passive cooling of buildings by using integrated earth to air heat exchanger

7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger

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Passive cooling of buildings by using integrated earth to air heat exchanger

and solar chimney

M Maerefat AP Haghighi

Department of Mechanical Engineering Faculty of Engineering Tarbiat Modares University Tehran 14115-143 Iran

a r t i c l e i n f o

Article history

Received 26 August 2009

Accepted 3 March 2010

Available online 26 March 2010

Keywords

Passive cooling

Earth to air heat exchanger

Solar chimney

a b s t r a c t

Passive cooling is being employed as a low-energy consuming technique to remove undesirable interiorheat from a building in the hot seasons There are numerous ways to promote this cooling technique and

in the present study the use of solar chimney (SC) together with earth to air heat exchanger (EAHE) is

introduced Consequently theoretical analyses have been conducted in order to investigate the cooling

and ventilation in a solar house through combined solar chimney and underground air channel The

1047297nding shows that the solar chimney can be perfectly used to power the underground cooling system

during the daytime without any need to electricity Moreover this system with a proper design may also

provide a thermally comfortable indoor environment for a large number of hours in the scorching

summer days Based on the required indoor thermal comfort conditions the numbers of required SCs

and EAHEs are calculated and some features of such a system is presented It is widely expected that the

proposed concept is useful enough to be incorporated with a stand-alone or a cluster of buildings

especially in some favorable climates

2010 Elsevier Ltd All rights reserved

1 Introduction

Environmental comfort economy and energy conservation are

some of the major functional considerations in the buildings So far

as institutional commercial and residential buildings are con-

cerned electrical air-conditioning systems are mainly employed for

the health and comfort of the occupants As matter of fact the

demand for air-conditioners is growing yearly However with the

increasing cost diminishing supply of nonrenewable energy and

environmental reasons there began a tremendous surge of interest

and research in solar and passive systems since the 1970s The use

of passive cooling techniques combined with a reduced cooling

load may not only result in a good thermal summer comfort but

they save cooling energy consumption too Here the two inter-

esting and promising passive cooling techniques are natural dayventilation and earth to air heat exchangers Natural ventilation is

usually employed in a region with mild climate and in spaces where

a little variation in indoor climate is tolerable A solar chimney on

the other hand is a good con1047297guration to implement natural

ventilation in buildings where solar energy is available

In the past decade solar chimneys had attracted much attention

of investigators and researchers As a matter of fact Bansal et al

analytically studied a solar chimney-assisted wind tower for

natural ventilation in buildings [1] The estimated effect of the solar

chimney was shown to be substantial in inducing natural ventila-

tion for low wind speeds Gan and Riffat also investigated solar-

assisted natural ventilation with heat-pipe heat recovery in natu-

rally ventilated buildings using a CFD technique [2] Hamdy and

Fikry examined theoptimum tiltangle of solar chimney system that

compromises between solar heat gain factor and stack high to

insure the best ventilation performance They also showed that the

air 1047298ow rate through roof solar chimney increases if the height

between inlet and outlet is increased [3] Khedari et al experi-

mentally investigated the feasibility of a solar chimney to reduce

heat gain in a house and the effect of openings on the ventilationrate The results showed that when the solar chimney was in use

room temperature was near that of the ambient air indicating

a good ability of the solar chimney to reduce house rsquos heat gain and

ensuring thermal comfort Opening a window or a door is less

ef 1047297cient than using solar chimneys [4] Mathur et al analytically

studied the effect of inclination of absorber on the air 1047298ow rate in

a solar induced ventilation system using roof solar chimney The

results showed that optimum absorber inclination varies from 40

to 60 depending upon the latitude of the location [5] Bassiouny

and Koura analytically and numerically studied the solar chimney

for improving room natural ventilation They found that the

Corresponding author Tel thorn98 21 8288 3360 fax thorn98 21 8288 3381

Mob thorn98 9123024381

E-mail address maerefatmodaresacir (M Maerefat)

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e w w w e l s e v i e r c o m l o c a t e r e n e n e

0960-1481$ e see front matter 2010 Elsevier Ltd All rights reserved

doi101016jrenene201003003

Renewable Energy 35 (2010) 2316e2324



chimney width has a more signi1047297cant effect on ACH compared to

the chimney inlet size [6]

The earth to air heat exchanger is applicable for improving

natural ventilation through a cooling effect which can also

contribute to decrease temperature in the building The earth to air

heat exchanger is a pipe buried in the ground through which air is

sucked into a building Since the ground exhibits high thermal

inertia temperature at a certain depth is almost constant

throughout the year which allows for its use either as a heat sink

(in summer) or a heat source (in winter) [7] In the summer soil

temperature of a hot and arid region at a few meters deep is lower

than the mean daily outdoor air temperature and signi1047297cantly

lower than the usual outdoor daytime air temperature So it can be

used as a heat sink to cool the exterior warm air [8] The proper

designing of the earth to air heat exchanger requires deeper

understanding of the heat andmoisture dynamics in the earth to air

heat exchanger Various analytical and numerical models have

contributed to investigate the thermal behavior and cooling or

preheating potential of EAHE [9e12]

