ditigal simulation of indoor temperatures of buildings with roof ponds

Solar Energy, Vol. 3I. No. 2. pp, 205-215, 1983 0038-092XI83/080205-11503.00/0 Printed in Great Britain. Pergamon Press Ltd.

DITIGAL SIMULATION OF INDOOR TEMPERATURES OF BUILDINGS WITH ROOF PONDS

RAJIV YADAV and D. F. RAO Department of Chemical Engineering, Indian institute of Technology Kanpur, Kanpur-208016, India

(Received 14 April 1982; accepted 6 August 1982)

Abstraet--A theoretical model is presented to predict the thermal performance of a building with roof ponds. Equations have been derived for the estimation of steady periodic heat fluxes through the roof slab and the outer walls. Energy storage and release by the partition walls and the floor has been considered. The other cooling loads have been estimated using the methods recommended in the ASHRAE Guide and Data Book. Hourly indoor temperatures are obtained by the numerical solution of the energy balance equation for the building. The algorithm that has been developed for digital simulation of the indoor temperatures is presented. The effectiveness of different kinds of roof-pond systems, i.e. shaded ponds, "Sky-therm", etc. for passive coolings have been examined. The studies indicate that the indoor temperatures of a building located in Delhi can be maintained below 30°C in summer while the maximum dry-bulb temperatures are above 40°C.

1. INTRODUCTION

The concept of using natural cooling, i.e. nocturnal radiation cooling and evaporative cooling for space cooling is quite old[l]. In recent times both nocturnal cooling[2, 3], and natural cooling[4] were utilised for space cooling. Hay and YeUott[5, 6] designed and constructed a proto- type building with roof ponds and successfully demon- strated the effectiveness of their (Sky-therm) system. Since then, several attempts have been made to assess experimentally the effectiveness of roof ponds for space cooling[7-10].

However, to gain an insight of the thermal behaviour of a building, for instance, to know the minimum attain- able indoor temperature, the effect of ambient parameters, etc. a theoretical analysis is warranted. Sodha et a/.[ll] computed the heat flux through the concrete roof with and without ponds for a constant indoor temperature. The evaluation of hourly indoor temperatures rather than the roof fluxes will reveal the effectiveness of roof ponds in space cooling. Recently, Balcomb et al.[12] and Prasad et a/.[13] predicted the indoor temperature using a simple thermal network analysis. Here we present a method to estimate the hourly indoor temperatures based on the steady periodic heat-transfer analysis.

2. TItEORETICAL MODEL

The estimation of indoor temperature of a building inolves (i) the heat transfer rates through the roof, the outer walls, the doors and the windows, (ii) the sensible energy storage and release due to the partition wall and the floor, (iii) cooling loads due to air infiltration, lighting, fans and occupants, etc. First the methods of estimation of these cooling loads are presented and then the energy balance equation for the building is given.

2.1 Heat flux through the roof

The roof is considered to be a homogeneous infinite slab of thickness L. It is assumed that a layer of water of

205

. . . . . . . . . . . . j W a t ~ r

L ~ ' / / / / / / / / / / / / / / , / / / / / ¢ ~ lqL

Fig. 1. Sketch of a roof slab with roof pond.

depth L', separated by a thin plastic film, is maintained over the roof slab. The sketch of the roof slab along with heat fluxes that are involved are shown in Fig. 1. We need to find the heat flux at the inner surface of the roof slab.

This requires the solution of one-dimensional heat conduction equation for the roof slab with the ap- propriate boundary conditions. The outside boundary condition involves the pond-water temperature. The pond-water temperature is obtained as shown below.

The Pond-water temperature. Considering the pond water to be at a uniform temperature and solar radiation entering the water is completely absorbed, the energy balance equation for the pond water is

mcdT.= " P" dt l ( 1 - p ) + q u , + q o - q , - q ~ - q c (1)

where t is time, mw is the amount of water per unit area of the pond, Cpw, T, are the heat capacity and temperature of water, respectively, I is insolation, p is the reflectivity of water, q~, is the downward atmospheric radiative flux, qo is the heat flux from the roof slab and q~, qc, q, are the evaporative, convective and radiative fluxes from the pond, respectively.

Equation (1) can be written as

mwC, w @ = I(1 - p) + qd~ + q(Tp) (2)

where

q(Tp) = - q~ - qc - q, + qo.

