Energy and Buildings 40 (2008) 2052–2058

Cooling load reduction by using thermal mass and night ventilation

Lina Yang *, Yuguo Li

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

A R T I C L E I N F O

Article history:

Received 6 May 2008

Accepted 26 May 2008

Keywords:

Cooling load

Cooling load ratio

Thermal mass

Night ventilation

Air-conditioning

A B S T R A C T

We provide a quantitative understanding of the relationship between thermal mass and cooling load, i.e.

the effect of thermal mass on energy consumption of air-conditioning in office buildings. A simple office-

building model with air-conditioning at daytime and free cooling at nighttime is analyzed in detail to

quantify the hourly and overall variation of cooling load of air-conditioning. As an important parameter,

an increase of time constant can effectively reduce the cooling load, by as much as more than 60% when

the time constant is more than 400 h. However, when the time constant is larger than 1000 h, a further

increase may slightly increase the cooling load, as a too large time constant may also postpone the heat

release of thermal mass until the daytime. For the most effective reduction of cooling load, the interior

and exterior convective heat transfer numbers need to be matched.

� 2008 Elsevier B.V. All rights reserved.

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1. Introduction

Buildings consume more than 30% of the primary energyworldwide. In China, buildings account for 23% in 2003 of the totalenergy use and is expected to increase to 30% by 2010 [1]. 65% ofthe building energy consumption in 2003 in China was due toheating, ventilation and air-conditioning [1]. Hence, improvingbuilding energy efficiency has become one of the critical issues foroverall national energy strategy in China.

The use of thermal mass in a building can reduce peak heatingor cooling load, and subsequently building energy consumption, inparticular when it is integrated with night ventilation. Thermalmass is defined as the thermal materials that can absorb heat, storeit and release it later. Thermal mass includes building envelope,furniture, internal walls, etc. Thermal storage capacity of buildingmass is one of the factors describing the building thermalperformance [2]. In naturally ventilated buildings, thermal massis effective for reducing the air temperature fluctuation [3].

Many studies investigated the relationship between thermalmass and indoor air temperature, and the effect of thermal massand night ventilation on cooling load; as reviewed by Balaras [4].16 different simplified models for estimating the cooling load of abuilding, considering the building’s thermal mass, were summar-ized and compared in Ref. [4]. Parameters describing the effects ofthermal mass include the effective heat storage capacity [5,6],diurnal heat capacity [7], thermal effectiveness parameter [8],

* Corresponding author. Tel.: +852 2816 2625; fax: +852 2858 5415.

E-mail address: liyg@hku.hk (L. Yang).

0378-7788/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2008.05.014

admittance factor [9], and total thermal time constant [10]. Theeffective layer thickness of external walls [11] and the surface areaof thermal storage [12,13] also significantly affect the thermalmass performance.

Existing studies showed that the reduction in cooling load byusing thermal mass vary between 18 and 50% [8,14–16]. But thesestudies were mostly based on the laboratory monitoring or fieldexperiments, without systematic theoretical studies. Hence thispaper aims to provide a detailed theoretical analysis on therelationship between use of thermal mass and reduction of coolingload. Through a simple building model, all parameters affecting thethermal mass performance are quantitatively evaluated andanalyzed.

2. A simple building model

Here only the warm climates are considered, while the resultsand analysis can also be easily extended to the cold climates. Fig. 1shows a simple office-building model with daytime air-condition-ing and night ventilation. The air temperature distribution in thebuilding is uniform. Both internal and external thermal storagematerials are modeled as a thermal mass wall. All buildingenvelope except the thermal mass wall is perfectly insulated. Asshown later, the location of thermal mass relative to insulation andeffect of insulation may be analyzed by changing the interior andexterior convective heat transfer numbers. Thermal radiationbetween room surfaces is ignored. All heat gain (including solarheat gain) and heat generation in the building is lumped into oneheat source term, i.e. E at daytime and no indoor heat gain isconsidered at nighttime. The temperature distribution in the

Nomenclature

Ai interior surface area of thermal mass (m2)

Ao exterior surface area of thermal mass (m2)

cm heat capacity of the thermal mass (J/kg K)

cp heat capacity of air (J/kg K)

E heat generation rate (W)

g acceleration of gravity (m/s2)

hi interior convective heat transfer coefficient

(W/m2 K)

ho exterior convective heat transfer coefficient

(W/m2 K)

M mass of the thermal mass (kg)

qv night ventilation rate (m3/s)

