Determination of optimum insulation and cement plaster thickness for bungalow buildings through a simulation-statistical approach using response surface methodology

Insulating interior side of external wall and finishing by cement plaster is one of the most appropriate methods of reducing annual energy consumption in available buildings. The aim of this study is to determine the optimum expanded polystyrene (EPS) and cement plaster thickness for bungalow building in Malaysia. The present study evaluates the effect of different thermal insulation and interior cement plaster thicknesses on the annual cooling energy consumption. Furthermore, the optimum thickness of EPS and plaster is estimated based on wall type and building orientation. Two different types of walls made of concrete and brick are considered. EPS and plaster were used in the range of 20 to 100 mm and 0 to 20mm, respectively. The results show that both thermal insulation and plaster thickness have a direct effect on annual cooling energy consumption, however, the influence of wall thermal insulation thickness is more significant than cement plaster thickness. Further, the optimum EPS thickness decreases with the increment in cement plaster thickness for different orientations and wall types. The optimum EPS thickness ranges from 31.5 mm to 53.1 mm based on wall type, orientation and cement plaster thickness. Utilizing optimum EPS and cement plaster thicknesses can thus reduce annual energy consumption by about 6 to 12% in different directions.


INTRODUCTION
Total end-user energy consumption is linked to the transportation, industrial, residential, commercial and other sectors with contributions of 30%, 29%, 27%, 9% and 5%, respectively (Parameshwaran et al., 2012). One-third of the total energy consumption and 30% of greenhouse gas emissions are attributed to buildings in most countries (Martínez-Molina et al., 2016; D. Zhang et al., 2004). Finding new means of saving energy in the building sector is essential due to the limited natural energy sources and rise in population  . Fabric and ventilation heat transfer are two reasons for heat loss in buildings. Fabric heat loss is related to conduction heat transfer through walls, roofs, windows and floors.
Ventilation heat loss is a type of convective heat transfer whereby air is replaced by heating, ventilation, and air conditioning systems.
In Malaysia, residential buildings consume about 19% of the total energy (Saidur et al., 2007). The average building energy index (BEI) in south-east Asia is about 233 KWh/m 2 /year, whereas the Malaysian average is 269 kWh/m 2 /year. Around 45% up to 70% of the energy consumed by Malaysian buildings is attributed to cooling equipment (Hassan & Al-Ashwal, 2015;Rahman et al., 2008). However, cooling energy consumption may be reduced by limiting the amount of heat transfer through the building envelope (Mirrahimi et al., 2016). Using materials with high heat resistance in the building envelope is a suitable method of reducing the annual cooling load and peak cooling demand for buildings in hot and humid regions. Hassan and Al-Ashwal (Hassan & Al-Ashwal, 2015) reported that exterior wall thermal insulation facilitates significant reductions in annual cooling energy by up to 20% in Malaysian buildings. However, Iqbal et al. (Iqbal & Al-Homoud, 2007) reported only 2% energy savings by increasing the insulation thickness from 50 to 75 mm.
Thick insulation reduces energy consumption, although it increases construction costs and reduces internal spaces. Hence, it is vital to identify the optimum thickness for thermal insulation. Mahlia and Iqbal (Mahlia & Iqbal, 2010) revealed that the optimum insulation thickness is between 15 to 60 mm depending on the air gap thickness and insulation material. Dombaycı (Dombaycı, 2007) reported that the optimum insulation thickness is about 95 mm in buildings in Turkey. However, another study indicated that the optimum insulation thickness in Turkey ranges from 10 to 70 mm depending on fuel type and weather conditions (Ucar & Balo, 2009). Yu et al. (Yu et al., 2009) reported optimum thicknesses of different insulation types in the range of 50 to 230 mm. Ashouri et al. (Ashouri et al., 2016) found that the optimum thickness varies from 94 to 220 mm based on wall thickness and insulation type.
Mahlia et al. (Mahlia et al., 2007) reported that the optimum insulation material thickness is around 40 to 100 mm. In addition, they proposed the following correlation between thermal conductivity and thermal insulation material thickness: xopt = a + bk + ck 2 (1) Where x is the insulation thickness (m), k is the thermal conductivity of the insulation (W/m֠ K), a = 0.0818, b = -2.973 and c = 64.6. EPS is a white foam plastic insulation material, which is manufactured by expanding polystyrene. The cost of EPS varies from 6.54 €/unit to 47.97 €/unit, while the commercial thickness ranges from 30 to 220 mm. The thermal conductivity, density and specific heat capacity of EPS are in the ranges of 0.029-0. Based on the available literature, the optimum thickness of insulation materials varies according to wall thickness, wall topology, building orientation, weather conditions, insulation type and wall type. It appears from the literature that no study has evaluated the effects of cement plaster thickness on the optimum wall insulation thickness and building energy consumption. In the most available studies the thickness of cement mortar considered constant and the effect of this layer of wall on total heat transfer through walls has not been considered. Hence, the aim of this study is to evaluate the effect of both thermal insulation thickness and cement plaster thickness on the annual energy consumption of an air-conditioned bungalow. Another objective of this research is to determine the optimum EPS thickness for Malaysian buildings based on wall type, orientation, and cement plaster applied within. The results indicate potential energy savings for bungalows with different orientations.
To fulfil the objectives, the annual energy consumption of a tropical single-story bungalow is simulated while the walls containing EPS and cement mortar in different thicknesses. Then, the achieved data of simulation are inserted to the design expert software to find the optimum thickness of EPS and cement mortar through RSM. Finally, the amount of energy consumption reduction of building in present of optimum thickness of EPS and plaster is calculated.