206

The function q(Tp) is nonlinear in Tp. It is linearised using the Taylor series expansion about Tpo. Then, eqn (2) is solved to obtain

S _ e_e,) T, = Tpo- F(1 (3)

where

S - - I(1 - p) + qa. + q(Tpo) mwCpw

UL p = - - / ~ / w f p w

dq(T,) UL = ~ ,t Yp=Tpo

T . o = T~I . . . . o.

The equations employed in evaluating the various fluxes are given in Table 1. Equation (3) has been subjected to experimental verification and the agreement is found to be good. The details are reported elsewhere by Kishore et a/.[14].

Roof slab. The inner surface of the roof slab is exposed to the air whose temperature is Tn. Both TR and Te are continuously varying with time. The transfer of heat by radiation between the roof and the interior of the building is neglected. Under these conditions, qL, the heat flux at the inner surfaces of the roof slab can be obtained as shown below.

OT 02T 0-7 = ar ~x (4a)

and the boundary conditions are

- Kr 0I" = hL(TL - TR) (4b) OX x~L

- K" OT =o= ~e~(T°- T") (4c)

where m, K~ are the thermal diffusivity and thermal conductivity of the roof slab, Kp, 4 are the thermal conductivity and thickness of the plastic film and To, TL, are the roof slab temperatures at x - - 0 and at x = L, respectively•

Rmiv YADAV and D. P. RAO

Alford et al. [15] presented the solution of eqn (4) for a general case which formed the basis for the evaluation of periodic fluxes through walls using the concept of sol-air temperature. Their solution adapted for our case is given below. It requires that T[.( = T. - TR) be expressed as a fourier series:

I _ ¢ Tp - T,,,. + T ~ cos(W,t + ¢,)+ . . . + T; . cos(w.t + G) + . . . (5)

1 f24 N,, T ; , . = ~ j 0 T[,dt, tanG=M-- ~,

1 (24 T;,, =(M.2+M,,2) '/z, M. = ~ J o T;cos w,,tdt

N. = T; sin w.t dt, w. = ~ .

The solution in terms of qL is

q,~ = U[T[,m + t,T[~, cos(wd - t)~- ~b,) + . . • + A,,T[,,, cos (w,,t - t), - d~,,) +" ' ']

where

(6)

1 V. = hLKp U = 1 L Kp' o',,Kr(Y. 2 + Z.2)'I2G

h-;+~ + ~-T

~r. = , d'. = tan- ' , h. = V./U

y . = \~-[ hLK,, 1)cos ~r.L sinh o-,,L + \~-{ h2ho 1)

K. h2 q- ~ - 6p

sin ¢ .L sinh o-.L + ~ cos o'.L cosh ¢ .L

Z. = ~ , ~ h 2 K ~ + 1) sin cr.L cosh or.L- \ ~ [ hLKp _ 1~/

• - ho + K d G sin •.L sinh •.L. cosh o-.L sin O'nL + ¢r.Kr

In the above, 6 . is evaluated such that sin ~b. has the sign of Zn ; COS ~b., of Y..

Table 1. Equations used for the heat fluxes

NO. EQUATION

I. qda = T:(1-s+b Pa ~12)

2. qc = hc(Tp-Ta)

h c = 5.7 + 3.8V

3. % - ~ s ( P s - P s )

B 4. In ps = A -

5. qr = ~ ~- T4

SOURCE

The Brunt Equation

18

Duffle and Beckman

19

Treybal 23

Antonle Equstlon

REMARKS

The c o n s t a n t s s= 0.53, b=-O.61 are proposed by Ramanathan & Desal for the Indian conditions

Validity is doubtful (is not a sensity parameter )

Digital simulation of

Equation (6) is used to evaluate qL as well as qo. While evaluating the latter, L in eqn (6) is replaced with zero.

2.2 Heat fluxes through outer walls One can use the concept of sol-air temperature[16] to

estimate the periodic heat fluxes through outer walls. However, for the sake of convenience in computation, the same set of equations used to estimate the roof fluxes were employed. While evaluating the heat fluxes through outer walls we have set Kp/a w, = 10,000WK/m 2, L '= 0.0015 m, p = 0.2 and h~, = 0. Since the water film is taken to be at a uniform temperature it does not offer any thermal resistance. It merely contributes to the increase the heat capacity of the wall which can be safely ignored. Validity of this model is justified later.

