Effect of thermal mass on performance of insulated building walls and the concept of energy savings potential

Applied Energy 89 (2012) 430–442

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Effect of thermal mass on performance of insulated building walls and the concept of energy savings potential Sami A. Al-Sanea a,⇑, M.F. Zedan a, S.N. Al-Hussain b a b

Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia SABIC’s Technology and Innovation (T&I) Division, P.O. Box 42503, Riyadh 11551, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 31 January 2011 Received in revised form 31 July 2011 Accepted 7 August 2011 Available online 6 September 2011 Keywords: Thermal mass Heat transfer characteristics Insulated building walls Steady periodic conditions Energy savings potential

a b s t r a c t Effects of varying amount and location of thermal mass on dynamic heat-transfer characteristics of insulated building walls with same nominal resistance (Rn-value) are investigated numerically under steady periodic conditions using climatic data of Riyadh. Concepts of ‘‘thermal-mass energy-savings potential’’ (D) and ‘‘critical thermal-mass thickness’’ (Lmas,cr) are developed and utilized in order to determine thermal mass thickness (Lmas) required for a selected desirable percentage of energy savings. Results show that daily transmission loads are not affected by Lmas for representative days of months in summer and winter. However, for moderate months, daily cooling and heating transmission loads decrease with increasing Lmas and either diminish to zero or be reduced asymptotically to constant values. For all months, peak transmission loads and decrement factor decrease, while time lag increases, with increasing Lmas. For a given Lmas, a wall with outside insulation gives better overall performance than a wall with inside insulation. While Rn-value is constant, wall dynamic resistance (Rd-value) changes and represents actual variations in transmission loads. For D in the range 70–99%, Lmas,cr ranges between 6 and 30 cm by using heavyweight concrete. It is found that maximum savings in yearly cooling and heating transmission loads are about 17% and 35%, respectively, as a result of optimizing Lmas for same Rn-value. It is recommended that building walls should contain Lmas,cr that corresponds to high D (95%) and with insulation placed on outside for applications with continuously operating year-round AC. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The demand for electricity is increasing as a result of increasing population, expansion and development plans, and maintaining a good indoor thermal comfort conditions. Besides, the increasing cost of energy and adverse impact on the environment by energy production plants, all contribute to the need to find means to substantially reduce energy consumption. Buildings, through cooling and heating requirements, are major contributors to energy consumption worldwide. It is estimated that about two-thirds of the electric energy generated in the Kingdom of Saudi Arabia is used in buildings and two-thirds of that is used by air-conditioning (AC) equipment [1]. A major part of the energy consumed by AC is due to heat transmission through the outer walls. Therefore, reducing this load becomes one of the most effective energy conservation measures in buildings. The use of special building materials, thermal insulation, as well as employing good design practices should serve this objective. Insulated building walls are integrated parts of a building envelope. They protect the inner space from extreme weather conditions ⇑ Corresponding author. Tel.: +966 1 4676682; fax: +966 1 4676652. E-mail address: [email protected] (S.A. Al-Sanea). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.08.009

and damp down large fluctuations in temperature. As such, the building envelope should provide the necessary thermal comfort for the occupants as well as reduce energy consumption requirements for cooling and heating. This is usually done through increasing thermal resistance (R-value) of this envelope and, hence, reducing transmission loads. Therefore, addition of thermal insulation is important, particularly in regions with extreme climates. Of importance too is to provide means to increase time lag and decrease decrement factor through increasing thermal energy storage capability. The latter is usually regulated through thermal mass in the building envelope. Using heavy thermal masses in building walls is well known in moderate climates (e.g. Mediterranean climate) as means of regulating indoor temperature through nighttime natural ventilation. However, such an advantage cannot be utilized in dusty climates in which reliance is made on the AC equipment (for cooling and heating) for almost all days of the year. While thermal mass controls the amount and rate of heat storage in building components and reduces temperature fluctuations and increases time lag, it does not often preclude the need for using thermal insulation. Accordingly, two important issues must be dealt with; firstly, means of increasing the R-value usually by adding thermal insulation, and secondly, means of increasing thermal energy storage

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Nomenclature c df hc,i hc,o hi Is k L Lins Lmas Lmas,cr N n Qi qc,o qi qpeak qr,o qst Rd, Rn T

specific heat capacity (J/kg K) decrement factor convection coefficient at inside surface (W/m2 K) convective coefficient at outside surface (W/m2 K) combined convection and radiation coefficient at inside surface (W/m2 K) solar radiation flux (W/m2) thermal conductivity (W/m K) layer thickness (m) insulation thickness (m) thermal mass (masonry) thickness (m) critical thermal mass thickness (m) number of layers number of nodes total transmission load (kW h/m2 day) or (kW h/m2 yr) outside convection heat transfer rate (W/m2) instantaneous transmission load (W/m2) peak transmission load (W/m2) long wave radiation exchange (W/m2) rate of energy stored dynamic and nominal (static) thermal resistances (m2 K/W) temperature

capability typically by increasing thermal mass. Insulation materials, while they increase R-value, are not commonly been looked upon as elements that can increase time lag and decrease decrement factor; these are usually associated with thermal mass. On the other hand, thermal masses, while they increase energy storage capability, are not commonly been looked upon as materials that can effect substantial reduction in daily transmission load; the latter is commonly associated with thermal insulation. These common beliefs are based upon facts that increasing amount of mass would not much increase the R-value and increasing amount of insulation would not much increase energy storage capability. This view is simply based upon thermal properties and behavior of building and insulation materials under static (steady state) conditions. Studies under dynamic conditions have shown that these issues are rather complicated and interactive; both insulation and thermal mass have wider effects on thermal characteristics than commonly believed. There are indeed common effects between insulation and thermal mass as well as much interaction between them with regard to their amounts and relative locations within the building structure as can be appreciated next in the literature review. Effects of climatic conditions and operating conditions of AC equipment add to the complexity of the problem. Building elements are, in general, subjected to either steady periodic conditions or initial transient conditions both of which are dynamic in nature. Steady periodic conditions are often reached after a sufficiently long time from start of AC operation and when initial transient effects subside. Practically, steady periodic conditions take place when daily climatic conditions prevail in a periodic manner, or approximately so, and when AC system operates continuously. Short intermittent periods of AC shutdown, as controlled by thermostat settings, should not upset reaching steady periodic conditions. Initial transient conditions, on the other hand, often prevail before reaching steady periodic behavior and take place when AC system is shutdown for prolonged periods of time. Thermal characteristics and roles played by insulation and thermal mass are so much dependent on climatic conditions and operating conditions of AC equipment.