Climate conditions and comfort temperature
The geographic location of Kuala Lumpur as the capital of Malaysia is at latitude 3.13֠ N and longitude 101.68֠ E (Fig. 1). Malaysia's tropical climate is hot and humid. The insolation (solar radiation energy shining on a horizontal surface) in Malaysia is depicted in Fig. 3. Data obtained for a ten-year period shows that outdoor temperatures are relatively uniform with average temperatures between 23.7֠ C and 31.3֠ C throughout a day with the highest maximum recorded of 36.9֠ C. The average relative humidity throughout a day is between 67% and 95% (Asadi et al., 2014b). Regarding the Malaysia climate, cooling systems are considered among the principal energy consumption aspects in the building sector.

Governing heat transfer equations
Heat transfer is a vector quantity that occurs through conduction, convection and radiation (Incropera & DeWitt, 1985). Conduction heat transfer in solids is a mixture of molecule vibrations and energy transport by free electrons (Bhattacharjee & Krishnamoorthy, 2004). The energy consumption in buildings is extremely dependent on the thermal conductivity values of the building materials. Thermal conductivity is a property of a material, which demonstrates its heat conduction capability (Asadi et al., 2018; W. Zhang et al., 2015). In convection, heat flows through the movement of liquid or gas molecules (between solids and fluids). In radiation, heat flows through electromagnetic waves.
The rate of total heat lost or gained by a building surface through conduction, convection and radiation can be calculated using Eq. 2.
Where is the building component surface area, Ui is the U value of each building component, Ti is the indoor temperature and To is the temperature of the ground and the outside air.
The U value of a wall is calculated by: Where is the wall's total heat resistance given by: Where hi and ho are the inside and outside heat transfer coefficients, L is the layer thickness and k is the thermal conductivity of the related material.

Wall configuration
Two different walls were designed for use as exterior walls in a bungalow building. The first consists of 200mm concrete and the second is made of 200mm brick. Both walls' exterior surfaces were covered with 10 mm of cement plaster. The interior surfaces contained expanded polystyrene (EPS) as the thermal insulation material and cement plaster coating ranging from 20 mm to 100 mm and 0 mm to 20, respectively (Fig. 4). The length and thermal properties of the designed walls are summarized in Table 1.

Statistical analysis and optimization
Factorial design analysis and response surface methodology (RSM) are deemed suitable tools to determine the optimal conditions (Gheshlaghi et al., 2008). RSM was originally presented for modeling in experimental studies and was subsequently utilized to address numerical simulation modeling. RSM prospect the relation between the variables and one or more response.
RSM includes statistical and mathematical techniques based on the fit of obtained data to the polynomial equation.
In experimental tests, inaccuracies during measurements can be the result of errors. Though in computer simulation, round-off errors, inadequate convergence of iterative processes, or the discrete representations of continuous physical phenomena are sources of numerical noise (Tabatabaeikia et al., 2016).
Design-Expert software version 7.0.0 was used to design a simulation model as well as to analyze and optimize the statistical results. The impact of four factors, including indoor cement plaster thickness, heat insulation thickness, wall type, and building orientation on the annual cooling energy consumption was examined using analysis of variance (ANOVA).
The simulation design employed in this study is the Central Composite Design (CCD) with three levels (+1, 0, -1) for two numeric factors including cement plaster and thermal insulation thicknesses. In addition, the model consists of wall type and building orientation as the categorical variables.

Sample building
A typical sample of a tropical single-story bungalow constructed in Malaysia is shown in Fig. 5. The footprint area of the building is about 180 m 2 . It consists of three bedrooms (one master room + two normal rooms), one small room, kitchen, restrooms, a dining room and a living room.