2.3 Floor The floor can be assumed to be a semi-infinite homo-

geneous solid. Further; the variation of indoor-air temperature is approximated by the relation

TR = Trim c o s wt.

The boundary condition imposed at the floor surface is

aT I 2~r - Kt ~ x =o = hI(T - T~) and w = 2-4-

where hi is the heat-transfer coefficient and is assumed to be constant with time. For this case, Luikov[17] gives a solution from which the heat flux to the floor, ql, can be obtained as

ql = - KITRmAo [sin(wt - M) - cos(wt - M)]

(7) where

[ 1 + 2 [ w ~ ' / 2 w ] ,/2 Ao

L

M = tan-'[1 + hi(2af/w)m] -'.

2.4 Energy storage in partition walls Due to steady periodic indoor temperature variation,

the partition walls, the furniture, etc., get heated and cooled during a cycle. Depending on the phase difference between TR and the surface temperature of the partition walls, transfer of heat takes place between the inside air and the walls. The resultant heat fluxes influence the amplitude of the oscillations of the hourly indoor temperature. The method of estimation of these fluxes is given by Luikov[17]. But the contribution of heat fluxes due to the furniture and other indoor items are difficult to estimate. In order to understand the influence of these heat fluxes on the indoor temperature swings, a parametric study has been carried out employing the equation

qR = qmR COS(Wt -- L + 1/4~r) (8)

where qR is the heat transfer rate from air to the partition walls, q~,R is the amplitude of qR and L is the

indoor temperatures 207

phase difference between TR and the surface temperature of the walls. Equation (8) has the functional form for the heat flux to a semi-infinite solid whose surface temperature varies sinusiodally.

2.5 Energy balance for building Assuming that the air inside the building is at a uni-

form temperature (a reasonable assumption as the cooling is taking place through the roof) and the net radiation exchange between the internal surfaces is negligible, the energy balance for the building is

dTR - mACpA ~ - = qr + (:lw + qa,,. + Or + q, + qR + q/,, (9)

where CPa, ma are the heat capacity and the mass of air inside the building, the symbols with bar ( - ) represents the heat transfer rates through roof, walls, doors and windows, and floor, respectively, q~ is the internal cooling load due to lights, fans, occupants etc., qA~ is the cooling load due to air infiltration.

Equation (9) is solved numerically using an iterative scheme. The details are given in the following section.

3. ALGORITHM

The numerical solution of eqn (9) is obtained as fol- lows. A set of hourly indoor temperatures for 24hr is assumed. Using these temperatures, the heat transfer rates through outer walls, roof, floor and the contribution due to q~ are computed. The heat transfer rates through doors and windows, and the cooling load due to air infiltration, lights, fans, occupants, etc. are estimated according to the procedures given in the ASHRAE Guide and Data Book[20]. Then, the revised hourly temperatures are obtained from the equation

t Tm.~+l = TRI, I + m------A~A [q, + qw + qa~ + ql + q~ + qR

+qa, ] (10)

where t is the time interval (1 hr is used) and the subscripts J stands for the hr of the day and L for the iteration number. A convergence criteria

(T~, I+, - TRj, 1) < 3.0°C

is used. If the criterion is not satisfied a new set of temperatures is obtained using the regula falsi method, treating the temperature of each hr to be independent of others. Though this procedure resulted in faster convergence than the method of direct substitution, it required some times more than 30 iterations for convergence. A maximum temperature correction of 3°C is allowed from iteration to iteration to prevent divergence. Since the convergence is attained by this procedure, the more efficient techniques like the Newton-Raphson or the multivariable Wegstien were not tried. The algorithm is shown in Fig. 2.

For a given set of indoor temperatures, the eqns (3) and (6) are solved iteratively to obtain q, and qw, since qo is now known a priori. The algorithms for evaluating these fluxes are shown in Figs. 3 and 4.

208 RAJIV YADAV and D. P. RAO

r . . . . .

I [Compute he* 1 I JTr (J, i) using / I /moditie d I Jregula falsi I

L . . . .