Qcl cooling load (W)

t time (s)

TE temperature rise due to internal heat gain (K)

Ti indoor air temperature (K)

Tm thermal mass temperature (K)

To outdoor air temperature (K)

Tset indoor air setting temperature at daytime (K)

T̃o mean outdoor temperature (K)

DT̃o amplitude of outdoor air temperature fluctuation

(K)

Greek symbolsb phase shift (s)

li interior convective heat transfer number

lo exterior convective heat transfer number

j cooling load ratio

jt total cooling load ratio

r air density (kg/m3)

t time constant (s)

v frequency of outdoor temperature variation (1/s)

Fig. 1. A simple one-zone building model with periodic outdoor air temperature

variation when: (a) daytime, the air-conditioning (AC) system is on and the indoor

air temperature is kept constant and (b) nighttime, AC is off and the building is

ventilated at a constant ventilation rate.

L. Yang, Y. Li / Energy and Buildings 40 (2008) 2052–2058 2053

thermal mass is also assumed to be uniform, i.e. Tm. This meansthat the thermal conduction process within the materials is muchfaster than thermal convection at surface. At daytime, the indoorair temperature is kept constant, i.e. Tset; see Fig. 1a. At nighttime,the ventilation rate, qv, is constant; see Fig. 1b.

2.1. Daytime

The heat balance equations for thermal mass and room air are

Mcm@Tm

@tþ hoAoðTm � ToÞ þ hiAiðTm � T iÞ ¼ 0 (1)

Q cl þ hiAiðTm � T iÞ þ E ¼ 0 (2)

where Qcl is the heat removed by air-conditioning equipment, i.e.the cooling load.

We assume that the outdoor temperature can be expressed byFourier analysis as the sum of sinusoidal components of periods 24,12, 8, 6 h, etc. We consider the main sinusoidal component ofperiod 24 h.

To ¼ T̃o þDT̃o sinðvtÞ (3)

where DT̃o and T̃o are independent of time and DT̃o�0; v is thefrequency of the outdoor temperature fluctuation with a value of2p/24 h�1.

Substituting Eq. (3) into Eq. (1), we get

vt@Tm

@ðvtÞ þ ðlo þ liÞTm ¼ loT̃o þ liT i þ loDT̃o sinðvtÞ (4)

where t ¼ Mcm=rcpqv is the time constant based on a referenceventilation rate qv, which is chosen to be the night ventilation flowrate. lo ¼ hoAo=rcpqv is the non-dimensional exterior convectiveheat transfer number, and li ¼ hiAi=rcpqv the interior convectiveheat transfer number.

Two convective heat transfer numbers li and lo measure therelative strength of interior and exterior convective heat transfer atthe thermal mass surfaces. A small thermal resistance (largeinterior or exterior convective heat transfer number) representsthe interior or exterior convective heat transfer is very effectivecompared to the flow mixing in the room. In such situations, thethermal mass is considered to be in thermal equilibrium with theroom air or outdoor.

The general solution of Eq. (4) is

TmðvtÞ ¼ lo

lo þ liT̃o þ

li

lo þ liTset

þ loDT̃offiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlo þ liÞ2 þv2t2

q sinðvt � b1Þ

þ C1 e�ððloþliÞ=vtÞvt (5)

L. Yang, Y. Li / Energy and Buildings 40 (2008) 2052–20582054

where Tset is the indoor temperature set point, which is maintainedby the air-conditioning system (Ti = Tset = constant at daytime),and C1 is a constant. For the thermal mass, the phase shiftb1 = tan�1(vt/(lo + li)) with a value between 0 and p/2, i.e. 0 and6 h. Here the warm climates are defined as T̃o� Tset, however, theanalysis can also be extended to the cold climates (i.e. T̃o < Tset).

Substituting Eq. (5) into Eq. (2) and we have the cooling load

Q clðvtÞ ¼ �rcpqv TE þlilo

lo þ liðT̃o � TsetÞ þ

liloffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlo þ liÞ2 þv2t2

q DT̃o sinðvt � b1Þ þ C1li e�ððloþliÞ=vtÞvt

8><>:

9>=>; (6)

where TE ¼ E=rcpqv is the temperature rise due to the heat source.A negative/positive Qcl means that cooling/heating is needed.