Tf,i Tf,o t tlag x

indoor air temperature (°C) outdoor air temperature (°C) time (s or h) time lag (h) coordinate distance normal to wall surface (m)

Greek letters a thermal diffusivity (m2/s) D thermal-mass transmission-load-savings potential (%) Dt time step (s) Dx internodal distance (m) k surface absorptivity of solar radiation q density (kg/m3) Subscripts c cooling or convection f fluid (ambient) h heating i inside surface or nodal point j layer number N outside layer o outside 1 inside layer or nodal point 1

The main objective of the present study is to investigate effects of thermal mass on transmission loads, energy storage rate, dynamic thermal resistance, time lag, and decrement factor in building walls for same Rn-value. Besides, these thermal characteristics are investigated for cases of outside and inside insulation under steady periodic conditions (i.e. continuous operation of AC system) using climatic data of Riyadh. Concepts of ‘‘thermal-mass energysavings potential’’ and ‘‘critical thermal mass’’ are introduced and developed for the first time in order to determine the thermal mass required for a selected desirable percentage of energy savings.

2. Previous studies Early studies on optimum locations of insulation and concrete layers in building walls and roofs, with the objective to obtain conditions for best load leveling, are those of Sodha and coinvestigators in the late 1970s [2]. In their Fourier series analysis, the authors used the sol–air temperature for a typical hot summer’s day in Delhi and ignored long wave radiation effect. The heat flux to the inside space was evaluated for two configurations: (i) concrete/insulation/air–gap/concrete and (ii) concrete/air–gap/ insulation/concrete. They showed that, for a given total thickness of concrete, best load leveling was achieved when the thickness of the outer concrete layer was as small as possible. Interchanging position of insulation and air gap did not significantly affect optimum condition for best load leveling. The air gap had no significant effect on the time lag but reduced the heat flux markedly. Using the same analysis, Seth et al. [3] investigated optimum distribution of insulation and concrete in an insulation/air–gap/concrete/air– gap/insulation (IACAI) slab and in a concrete/air–gap/insulation/ air–gap/concrete (CAIAC) slab. It was shown that, for a typical hot summer’s day in Kuwait and for given total thicknesses of insulation and concrete, the best load leveling was obtained (i) in IACAI, when the insulation thicknesses on the outside and inside were identical and (ii) in CAIAC when the thickness of the outside concrete layer was least. Of the two structures, IACAI was better from a load leveling point of view.

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Zaki and Hassan [4] determined thermal performance of a twolayered wall with periodic change of outside air temperature and solar radiation taking into consideration effects of building materials, orientation, and relative position of insulating layer. Average heat flux was shown not to be affected by the relative position of layers. Effect of insulation and energy storing layers upon cooling load was investigated by Al-Turki and Zaki [5]. Analysis showed that dispersion of insulation material within building material was less effective than using a continuous equivalent insulation layer placed on the outdoor facade. A whole building energy analysis, based on thermal response factor method, was performed by Eben Saleh [6,7] to investigate effect of insulation material, thickness, and arrangement on the thermal performance of buildings in a hot–dry climate. Results showed that better performance was achieved by locating the insulation on the outer side of building envelope. Balaras [8] reviewed design tools for calculating cooling loads and indoor air temperatures in buildings accounting for thermal mass effects. The review demonstrated the effectiveness of thermal mass in providing more comfortable indoor conditions and energy conservation particularly for locations with large diurnal temperature swings. In general, a high mass building reduces interior air temperature variation, increases time lag, and decreases peak load compared to a low mass building. Keeping overall thickness and U-value of a three-layered building envelope constant, Bojic and Loveday [9] investigated influence of layer distribution of insulation/masonry on thermal behavior. It was shown that for intermittent heating, the insulation/masonry/insulation structure was better. However, for intermittent cooling, it was preferable for the slab to be of the masonry/insulation/masonry structure. If cooling was continuous, then the slab structure did not matter. Bojic et al. [10] investigated influence of insulation position in walls on the cooling load in residential flats in high-rise buildings in Hong Kong. They found that the peak cooling load was decreased by about 7% when a 5 cm polystyrene insulation was used facing either the inside or outside depending on the flat orientation. However, no much reduction in load was observed when the thickness of insulation was increased above 5 cm and that of concrete above 10 cm. Kossecka and Kosny [11] and Kossecka [12] presented concept of ‘‘thermally equivalent wall’’ which is a plane 1-D multilayer structure of dynamic characteristics similar to those for complex structure in which 3-D heat flow occurs. It was shown that the response factor, which represented heat flux at one surface due to temperature excitation at the opposite surface, decayed relatively quickly when the thermal mass was placed on the outside and/or the inside of wall structures. Kossecka and Kosny [13,14] analyzed effect of mass and insulation location on heating and cooling loads in a continuously used residential building. They concluded that material configuration of exterior wall could significantly affect annual thermal performance depending on climate. They found that walls with massive internal layers had better annual thermal performance than those with inside insulation. However, for intermittent heating and cooling, inside insulation could result in better performance. Al-Sanea [15] developed and applied a computer model, based on the finite-volume implicit procedure, to evaluate dynamic thermal characteristics of building walls. Concept of dynamic thermal resistance (Rd-value) was developed in order to account for influences of wall orientation, long wave radiation exchange, thermal energy storage, as well as nominal (static) thermal resistance parameters. It will be shown later that this Rd-value is very much indicative of effects of varying amount and location of thermal mass, the main subject of the present paper. The same computer model was utilized by Al-Sanea and Zedan [16] to study effects of insulation location on thermal performance of building walls