1 Set room temp

J Tr(J.L)~ ta(J ) 1

+ Calculate qL &q~ t Subroutin42 room

floor

1 Compute q L,qv,,qfJ q ,qs,qai J

I [Calculat~ ~r (J,i .~C~. u

1 J EP=EP*I Tr (').it 1)-J

Tr(J,~)l~

F ~ - . . . . . .

Fig. 2. Algorithm for the indoor temperature computation.

r I

I

II JCatcuLote tN, J J

h . . . . . ( ~ . . . . . . . . Y

Calculate Tpjj

Tpo,~-TpJ Jqo(J i) ~ qo( ," .I ) I

2 0 ' . . . . J JEPZ~EPZ. lqo(J, .U-qo(J.i I 1

EPS -Tp24 TFOO.~Tp24

F ~ Calculate q L(j)qo(J,i ..).l x, . . . . . ,,, r-, ~ vD [(subroutine flux

Fig. 3. Algorithm to find roof and wall heat fluxes.

I Express Tp as a Fourier series I

I n > - . . . . . . . . .

I Catculat¢ Tpn,Tpn ~n ,~n ,~n J

. . . . . .

I Calculate qL[Jl, qo(Li .1)

TLj,ToJ

Fig. 4. Algorithm for subroutine flux.

DIGITAL SIMULATION

A building of the size 10 m x 10 m x 4 m with 0.30 m thick brick walls and with a door and two windows on each of the four walls is chosen for the simulation. The walls are assumed to be aligned with east, west, north and south directions. The equations employed in evaluating the fluxes qc, qv, etc. are listed in Table 1. The insolation on the walls is found using the procedure given in Ref.[19]. The diffuse radiation is taken to be 10 per cent of the total solar radiation. In evaluating the net thermal flux, the ground is considered to be at the ambient temperature. The numerical values of the parameters used are given in Table 2. It may be men- tioned that the qR in eqn (8) is treated as a product of the amplitude of indoor temperature variation and CR the apparent heat capacity of the partition walls and other indoor items. The phase difference, L, in eqn (8) is so chosen as to minimise the amplitude of indoor temperature oscillations. The heat flux through roof can be increased either by increasing hL by running ceiling fans or by enhancing the surface area by means of fins or corrugations. This effect on space cooling is studied by parametric variation of hr.

The hourly solar radiation and the three-hourly ambient temperature, wind velocity, humidity data are used in evaluating the various heat fluxes. The data used in this work was monitored by the Indian Meteorological Department at Delhi for the year 1974. The hourly ambient temperatures are obtained by interpolation of the 3-hr data. It is found that the absolute humidity remained more or less constant over a day for the days considered here. The daily average wind velocity is used in the computation. The meteorological data of a typical day for each of the summer months of April-June are used in this study and these are given in Table 3.

Digital simulation of indoor temperatures

Table 2. Numerical values of the parameter used in the computer simulation

I,

2.

Anionic constants of water: A = 18.3443, B= 3841.2, C= -45.15

Thermal properties:

Emissivity of water (thermal)

Reflectivity of water(solar)

Emissivity of brick wall

Properties of metal(Iron

Density kg m -3 7000

Thermal conductivity

W m-IK "I 45.7

Specific heat

J kg'IK -I 402

3. Heat transfer coefficients

Inside roof (h L)

Windows(glass,U)

Doors (u)

Floor (hf)

Plastic f i lm (k/gp) 4. Details of Building

Dimena ions

Doors No .4

Windows No .8

Thickness walls

m 0.3

Air changes per hour

Window shads coefficient

Heating load

Pond depth

Pond depth (Sky-therm)

O .95

0.10

0.80

concrete walls floor

2020 1922 2240

1.73 0.72 1.73

872 837 872

6.~Wm'2K -1

6.02 W m'2 K -I

3.12 W m-2 K -I

22.72 W m-2 K -I

5000 W m-2 K "I

10m x 10m x 4m

2m x Im

Im x Im

metal roof concrete roof

0.001 0.15

2.0

0.5

860 W (5 persons+ 5OOW lighting and fans)

0.05 m

0.20 m

209

Three types of roof-pond systems namely open pond, shaded pond and the sky-therm have been studied. In the open-pond system, the pond is exposed to the sky all the time. In the shaded-pond system, a shade over the pond is provided to cut off solar radiation from reaching it using a permanent structure with a configuration similar to the venetian blinds. Thus, while the water is exposed to wind, the direct exchange of radiation between the sky and the water is prevented. In computations it is assumed that he, h~ are unaffected by the shade. The net thermal flux due to radiation between the water and the shade is estimated, considering the inside surface of the shade is black and it is at the ambient temperature. Depth of the water is taken to be 5 cm for the open and the shaded ponds, and 20 cm for the sky-therm system. In the sky-therm system it is considered that the pond is covered with movable insulation panels from 7 a.m. to 5 p.m. During this period, it is assumed no heat exchange takes place between the ambient and the pond water. The ponds over metal and concrete roofs have been studied.