Krarti and Kreider [9] developed a simpli1047297ed analytical model to

determine the energy performance of an underground air tunnel

The model assumed that the air tunnel-ground system reaches

periodic and quasi-steady state behavior after some days of oper-ation Also parametric analysis was conducted to determine the

effect of tunnel hydraulic diameter and air 1047298ow rate on the heat

transfer between ground and air inside the tunnel Hollmuller [10]

considered a periodic input for the air in the buried pipe yielding

a physical interpretation of the amplitude-dampening and the

phase-shifting of the periodic input signal Al-Ajmi et al [11]

developed a theoretical model of an eartheair heat exchanger for

predicting the outlet air temperature and cooling potential of these

devices in a hot arid climate The results showed that the EAHE

have the potential for reducing cooling energy demand in a typical

house by 30 over the peak summer season Kumar et al [12] used

the concept of arti1047297cial neural network and goal oriented design to

propose a computer design tool that can help the designer to

evaluate any aspect of earth to air heat exchanger and behavior of

the 1047297nal con1047297guration The results showed that there are six vari-

ables in1047298uencing the thermal performance of the earth to air heat

exchangers These variables are length humidity ambient air

temperature ground surface temperature ground temperature at

burial depth and air mass 1047298ow rate

The technique for passive cooling that is introduced and inves-

tigated in the present paper is integrated earth to air heat

exchanger and solar chimney (EAHE-SC) system A schematic plan

of the passively cooled room is shown in Fig 1 This system realizes

both cooling and ventilation during daytime with the help of solar

energy thus it is natural day ventilating technique

The proposed solar system consists of two parts the solar

chimney and the earth to air heat exchanger The solar chimney

consisted of a glass surface oriented to the south and an absorber

wall that works as a capturing surface The air is heated up in the SC

by the solar energy and 1047298ows upward because of the stack effect It

causes driving force which sucks the outside air through the cool-

ing pipe

The EAHE consists of horizontal long pipes that areburied under

the bare surface at the speci1047297c depth The pipes are spread under

the ground in a parallel manner The pipe spacing is considered

more than the thickness of the heat penetrating depth to increasethe heat exchange between the soil and the air

It will be shown this system can provide good indoor condition

in accordance with the Adapted Comfort Standard (ACS) speci1047297ed

for thermal comfort in naturally ventilated buildings The required

indoor temperatures according to the adaptive comfort model are

shown in Fig 2 The 1047297gure only shows the acceptable temperature

of indoor air when the outdoor temperature is within the range of

0e40 C and it does not recommend the ventilation rate [13]

Ventilation standards require a minimum of 3 air changes per

hour for residential buildings in India [14] Therefore the minimum

ventilation rate is set approximately around 3 ACH It will be

consequently shown that how this ventilation rate suitably

provides the required cooling loads of a room

Fig 1 Schematic diagram of integrated earth to air heat exchanger and solar chimney

M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2317



2 Modeling the system

Themodeling includes models of solarchimney(Fig3) and earth

toair heat exchanger (Fig4) In estimating theventilationrateof theproposedsolarhouse as a wholeit is important to determine theair

1047298ow rate which can be handled under a particular design and

operating conditions For this an overall energy balance on the

chimney is considered This includes the energy balances of glass

cover wall the black absorber wall and the air in between Writing

energy balance equations for absorber surface glass surface and air

column and solving them for T g T abs and T f to calculate air 1047298ow rate

have sought a mathematical solution Chimney modeling has been

done in accordance with Ong model [15]

The EAHE system presented in this paper is modeled as two

coupled heat transfer processes namely convection heat transfer

between air 1047298owing in the pipe and the pipe inner surface and

conduction heat transfer between the pipe inner surface and the

surrounding soil

The major assumptions that are used in the modeling may be

summarized as follows

1 Air inlet to the chimney is considered to have the same room

air average temperature

2 Only buoyancy force is considered wind induced natural

ventilation is not included

3 The 1047298ows in the channels are hydrodynamically and thermally

fully developed

4 The glass cover is opaque for infrared radiation

5 Thermal capacities of glass and absorber wall are negligible

6 The air 1047298ow in the channel is radiative non-participating

media

7 All thermophysical properties are constant evaluated at an

average temperature

8 The soil is homogeneous and the soil type does not changealong the channel

9 The system is at steady-state condition

21 Mathematical modeling of solar chimney

An element of the model for SC is shown in Fig 3 In principle

and based on the energy conservation law a set of differential

equations are obtained along the length of SC The energy balance

equation for glass cover is

S g A g thorn hrabsg Aabs

T abs T g

frac14 hg Ag

T g T fsc

thorn U ga AgT g T fsc (1)

The overall top heat loss coef 1047297cient from glass cover to ambient

air U ga can be written as

U ga frac14 hwind thorn hr gsky thorn hga (2)

The convective heat transfer coef 1047297cient due to the wind hwind is

given by [16]

hwind frac14 28 thorn 30uwind (3)

The solar radiation heat 1047298ux absorbed by the glass cover S g is

given by

S g

frac14 ag

I (4)

Fig 2 Adaptive standard for naturally ventilated buildings

Fig 3 Schematic diagram of the heat transfer in the solar chimney

Fig 4 Cross section of an EAHE with heat penetration depth

M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242318



The radiative heat transfer coef 1047297cient from the outer glass

surface to the sky referred to the ambient temperature is obtained

from [15]

hr gsky frac14s3g

T g thorn T sky

T 2g thorn T 2

sky

T g T sky

T g T a

(5)

Where the sky temperature is T sky frac14 00552T a15[16]The radiation heat transfer coef 1047297cient between absorber plate

and glass cover may be obtained from [15]

hr absg frac14s

T 2g thorn T 2abs

T g thorn T abs

1=3g thorn 1=3abs 1 (6)

The convective heat transfer coef 1047297cient between the glass cover

and air 1047298ow in the chimney

hg frac14 Nugkfsc=Lg (7)