under steady periodic conditions using climatic data of Riyadh. Results showed that insulation location had a minimal effect on daily total transmission load. However, outside insulation gave smaller amplitude of load fluctuation and, hence, peak load in both summer and winter for all wall orientations. Under initial transient effects, on the other hand, Al-Sanea and Zedan [17] showed that insulation layer location had a significant effect on instantaneous and daily total loads. It was recommended that for spaces where AC system is switched on and off intermittently, the insulation should be placed on the inside. In [16,17], attention was focused on effect of insulation/mass location for same amount of thermal mass and insulation. The finite difference method was used by Asan [18] and by Ozel and Pihtili [19] to determine optimum distribution of multi insulation layers in walls for maximum time lag and minimum decrement factor. Al-Sanea and Zedan [20] carried out thermal analysis of walls consisting of one, two and three layers of insulation in which locations of insulation layers were varied with the objective of achieving best overall dynamic performance under optimum thickness of insulation. Ogoli [21] measured temperatures in buildings with low and high thermal mass and showed that materials with high mass had long time lag and moderating effects on temperature swings and thus were effective in lowering indoor maximum temperatures below high outdoor maxima. Cheng et al. [22] presented results of experiments for effects of envelope color and thermal mass and showed that use of lighter surface color and high mass could dramatically reduce maximum indoor temperature. However, the benefit of applying thermal mass depended on AC operation mode and occupancy pattern. Tsilingiris [23] used the implicit finite-difference method to evaluate daily quasi steady-state energy losses from walls and showed that when heating was intermittent the insulation performed better when installed at the interior wall side. Tsilingiris [24] investigated effect of space distribution of heat capacity and thermal resistance on transient behavior of a wall exposed to harmonically time-varying conditions. Results showed that using large heat capacity walls with insulation at ambient side led to a substantial increase of thermal time constant and suppression of room temperature swings. In another study, Tsilingiris [25] fixed wall R-value and investigated effects of spatial distribution of heat capacity. Analysis was carried out using climatic data of Athens for typical days in January and July, while neglecting radiation. It was concluded that spatial distribution of heat capacity strongly influenced transient wall heat flux and asymptotic approach to quasi steady-state periodic behavior but had no effect on time-average quasi steady-state heat flux. Gregory et al. [26] studied impact of thermal mass on performance of Australian residential constructions by using the commercial AccuRate energy rating tool which is based on the frequency response method. They found that thermal mass had a dramatic impact on thermal behavior of modules studied, particularly in those where mass was within a protective envelope of insulation. Zhou et al. [27] developed a simple heat balance model to estimate impact of external and internal thermal mass on indoor air temperature of naturally ventilated buildings. Different walls were compared and found that use of heavy wall with external insulation had the lowest amplitude of indoor air temperature. Effects of thermal mass and thermal insulation must be considered simultaneously since, under dynamic conditions, their effects are interactive. Type, thickness, and location of thermal mass and insulation layers are crucial parameters that affect the thermal behavior of the building envelope. Research in the last 10 years has concentrated more on optimization of insulation layer thickness than on thermal mass. For example, Al-Sanea and Zedan [28] determined optimum thickness of insulation (Lopt) in walls under steady periodic conditions using the climatic data of Riyadh.

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It was found that Lopt increases with cost of electricity, building lifetime and inflation rate; and decreases with increasing cost of insulation material, coefficient of performance of AC equipment and discount rate. Wall orientation was found to have a significant effect on thermal characteristics but a relatively smaller effect on Lopt. Recently, Daouas [29] calculated Lopt in walls under the climatic conditions of Tunisia, while Ozel [30] calculated Lopt under the climatic conditions of Elazig, Turkey. In both studies [29,30], the authors obtained effects of wall orientation on transmission loads and Lopt similar to those obtained earlier by Al-Sanea and Zedan [28]. In a recent study, Taleb and Sharples [31] assessed energy consumption in an apartment complex under the climatic conditions of Jeddah, Saudi Arabia. They used DesignBuilder; a building energy simulation software package based on EnergyPlus. It was estimated that by improving thermal insulation, using more efficient glazing, and fitting external shading devices, energy consumption reduction of over 30% could be achieved. The present authors would like to emphasize here that additional energy savings are possible by using nontraditional energy conservation measures such as the newly developed design practices concerning the optimum use of thermal insulation [20] and the use of optimum thermal mass; the concept of the latter is developed and quantified in the current paper. In summary, it can be concluded that there is a growing interest in determining optimum locations of insulation and thermal mass layers in building walls. However, there is still a need for detailed and systematic studies to investigate effects of thermal mass on energy storage, transmission loads, time lag, and decrement factor. Quantifying effects of amount and location of thermal mass on energy savings potential is obviously lacking. The present study aims at addressing these issues as well as utilizing wall dynamic R-value as an indicative of transmission loads under dynamic conditions. 3. Mathematical formulation and calculation procedure A wall of N layers is shown in Fig. 1. The outside is exposed to convection heat transfer (qc,o), long wave radiation exchange with surroundings (qr,o), and solar radiation (Is). The inside is exposed to combined convection and radiation (qi) which gives the cooling or heating transmission load in terms of the indoor air temperature (Tf,i). Assuming no heat generation, constant properties, and 1-D heat transfer, the governing equation becomes:

@2T j 1 @T j ¼ @x2 aj @t

ð1Þ

where aj is the thermal diffusivity (=k/qc) of layer j. The initial temperature distribution is taken uniform across the whole wall as:

T j ðx; 0Þ ¼ T 0

433

ð2Þ

where T0 is equal to mean outdoor air temperature (Tf,o,mean). It is noted that the steady periodic solution is independent of initial temperature conditions, and that Tf,o,mean is a convenient value to start calculations. The boundary conditions are:

k1

 @T  ¼ hi ðT f ;i  T x¼0 Þ @x x¼0

ð3Þ

at the inside surface, where k1 is the thermal conductivity of the wall inner layer and hi is the combined convection and radiation heat-transfer coefficient, and

kN

 @T  ¼ hc;o ðT x¼L  T f ;o Þ  kIs  qr;o @x x¼L

ð4Þ

at the outside surface, where kN is the conductivity of the wall outer layer, hc,o is the outside convection coefficient, and k is the solar absorptivity taken as 0.4 for light-colored surfaces. The heat transfer coefficients (hi and hc,o) were determined from correlations, Kusuda [32]. The outdoor air temperatures (Tf,o) were obtained from hourly measurements in Riyadh averaged over a number of years. The solar radiation (Is) was calculated from the ASHRAE clear-sky model [33] with results adjusted to account for local dust and cloud conditions, Al-Sanea et al. [34]. The nonlinear long wave radiation exchange with the sky and ground (qr,o) was accounted for rigorously including refined means for estimating the sky temperature. Calculations of these parameters are given by Al-Sanea et al. [35]. The indoor temperature (Tf,i) was fixed for the representative day of each month of the year but varied between the months according to appropriate monthly thermostat settings as summarized in Table 1. These indoor air temperatures, and those in their proximity, were selected to give low operational cost while maintaining thermal comfort in dry climates, Al-Sanea and Zedan [36]. The present nonlinear problem was solved by a control volume finite-difference method using the implicit formulation. A wall of N layers was discretized into a number of nodes, see Fig. 1, and the finite-volume equations were derived by applying the overall energy balance. These equations can be represented by the general form:

ai T i ¼ bi T iþ1 þ ci T i1 þ di

ð5Þ

and were solved by the TDMA for i = 1, 2, . . . , n. The temperature Ti at node i is linked to neighboring temperatures, Ti+1 and Ti1, and the previous time-step temperature through coefficients ai through di. Expressions for these coefficients are given in [35]. Results were checked to be fully converged, and grid and time step independent. Besides, solution was carried through a number of periods (each lasting 24 h) until a steady periodic state was fully obtained. The numerical model has been validated in previous

Fig. 1. Composite wall of N-layers showing boundary conditions and grid arrangement.