A computer program has been written in FORTRAN-

10 for simulation of thermal behavior of the building and it is implemented on a DEC 1090 system. Extensive studies have been carried out and are reported elsewhere[21] in detail. The significant results are presented below.

RESULTS AND DISCUSSIONS The hourly indoor temperatures of the building with

the open and shaded ponds under different design conditions are presented in Tables 4-6 for the 3 days. It can be seen that the open-pond system is not very effective from the comfort point of view though it is found to be better than the bare roof. On the other hand, the indoor temperatures are below 30°C in the case of shaded pond even for the concrete roof for all the three days.

Thermal performance of the sky-therm system is compared with that of the shaded-pond system in Fig. 5. In evaluating the indoor temperatures, hL is taken to be 12.18Wm -2. The effectiveness of the both systems equally good. The sky-therm system is a shade better than the other. This is because the pond water exchanges thermal radiation with the night sky in the sky-there


Table 3. Meteorological data for Delhi 1974

APRIL MAY JUNE

Hour Amblpnt Solar Ambient Solar Ambient Solar Temp. °0 Raeiatlon Temp. °C Radiation Temp. eC Radiation

-2 -2 W m -2 Wm Wm

I 23.8 33.6 - 26.9 -

2 22.3 32.0 25.2 -

3 21 . I 30.8 23.7 -

4 20 .0 30.0 22.6 -

5 20.0 29.2 22.7 -

6 21 .2 6 .98 28 .8 8 .14 24 .2 51.16

7 22.6 131 .39 28.7 155.81 25.6 206.97

8 24.2 369.76 29.4 395.34 27.0 430.23

9 26.4 601.16 31.0 648.85 28.8 631.39

I0 29.4 790.69 33.4 844.18 30.4 779.06

11 30.9 903.48 36.5 961.62 51.8 884.87

12 33.4 949.99 38.0 1025.57 33.2 939.52

13 34.6 932.55 39.2 1005.80 34.1 924.41

14 35.4 845.34 39.8 937.20 34.8 859.29

15 36.0 712.78 40.4 811.62 35.4 726.74

16 36.4 509.30 40.6 604.64 36.0 579.06

17 36.4 300.00 40.2 387.20 36.0 369.76

18 54.9 100.00 38.5 161.63 35.0 169.77

19 33.1 I .16 36.5 13.95 33.7 43.02

20 31.2 0 34.8 - 32.3 -

21 29.7 - 35.3 - 31.6 -

22 27.9 - 32.5 - 31.0 -

23 26.5 - 31.8 - 30.8 -

24 25.6 - 31.4 - 30.4 -

Average Wind velocity, ms -I 3.2 4.0

Abs. Humidity, kg H20/kg Air 0.006 0.005

0.6

O.013

Table 4. Computer simulated indoor temperatures under different design conditions. Day: April 4th 1974, Place: Delhi