Where Nusselt number Nug frac14 06(Grgcos qPrfsc)02 Grashof

number Grg frac14

( g bS g

(Lg

)4(kfscn

fsc

2 )) [5] The convective heat transfer

coef 1047297cient between inclined absorber wall and the air 1047298ow in the

chimney is given by

habs frac14 Nuabskfsc=Lsc (8)

Where Nusselt number Nuabs frac14 06(Grabscos qPrfsc)02 and Grashof

number Grabs frac14 ( g bS abs(Labs)4(kfscnfsc2 )) All property values are

evaluated at average surfaceeair temperatures

The energy balance equation for air 1047298ow in the chimney is

habs Aabs

T abs T fsc

thorn hg Ag

T g T fsc

frac14 mC fsc

T fsc T r

g

(9)

The axial mean air temperature was experimentally determined

to follow the non-linear form [15]

T fsc frac14 gT fsco thorn eth1 gTHORNT fscin (10)

Value of the constantg is taken as 074 according to Ref [17] The

energy balance equation for the absorber plate is written as

S abs Aabs frac14 habs Aabs

T abs T fsc

thorn hr absg Aabs

T abs T g

thorn U absa AabsethT abs T aTHORN (11)

The overall heat transfer coef 1047297cient from the rear of the

absorber wall to the ambient U absa is given by

U absa frac14

1=eth

1=

ha thorn

t ins=

kinsTHORN

(12)

In the above equation ha has been taken as 28 Wm2 K [16]

22 Mathematical modeling of EAHE

In orderto determinethe system cooling capabilityone is mainly

interested in the cool air temperature supplied by the EAHE

Therefore detailed modeling of the EAHE is required The cross

section of EAHE used in the model and the thermal network of the

systemare shown in Figs 4 and5 respectively In order to impose the

ground thermal loads as boundary conditions at the EAHE wall the

undisturbed soil temperature (T su) has been used The soil temper-

ature is nearly constant at the penetration depth (Fig1) The pene-

tration depth is de1047297

ned when the surface of the soil is subjected to

a periodic temperature It depends on the soil diffusivity and the

temperature cycle frequency through equation (13) [10]

d frac14

ffiffiffiffiffiffiffi2ls

u

r (13)

Where ls frac14 ks(rsC s) for daily variation u frac14 (2pday) and for annualu frac14 (2p(year)) The penetration depths are used to calculate the

thermal resistance only and the rest of the analysis is carried out at

steady-state condition The model includes two equations one is

related to the energy balance of the circulating 1047298uid and the other

equation describes heat transfer in the soil region

The energy balance for d x a differential length of EAHE can be

expressed in the following form

T ft T su frac14 dQ Rtotal

d x (14)

Where Rtotal represents the overall thermal resistance which can

be de1047297ned by the resistance network as shown in Fig 5

Rtotal frac14 Rc thorn Rt thorn Rs (15)

Where Rc is the thermal resistance due to convection heat

transfer between air in the pipe and the pipe inner surface It may

be expressed as

Rc frac14 1

2pLt h ft (16)

The convection heat transfer coef 1047297cient inside the pipe is

de1047297ned by

hft frac14 Nutkft

2r ti(17)

The Nusselt number for air 1047298ow in pipe with smooth internalsurface depends on Reynolds number and it is given by [18]

Nu frac14 366 if Re lt 2300 (18a)

Nu frac14 x=8ethRe 1000THORNPr

1 thorn127 ffiffiffiffiffiffiffiffiffiffiffi

ethx=8THORNp

Pr2=3 1 if 2300 Relt5 106 (18b)

Where

x frac14 eth182log Re 164THORN2 if Re 2300 (19)

Rt is the thermal resistance of the pipe Steady-state analysis gives

the thermal resistance of the pipe annulus as

Fig 5 Thermal resistance between air 1047298ow and surrounding undisturbed soil




Rt frac14 ln

r ti thorn t t

r ti

2pktLt (20)

Rs is the thermal resistance between EAHE and undisturbed soil

surface it is given by

Rs frac14 1

2pksLt

ln01 thorn d

r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn

d

r ti thorn t t

2

1s 1A (21)

The energy balance of the circulating 1047298uid is given by

dQ frac14 mC f dT ft

d x d x (22)

Eqs (14) and (22) give the differential overall energy balance

equation in the form8gtlt

gt

dT ft

d x thorn

T f t

mC ftRtotalfrac14 00

T ft frac14 T a x frac14 00

(23)

The solution of equation (23) can be expressed as

T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp

x

mC ftRtotal

(24)

23 Room ventilation and temperature

Chimney effect causes the movement of air into and out of

buildings and is driven by buoyancy Buoyancy occurs due to

a difference in indoor-to-outdoor air density resulting from

temperature and moisture differences A chimney heated by solar

energy can be used to drive the chimney effect without increasing

room temperature The driving potential for the air 1047298ow through

the solar house is function of the pressure difference between the

inlet of the EAHE and the SC outlet The buoyancy pressure due to

increasing air temperature in SC sucks the cooled and heavy air

through the EAHE The friction losses due to 1047298uid 1047298ow through the

channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the

buoyancy pressure overcomes the sum of all 1047298ow pressure losses

the natural ventilation may take place

A mathematical model based on Bernoullirsquo s equation has been

used to estimate the system 1047298ow rate Thus the chimney net draft

Draftsccan be calculated by the following equation [19]

Draftsc frac14rfa rfsco

gLscsin q

0X7

j frac14 6

c j thorn xscLsc

dhyd

sc

1A

r

fscou

2

sc2

eth25THORN

Where the c j is the pressure loss coef 1047297cients at the locations which

are indicated in Fig 1

In right hand side of equation (25) the 1047297rstclause is thechimney

theoretical draft and the second one is the chimney pressure loss

The EAHE pressure loss DP EAHE is [20]