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Table 1 Monthly settings of indoor air temperature [36]. Month

January

February

March

April

May

June

July

August

September

October

November

December

Tf,i (°C)

21

21

21

24

26

26

26

26

26

24

21

21

studies and was shown to produce very accurate results under dynamic conditions by comparison with exact analytic solution for a one-layered wall [15] and semi-analytic solutions for a threelayered wall [16,17].

temperatures at previous and current time steps. It is noted that, for a given thermal mass, qst reflects average wall temperature fluctuation with time. 4.7. Nominal thermal resistance (Rn-value)

4. Definition and calculation of parameters All the following parameters are calculated after solution has reached a steady periodic state.

Rn ¼

4.1. Time lag (tlag)

Is amplitude of temperature fluctuation on inner surface of wall divided by that on outer surface. This is calculated for the representative day of each month of the year. The yearly average decrement factor is then determined as the arithmetic average of these monthly values. 4.3. Instantaneous cooling and heating transmission loads (qi) These are calculated from wall inner surface temperature (Tx=0) obtained from the solution as:

qi ¼ hi ðT x¼0  T f ;i Þ

ð6Þ

4.4. Daily total cooling and heating transmission loads (Qi) These are calculated from qi by integration over a 24-h period as: 24h 0

qi dt

ð7Þ

It is noted that values of qi are summed up separately for cooling and for heating. 4.5. Yearly total cooling and heating transmission loads These are calculated from the corresponding daily total values. The daily value of the representative day of each month is multiplied by the number of days in that month and then summed up over the whole year. Of course, cooling and heating transmission loads (Qi,c and Qi,h, respectively) are summed up separately. 4.6. Wall energy storage rate (qst) This is calculated from:

qst ¼

N X n X j¼1

i¼1

qi;j ci;j Dxi;j

T new  T old i;j i;j Dt

k

j

þ

1 1 þ hi hc;o

ð9Þ

4.8. Dynamic thermal resistance (Rd-value) The daily average dynamic thermal resistance is calculated for the representative day of each month of the year as follows:

R 24h

4.2. Decrement factor (df)

Z

N   X L j¼1

Is time span between attaining peak temperatures at outside and inside surfaces of wall. This is calculated for the representative day of each month of the year. The yearly average time lag is then determined as the arithmetic average of these monthly values.

Qi ¼

This is equal to 2.86 m2 K/W and is calculated as the sum of the following resistances:

ð8Þ

where i refers to node in layer j, n is total number of nodes in this layer, N is total number of layers in wall, Dx is internodal distance, Dt is time interval, and superscripts old and new refer to

jðDTÞjdt Rd;day ¼ 0R 24h jqi jdt 0

ð10Þ

where DT = Tf,o  Tf,i. The yearly average dynamic R-value is then determined as the weighted average of these monthly values with respect to transmission loads. As will be seen later, Rd is not constant for a wall with a given Rn and its variation represents the dynamic nature of the problem in an informative way. 5. Presentation and discussion of results Firstly, effects of amount and location of thermal mass on transmission loads, energy storage rate, dynamic resistance, time lag, and decrement factor are dealt with. Secondly, concepts of critical thermal mass and thermal-mass energy-savings potential are developed and utilized. Climatic data of Riyadh are used and a west-facing wall is considered. It is noted that the thermal mass is basically the mass times specific heat. For a 1-D problem, this boils down to density  specific heat  thickness of layer. In the present study, heavyweight concrete is the masonry material used which means that the density and specific heat are fixed and, therefore, the thermal mass can be characterized by layer thickness. 5.1. Wall configurations (W1 and W2) and conditions of constant Rnvalue Two walls are considered: wall W1 with the insulation placed on the outside and wall W2 with the insulation placed on the inside. The thermal mass (heavyweight concrete) and thermal insulation (molded polystyrene) are sandwiched by thin plastering layers as shown in Fig. 2a and b. Table 2 summarizes properties of materials used, [33,37]. The thermal mass thickness is varied in the range 0 6 Lmas 6 50 cm while keeping the wall Rn-value constant. This is done by corresponding adjustments made to the insulation layer thickness (Lins), see Table 3. Since kmas  kins, an increase in Lmas by 100 mm, for example, would correspond to a mere reduction in Lins by about 2 mm. 5.2. Instantaneous thermal characteristics variations with time of day Instantaneous transmission loads (qi) are presented versus time for wall W1 in Fig. 3a for representative days of August, January,

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Inside

(a) 9

Outside

Cement plaster (1.5 cm)

Aug., 20 cm Jan., 20 cm Nov., 20 cm Aug., 5 cm Jan., 5 cm Nov., 5 cm

7

Cement plaster (1.5 cm)

5

Thermal mass

qi (W/m2)

Thermal Insulation

3

1

-1

(a) Wall W1 -3

Inside

Outside -5 0

6

Cement plaster (1.5 cm)

Cement plaster (1.5 cm)

(b) 9 Thermal Insulation

12

18

24

18

24

Time (h)

Thermal mass

Aug., 20 cm Jan., 20 cm Nov., 20 cm Aug., 5 cm Jan., 5 cm Nov., 5 cm

7

qi (W/m2)

5

(b) Wall W2

3

1

Fig. 2. Schematic of wall configurations with same and constant Rn-value; (a) wall W1 with outside insulation and (b) wall W2 with inside insulation.

-1 Table 2 Material properties [33,37].

-3

Material

k (W/m K)

q (kg/m3)

c (J/kg K)

Cement plaster Molded polystyrene Heavyweight concrete

0.72 0.034 1.73

1860 23 2243

840 1280 840

Table 3 Adjustments made to insulation layer thickness (Lins) by varying thermal mass thickness (Lmas) in order to keep Rn-value constant. Lmas (m)

Lins (m)

0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.400 0.500

0.0900 0.0890 0.0880 0.0871 0.0861 0.0851 0.0841 0.0821 0.0802

and November. Results are also compared for Lmas = 20 cm and 5 cm, corresponding to heavyweight and lightweight structures. It is seen that qi has a periodic variation and oscillates with positive values in August (representing heat transmission to space), negative values in January (representing heat transmission out of space), and both positive and negative values in November. Load

-5

0

6

12

Time (h) Fig. 3. Transmission load variation with time of day in August, January, and November with Lmas = 20 cm and 5 cm; (a) for wall W1 (outside insulation) and (b) for wall W2 (inside insulation).

fluctuations are damped down appreciably by using the heavyweight structure (Lmas = 20 cm). Peak transmission load is, hence, reduced and its time of occurrence is delayed giving longer time lag. These are clear advantages of using increased thermal mass. Corresponding results for wall W2, presented in Fig. 3b, show similar trends but with larger fluctuations. Therefore, placing insulation on outside provides more damping of load fluctuation and smaller peak load. Integrated values of qi over a 24-h period give the daily total transmission loads (Qi), see Eq. (7). Table 4 summarizes and compares these daily total cooling and heating loads. Any of these loads is also represented by the area enclosed under its corresponding curve in Fig. 3a and b and the zero datum line shown. It is noted that the daily cooling loads are practically the same in August for both thermal masses and for both walls with a value of about 0.085 kW h/m2 day. The same can be said about the daily heating loads in January with a value of about 0.06 kW h/m2 day. However, this is not true for the daily loads in November, where both cooling

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Table 4 Daily total cooling and heating transmission loads for walls W1 and W2 using Lmas = 5 cm and 20 cm for representative days of August, January, and November. Qi (kW h/m2 day)

Cooling  100 Heating  100

45

Wall W1

Wall W2

Lmas = 5 cm

Lmas = 20 cm

Lmas = 5 cm

January

November

August

January

November

August

January

November

August

January

November

8.511 0.000

0.000 5.999

1.064 1.722

8.509 0.000

0.000 6.001

0.126 0.786

8.522 0.000

0.069 6.061

1.478 2.126

8.539 0.000

0.000 5.983

0.351 0.986

(a)

Aug. Jan. Nov.

