-- Experimental and theoretical investigation of effects of wall’s thermophysical properties on time lag and decrement factor

7/29/2019 -- Experimental and theoretical investigation of effects of walls thermophysical properties on time lag and decre

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Experimental and theoretical investigation of effects of wall'sthermophysical properties on time lag and decrement factor

Koray UlgenSolar Energy Institute, Ege University, 35100 Bornova Izmir, Turkey

Received 22 May 2001; accepted 2 June 2001

Abstract

Energy saving policies are necessary to control energy consumption, use energy efciently and effectively, and reassess available

production and consumption systems. In this context, the objectives of this study are to investigate the thermal behaviours of opaque wall

materials under solar energy change, and the interaction between thermophysical characteristics of opaque wall materials and solar energy

falling onto exterior surface of the wall affects interior environment. Parameters of characteristics used in wall formation, their positions,

wall thermal behaviours, and ``time lag'' and ``decrement factor'' having effect on the changes of conditions of interior space were

investigated experimentally for different wall formations. The experimental ndings were compared with the results of equations derived by

using an analytic methodology. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Thermophysical properties; Time lag; Decrement factor; Solair temperature

1. Introduction

Fossil fuel consumption in buildings to provide comfort

conditions destroy ecological balance and environmentalpollution endangers life. In order to minimise this negative

impact, it is inevitable to higher the level of renewable

energy sources usage. It is also very essential to take new

measures to use more renewable energy sources in order to

minimise this negative impact. Solar energy is a clean and

renewable energy source, creating no waste.

Climatisation of buildings could be managed by passive

and active solar systems. Active systems need heat transfer

and store uids, control and transfer elements in order to

collect and store solar energy. Building components in

passive systems collect and transfer heat. Massive building

elements such as walls and oors work as thermal masses.

Solar energy storage in sunny periods is used to heat building

spaces when needed [13].

Daily temperature prole changes inside opaque wall

elements can be observed depending on the temperature

difference internal space and the environment. The absorption

of solar radiation from the external opaque wall causes a

gradual rise in the temperature distribution through the wall

until an equilibrium state is being reached. This process is

called the thermal inertia of the internal space and wallsystem [4,5].

On this transient period, temperature prole on the wall

cross-section has been assumed to be sinusoidal wave. This

observed change depending on thermophysical properties,

and on the inner side of wall, it reaches the lowest level

sinusoidal change in reaching from outside to inner face

dened as time lag or phase lag (f). Lowering entity of

amplitude is dened as decrement factor and attenuation

factor(f) [6]. A schematic of time lag and decrement factor

are shown in Fig. 1.

Depending on the thermophysical properties and thick-

ness of opaque wall elements, approximately 12 h time lag

values can be observed. So, passive energy storage applica-

tions during the day can be also used at night. Further, the

decrease in the indoor temperatures can be prevented when

the heating system was switched off. In hot and arid climate

zones using specially designed walls, the variation of the

outdoor temperatures has a very little effect on the indoor

temperature [7].

The heat ux within the envelope of the building occurs in

the transient regime under the effect of solar radiation.

Various analytical and numerical methods have been devel-

oped for the solution of the differential equation, which

represents this form of the heat transfer [814].

Energy and Buildings 34 (2002) 273278

Abbreviations: VCbrick, vertical cavernous brick; HCbrick, horizontal

cavernous brick; Cbrick, coat brick; TCbrick, thin coat brick; EPfoam,

extrude polystren foam; Ppanel, prefabricated panel; Styrofoam, expanded

polystren foam; Kapipane, permeable insulation material

E-mail address: [email protected] (K. Ulgen).

0378-7788/02/$ see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 7 7 8 8 ( 0 1 ) 0 0 0 8 7 - 1


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In this study, the behaviour of opaque wall materials

constituting building surfaces under solar energy is inves-

tigated both experimentally and theoretically in order to nd

time lag and decrement factor for different wall composi-

tions. The main aim in doing this study is to determine

proper wall compositions used in passive solar buildings.

2. Analysis

In this study, in order to obtain the theoretical results of

opaque wall systems studied, it is assumed that wall ele-

ments have a nite length, and one-dimensional transient

heat conduction through the wall. One-dimensional transient

heat conduction equation is as follows:

rc@T

@t k@

2T

@x2: (1)

The Fourier equation describes the temperature at a point in

the wall and at some instant. To solve Eq. (1), it is necessary

to specify an initial condition and two boundary conditions.