DP EAHE frac14

0X5

j frac14 1

c j thorn xtLEAHE

dti

1Arftu2

f t

2

(26)

The air temperature variation in the vertical pipe is ignored The air

temperature at the solar chimney inlet is assumed to be same as the

room air temperature which is higher than the cooled air

temperature at the pipe outlet So the chimney effects DraftEAHE

and DraftRoom can be expressed as

DraftEAHE frac14rfr rft

gH tr (27)

DraftRoom frac14

rfscin rfr

gH rinscin (28)

The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and

DraftRoom

DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)

Under steady-state conditions we can write

DraftSystem frac14 Draftsc (30)

The air mass 1047298ow rate at the chimney and EAHE are the same if

there is no air in1047297ltration

m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)

By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as

usc frac14

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms

Friction Terms

r (32-a)

Where

Bouyancy Terms frac14 2

rfa rfsco

gLscSinethqTHORN

rfscin rfr

gH rinscin

rft rfr

gH tr

(32-b)

Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin

2

rfr thornn

ethc THORN7thornxsc Lsc

ethdhydTHORNsc

orfscothorn( P5

j frac14 1

c j thorn xtLtthornH trthornBurried depth of EAHE

dt

rfsco Asco

rft At

2)rft

(32-c)

The main criteria for thermal comfort condition are affected by two

factors the ACH and room air temperature The ACH is calculated

under steady-state conditions by the following equation [5]

ACH frac14 3600m

rfscV (33)

The room air temperature which depends on room heat gain is

obtained by the following equation

T r frac14 T ftot thorn Q rmC ft

(34)

Where Q r is sum of the heats that the room gains through the walls

and the heat generated by internal heat sources

3 Analysis

The system capability to provide the desired indoor condition

depends on parameters such as the ambient conditions (tempera-

ture solar radiation) dimensions of SC and EAHE and cooling

demand Parametric study is carried out to 1047297nd the effects of

geometrical dimensions of the SC and EAHE and outdoor envi-

ronmental conditions The following dimensions and speci1047297

cations




are used in the modeling The room 40 40 3125 m in

dimensions without air in1047297ltration and has a minimum cooling

demand of Q frac14 116 W This is the demand of a room with adiabatic

walls which one person is resting in it The cooling demand is

changed at the range of 116e1500 W in the calculations

A solar chimney with the length of 40 m width of 10 m air gap

depth of 03 m and inlet of 04 04 m is considered These

dimensions are chosen based on studies of Ref [22] and may be

changed in the calculation A detailed study on a south facing solar

chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers

of solar chimneys are adequate to provide the required stack effect

for the system

The cooling pipe of EAHE is a PVC pipe with 250 m length

001 m thickness and inside diameter of 05 m and is buried 30 m

below the soil surface According to the model developed by Bansal

et al [21] undisturbed soil temperature at a depth of 30 m is

approximated to be 19 C for a dry shaded soil surface condition

and it is considered to be the heat sink temperature These

dimensions have a decisive in1047298uence on cooling load and system

performance which will be investigated here Usually only one

EAHE suf 1047297cesto provide the necessarycooling load but in sever hot

conditions more cooling pipes may be employed

The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet

level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m

above the buried horizontal pipes of the EAHE The ambient

outdoor temperature is 34 C The thermophysical properties of the

materials included in the modeling are given in Table 1 The values

of the properties speci1047297ed in the table are kept constant in the

computation unless speci1047297cally noted otherwise

A computer program was written in MATLAB software to solve

the mathematical model The governing equations (1 9 11 24 and

32) have to be solved iteratively until convergence of the results

There is no experimental data to validate the results of theo-

retical model for the integrated system So the calculation has been

carried out for SC and EAHE separately under same conditions of

experimental studies of [22] and [23] to check the mathematical

model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical

and experimental results of Mathur et al [22] for different combi-

nations of solar radiation SC height and chimney inlet dimensions

The quantitative comparison shows a reasonable agreement

between the results obtained by the present study and the pub-

lished results of [22] The results of present study are closer to the

experimental results than the theoretical results of Ref [22] It

should be noted that the calculation carried out at the same

conditions of Ref [22] in which the roomvolume is 27 m3 and other

experimental conditions are given in Table 2

Fig 6 shows the air temperature variation along the cooling

pipe The results of the present work are calculated at the condi-

tions of experiments of Ref [23] given in Table 3 As the 1047297gure

shows there is good agreement between the present theoretical

results and the experimental results of Ref [23]

However it is reasonable to conclude that the mathematical

model can predict air temperature quite accurately and the calcu-

lated results are reliable

4 Result and discussion

41 Capability of the system to provide thermal comfort

Theoretical calculations are performed at various solar radia-

tions and room cooling demands The results are summarized in

Table 4 It is found that an integrated system of a few number of

solar chimneys with one (or at most two) EAHE cooling pipe can

Table 1

Thermophysical properties

Parameters Values

1 Transmissivity of glass 084 (d)

2 Absorptivity of glass 006 (d)

3 Emissivity of the glass 090 (d)

4 Absorptivity of absorber wall 095 (d)

5 Emissivity of the absorber wall 095 (d)

6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)

8 Thermal conductivity of the Soil 052 (Wm K)

9 Speci1047297c heat of soil 1840 (Jkg K)

Table 2

Comparison of experimental and theoretical results for solar chimney induced ACH number

Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)

ACH Errors of [22] Errors of present

studyEXP [22] Theo [22] Theo (present study)

300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

Fig 6 Comparison present results with experimental data




provide the indoor thermal comfort conditions so the temperature

is retained at 2815e3194 C which is within the acceptable range

according to Ref [14] with 3e7 ACH which secures the required

ventilation rate As can be seen for higher cooling demands longer

and more cooling pipes of the EAHE are required

42 Effective dimensions of the system

There are many geometrical dimensions in the system that

affect its performance Some of them such as dimensions of the

inlet of the SC cross area of the SC etc have minor effects these

in1047298uence the 1047298ow rate slightly by changing the resistance to the

1047298ow While two geometrical dimensions have the substantial

effects i) absorbing surface area of the SC which provide the

energy for stack effect at the SC ii)cooling surface area of the EAHE

which facilitates heat removal from the air 1047298ow to soil

In the present study effects of variations of all dimensions are

investigated Based on the obtained results the dimensions

described in the section 3 have been chosen as suitable working

dimensions The details of the results are not given in the present

paper to save time However effects of changing the two ef 1047297cacious

dimensions are reported here

i) Absorber surface area is increased by increasing the length of

the chimney This increase results in higher ventilation rate or

higher ACH number On the other hand higher ventilation

rate with a constant cooling source results in higher indoor

temperature Thus more number of buried pipes are required

to cool the room and satisfy the thermal comfort require-

ments as shown in Table 5

ii) The lateral surface area of the buried pipe is serving as heat

exchange surface area of the heat sink of the system Gener-

ally larger cooling area provides more cooling effect to the

system In order to increase the cooling surface one may

increase the diameter andor the length of the pipe Table 6

shows the effect of EAHE length on system performance at

two different cooling demands For the length of EAHE less

than 20 m the comfort temperature may not be provided and

longer EAHE should be employed

Resultsof the study on thediameterof cooling pipes are shown in

Table 7 A comparative surveyshows that the required number of SCs

and EAHEs are minimums when the diameter is 05 m Therefore

this value is adopted as default valueof diameterand thevariation in

lateral area surfaces are made by increasing the length of the pipe

43 Effects of environmental conditions on the system performance

The environmental conditions are comprised of solar radiation

and outdoor ambient temperature in the present study Table 8

Table 3

Properties and conditions of experiment [23]

1 Length of EAHE 2500 (m)

2 Buried depth of EAHE 256 (m)

3 Radius of pipe 0305 (m)

4 Thickness of pipe 0002 (m)

5 Thermal conductivity of pipe 033 (Wm K)

6 Thermal conductivity of soil 116 (Wm K)

7 Thermal diffusivity of soil 645 107 (m2s)

8 Air velocity 147 (ms)

9 Air density 1214 (kgm3)

10 Air viscosity 178 107 (kgs m)

11 Speci1047297c heat of air 1205 103 (Jkg K)

12 Air Prandtl number 065 (d)

13 Thermal conductivity of air 028 (Wm K)

Table 4

Performance of the system at various cooling demands and solar radiations

Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2

Note Ambient air temperature frac14 34 C

Table 5

Effects of absorber length on system performance

Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6

Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)

Table 6

Effects of length of EAHE on system performance

Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1

800 40 400 150 Thermal comfort cannot be

provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2




shows the summary of results of the theoretical calculations fordifferent environmental conditions

The buoyancy driving force increases with an increase of solar

intensity and it causes higher ACH Thus less number of SCs are

required to drive the cool and heavy air through the EAHEs and to

compensate the pressure drops The results of calculations also

show that the required number of EAHEs should be increased to

retain the thermal comfort condition when the number of ACH and

indoor air temperature are increased at high solar radiation

The effect of ambient airtemperature on stack effect of SC is vice

versa The stack effect decreases when the ambient outdoor

temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room

The results show that the system can provide the required

indoor temperature and ACH number even at harsh environmental

condition of high temperature of 45 C and low solar radiation of

100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be

able to provide the stack effect and in this condition the use of

a small fan can help the cool air to 1047298ow from EAHE in to the room

and to realize thermal comfort condition

It should be noted that in this system all air 1047298ow is fresh air and

a reduction about 23 C in the inlet air is praiseful achievement of

the present passive cooling system

5 Conclusions

A passive solar system comprises of solar chimneys and earth to

air heat exchangers is proposed and studied in the present paper

The present study shows that the performance of the system

depends on solar radiation outdoor air temperature as well as

con1047297guration of both the SC and the EAHE

The results showed that the number of required SCs decreases

with the use of taller SCs The use of taller SCs lead to thermal

discomfort therefore more number of buried pipes should be

employed to cool air 1047298ow and satisfy the thermal needs

Results of the study on diameter of EAHE show that there is an

optimum diameter for cooling pipes (05 m) which gives the

minimum required number of SCs and EAHEs It has also been

found that the long EAHE with the length of more than 20 m should

be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and

cooling demand are high although providing thermal comfort is

dif 1047297cult proper con1047297gurations could provide good indoor condi-

tion even in the poor solar intensity of 100 Wm2 and high ambient

air temperature of 50 C

References

[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500

[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87

[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814

(1e

4)381e

6

Table 7

Effects of diameter of EAHE on system performance

Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8

800 40 400 03 Thermal comfort cannot be provided

05 314 2900 3 5

07 443 2986 4 7

09 Thermal comfort cannot be provided


05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8

System performance at different indoor and outdoor conditions

Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900




[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93

[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63

[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73

[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18

[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-

mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7

[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74

[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17

[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44

[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55

[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8

[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7

[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60

[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980

[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and

1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011

[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346

[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45

[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35

[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5

Nomenclature

A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)