40

Lmas = 20 cm

August

40

20

35

Tf,o

Tf,i for Aug.

qst (W/m2)

T (ºC)

0

Tf,o

30

Tf,i for Aug.

25

Tf,i for Jan. & Nov. Tf,i for Jan. & Nov.

-20 Aug., 20 cm

20

-40

Tf,o

Jan., 20 cm Nov., 20 cm

Tf,o

15

Aug., 5 cm

Tf,o

-60

Tf,o

10

Jan., 5 cm Nov., 5 cm

-80

5 0

6

12

18

0

24

6

Time (h)

and heating loads are present and are quite different between the two thermal masses as well as between the two walls, as can clearly be seen in Table 4. These loads are substantially reduced by increasing mass for the same Rn-value. It may also be noted that these loads are smaller for wall W1 compared to wall W2. The variations of qi with time presented earlier in Fig. 3a and b are very much the outcome of effects of outdoor and indoor air temperatures (Tf,o and Tf,i) presented in Fig. 4. It is seen that Tf,o is always above Tf,i in August; the opposite is true in January. However, in November Tf,o variation crosses Tf,i; i.e. it is higher during part of day (10:00 < t < 20:00) and is lower during the rest of the day. This explains the occurrence of both cooling and heating transmission loads in November and, as will be seen later, is the reason behind potential energy savings due to thermal mass in moderate months or, indeed, moderate climates. Further insight into results is made by examining variations of thermal energy storage rate with time. These are shown for wall W1 in Fig. 5a for August, January, and November for Lmas = 20 cm and 5 cm. Positive values signify energy storage, while negative values signify energy loss. As seen, the wall gains energy during daytime (7:00 < t < 16:00) and dissipates it predominantly during the evening and night time. The dominant source of energy gain is solar radiation absorbed by the wall outer surface, a large percentage of which is stored in the wall and is ultimately dissipated to outside through the same surface. Daily total storage rate is the area under the curve using positive values of qst, while daily total dissipation rate is the area under the curve using negative values of qst. These two quantities must be equal under steady periodic conditions, i.e. net heat storage over 24 h must be zero. It is interesting to note that energy storage and dissipation rates have similar time variations in August, January, and November, and that these rates are not much affected by varying amount of thermal

(b) 150

18

24

18

24

Aug., 20 cm Jan., 20 cm

120

Nov., 20 cm

90

Aug., 5 cm Jan., 5 cm

60

qst (W/m2)

Fig. 4. Outdoor air temperature (Tf,o) variation with time of day in August, January, and November showing fixed thermostat settings of indoor air temperature (Tf,i).

12

Time (h)

Nov., 5 cm

30 0

-30 -60 -90 -120 0

6

12

Time (h) Fig. 5. Energy storage rate variation with time of day in August, January, and November with Lmas = 20 cm and 5 cm; (a) for wall W1 and (b) for wall W2.

mass. It seems surprising at first that increasing thermal mass does not really increase heat storage rate; however, a careful look at Eq. (8) shows that the average wall temperature fluctuation drops with increasing thermal mass. The corresponding results for wall W2, presented in Fig. 5b, show that qst variations with time have rather similar trends to those of wall W1 but with larger fluctuations. Moreover, the effect of thermal mass on qst is much more noticeable for wall W2. Therefore, placing the insulation layer on the outside has very much reduced energy storage rates and damped temperature fluctuations.

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10

2

W1, cool.

W2, cool.

W1, heat.

W2, heat.

W1, cool. 9

Qi,c (kWh/m2.day) × 100

1

Qi (kWh/m2.day) × 100

W2, cool.

0

-1

-2

8

7

6

-3

5

0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

Fig. 6. Daily cooling and heating transmission loads variation with masonry thickness in November for walls W1 and W2.

0.3

0.4

0.5

Lmas (m)

Lmas (m)

Fig. 7. Daily cooling transmission load variation with masonry thickness in August for walls W1 and W2.

5.3. Effect of thermal mass on daily thermal characteristics 12

10

Rd (m2.K/W)

Fig. 6 presents variations of the daily total transmission loads (Qi) with masonry thickness (Lmas) for the representative day of November. Positive values signify cooling loads (Qi,c), while negative values signify heating loads (Qi,h). It is seen that Qi,c decreases with increasing Lmas and diminishes to zero at Lmas  0.25 m for W1 and Lmas  0.35 m for W2. Similarly, the magnitude of Qi,h decreases with increasing Lmas but reaches asymptotically a constant value at Lmas  0.3 m. For Lmas < 0.3 m, and for both cooling and heating, wall W1 gives smaller Qi than wall W2 for any given Lmas. Corresponding results for August, presented in Fig. 7, show that values of Qi,c stay practically constant with increasing Lmas and are practically equal for both walls. These behaviors are attributed largely to the swing of the outdoor temperature (Tf,o) relative the indoor temperature (Tf,i) as shown earlier in Fig. 4. Similar trend of variation is obtained for January to that obtained for August but for Qi,h. The variations of the daily average Rd-value with Lmas for the representative days of August, January, and November are presented in Fig. 8. It is seen that Rd-values in August stay practically constant with increasing Lmas. This reflects the daily transmission load behavior already shown in Fig. 7. The same is true for January. For these months, Rd-values can hardly be distinguished from the Rn-value which is 2.86 m2 K/W. In November, however, it is seen that while the Rn-value is constant, the Rd-value increases with Lmas. This reflects decreasing daily cooling and heating transmission loads with increasing Lmas as shown in Fig. 6. Besides, for a given Lmas, Rd-value for wall W1 is greater than that for wall W2 up to Lmas  0.4 m, beyond which Rd-values of the two walls are approximately the same. This also reflects Qi versus Lmas behavior presented in Fig. 6. It is concluded, therefore, that the Rd-value gives a true and indicative representation of the actual daily transmission loads while the Rn-value falls short of such a complete representation, as expected. Fig. 9a compares Rd-values for the representative days in all months. This is done for both walls with Lmas = 5 cm while showing Rn-value as a reference. For this light structure, it is seen that Rd-values are generally smaller than the Rn-value and that they are different for the two walls in the moderate months with wall W1 having the larger values. The picture changes significantly for

8

6

W1, Aug. W1, Jan. W1, Nov.