~ v ~ N F 0 f! D S HA D ED POND

Concrete M~t~] Concrete Metal Slab 0.15m O.OClm 0.15m O.OO1m

C R 0.0 2000 0.0 2000 0.0 0 .0 2000 0.0 O.O 2000

h L 6.09 12.18 6.09 12.18 6.09 12.18 12.18 6 .O9 12.18 12.18

HO[~ Ta°C INDOOR T~MPE~ATVRES °C

1 23.8 20.1 24.4 19.6 20.8 22.0 21.3 24.9 21.6 20.3 22.1

3 21.1 18.3 21.6 17.2 18.6 20.0 19.2 22.3 19.4 18.2 20.1

20.0 16.9 18.2 15.7 16.6 19.6 17.9 19.6 17.8 16.5 18.0

7 22.6 20.4 19.3 19.7 19.4 21.5 20.5 20.4 20.1 18.7 19.2

9 26.4 25.4 22.5 25.5 25.9 24.7 23.3 21.3 22.7 20.8 20.5

11 ~0.9 ~1.0 26.5 ~0.2 27.7 27. ! 25.5 22.5 24.8 22.6 21.4

13 34.6 34.5 29. t 33.1 2~.3 28.9 27.2 23.6 26.4 24.1 22.3

I~ ~6.0 35.8 30.6 3~.4 2o.0 ~0.7 29.1 26.1 28.6 26.2 24.4

17 36.4 34.0 30.1 ~1.2 26.9 ~1.3 30.0 28.4 29.8 27.5 26.1

la ~.I 27.2 25.7 28.2 21.9 27.6 26.5 26.7 26.5 24,5 23.8

21 29.7 23.3 24.6 22.3 20.7 25.3 24.7 26.5 24.7 23.O 23.3

2~ 26.~ 21.2 24.8 20.9 21.0 23.6 22.9 26.1 23.5 21.6 22.8

Digital simulation of indoor temperatures

Table 5. Computer simulated indoor temperatures under different design conditions. Day: May 8th 1974, Place: Delhi

211

OPEN POND SHADED POND

Concrete Metal Concrete Metal Slab O.15 O.OO1m 0.15m O.O01m

C~ O.O 2000 O .O 2000 0.0 0.0 2000 O .0 0.0 2000

h L 6.09 12.18 6.09 12.18 6.09 12.18 12.18 6.09 12.18 12.18

HOURS Ta°C INDOOR TEMPERATURES °C

1 35.6 26.4 29.1 24.8 24.7 28.2 27.0 29.7 26.8 24.7 26.1

3 30.8 24.8 26.8 23.0 22.9 26.4 25.2 27.5 25.2 23.1 24.5

5 29.2 23.2 23.7 21 .8 21 .4 24.8 23.7 24.9 23.5 21.6 22.7

7 28.7 24.5 23.2 23.8 22.6 25,5 24.2 24.1 24.0 21 .9 22.4

9 31.0 28.6 25.7 28.2 26.1 27.6 26.2 24.7 25.6 23.2 23.0

11 36.5 34.4 50.1 33.5 30.5 50.9 29.2 26.7 28.2 25.6 24.7

13 59.2 37.2 32.2 35.3 51.5 31.9 30.0 27.3 29.1 26.2 25.0

15 40.4 38.1 35.2 35.3 30.9 33.3 31.3 29.1 30.9 27.9 26.6

17 40.2 36.3 32.5 33.5 29.2 33.7 32.1 30.8 32.1 29.2 28.2

19 36.5 29.3 27.6 27.3 23.8 29.6 29.4 28.4 28.4 25.9 25.4

21 53.3 25.8 26.5 24,4 22.3 27.7 26.7 28.2 26.7 24.5 24.7

23 31 .8 24.8 27.5 23.6 22.8 26.9 26.0 28.4 25.8 23.8 24.7

Table 6. Computer simulated indoor temperatures under different design conditions. Day: June llth 1974, Place: Delhi