I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)

U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)

xy coordinate system (m) Z height of chimney inlet (m)

Greek symbols

a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor

r density (kgm

3

)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)

Dimensionless terms

Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]

Subscripts

a ambientabs absorber wallc convective

f air 1047298ow g glasshyd hydraulici internalin inletins insulation

j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe




chimney width has a more signi1047297cant effect on ACH compared to

the chimney inlet size [6]

The earth to air heat exchanger is applicable for improving

natural ventilation through a cooling effect which can also

contribute to decrease temperature in the building The earth to air

heat exchanger is a pipe buried in the ground through which air is

sucked into a building Since the ground exhibits high thermal

inertia temperature at a certain depth is almost constant

throughout the year which allows for its use either as a heat sink

(in summer) or a heat source (in winter) [7] In the summer soil

temperature of a hot and arid region at a few meters deep is lower

than the mean daily outdoor air temperature and signi1047297cantly

lower than the usual outdoor daytime air temperature So it can be

used as a heat sink to cool the exterior warm air [8] The proper

designing of the earth to air heat exchanger requires deeper

understanding of the heat andmoisture dynamics in the earth to air

heat exchanger Various analytical and numerical models have

contributed to investigate the thermal behavior and cooling or

preheating potential of EAHE [9e12]

Krarti and Kreider [9] developed a simpli1047297ed analytical model to

determine the energy performance of an underground air tunnel

The model assumed that the air tunnel-ground system reaches

periodic and quasi-steady state behavior after some days of oper-ation Also parametric analysis was conducted to determine the

effect of tunnel hydraulic diameter and air 1047298ow rate on the heat

transfer between ground and air inside the tunnel Hollmuller [10]

considered a periodic input for the air in the buried pipe yielding

a physical interpretation of the amplitude-dampening and the

phase-shifting of the periodic input signal Al-Ajmi et al [11]

developed a theoretical model of an eartheair heat exchanger for

predicting the outlet air temperature and cooling potential of these

devices in a hot arid climate The results showed that the EAHE

have the potential for reducing cooling energy demand in a typical

house by 30 over the peak summer season Kumar et al [12] used

the concept of arti1047297cial neural network and goal oriented design to

propose a computer design tool that can help the designer to

evaluate any aspect of earth to air heat exchanger and behavior of

the 1047297nal con1047297guration The results showed that there are six vari-

ables in1047298uencing the thermal performance of the earth to air heat

exchangers These variables are length humidity ambient air

temperature ground surface temperature ground temperature at

burial depth and air mass 1047298ow rate

The technique for passive cooling that is introduced and inves-

tigated in the present paper is integrated earth to air heat

exchanger and solar chimney (EAHE-SC) system A schematic plan

of the passively cooled room is shown in Fig 1 This system realizes

both cooling and ventilation during daytime with the help of solar

energy thus it is natural day ventilating technique

The proposed solar system consists of two parts the solar

chimney and the earth to air heat exchanger The solar chimney

consisted of a glass surface oriented to the south and an absorber

wall that works as a capturing surface The air is heated up in the SC

by the solar energy and 1047298ows upward because of the stack effect It

causes driving force which sucks the outside air through the cool-

ing pipe

The EAHE consists of horizontal long pipes that areburied under

the bare surface at the speci1047297c depth The pipes are spread under

the ground in a parallel manner The pipe spacing is considered

more than the thickness of the heat penetrating depth to increasethe heat exchange between the soil and the air

It will be shown this system can provide good indoor condition

in accordance with the Adapted Comfort Standard (ACS) speci1047297ed

for thermal comfort in naturally ventilated buildings The required

indoor temperatures according to the adaptive comfort model are

shown in Fig 2 The 1047297gure only shows the acceptable temperature

of indoor air when the outdoor temperature is within the range of

0e40 C and it does not recommend the ventilation rate [13]

Ventilation standards require a minimum of 3 air changes per

hour for residential buildings in India [14] Therefore the minimum

ventilation rate is set approximately around 3 ACH It will be

consequently shown that how this ventilation rate suitably

provides the required cooling loads of a room

Fig 1 Schematic diagram of integrated earth to air heat exchanger and solar chimney



















surrounding soil








fully developed




media


average temperature









T abs T g

frac14 hg Ag

T g T fsc






given by [16]



given by

S g

frac14 ag

I (4)









from [15]

hr gsky frac14s3g

T g thorn T sky

T 2g thorn T 2

sky

T g T sky

T g T a

(5)



hr absg frac14s

T 2g thorn T 2abs

T g thorn T abs

1=3g thorn 1=3abs 1 (6)





number Grg frac14

( g bS g

(Lg

)4(kfscn

fsc



chimney is given by






habs Aabs

T abs T fsc

thorn hg Ag

T g T fsc

frac14 mC fsc

T fsc T r

g

(9)







T abs T fsc

thorn hr absg Aabs

T abs T g




U absa frac14

1=eth

1=

ha thorn

t ins=

kinsTHORN

(12)















d frac14


u

r (13)









d x (14)






be expressed as

Rc frac14 1

2pLt h ft (16)


de1047297ned by

hft frac14 Nutkft

2r ti(17)


Nu frac14 366 if Re lt 2300 (18a)



ethx=8THORNp

Pr2=3 1 if 2300 Relt5 106 (18b)

Where








Rt frac14 ln

r ti thorn t t

r ti

2pktLt (20)