Eq. (6) shows that the cooling load is the sum of three parts. Thefirst is the mean load Q̃ cl, which comprises the steady state coolingload due to steady heat source, and the heat gain or loss throughconvective heat transfer due to the temperature differencebetween mean outdoor and indoor air temperature (as thermalconduction through the thermal mass is assumed to be infinite).The second part is the periodic fluctuating load DQ̃ cl with itsamplitude depending on the outdoor air temperature swing DT̃o,the convective heat transfer number (li and lo), and the timeconstant t. b1 is the phase lag of the cooling load swing withrespect to the outdoor air temperature; and the third part (theexponent term) is due to initial condition and it decays to zero astime or exterior convective heat transfer increases, or timeconstant decreases.

The cooling load increases as heat source (TE), or temperaturedifferences between indoor and mean outdoor air ðT̃o � TsetÞ, orfluctuation of outdoor air temperature ðDT̃Þ increase. On the otherhand, the time constant t and the convective heat transfercoefficient with surrounding air (li and lo), are also importantparameters affecting the cooling load. Undoubtedly, the peak-cooling load can be reduced with heavy thermal mass, i.e. largetime constant t. The phase shift of cooling load is b1 = tan�1(vt/(lo + li)) with a value between 0 and p/2 (i.e. 0 and 6 h).

When there is no thermal mass, i.e. t = 0, we can easily obtainthe cooling load Qcl0:

Q cl0ðvtÞ ¼ �rcpqv TE1 þlilo

lo þ liðT̃o � TsetÞ þ

lilo

lo þ liDT̃o sinðvtÞ

� �

(7)

The effect of thermal mass can be seen from the lack of thetime constant terms in Eq. (7). A cooling load ratio j = Qcl/Qcl0 isdefined here to represent the ratio of cooling load in buildingwith thermal mass to the load in building without thermal massat daytime.

j ¼ Q cl

Q cl0¼

TE1 þ ðlilo=lo þ liÞðT̃o � TsetÞ þ ðlilo=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlo þ liÞ2 þv2t2

qÞDT̃o sinðvt � b1Þ þ C1li e�ððloþliÞ=vtÞvt

TE1 þ ðlilo=lo þ liÞðT̃o � TsetÞ þ ðlilo=lo þ liÞDT̃o sinðvtÞ(8)

The cooling load ratio is a time-dependent parameter. Thesmaller the ratio, the more energy saved. The cooling load ratiodecreases when the heat source E, temperature difference betweenindoor and outdoor air ðT̃o � TsetÞ, or the outdoor temperatureswings DT̃o decrease.

To understand the total energy conservation potential, the totalcooling load ratio is introduced to represent the ratio of totalcooling load in building with thermal mass to that without thermal

mass.

jt ¼Rvt2

vt1Q clj jdðvtÞRvt2

vt1Q cl0j jdðvtÞ

(9)

2.2. Nighttime

The two heat balance equations for the thermal mass and roomair are

Mcm@Tm

@tþ hoAoðTm � ToÞ þ hiAiðTm � T iÞ ¼ 0 (10)

rcpqvðTo � T iÞ þ hiAiðTm � T iÞ ¼ 0 (11)

Let l0i ¼ li=ð1þ liÞ, we have

vt@Tm

@ðvtÞ þ ðlo þ l0iÞTm ¼ ðlo þ l0iÞT̃o þ ðlo þ l0ÞDT̃o sinðvtÞ (12)

The general solution of Eq. (12) is

TmðvtÞ ¼ T̃o þðlo þ l0iÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðlo þ l0iÞ2 þv2t2

q DT̃o sinðvt � b2Þ

þ C2 e�ððloþl0iÞ=vtÞvt (13)

where C2 is a constant. The phase shift b2 ¼ tan�1ðvt=ðlo þ l0iÞÞ.The solution for indoor air temperature is

TðvtÞi ¼ T̃o þl0ili

DT̃o sinðvtÞ þ l0ilo þ l0iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðlo þ l0iÞ2 þv2t2

q

DT̃o sinðvt � b2Þ þ l0iC2 e�ððloþl0iÞ=vtÞvt (14)

2.3. Matching conditions

We assume that in 24 h, the daytime is from t1 to t2. The thermalmass temperatures at t2 and t1 + 24 should be continuous.

At t = t2, we have

T̃o þlo þ l0iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðlo þ l0iÞ2 þv2t2

q DT̃o sinðvt2 � b2Þ þ C2 e�ððloþl0Þi=vtÞvt2

¼ lo

lo þ liT̃o þ

li

lo þ liTset þ

loDT̃offiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlo þ liÞ2 þv2t2

q

� sinðvt2 � b1Þ þ C1 e�ððloþliÞ=vtÞvt2 (15)

Fig. 2. The temperature profiles of indoor air and thermal mass with different mean

outdoor air temperatures: (a) T̃o ¼ 308:15 K; (b) T̃o ¼ 303:15 K; (c) T̃o ¼ 297:15 K.