The boundary condition at the exterior surface is

k@T@x

x0

houtTsa Tout: (2)

Eq. (2) includes the gain due to the absorbed incident solar

radiation for the exterior surface of the opaque wall and the

heat loss by convection to the ambient air from the exterior

surface. Similarly, the boundary condition at the interior

surface can be written as

k@T

@x

xL hinTs;i Tin: (3)The first term of Eq. (3) represents the conduction heat

transfer through the wall, while the second term represents

the convective heat transfer between the interior surface

of the opaque wall and the indoor air. The temperature values

at the time t 0 can be taken as initial condition. For the

Nomenclature

a thermal diffusivity (m2 s1)

A amplitude

c specific heat (kJ kg1 K1)

f decrement factor

fexperiment experimental decrement factorftheoric theoretical decrement factor

h convective heat transfer coefficient

(W m2 K1)

I total solar radition for vertical surface

(W m2)

k thermal conductivity (W m1 K1)

P period (24 h)

R thermal resistance (W1 m2 K)

S heat storage capacity (W s1/2 m2 K1)

t time (h)

T temperature (8C)

w angular speed (rad s1)

x thickness (m)

Greek letters

a absorptivity

b surface tilt angles (8)

f time lag (h)

fexperiment experimental time lag

ftheoric theoretical time lag

r mass density (kg m3)

Subscripts

a,in indoor amplitude

a,out outdoor amplitudein indoor

out outdoor

sa solair

s,i indoor surface

s,o outdoor surface

Fig. 1. The schematic representation of the time lag, f, and decrement factor, f

Ain=Aout.

274 K. Ulgen / Energy and Buildings 34 (2002) 273278


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temperature affecting the exterior surface of the opaque

wall, a theoretical temperature referring to the joint effect

of the outdoor air temperature and the absorbed solar

energy and indicating periodical change by time has been

used. In the literature, this temperature is called solair

temperature [9].

Tsa Tout ahout

It eDRhout

: (4)

ASHRAE recommends that the correction factor, eDR=hout,be given a value 48C for horizontal surfaces facing up. Thus,

the solair temperature is 48C cooler due to reduced infrared

radiation coming from the sky. The correction factor is

specified to be 0 for vertical surfaces, as the warmer sunlit

surfaces compensate for the cooler sky temperature. An

estimate of the correction factor for other tilt angles based

upon radiation shape-factor geometry is

eDR

hout 4cosb; (5)

where b is the surface tilt angles measured between the

surfaces normal and vertical [9].

Under the initial and boundary conditions given above,

the following Eq. (6) can be obtained from the solution of the

equation of heat conduction, which is one-dimensional and

dependent on time:

Tx; t

X21 X22q

sinwt f: (6)Eq. (6) is the analytical solution to the problem. X1 and X2are function of x and can be calculated from the following

equations:

Srck

p: (9)

At the same time, the ratio of X1 to X2 gives the time lag

between interior and exterior surfaces of the opaque element.

f arctan X2X1

: (10)

In addition, the square-rooted term of Eq. (6) refers to the

reduction in the amplitude of the surface temperatures,

which is decrement factor.

f

X21 X22q

: (11)

The results of the analytical solution are given in Table 1. For

the convective heat transfer coefficient values considered in

analytical solutions are measured experimentally.

3. Experimental studies

Based on the earlier studies given in the literature, the

experimental set-up whose subsections are given below has

been developed in this study [15]. It is aimed at determining

the behaviour of the envelope of the building under the effect

of solar radiation [16]:

simulation unit; datalogger (for storing data and controlling the system); computer (for organising the data stored); temperature sensors (used for measuring wall surface and

environment temperatures);

test samples (wall structures to be tested and having1 m 1 m surface area on each side).The simulation unit shown schematically in Fig. 2 con-

sists of three parts. The space A represents the environment,

and the temperature change in the space A is assumed to be

sinusoidal. A heating unit, a cooling unit and fan are placed

inside the space A. The goal is to create a sinusoidal

temperature change by changing the energy level at certain

time intervals, keeping the energy level by which is given

heater and cooler into the volume xed (Fig. 3a). In order for

periodical change to have some time intervals, simulation

time is taken as 32 h. First 2 h are the time elapsed for the

system to reach equilibrium; the last 30 h are a change

process having ve periods to reach the steady state regime.

Each period represents a day. Measurements are made to

determine how periodical temperature change, simulated in

the space A, is reected into the space B (Fig. 3b). In the wall

part, there are 10 wall samples, which form the context of

the study and are designed for different climate conditions.