Rs frac14 1

2pksLt

ln01 thorn d


d

r ti thorn t t

2

1s 1A (21)



d x d x (22)



gt

dT ft

d x thorn

T f t



(23)



x

mC ftRtotal

(24)



















gLscsin q

0X7

j frac14 6

c j thorn xscLsc

dhyd

sc

1A

r

fscou

2

sc2

eth25THORN






DP EAHE frac14

0X5

j frac14 1

c j thorn xtLEAHE

dti

1Arftu2

f t

2

(26)







gH tr (27)

DraftRoom frac14

rfscin rfr

gH rinscin (28)


DraftRoom








usc frac14


Friction Terms

r (32-a)

Where


rfa rfsco

gLscSinethqTHORN

rfscin rfr

gH rinscin

rft rfr

gH tr

(32-b)


2

rfr thornn


ethdhydTHORNsc

orfscothorn( P5

j frac14 1


dt

rfsco Asco

rft At

2)rft

(32-c)




ACH frac14 3600m

rfscV (33)




(34)



3 Analysis







cations















for the system

















































Table 1


Parameters Values









Table 2


Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)



300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts






















surrounding soil








fully developed




media


average temperature









T abs T g

frac14 hg Ag

T g T fsc






given by [16]



given by

S g

frac14 ag

I (4)









from [15]

hr gsky frac14s3g

T g thorn T sky

T 2g thorn T 2

sky

T g T sky

T g T a

(5)



hr absg frac14s

T 2g thorn T 2abs

T g thorn T abs

1=3g thorn 1=3abs 1 (6)





number Grg frac14

( g bS g

(Lg

)4(kfscn

fsc



chimney is given by






habs Aabs

T abs T fsc

thorn hg Ag

T g T fsc

frac14 mC fsc

T fsc T r

g

(9)







T abs T fsc

thorn hr absg Aabs

T abs T g




U absa frac14

1=eth

1=

ha thorn

t ins=

kinsTHORN

(12)















d frac14


u

r (13)









d x (14)






be expressed as

Rc frac14 1

2pLt h ft (16)


de1047297ned by

hft frac14 Nutkft

2r ti(17)


Nu frac14 366 if Re lt 2300 (18a)



ethx=8THORNp

Pr2=3 1 if 2300 Relt5 106 (18b)

Where








Rt frac14 ln

r ti thorn t t

r ti

2pktLt (20)



Rs frac14 1

2pksLt

ln01 thorn d


d

r ti thorn t t

2

1s 1A (21)



d x d x (22)



gt

dT ft

d x thorn

T f t



(23)



x

mC ftRtotal

(24)



















gLscsin q

0X7

j frac14 6

c j thorn xscLsc

dhyd

sc

1A

r

fscou

2

sc2

eth25THORN






DP EAHE frac14

0X5

j frac14 1

c j thorn xtLEAHE

dti

1Arftu2

f t

2

(26)







gH tr (27)

DraftRoom frac14

rfscin rfr

gH rinscin (28)


DraftRoom








usc frac14


Friction Terms

r (32-a)

Where


rfa rfsco

gLscSinethqTHORN

rfscin rfr

gH rinscin

rft rfr

gH tr

(32-b)


2

rfr thornn


ethdhydTHORNsc

orfscothorn( P5

j frac14 1


dt

rfsco Asco

rft At

2)rft

(32-c)




ACH frac14 3600m

rfscV (33)




(34)



3 Analysis







cations















for the system

















































Table 1


Parameters Values









Table 2


Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)



300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts









from [15]

hr gsky frac14s3g

T g thorn T sky

T 2g thorn T 2

sky

T g T sky

T g T a

(5)



hr absg frac14s

T 2g thorn T 2abs

T g thorn T abs

1=3g thorn 1=3abs 1 (6)





number Grg frac14

( g bS g

(Lg

)4(kfscn

fsc



chimney is given by






habs Aabs

T abs T fsc

thorn hg Ag

T g T fsc

frac14 mC fsc

T fsc T r

g

(9)







T abs T fsc

thorn hr absg Aabs

T abs T g




U absa frac14

1=eth

1=

ha thorn

t ins=

kinsTHORN

(12)















d frac14


u

r (13)









d x (14)






be expressed as

Rc frac14 1

2pLt h ft (16)


de1047297ned by

hft frac14 Nutkft

2r ti(17)


Nu frac14 366 if Re lt 2300 (18a)



ethx=8THORNp

Pr2=3 1 if 2300 Relt5 106 (18b)

Where








Rt frac14 ln

r ti thorn t t

r ti

2pktLt (20)



Rs frac14 1

2pksLt

ln01 thorn d


d

r ti thorn t t

2

1s 1A (21)



d x d x (22)



gt

dT ft

d x thorn

T f t



(23)



x

mC ftRtotal

(24)



















gLscsin q

0X7

j frac14 6

c j thorn xscLsc

dhyd

sc

1A

r

fscou

2

sc2

eth25THORN






DP EAHE frac14

0X5

j frac14 1

c j thorn xtLEAHE

dti

1Arftu2

f t

2

(26)







gH tr (27)

DraftRoom frac14

rfscin rfr

gH rinscin (28)


DraftRoom








usc frac14


Friction Terms

r (32-a)

Where


rfa rfsco

gLscSinethqTHORN

rfscin rfr

gH rinscin

rft rfr

gH tr

(32-b)


2

rfr thornn


ethdhydTHORNsc

orfscothorn( P5

j frac14 1


dt

rfsco Asco

rft At

2)rft

(32-c)




ACH frac14 3600m

rfscV (33)




(34)