4

W2, Aug. W2, Jan. W2, Nov.

2

0 0

0.1

0.2

0.3

0.4

0.5

Lmas (m) Fig. 8. Daily average dynamic R-value variation with masonry thickness in August, January, and November for walls W1 and W2; Rn-value = 2.86 m2 K/W.

the heavier mass (Lmas = 20 cm) shown in Fig. 9b. Here, Rd-values increase substantially above the Rn-value in March, April, October, and November. It is also noted that wall W1 has higher Rd-values than wall W2 in March and November. These results emphasize the importance of both amount and location of thermal mass and indicate that the moderate months are responsible for achieving energy savings due to sole effect of mass for a given wall Rn-value. The relationship between amount of thermal mass and percentage energy savings is dealt with later.

5.4. Concept and significance of dynamic R-value The present authors have developed, refined, and adopted the concept of the dynamic R-value for a while now. Its advantage over the nominal R-value has been noticed. However, it has now been realized through the present work that it has a much wider scope

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(a)

3.5

3

R (m2.K/W)

2.5

2

1.5

1

W1, dyn. R W1, nom. R W2, dyn. R W2, nom. R

0.5

0 1

2

3

4

5

6

7

8

9

10

11

12

Month

(b)

9

W1, dyn. R W1, nom. R W2, dyn. R W2, nom. R

8 7

R (m2.K/W)

6 5 4

thermal mass and reaches asymptotically a constant value at large thermal mass, see Fig. 8. Due to these moderate months, the same trend is obtained for the yearly average dynamic R-values as will be seen later. With reference to Table 4, and by considering for example wall W1 with Lmas = 5 cm, it is clearly noted that the sum of the absolute values of daily cooling and heating transmission loads for the representative day of November is much less than either the cooling load in the representative day of August or the heating load in the representative day of January. This is attributed to two factors; the first factor is related to reduction in difference between outdoor air and indoor air temperatures in November compared to August and January, see Fig. 4. The second factor is related to the dynamic nature of the problem, i.e. thermal energy storage and time lag effects in the wall and their interaction with varying amount of thermal mass. This second factor cannot be accounted for by the nominal R-value during the moderate months where both cooling and heating are present during the day, in which heat transfer to the inner space reverses direction accordingly. The dynamic R-value, on the other hand, has responded to this effect by showing changes, see Fig. 9a, reflecting variations in both transmission loads and the driving temperature differences between outdoor and indoor over the representative days in the months. By referring to the same previous variables in Table 4 but at Lmas = 20 cm, results reveal much reduced cooling and heating transmission loads in November; this may also be noted in Fig. 6. Since the driving temperature differences between outdoor and indoor are the same, the dynamic R-value must have increased appreciably to represent such large reduction in transmission loads. This is exactly what the results in Fig. 9b indicate. This may be looked upon as an enhancement in dynamic R-value as a result of increasing thermal mass for same nominal R-value.

3

5.5. Effect of thermal mass on yearly thermal characteristics

2 1 0 1

2

3

4

5

6

7

8

9

10

11

12

Month Fig. 9. Daily average dynamic and nominal R-values for walls W1 and W2 for representative days in months; (a) with Lmas = 5 cm and (b) with Lmas = 20 cm.

of use than had been anticipated. The following account highlights its advantage and importance. The R-value employed exclusively in the literature is the static R-value. It is presently termed nominal R-value [Eq. (9)] in order to distinguish it from the dynamic R-value [Eq. (10)]. This nominal R-value, which represents transmission load under steady-state conditions, is merely used here as a datum for comparison. Caution must be exercised in using this R-value under dynamic conditions. The present results have demonstrated that both dynamic and nominal R-values are close for winter and summer months in which only heating or cooling is present during the whole day, see Figs. 8 and 9, and therefore both R-values give adequate representation of the transmission loads. In contrast, during the moderate months in which both heating and cooling are present during the day, only the dynamic R-values have responded and proportionately represented corresponding changes in transmission loads while the nominal R-value completely fails to do that. As a consequence, there is no physical reasoning to why, in the moderate months, the nominal R-value is greater than the dynamic R-values for lightweight walls and is smaller than the dynamic R-values for heavyweight walls, cf. Fig. 9a and b. Indeed, in the moderate months, the dynamic R-value increases all the way with increasing

Variation of yearly total cooling transmission load (Qi,c) with Lmas is presented in Fig. 10a. It is seen that Qi,c decreases sharply with increasing Lmas reaching asymptotically a constant value for either wall. The asymptotic values are represented by the two lower dotted horizontal lines. The two upper dotted horizontal lines will be referred to later when considering the critical thermal mass thickness. Similar behavior is obtained for the yearly total heating transmission load (Qi,h) shown in Fig. 10b. It is noted that for a given Lmas, wall W1 gives lower yearly cooling and heating loads. For Lmas > 30 cm, the two walls give practically the same yearly loads. At the other end, when Lmas = 0, Qi is the same since both walls would have identical configurations; see Fig. 2. By comparing values of Qi at the asymptotes with those at Lmas = 0 in Fig. 10a and b, the maximum possible savings in yearly transmission loads affected by thermal mass alone are estimated at about 17% for cooling and 35% for heating. Such potential savings in transmission loads are quite substantial and, as emphasized earlier, are caused by reduction in loads with increasing Lmas while keeping Rn-value constant. These results are consistent with the traditional practice of constructing walls with large masses in regions with moderate climates. Nevertheless, this does not preclude the need for using sufficient amount of thermal insulation. The use of even heavily insulated but lightweight walls must, therefore, be carefully scrutinized under different climatic conditions. Fig. 11 displays the variations of the peak cooling (August) and peak heating (January) transmission loads with Lmas. It is seen that qpeak decreases appreciably with increasing Lmas and resembles variations of the yearly total cooling and heating transmission loads presented above. However, a main difference is that qpeak continues to decrease and does not seem to reach an asymptotic value with increasing Lmas over the range considered. For Lmas < 0.4 m, wall

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(a) 15

10

W1, cool.

W2, cool. 8

W1, cool.

W2, cool.

W1, heat.

W2, heat.

14.5

6

qpeak (W/m2)

Qi,c (kWh/m2.yr)

14

13.5

4 2 0

13

-2 12.5

-4 -6

12 0

0.1

0.2

0.3

0.4

0

0.5

0.1

0.2

0.3

0.4

0.5

Lmas (m)

Lmas (m)

Fig. 11. Yearly peak cooling and heating transmission loads variation with masonry thickness for walls W1 and W2.