OPEN POND SHADED POND

Concrete Mete] Concrete Metal Slab 0.15m O.O01m Slab 0.15 m O.O01m

O R O.O 2000 0 .O 2000 O.O 0.O 2000 0.0 0.O 2000

h L 6.09 12.18 6.09 12.18 6.09 6.09 12.18 6.09 12.18 12.18

HO[~ A~'BIENT~C TEMPERATURE °0

1 26.9 24.3 29.2 24.1 26.2 27.0 26.6 29.8 27.1 26.3 27.8

3 23.7 21.5 25.7 21.0 23.6 24.0 23.7 26.4 24.2 23.5 25.2

5 22.7 20.3 22.6 19.9 22.0 22.8 22.5 24.0 22.4 21.9 23.2

? 25.6 24.6 24.2 24.9 25.7 25.9 25.2 25.2 25.0 24.2 24.7

9 28.8 29.9 27.1 31.1 30.5 28.4 27.2 25.6 26.7 25.6 25.4

11 31.8 34.7 30.6 36.2 34.4 29.2 28.1 25.4 27.7 26.2 25.2

13 54.1 38.8 34.0 39.0 36.3 30.5 29.1 26.1 28.7 27.2 25.7

15 55.4 41.0 56.3 39.6 36.3 52.4 51.6 28.8 31.1 29.7 28.0

17 36.0 39.5 56,0 37.1 33.6 33.9 33.1 31.6 32.9 31.3 30.1

19 33.7 ~2.1 30.8 2q.9 27.5 50.7 30.0 50.1 29.9 28.5 28.0

21 31.6 27.6 29.2 26.3 25.3 29.2 28.7 30.3 28.7 27.7 27.8

2~ 50.8 26.4 30.5 26.0 26.9 29.1 28.8 31.6 29.0 28.1 29.2

system whereas, in the other, it exchanges with the shade which is at the ambient temperature. If space cooling is the only objective it appears the shaded-pond system is advantageous as it does not require daily attention.

The heat transfer rates through the outer walls and the roof as well as the cooling loads are shown in Figs. 6 and 7 for the shaded-pond systems with a concrete roof and a metal roof. The trend and magnitude of the heat fluxes through outer walls are in agreement with the heat fluxes through a 16in. brick wall computed by Mackey and Wright[22]. It can be seen that the dominant cooling loads are those due to air infiltration and due to heat transfer through doors and windows. The heat transfer

rates through outer walls are insignificant to warrant insulation.

The effect of the absolute humidity on the thermal performance of the building with shaded ponds is shown in Table 7. It deteriorates with increase in humidity and becomes more or less ineffective if the relative humidity is above 50 per cent, computed based on the ambient temperature at 3 p.m. It may be noted that the effect of the humidity on sky-therm cooling is similar.

The effects of variation of the air infiltration rate and the CR on the indoor temperature have been studied and the results are presented in Table 8. The system is rendered ineffective if the air infiltration is more than 5


~0

35

u o

o 30

E

25

20

ShQded pond,concrcztcz roof, ~, _CR=2000

Skyther m,cOncr~te rOOf cn=o .o

",.•eed pond ; tal roo f

$kyfhcrm ; metal roof

2 4 6 8 10 12 14 16 18 20 22 24 Ti me, h

Fig. 5. Simulated indoor temperature with shaded pond and sky-therm.

26

14

,12

4

%0 O -/4

~-~

-12

-16

-20

-24

-26

3

J I I 1 I i i 1 J I i i 1 2 4 6 8 10 12 IZ. 16 IB 20 22 24

ROOf hckn~ss=O00 m h L = 2.)8W- m-2 IK -1 CR =2000.0 k J- K 1 Air in f i l t ra t ion 2 W e s t w a l t

3 EosI wol l 4. North wol[ 5 Doors and w{iqdows 6 Roofs

T i m c h

Fig. 6. Heat fluxes with shaded pond on metal roof.

Digital simulation of indoor temperatures 213

12

0 ~-- I ! -- I I I^ ? , , r .I,, ,L

O

o -S

~_~2

-16

-2C

-24

2 4, 6 8

ROOf thickness=O 15m h L = 12.18 W- r~ 2 I~ 1 CR = 2000.0 kJ - K -1 1 Air infiltration 2 West wall 3. East wall 4, South wall 5. Doors and windows 6 Roof

10 12 14 16 18 20 22 24,

Time h

Fig. 7. Heat fluxes with shaded pond on concrete roof.

Table 7. Effect of humidity on indoor temperatures. Day: May 8th 1974 Metal roof hL= 12.18Wm-2K - ' . CR = 2000 kJ K- '

Shaded Pond Sky therm

Humidity 0.012 0.019 0.026 0.025

Hour Amblem% Temperature eC

Temp.°C

1 3 3 . 6 29.1 31 .7 34 .1 31 .9

3 30 .8 27 .6 30 .3 32 .5 30 .5

5 29.2 25.8 28.6 30.9 29.3

7 28.7 25.8 28.4 30.8 29.5

9 31.0 26.3 29.1 31.5 30..5

11 36.5 27.9 30.5 32.8 31.8

13 39 .2 28 .0 30 .6 3 2 . 7 32 .7

15 40.4 29.5 32.0 34.0 34..5

17 40 .2 31.1 33.5 35 .7 36.2

19 36 .5 28 .4 30 .9 33 • 1 33 • 1

21 33 .3 27 .8 30 .4 32 .6 30 .8

23 31 .4 27.7 30.4 32 .6 30.8

214 RAJ]V YADAV and D. P. RAO

Table 8. Effect of air infiltration rate and CR on indoor temperatures. Day: May 8th 1974, Shaded pond over metal roof hL=6.08Wm ~K -~

