:8974T 0:0699T2þ0:0012T35:8511106 T4 ð16

In modelling the floor elements, the earth temperature at 60 cm depth below the

floor is considered constant and equal to the daily average temperature of the

region

[2]

In the above equations, the number of unknowns is greater than the number of

equations; these equations were solved by proposing the initial inside air temperature

at start time

t. This initial temperature TalðtÞ

will not be correct and it is

necessary to simulate the model with the same daily repetition of air temperature

and solar radiation until the temperature of each node returns to the same value at

the same time in each day’s simulation. At this point, the building is in thermal

harmony with the environment.

5. Results and discussion

Analysis of the results shows that the most significant factors affecting the cooling

power of the passive cooling roof were the rocks, water volume, aluminium

roof thickness and roof air space width. The simulation was done for two models,

room with cooling roof system as shown, and room with bare roof. The model was

assumed to be located in Laghouat city at latitude 33.43

v N and longitude 2.56v

H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–18 86

1883

Fig. 3. Comparison of room air temperatures with cooling roof system and with bare roof (for ventilated

room case).

Fig. 2. Comparison of room air temperatures with cooling roof system and with bare roof (for nonventilated

room case).

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H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–1886

for an elevation of 767 m above sea level. The simulated day was 26 July; the

maximum and the minimum temperature were respectively 42.7 and 24.5

vC.

Fig. 2

shows a comparison of room air temperatures with cooling roof system and with

bare roof without room ventilation. It can be seen from this figure that the evaporative

reflective roof can reduce the internal room air temperatures during the day

up to 8

C in comparison to the air temperatures for a bare roof over the room.

Fig. 3

is the comparison of room air temperatures with cooling roof system and

with bare roof when room ventilation is allowed. The ventilation was allowed from

8 pm till 9 am, a period when the outside air temperature is relatively low. This can

significantly improve cooling of room air temperatures, as shown in

Fig. 4

6. Conclusion

A dynamic mathematical model for an evapo-reflective roof used to improve

space cooling in buildings in hot arid climates has been developed. The analysis

theoretically examined the effectiveness of such a roof cooling system in comparison

to a bare roof. The results showed that cooling inside buildings can be

improved by the application of such a cooling design. It was also seen that combining

evapo-reflective roof with night ventilation increases such cooling more significantly.

Fig. 4. Comparison of room air temperatures with cooling roof system (for ventilated and nonventilated

room case).

H. Ben Cheikh, A. Bouchair / Renewable Energy 29 (2004)1877–18 86

1885

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