Energy modeling in eQUEST
Recently, several building performance simulation software with different simulation engines have been utilized to analyze the energy consumption of buildings. Building energy simulation is an adequate technique to evaluate diverse construction material choices and architectural design decisions and to analyze the energy performance of buildings (Asadi et al., 2017). Data exchange reliability and userfriendly interface are the main features of a practical simulation software.
eQUEST is a helpful graphical user interface for the DOE-2 engine. DOE-2, as one of the greatest general programs for building simulation. This software is capable of modeling building energy consumption in reasonable of short time in case of large buildings. In the present study, eQUEST 3.65 was applied. First, the schematic design wizard (SD) was selected to simulate the building envelope. A summary of the input data is available in Table 2. The building envelope designed was transferred to the design development wizard (DD) to define different HVAC systems and assign related thermal zones.
To simplify the model, two thermal zones were designed. One zone consists of the living, dining and master rooms as the air-conditioned zone and the second zone entails the rest of the house as mechanically ventilated areas. Based on the literature, most air-conditioned houses in Malaysia utilize cooling systems in the master bedroom and living area, especially during the night. A daily average of 6 hours of air conditioning have been reported (Sabouri & Zain, 2011). In this study, a split system with DX cooling and a direct return air path was designed for the air-conditioned zone. The cooling thermostat was designed with 24֠ C while the fan (on) mode is intermittent. The simulated building is occupied from 6 pm to 9 am on weekdays and the entire day on weekends. A summary of HVAC systems is presented in Table 3. The building and HVAC system simulated by eQUEST for energy consumption analysis are shown in Fig. 6. Finally, detailed eQUEST data were employed to simulate annual cooling energy consumption. eQUEST was run 72 times for different U values of the external walls and different orientations according to design expert suggestions.

Statistical results
The results obtained from eQUEST were inserted into the Design-Expert software to carry out the statistical analysis and optimization based on RSM. Analysis of variance (ANOVA), a reliable way to analyze fitted model quality, makes a comparison between the deviation caused by the treatment and variation caused by random errors. The design summary is given in Table 4. Design-Expert software suggested a quadratic model to generate the response surface. This suggestion is based on the amount of adjusted R 2 (0.989) and predicted R 2 (0.986), which are close to 1 ( Table 5). The mathematical models between the response (annual cooling energy consumption) and independent variables (type of wall, orientation, cement plaster thickness, and thermal insulation thickness) are represented in Table 6.  Table 6 -Correlation between annual cooling energy consumption and cement plaster thickness, and thermal insulation thickness for different walls with different orientations  Fig. 7 and Fig. 8 represent the interaction effects of cement plaster thickness and thermal insulation thickness for different orientations and walls on annual cooling energy consumption. The 3D surface graphs indicate that the influence of thermal insulation thickness is more significant than cement plaster thickness on the amount of annual cooling energy consumption.

Optimization
Although thick insulation reduces annual energy consumption, material costs and indoor space are two controversial issues. In order to achieve minimum annual energy consumption, a precise design optimization study was carried out by utilizing RSM, which consists of mathematical and statistical optimization methods. The optimized design is based on minimum usage of thermal insulation between 20 and 100 mm and minimum energy consumption, while the cement plaster thickness ranges from 0 to 20 mm for various orientations. The results indicate that minimum energy consumption is achievable for the east-oriented bungalow constructed with brick wall containing 31.51mm EPS and 16.39mm cement plaster in the wall interior (Fig.  9). To determine the optimum insulation thickness for the available buildings, the optimization process was repeated for each orientation and type of wall. The optimized design is based on minimum usage of thermal insulation between 20 and 100 mm and minimum energy consumption, while the cement plaster thickness ranges from 0 to 20 mm for the selected orientations and walls (Table 7). Fig. 10 and Fig. 11 present the relations between optimum insulation thicknesses and indoor cement plaster thicknesses in the 0 to 20 mm range. Figure 9 -Optimum design suggested based on optimization.   Finally, the amount of annual cooling energy reduction was achieved by comparing the energy consumption in buildings when excluding EPS and cement plaster, and including EPS and cement plaster in optimized amounts. According to Fig. 12 and Fig. 13, using optimum EPS insulation thicknesses can reduce energy consumption by about 9 to 12% and 6 to 9% with concrete and brick walls, respectively.

CONCLUSIONS
Residential buildings in Malaysia are responsible for about 19% of the total energy consumption. Heat transfer through the building envelope is considered one of the main reasons for energy expenditure in the building sector. Wall material type and topology, building orientation and material type, insulation thickness and wall finishing affect the heat transfer and energy consumption of buildings.
Adding thermal insulation to the interior surface of external walls and covering the interior and exterior sides of walls with some finishing such as cement plaster are useful strategies to reduce energy consumption of existing buildings. It is vital to consider the optimum thickness of thermal insulation to reduce material costs keeping in view environmental impacts and internal spaces. without EPS and plaster Included EPS and plaster 8% 7.5% 6% 9% This study was carried out to examine the effects of thermal insulation and cement plaster thickness on the annual cooling energy consumption of a bungalow building in Malaysia and to find the optimum thickness of EPS based on wall type, building orientation and cement plaster thickness. eQUEST software was used to simulate the annual cooling energy consumption of a bungalow building based on different U values of two types of walls of different sizes and orientations. Design-Expert software was used to design, analyze and optimize the statistical results.
The quadratic equations and 3D surface graphs indicate that the influence of EPS thickness is more significant than cement plaster thickness on annual cooling energy consumption. The optimum EPS thickness decreases with the increment in cement plaster thickness for different orientations and wall types. The optimum EPS thickness ranges from 31.5 mm to 53.1 mm based on wall type, orientation and cement plaster thickness. Therefore, utilizing the optimum EPS thickness and cement plaster on the interior side of external walls decreases the annual cooling energy consumption from 6 to 12% according to wall type and orientation.