(b) -4 0

0.1

0.2

0.3

0.4

0.5

-4.5

W2

12

-5.5 10

-6

tlag (h)

Qi,c (kWh/m2.yr)

W1

14

-5

-6.5

8 6

-7

4

W1, heat.

W2, heat.

-7.5

Lmas (m) Fig. 10. Yearly cooling and heating transmission loads variation with masonry thickness for walls W1 and W2 showing asymptotes and corresponding critical thermal mass thicknesses by using 5% criterion; (a) cooling load and (b) heating load.

W1 gives lower qpeak. At Lmas > 0.4 m, the two walls give practically the same qpeak; this suggests that qpeak is not sensitive to insulation layer location at large Lmas. The yearly average time lag (tlag) variations with Lmas are presented in Fig. 12. It is seen that for Lmas > 10 cm, tlag increases linearly with Lmas. For a given Lmas, wall W1 gives a time lag that is about half an hour longer compared to wall W2. It is estimated that tlag increases at a rate of about 1 h per 4 cm increase in Lmas. Fig. 13 presents the variations of the yearly average decrement factor (df) with Lmas. It is seen that df decreases with increasing Lmas. The initial rate of decrease is steeper for wall W1 which is an advantage for the outside insulation. At Lmas = 0, df  0.04; this is reduced by an order of magnitude for wall W1 when Lmas = 30 cm compared to a reduction by a factor of 5 for wall W2. The yearly average Rd-value variations with Lmas are presented in Fig. 14 and compared with the Rn-value. These are weighted average with respect to transmission loads. It is seen that Rd-values of both walls increase with Lmas and reach asymptotically the same value at Lmas > 0.3 m. For a given Lmas, and for Lmas < 0.3 m, wall W1

2 0 0

0.1

0.2

0.3

0.4

0.5

Lmas (m) Fig. 12. Yearly average time lag variation with masonry thickness for walls W1 and W2.

gives larger Rd-value over that of wall W2. The increase in Rd-value with Lmas is consistent with the decrease in Qi and qpeak with increasing Lmas presented earlier in Figs. 10a and b, and 11. As seen from the latter figures, Qi,c, Qi,h, and qpeak practically cease to decrease with increasing Lmas beyond 0.3 m; this is exactly reflected by Rd-value becoming constant for Lmas > 0.3 m as seen in Fig. 14. Compared to the constant Rn-value, it is clear that the Rd-values are in harmony with varying values of Qi and qpeak; as such, they better represent the dynamic nature of the problem. It is interesting to note that the nominal R-value is still in common use in the literature and in building codes and standards under the name of ‘‘recommended R-value’’. In view of the present results, the accuracy and legitimacy of using the nominal R-value under dynamic conditions may be quantified under the present conditions with reference to Fig. 14. As seen, noticeable differences exist between the dynamic R-values and the constant nominal R-value depending on the amount of thermal mass present and

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S.A. Al-Sanea et al. / Applied Energy 89 (2012) 430–442 Table 5 Percentage criterion, energy savings potential, yearly cooling transmission load, and critical thermal mass thickness for wall W1a.

4

W1

W2

df ×100

3

2

a b

1

0 0

0.1

0.2

0.3

0.4

0.5

Lmas (m) Fig. 13. Yearly average decrement factor variation with masonry thickness for walls W1 and W2.

3.5

R (m2.K/W)

3

2.5

W1, dyn. R

W1, nom. R

W2, dyn. R

W2, nom. R

2 0

0.1

0.2

0.3

0.4

0.5

Lmas (m) Fig. 14. Yearly average dynamic and nominal R-values variation with masonry thickness for walls W1 and W2.

its location in the wall. If, for the sake of argument, the recommended R-value is taken as the nominal R-value shown in the figure, then in practice the wall would be under-designed for Lmas less than about 0.1 m and over-designed for Lmas greater than about 0.1 m because of dynamic effects. Accordingly use of lightweight walls, even when sufficiently insulated, must be scrutinized for proper thermal mass especially in moderate climates.

5.6. Critical thickness of thermal mass (Lmas,cr) and energy savings potential (D) Energy savings potential is short for ‘‘thermal-mass transmission-load-savings potential’’ and represents percentage savings on that part of energy caused by transmission load that can potentially be achieved by thermal mass. This excludes savings that are normally affected by thermal insulation. Based on yearly transmission load (Qi) variations with Lmas, a critical thermal mass thickness

% Criterion

D (%)

Transmission loadb (kW h/m2 yr)

Lmas,cr (cm)

30 20 15 10 7 5 3 2 1

70 80 85 90 93 95 97 98 99

13.223 12.972 12.847 12.721 12.646 12.596 12.545 12.520 12.495

6.5 8.4 9.8 12.1 14.2 15.9 18.2 20.0 23.7

Largest load = 14.98 kW h/m2 yr and asymptotic load = 12.47 kW h/m2 yr. Load = % criterion  (largest load  asymptotic load) + asymptotic load.

(Lmas,cr) is obtained corresponding to a percentage energy-savings potential (D). This is demonstrated with reference to Fig. 10a where the two lower horizontal dotted lines represent the asymptotic cooling loads for walls W1 and W2. An asymptotic load gives the minimum yearly total transmission load obtained at ‘‘large’’ thermal mass. Adding more mass will not further reduce this load, and is pointless as far as savings in energy consumption are concerned. This fact leads to the notion of optimum thickness of thermal mass to use in building walls. For the present demonstration, a ‘‘5% criterion’’ is chosen; this constitutes a 95% of the maximum possible savings on yearly cooling transmission load through using thermal mass alone for a given wall Rn-value. Firstly, the difference between yearly cooling load at Lmas = 0 and asymptotic load is calculated. Secondly, 5% of this difference is added to the asymptotic load. These new loads, for walls W1 and W2, are represented by the two upper dotted horizontal lines shown in Fig. 10a which cut the Qi,c versus Lmas curves at Lmas,cr. Fig. 10a shows that Lmas,cr = 15.9 cm and 22.7 cm for walls W1 and W2, respectively. By repeating the above procedure for the yearly total heating transmission loads, as shown in Fig. 10b, the Lmas,cr obtained are 15.6 cm and 22.5 cm for walls W1 and W2, respectively. By comparing these values with those for cooling, it becomes evident that Lmas,cr for cooling and heating are practically the same for a given D. This finding is quite important since, otherwise, one will have to compromise between what would have been two different Lmas,cr, one for cooling and one for heating. In order to construct a chart that can be used to obtain thermal mass required to achieve desired percentage savings in yearly transmission loads, critical thermal mass variations with energy savings potential are developed as shown in Table 5. The table summarizes values of critical thermal mass thickness (Lmas,cr) and energy savings potential (D) for cooling calculated for wall W1. The first column specifies the % criterion used. The second column contains energy savings potential which is simply 100%  % criterion used. The third column contains the transmission load calculated by using the % criterion. The fourth column contains Lmas,cr obtained from corresponding value of transmission load just calculated by using Qi,c versus Lmas curve presented in Fig. 10a. Due to space limitation, other such tables for heating and for wall W2 are not presented. Fig. 15 presents Lmas,cr variations with D and compares results between walls W1 and W2 for cooling and heating. It is seen that Lmas,cr increases with D; the increase is initially gradual and then becomes much steeper as a high energy savings potential is sought. Accordingly, if a high D is selected, this would be on the expense of having to use large Lmas,cr. The initial gradual increase of Lmas,cr with D is quite advantageous since much of the energy savings potential can be achieved by slightly increasing Lmas. Results also show that values of Lmas,cr are practically the same for cooling and heating

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35

30

W1, cool.