Air changes per hour Heat Capacity (CR=O) (Air changes=2)

I 2 5 500 1000 2000

Hour Ambient Temp.°C Temperature °C

I 33.6 26.0 26.8 28.6 27.4 28.1 28.9

5 30.8 24.6 25.2 26.5 26.0 26.4 27.3

5 29.2 22.6 23.5 25.1 24.1 24.6 25.2

7 28.7 23.3 24.0 25.2 24.2 24.5 24.8

9 31.0 25.3 25.6 26.8 25.5 25.4 25.2

11 36.5 27.0 2~.2 30.4 27.7 27.3 26.9

13 39.2 27.3 29.1 32.2 28.5 28.0 27.1

15 40.4 2q.4 30.9 33.5 30.1 29.7 28.8

17 40.2 31.2 32.1 34.0 31.5 31.1 30.4

19 36.5 27.1 28.4 30.8 28.1 28.0 27.6

21 33.3 25.6 26.7 28.5 26.8 26.8 27.0

23 ~I .4 25.1 25.~ 27.2 26.3 26.6 27.2

air changes per hr. Higher the value of CR smaller is the amplitude of the indoor temperature oscillations.

CONCLUSIONS

A model for evaluation of the thermal performance of buildings with roof ponds is proposed. Computer simulation studies indicate that the indoor temperatures can be maintained within the comfort zone using passive cooling even in the semi-arid zones with the conditions similar to New Delhi. However , carefully designed experiments are warranted to obtain the design parameters, to validate the model and to demonstrate the adaptability of the roof ponds to the low-cost housing.

Acknowledgement--The authors gratefully acknowledge Tata Energy Research Institute, Bombay, for the financial support for this work.

Ao A,B,C

c. CR Cs h k

kg I L L'

mw mA M

M.,N. P P q

NOMENCLATURE

defined by eqn (6) Antonie constants specific heat kJ kg t K i equivalent heat capacity of building kJ K humid heat capacity of air-water mixture kJ kg ' K -~ heat transfer coefficient Wm " K thermal conductivity Wm t K-, mass transfer coefficient kg s - ' m ~(mm of Hg) insolation Wm : roof slab thickness m or phase difference rad depth of pond water m mass of water kg m -2 mass of air kg defined by eqn (7) or molecular weight defined by eqn (5) vapor pressure of water mm of Hg defined by eqn (3) or pressure mm of Hg heat flux Wm -'

q(Tp) defined by eqn (2) S defined by eqn (3) T temperature K

Tb (Tp- TR) t timeh -~ors t

w radian h -~ UL defined by eqn (3) U overall heat transfer coefficient Wm -2 V wind velocity m s

V,, defined by eqn (6) x distance m

Y,, defined by eqn (6) Z,, defined by eqn (6) a thermal diffusivity m2s O density kg m ~" or reflectivity o- Stefan-Boltzman constant Wm -2K 4

o, defined by eqn (6) ,~ latent heat of vaporisation

A,, defined by eqn (6) 4 plastic film thickness, m e emissivity

~,, defined by eqn (5) ~b,, defined by eqn (6)

Subscripts a ambient A air C convective

da downward atmospheric f floor I iteration number J hour of the day 0 a t x = 0 L a t x = L m mean

n.l.2 number of harmonic components p pond water or plastic r roof. radiative

R room w water s saturated, sensible energy storage

Digital simulation of indoor temperatures 215

t atmospheric V evaporation

Wd walls and doors

Superscript - heat transfer rate through the wall or roof, etc. k Jh -~

R E F E R E N C E S

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of Solar Energy Society of. India, p. 482. Bombay (1980). 15. J. S. Alford, J. C. Ryan and F. O. Urban, Trans. ASHVE 45,

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phere. Pergamon Press, Oxford (1965). 19. J. A. Duffle and W. A. Beckman, Solar Energy Thermal

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SE Vo|. 31, No. 2~F

ditigal simulation of indoor temperatures of buildings with roof ponds

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