3 Analysis







cations















for the system

















































Table 1


Parameters Values









Table 2


Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)



300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts







Rt frac14 ln

r ti thorn t t

r ti

2pktLt (20)



Rs frac14 1

2pksLt

ln01 thorn d


d

r ti thorn t t

2

1s 1A (21)



d x d x (22)



gt

dT ft

d x thorn

T f t



(23)



x

mC ftRtotal

(24)



















gLscsin q

0X7

j frac14 6

c j thorn xscLsc

dhyd

sc

1A

r

fscou

2

sc2

eth25THORN






DP EAHE frac14

0X5

j frac14 1

c j thorn xtLEAHE

dti

1Arftu2

f t

2

(26)







gH tr (27)

DraftRoom frac14

rfscin rfr

gH rinscin (28)


DraftRoom








usc frac14


Friction Terms

r (32-a)

Where


rfa rfsco

gLscSinethqTHORN

rfscin rfr

gH rinscin

rft rfr

gH tr

(32-b)


2

rfr thornn


ethdhydTHORNsc

orfscothorn( P5

j frac14 1


dt

rfsco Asco

rft At

2)rft

(32-c)




ACH frac14 3600m

rfscV (33)




(34)



3 Analysis







cations















for the system

















































Table 1


Parameters Values









Table 2


Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)



300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts


















for the system

















































Table 1


Parameters Values









Table 2


Solar radiation

(Wm2)

Absorber

length (m)

Inlet chim dimens

(m m)

Ambient

temp (K)



300 07 10 03 295e302 4400 4173 4366 516 077

08 10 02 298e304 5330 4054 4757 2394 1075

09 10 01 294e296 2400 2704 2368 1266 133

500 07 10 03 295e302 4800 5160 4454 750 721

08 10 02 298e304 4530 4895 4816 806 631

09 10 01 294e296 2660 3461 2970 3011 1165

700 07 10 03 295e302 5600 5810 5404 375 35

08 10 02 298e304 5330 5175 5480 291 281

09 10 01 294e296 2930 3671 3217 2529 979

















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts



















































Table 3















Table 4


Cooling

demand (W)

Solar radiation

(Wm2)

Length of

EAHE (m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 400 25 634 2853 2 1

600 403 2814 1

800 506 2831 1

1000 584 2844 1

200 400 25 630 2935 2 1

600 356 2873 1

800 481 2935 1

1000 565 2933 1

400 400 30 569 2992 2 1

600 790 3015 2

800 388 2951 1

1000 487 3062 1

600 400 40 467 2827 2 1

600 721 3042 2

800 309 2777 1

1000 400 2902 1

800 400 40 520 2813 3 2

600 421 2764 2

800 533 2903 2

1000 627 3014 2


Table 5


Cooling

demand (W)

Absorber

length (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 30 440 2822 1 1

40 583 2844 1 1

50 706 2866 1 1

60 818 2886 1 1

800 30 236 2894 2 340 510 3098 2 3

50 662 3238 2 3

60 829 3363 2 3

800 30 312 2924 3 5

40 305 2941 2 4

50 351 2981 2 5

60 384 3019 2 6


Table 6


Cooling

demand

(W)

Ambient

air temp

( C)

Solar

radiation

(Wm2)

Length of

EAHE

(m)

ACH

d

Room air

temp

( C)

Number

of SC

Number

of EAHE

116 40 400 150 347 2968 4 10

250 602 2972 3 2

350 517 2700 3 2450 579 2861 3 1

116 40 1000 150 347 2987 2 9

250 649 2872 2 3

350 465 2877 1 1

450 356 2633 1 1


provided

250 314 2900 3 5

350 454 2950 3 2

450 427 2700 3 2


provided

250 335 2938 2 6

350 742 2952 2 3

450 559 2926 2 2

























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts




























5 Conclusions



















References




(1e

4)381e

6

Table 7


Cooling

demand (W)

Ambient

air temp (C)

Solar radiation

(Wm2)

Diameter of

EAHE (m)

ACH

d

Room air

temp (C)

Number

of SC

Number

of EAHE

116 40 400 03 430 2996 3 2

05 602 2972 3 2

07 301 2989 3 4

09 476 2998 4 8

116 40 1000 03 507 2770 3 205 649 2872 2 3

07 867 2996 2 4

09 785 2980 2 8


05 314 2900 3 5

07 443 2986 4 7



05 335 2938 2 6

07 321 2931 2 7

09 371 2994 2 12

Table 8


Coolingdemand (W)

Ambient airtemp (C)

Solarradiation

(Wm2)

ACHd

Room airtemp (C)

Numberof SC

Numberof EAHE

500 40 100 328 2961 5 3

500 516 3113 3 3

900 483 3140 2 3

500 45 100 301 3092 6 4

500 430 3112 3 4

900 402 3127 2 4

500 50 100 305 3102 6 6

500 345 3162 3 5

900 306 3152 2 5

1000 40 100 498 3051 8 6

500 410 3195 2 2

900 363 3069 2 4

1000 45 100 415 3000 8 6500 327 3115 3 5

900 300 3090 2 5

1000 50 100 418 3195 8 7

500 305 3198 3 6

900 315 3153 3 12

1500 40 100 520 3136 8 4

500 329 3061 3 5

900 300 3035 2 5

1500 45 100 395 3100 9 9

500 362 3170 4 9

900 317 3160 3 12

1500 50 100


900
























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts



























Nomenclature





Greek symbols


r density (kgm

3


Dimensionless terms


Subscripts





passive cooling of buildings by using integrated earth to air heat exchanger

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