These samples have 1 m 1 m surface area and are insu-lated from the side surfaces to realise one-dimensional heat

conduction only.

Datalogger unit consisted of an electronic card for gen-

erating periodical temperature changes and a storage card

for receiving the signals coming from sensors during mea-

surements. Sensors were used to measure the temperatures

of the environment and wall surfaces. The sensors were

produced specically concerted datalogger through electro-

nic chips. The calibration of the sensors, before each experi-

ment, was made on the calibration card placed in datalogger

unit. There were 12 sensors: two for measuring environment

temperature and the rest for measuring surface temperature.

Also there was transfer unit in the system to convey data

collected by the datalogger to the computer. Data transfer

X1 Ta;out hin=S

ip sinhSip=kL x coshSip=kL x

Sip=hout hin=Sip sinhSip=kL 1 hin=houtcoshSip=kL" #

; (7)

X2 Ta;in hin=S

ip sinhSip=kx hin=houtcoshSip=kx

Sip=hout hin=SipsinhSip=kL 1 hin=houtcoshSip=kL" #

; (8)

K. Ulgen / Energy and Buildings 34 (2002) 273278 275


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Table 1

Theoretical and experimental results

Wall

no.

Sheet type

(out towards in)

Thickness

(cm)

a k/rc(m2 s1 107)

S (krc)1/2(W s1/2 m2 K1)

R

(W1 m2 K)

Theoretical Experimental

Decrement

factor, f

Time lag,

f (h)

ftheoric ftheoric

(h)

fexperiment fexperiment

(h)

1 Outer plaster 3.00 3.63 481.66 0.863 2.974

VCbrick 19.00 5.95 453.65 0.855 4.001

Inner plaster 2.00 3.20 282.84 0.7713 0.913 2.411 0.676 9.39 0.392 10.50

2 Outer plaster 3.00 3.63 481.66 0.860 2.432

Gas concrete 20.00 3.35 242.02 0.875 3.716

Inner plaster 2.00 3.20 282.84 1.6570 0.917 3.275 0.690 9.42 0.375 10.27

3 Outer plaster 3.00 3.63 481.66 0.835 2.861

EPfoam 3.00 8.25 32.70 0.935 2.099

VCbrick 19.00 5.95 453.65 0.744 4.125

Inner plaster 2.00 3.20 282.84 1.7814 0.912 2.392 0.529 11.48 0.357 10.10

4 Outer plaster 3.00 3.63 481.66 0.861 3.008

VCbrick 19.00 5.95 453.65 0.519 5.703

EPfoam 3.00 8.25 32.70 0.980 2.816Inner plaster 2.00 3.20 282.84 1.7814 0.903 2.988 0.395 14.52 0.281 11.28

5 Cbrick 9.00 4.93 825.88 0.347 5.804

Air space 3.00 0.02 5.61 0.954 2.469

HCbrick 13.50 4.10 476.24 0.820 4.137

Inner plaster 2.00 3.20 282.84 1.7340 0.922 1.915 0.250 14.33 0.332 11.44

6 Cbrick 9.00 4.93 825.88 0.407 5.676

Ppanel 3.00 18.20 29.66 0.944 2.307

HCbrick 13.50 4.10 476.24 0.839 4.038

Inner plaster 2.00 3.20 282.84 1.3302 0.923 2.073 0.299 14.09 0.351 11.56

7 Cbrick 9.00 4.93 825.88 0.351 5.782

Air space 3.00 0.02 5.61 0.925 1.702

EPfoam 3.00 8.25 32.70 0.970 2.718

HCbrick 13.50 4.10 476.24 0.826 4.110Inner plaster 2.00 3.20 282.84 2.7441 0.923 2.056 0.240 16.37 0.243 11.58

8 TCbrick 1.50 6.75 1380.26 0.821 3.168

Styrofoam 2.00 8.27 34.09 0.935 2.109

HCbrick 13.50 4.10 476.24 0.847 3.996

Inner plaster 2.00 3.20 282.84 1.0834 0.922 1.809 0.599 11.08 0.362 10.34

9 Outer plaster 3.00 3.63 481.66 0.779 2.908

Styrophore 15.00 28.13 26.83 0.992 2.942

Inner plaster 2.00 3.20 282.84 3.5618 0.922 3.780 0.714 9.63 0.365 10.30

10 Cam 0.40 5.90 1151.24 0.973 2.793

Kapipane 3.00 0.981 0.186

VCbrick 19.00 5.95 453.65 0.880 3.898

Inner plaster 2.00 3.20 282.84 1.0637 0.919 2.493 0.775 9.37 0.415 9.52

Fig. 2. The schematic representation of the simulation unit.