Fig. 3. Profiles of cooling load ratio and total cooling load ratio as a function of the

temperature differences between indoor and outdoor air T̃o � Tset: (a) cooling load

ratio; (b) total cooling load ratio.

L. Yang, Y. Li / Energy and Buildings 40 (2008) 2052–2058 2055

and at t = t1 + 24, we have

T̃o þlo þ l0iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðlo þ l0iÞ2 þv2t2

q DT̃o sinðvt1 þ 24v� b2Þ

þ C2 e�ððloþl0iÞ=vtÞv t1þ24ð Þ

¼ lo

lo þ liT̃o þ

li

lo þ liTset þ

loDT̃offiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlo þ liÞ2 þv2t2

q sinðvt1

� b1Þ þ C1 e�ððloþliÞ=vtÞvt1 (16)

The two constants C1 and C2 are determined from Eqs. (15) and(16). The expressions are lengthy and are not given here.

3. Results and discussion

As in Eqs. (8) and (9), the control parameters for the cooling loadratio include indoor air setting Tset, the outdoor air temperature

(mean outdoor temperature T̃o and temperature swing DT̃o), theinterior and exterior convective heat transfer numbers (li and lo),and as well as the time constant t.

For simplicity, we let t1 = 8:00, t2 = 18:00, v = p/12, roomvolume V = 32.4 m3 (4 m � 3 m � 2.7 m), lo = 30 (exterior con-vective heat transfer coefficient ho = 15 W/m2 K), li = 10 (interiorconvective heat transfer coefficient hi = 5 W/m2 K), t = 100 (com-mon concrete brick), DT̃o ¼ 7:5 K, E = 240 W (20 W/m2),Tset = 297.15 K (24 8C), and the reference night ventilation rate isgiven by qv=V ¼ 1 h�1. Then the phase shift b1 is about 2.21 h atdaytime and b2 = 2.68 h at night. The variation of cooling load canbe obtained by giving different outdoor climates, i.e. T̃o ¼ 308:15 K(35 8C), T̃o ¼ 303:15 K (30 8C); T̃o ¼ 297:15 K (24 8C, the referencecase).

3.1. Outdoor air temperature and cooling load

The temporal profiles of indoor/outdoor air temperature andthermal mass temperature are obtained for three different meanoutdoor air temperatures; see Fig. 2. The maximum temperature ofthermal mass at daytime occurs at around 16:00, then reachanother maximum at 19:00 after the air-conditioning is turned offand if the outdoor air temperature was higher than indoortemperature during this period. Heat is released from the thermalmass at nighttime and thermal mass achieves its minimumtemperature at around 4:00 in the following day. At nighttime theindoor air temperature reaches its minimum at around 3:00 whilethe minimum outdoor air temperature occurs at around 2:00. Alsothere is a gap for indoor air temperature between daytime and

Fig. 4. Profiles of cooling load ratio and total cooling load ratio as a function of

outdoor air temperature swing: (a) cooling load ratio; (b) total cooling load ratio.

Fig. 5. Profiles of cooling load ratio and total cooling load ratio as a function of time

constant: (a) cooling load ratio; (b) total cooling load ratio.

L. Yang, Y. Li / Energy and Buildings 40 (2008) 2052–20582056

nighttime at the time 8:00 and 18:00 when the air-conditioningsystem is on or off. The gap is smaller when the mean outdoor airtemperature is smaller.

Fig. 3 shows the cooling load ratio and total cooling load ratio asaffected by T̃o � Tset. The higher the temperature difference, thelarger the cooling load ratio and total cooling load ratio. In Fig. 3a,the cooling load ratio is less than one for most of the hours due toheat storage. After the heat storage capacity of the thermal massachieves its maximum at around 16:00, it begins releasing its heat,leading to an increase of the cooling load and the cooling load ratiobecomes greater than one after 16:00. The slightly excessiveenergy consumption at later hours is tiny, which can be offset bythe energy saving at earlier hours. Hence the total cooling loadratio can be less than one. The total cooling load ratio decreases asT̃o � Tset difference reduces. The maximum energy saving of closeto 30% is obtained when T̃o � Tset ¼ 0 K. It is noted that whenT̃o � Tset ¼ 0 K, the cooling load ratio is negative at early hours asthe night ventilation reduces the indoor air temperature to bebelow the setting temperature of 24 8C. In this case the heating isneeded rather than cooling.