W1, heat.

W2, cool.

W2, heat.

Lmas,cr (cm)

25

20

15

10

5

0 70

75

80

85

90

95

100

Energy savings potential, Δ (%) Fig. 15. Critical thermal mass thickness variation with cooling and heating energysavings potentials for walls W1 and W2.

energy-savings potentials as demonstrated by nearly perfect agreement between the solid and dashed lines. Trend of variations of Lmas,cr with D is very similar for both walls; however, for a given D, wall W1 gives about 5 cm less Lmas,cr. In other words, the energy savings potential of a wall with outside insulation is superior to that with inside insulation having the same thermal mass. Further examination of results in Fig. 15 reveals that the range of energy savings potential given by 70% 6 D 6 99% corresponds to a wide range of critical thermal mass given by 6.4 cm 6 Lmas,cr 6 29.6 cm. The precise value of Lmas,cr would, of course, depend on the selected value of D and thermal insulation location. It is noted that values of Lmas,cr corresponding to D < 70% are not presented since it is believed that under such conditions the walls would be wasting high percentage of valuable energy that could have easily been saved. Besides, walls with such correspondingly small Lmas,cr (e.g. Lmas,cr < 10 cm) would be highly under-designed with regard to peak loads, time lag, and decrement factor (cf. Figs. 11–13). From the practical application point of view, the use of Fig. 15 is simply to select a desired percentage of energy savings potential, and then determine the corresponding required thermal mass thickness. The present investigators suggest a minimum value of D of no less than 90% to be selected and recommend consideration of D in the range 90% 6 D 6 97%. 6. Conclusions and recommendations While keeping nominal resistance (Rn-value) constant, effects of amount and location of thermal mass in insulated building walls on total and peak transmission loads, time lag, decrement factor, and dynamic resistance (Rd-value) were investigated under steady periodic conditions using the climatic data of Riyadh. The concept of thermal-mass energy-savings potential was developed and utilized for the first time to construct a chart to determine the thermal mass thickness (Lmas) required to obtain desirable percentages of energy savings through using thermal mass alone for any thickness of insulation. The results show that: 1. Daily transmission loads are not affected by Lmas for summer and winter months. 2. For moderate months, daily cooling and heating loads decrease with increasing Lmas and either diminish to zero or be reduced asymptotically to constant values.

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3. Yearly cooling and heating transmission loads decrease with increasing Lmas and reach asymptotically constant values. 4. Peak cooling and heating transmission loads and decrement factor decrease with increasing Lmas, while the time lag increases with increasing Lmas. 5. While the Rn-value is constant, wall Rd-value changes with amount and location of Lmas and represents actual variations in transmission loads. 6. Relations between critical thermal-mass thickness (Lmas,cr) and thermal-mass energy-savings potential (D) are obtained by using heavyweight concrete. It is found that: (a) Lmas,cr increases with increasing D. (b) For a given Lmas, cooling and heating energy-savings potentials are the same. (c) For D in the range 70–99%, Lmas,cr ranges between 6 and 30 cm. (d) For a given D, Lmas,cr is smaller for a wall with outside insulation compared to a wall with inside insulation. Conversely, for a given Lmas,cr, higher D is obtained for the wall with outside insulation. 7. Maximum savings in yearly transmission loads are about 17% for cooling and 35% for heating as a result of optimizing thermal mass. 8. For a given thermal mass, a wall with outside insulation gives better overall thermal performance compared to a wall with inside insulation. It is recommended that building walls should contain as a minimum critical amount of thermal mass that correspond to energy savings potential in the range 90% 6 D 6 97% and that the insulation layer should be placed on the outside for applications with continuously operating AC. Future work may investigate effects of using different climatic conditions. Acknowledgments The authors would like to acknowledge the College of Engineering Research Center and Deanship of Scientific Research at King Saud University in Riyadh for support. References [1] Studies and Statistics Department, Electrical Affairs Agency: Electricity Growth and Development in the Kingdom of Saudi Arabia up to the year 1420 H (1999/ 2000 G), Ministry of Industry and Electricity, Kingdom of Saudi Arabia; 2002. [2] Sodha MS, Kumar A, Srivastava A, Tiwari GN. Thermal load levelling in a multilayered wall/roof. Energy Res 1981;5:1–9. [3] Seth SP, Bansal NK, Nayak JK, Seth AK. Optimum distribution of insulation and concrete in a multilayered wall or roof. Appl Energy 1981;9:49–54. [4] Zaki GM, Hassan K. Thermal performance of composite building components with periodic solar insolation and ambient temperature. Solar Wind Technol 1986;3:103–9. [5] Al-Turki A, Zaki GM. Cooling load response for building walls comprising heat storing and thermal insulating layers. Energy Convers Manage 1991;32:235–47. [6] Eben Saleh MA. Thermal insulation of buildings in a newly built environment of a hot dry climate: the Saudi Arabian experience. Int J Ambient Energy 1990;11:157–68. [7] Eben Saleh MA. Impact of thermal insulation location on buildings in hot dry climates. Solar Wind Technol 1990;7:393–406. [8] Balaras CA. The role of thermal mass on the cooling load of buildings. An overview of computational methods. Energy Build 1996;24:1–10. [9] Bojic MLj, Loveday DL. The influence on building thermal behavior of the insulation/masonry distribution in a three-layered construction. Energy Build 1997;26:153–7. [10] Bojic M, Yik F, Sat P. Influence of thermal insulation position in building envelope on the space cooling of high-rise residential buildings in Hong Kong. Energy Build 2001;33:569–81. [11] Kossecka E, Kosny J. Equivalent wall as a dynamic model for a complex thermal structure. J Therm Insul Build Env 1997;20(January):249–68. [12] Kossecka E. Relationships between structure factors, response factors, and ztransfer function coefficients for multilayer walls. ASHRAE Trans 1998;104(1A):68–77.

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