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unit was connected to the serial port of the datalogger. A

connection cable was used between the computer and the

transfer unit to transfer data from the serial port. Moreover, a

specically produced keypad was used to enter the com-

mand. In order to determine thermophysical behaviours

of opaque wall elements forming building shell under theeffect of solar energy showing periodical change, thermal

tests of 10 different types of walls were conducted in the

experimental simulation unit developed. Building materials

forming wall types and their positions are given in Table 1

[16].

4. Results and discussion

In the effective use of energy, the environmental tem-

perature, solar radiation intensity purpose of use of spaces

and characteristics, dimensions and formations of structureelements forming building shell are important parameters.

The walls, which are in interaction continuously with chan-

ging environmental temperature and solar radiation, can be

organised as single-layered or multi-layered in terms of their

formation.

As known, heat-spreading and storage features of the

material gain importance in time lag, decrement factor,

and magnitude of heat loss. Those features mentioned are

the functions of thermal diffusivity (a), mass density (r) and

specic heat (c) of the material. Atmospheric conditions and

purpose of use of spaces have some effects on passing of the

heat through the wall and on storage of the heat.

The walls in the study have different formations. Time lag

and decrement factorvalues of opaque wall elements form-ing building shell under the periodic change conditions are

illustrated in Table 1. Based on the experimental results and

theoretical calculations, as seen in Table 2, the best results

are obtained by using multi-layered insulated and air-caver-

nous wall formations (wall no.: 7), followed by insulated

(interior and exterior) formations (wall nos.: 4, 5, 6, 3, 8),

and single-layered formations (wall nos.: 1, 2, 9, 10).

Characteristic magnitude oftime lag and decrement factor

that will inform the designers concerning material charac-

teristics and their positions forming wall formations are

affected by heat storage (S) and thermal diffusivity (a) of

the material. The increase in both mass density and specicheat values has a positive effect on the results. On the

contrary, increase of the thermal conductivity causes heat

storage coefcient to change positively (increase in value),

but causes heat-spreading coefcient to change negatively

(increase in value). It means that it is impossible to obtain

positive results for both characteristics. Thus, it is inevitable

to consider composite types of walls formed by layers

having different features in design for the best results. A

Fig. 3. Internal view of (a) space A and (b) space B.

Table 2

The order of evaluation of wall formation tested by their theoretical experimental examinations (by wall numbers)

Evaluation rank Theoretical Experimental Results Evaluation rank

Decrement factor Time lag Decrement factor Time lag

1 7 7 7 7 7 1

2 5 4 4 6 5 2

3 6 5 5 5 4 3

4 4 6 6 4 6 4

5 3 3 3 1 3, 8 5

6 8 8 8 8 3, 8 5

7 1 9 9 9 1, 9 7

8 2 2 2 2 1, 9 7

9 9 1 1 3 2 9

10 10 10 10 10 10 10

K. Ulgen / Energy and Buildings 34 (2002) 273278 277


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small thermal diffusivity having effects on decrement factor

and increases in time lag that is a large mass density (r) and

specic heat (c) have a positive impact on the interior

environmental conditions.

5. Conclusions

Appropriate building shell can be obtained with massive

block having heat storage feature and composite types of

walls formed by light and non-heat conducting materials, by

giving attention to the function of interior space, and to the

position of the material in wall formations. Utilisation

period is also effective in terms of selection of opaque wall

materials forming building shell.

In the spaces used for short time and limited time inter-

vals, a lower level of heat storage capacity of the building

shell is preferred, while a higher level is preferred in

buildings used for long periods of time. This is very essential

for keeping the temperature changes of interior space at

minimum level.

In conclusion, many parameters should be taken into

consideration for providing comfort in spaces. In the build-

ings used for all day long (houses, ofces, etc.), multi-

layered and insulated wall formations are suggested, while

single-layered formations are suggested for the buildings

used for specic time intervals.

Acknowledgements

The author is grateful to the Research Fund of EgeUniversity for substantial support in realising this study,

and to the Association of Turgutlu Brick and Tile Producers

for contributions in providing the experiment mechanisms to

the Ege University Solar Energy Institute.

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-- Experimental and theoretical investigation of effects of wall’s thermophysical properties on time lag and decrement factor