Large diurnal temperature variations benefit thermal mass.Fig. 4 shows the effect of three different temperature swings of 5,7.5, and 10 K. The cooling load ratio and total cooling load ratiodecrease as the temperature fluctuation increases, as theamplitude of cooling load is proportional to the outdoortemperature swing as shown in Eq. (6). When the swing is larger,the reduced amplitude in the case with thermal mass is larger thanthat without thermal mass; see Eq. (8). The effect of indoor heatgain can also be shown (not done here). It is obvious that thecooling load is dominated by the heat gain when the daytime heatgain is large; hence the relative contribution of thermal mass isreduced.

3.2. Time constant/convective heat transfer and cooling load

The time constant t is a very important parameter fordescribing the thermal properties of thermal mass. The magnitudeof the time constant determines the heat storage capacity ofthermal mass and phase shift of the peak-cooling load. The effect ofthe time constant t on the cooling load ratio and total cooling loadratio is shown in Fig. 5.

The cooling load ratio and the total cooling load ratio decreasefirst and then increase as the time constant increases. When t = 0,both ratios equal to one. When the time constant t increases, thephase shift of thermal mass for both day and night time increasesas time constant increases, hence the phase shift for the coolingload increases correspondingly, see Eq. (6). The peak cooling load isdelayed and the energy saving is realized. On the other hand, sincethe amplitude of cooling load with thermal mass (see Eq. (6)) isinversely proportional to the time constant, the cooling load ratioand total cooling load ratio decrease as the time constant increases.That is why the total cooling load ratio reduces when t < 1000 inFig. 5. However, there is a slight increase in the total cooling loadratio when t > 1000 and increases to infinity. This may be due tothe fact that at nighttime, the heat release process of thermal massalso slows down due to the very large time constant but relativelysmaller night ventilation, which may lead to that the thermal massis kept at high temperature at night, and hence slightly increasedcooling load next day. Hence due to the phase shift approaches themaximum value of p/2, i.e. 6 h for the time constant to approachinfinity; there is minor increase for the total cooling load ratiowhen the time constant is greater than 1000.

Fig. 6. Profiles of cooling load ratio and total cooling load ratio as affected by the

interior convective heat transfer number: (a) cooling load ratio; (b) total cooling

load ratio.

Fig. 7. Profiles of cooling load ratio and total cooling load ratio as affected by the

exterior convective heat transfer number: (a) cooling load ratio; (b) total cooling

load ratio.

L. Yang, Y. Li / Energy and Buildings 40 (2008) 2052–2058 2057

It is obvious that when there is a mismatch between the twoconvective heat transfer numbers, an increase of any one of themwill not make any significant impact. Figs. 6 and 7 show thatneither small nor large convective heat transfer numbers reducethe cooling load ratio. For interior convective heat transfer numberli, the zero value of this number means there is no heat transferbetween indoor air and thermal mass. In this case, there is nothermal mass in building and the cooling load ratio or the totalcooling load ratio are equal to 1; see Fig. 6. A zero exteriorconvective heat transfer number lo means there is no heat transferbetween outdoor air and thermal mass. In this case, only interiorthermal mass contributes.

4. Conclusions

The effect of thermal mass on cooling load reduction inbuildings is studied in detail using a very simple building model,which allows us to examine the hourly benefits in using thermalmass and night ventilation. The cooling load ratio and the totalcooling load ratio are introduced to represent the effect of thermalmass on cooling load reduction. Our analysis quantified thedependence of the cooling load on the thermal properties ofthermal mass, including the time constant t and the convectiveheat transfer factors (both interior number li and exterior numberlo), the outdoor air temperature, and as well as the indoor heatgain. Our results show that only appropriate amount of thermalmass in terms of both thermal properties and convective heattransfer together with suitable outdoor climates will benefit most.The present work provides a simple model for designing thermalmass and night ventilation.

Acknowledgments

The work was supported by a grant from the Research GrantsCouncil of Hong Kong SAR, China (Project No. 7154/05E). Theauthors thank Dr. Pengcheng Xu for his assistance in mathematicalderivations. The work is a part of the International Energy Agency(IEA) Annex 44 project on Integrating Environmentally ResponsiveElements in Buildings.

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