ANALYTICS FOR A CONTROLLED EXPERIMENT TO DETERMINEOPTIMAL THERMAL INSULATION FOR BUILDING ENVELOPES

Manoj Autade1, Avani Goyal2, Gagan Deep Singh3, Punit Desai3

Bipin Rajendran1 and Monika Jain2

1Department of Electrical Engineering, Indian Institute of Technology Bombay, India2Centre for Urban Science and Engineering, Indian Institute of Technology Bombay, India

3Infosys Limited, Bengaluru, India

ABSTRACTWe present a controlled experimental study to analyzethe effect of the envelope of a building on its energyconsumption. Our study was based on a specially con-structed standard concrete wall room and two insu-lated rooms of different wall compositions. Energymodeling and calibration studies are carried out usingDesignBuilder simulation software and a newly devel-oped electrical equivalent circuit model based on equa-tions of heat transfer. Our model gives fundamentalinsights for optimizing parameters that determine theenergy consumption in buildings. We critically ana-lyze the results of our model demonstrating its use forinforming design decisions and improving overall en-ergy efficiency.

INTRODUCTIONIndia, like many other developing countries is experi-encing unexpected building boom. According to thereport of US Department of Energy (Yu et al.), build-ings account for 35% of the total energy consumed inIndia and is expected to increase by 8% every year.HVAC contributes to about 60% of a building’s over-all energy budget. Energy consumed by HVAC sys-tem depends on many factors such as orientation ofbuilding, climate, type of natural ventilation, shading,occupants activity and material composition of build-ing envelope (Nayak and Prajapati). The direct impactof one factor can be judged accurately in a controlledexperiment where one parameter is varied keeping allother parameters constant. Since building envelopeis one of the key parameters, we conducted a con-trolled experiment to analyze the impact of wall androof composition on overall energy performance. Inthis paper, we present an integrated approach of an-alytical modeling along with the actual constructionof three experimental rooms (I,II & III) for determin-ing optimal thermal insulation for buildings. The firstmodeling approach is using the DesignBuilder(DB)simulation software and the second is through an elec-trical analogy (EA) approach that gives more detailedinsights on the heat transfer through the various sur-faces of the room. A major issue in the building energymodeling field has been the lack of detailed and com-prehensive validation and verification studies (Ryanand Sanquist, 2012). The construction of the test setupwith sensors and energy meters enables proper valida-tion of the models developed in this work.

Several analyses have been done on the effect ofwall insulation on thermal behaviour (Kim and Moon,2009) (Jin et al., 2012). However, they are either per-formed by treating each wall as a separate componentor taking a sample sinusoidal wave as input instead ofthe actual solar radiation data. These approximationswill ignore the effect of one wall on the other walls,roof and floor and will not consider the effect of sur-face orientation. This paper treats the simulation ofthe entire room as a whole and uses the solar radiationdata as input to get more accurate insights on heat gainbehavior. Individual component of heat transfer suchas conduction, convection and radiation can be calcu-lated, to explain various aspects of heat gain behaviorof the rooms in conditioned and unconditioned days.This granular level information aids in understandingthe specific reasons for the thermal behavior demon-strated in the modeling results and accordingly makedesign decisions in a more efficient manner.

EXPERIMENTAL SETUPThree isolated test rooms are built with identical orien-tation and exposure conditions, but different wall androof compositions (Fig. 1). The setup is based in Ben-galuru city of India, which has a tropical savannah cli-mate throughout the year. All rooms have similar di-mensions and have an airtight door and one split air-conditioner, which is operating on a set temperatureof 20o C. During measurements, rooms are sealed andunoccupied at all times.

Figure 1: Wall composition of the standard room I andexperimental rooms II and III insulated with XPS (Ex-truded Polystyrene Foam) sheets.

Envelope dataThe standard control room (room I) is a 9.29 sq.menclosed area (3.048 m x 3.048 m x 4.267 m) with con-crete solid block (thickness = 200 mm) used as the pri-mary construction material for walls and RCC (rein-

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forced cement concrete) roof. All the wall composi-tions have been plastered from both inside and out-side (Fig. 1). The roof for both the insulated exper-imental rooms is made of a coated sandwiched insu-lation 100 mm thick, with 20 mm PIR (polyisocyanu-rate) panel and silver reflective sheet on top (Fig. 2).The thermo-physical properties of materials used inour buildings is listed in Table 1.

Figure 2: Normal RCC roof with plastering used inRoom I; rooms II and III have a sandwiched insula-tion with PUF (polyurethane) foam and PIR (polyiso-cyanurate) reflective panel on top.

Table 1: Material properties used in modeling.

Layer Conductivityk (W/m-K)

Specific heat ca-pacity Cs(J/Kg-K)

Density ρ

(Kg/m3)Plaster 0.72 840 1760

Concrete 0.97 1000 1400

RCC 2.3 1000 2300

XPS 0.027 1300 40

PUF 0.028 1470 30

PIR 0.021 1470 45

Sensor Network

To monitor environmental conditions, a total of 27 sen-sor motes are installed along the inside and outsidesurfaces of the walls and roof in each room. Threesensors are placed on each side of each wall surfaceto measure the surface temperatures and an air tem-perature sensor in the centre of the room is placedat a height of 0.6 m from floor to monitor the indoorair temperature of the room. Monitoring experimentshave been done with a single sensor for air temperaturekept in centre of the room assuming uniform temper-ature distribution for small confinements (Barbaresiet al., 2015) (Pereira et al., 2014). An energy meteris installed to measure the energy consumption of theair-conditioner for every room.

Experimental Results

The experiment data is spread over days in Augustand September, 2014. The AC is continuously onin August, while it was turned on and off as per apre-determined schedule in September for determiningtransient heat transfer behavior of the system. Some ofthe measurements are shown in Figures 3-6.

Figure 3: a) Indoor air temperature of conditionedrooms with set temperature 20o C b) Increase in in-door air temperature when AC is turned off.

Figure 4: Exemplary variation in inside surface tem-perature of the rooms with air-conditioning.

Figure 5: Exemplary variation in surface temperatureof the rooms with no air-conditioning.

Figure 6: Experimental rooms II and III show around60% energy savings compared to Room I. Room IIIhas a better energy performance than room II by 24%.

ANALYSIS & MODELINGThe inside surface temperatures of walls and roof areindicative of the heat gain in the room. We observethat over the course of a day, east and south wallsattain their peak temperatures before the other walls,followed by west wall with relatively higher magni-tude. The north wall also attains its peak value along

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with the south wall, but has a much lesser magnitudethroughout the day. This can be attributed to the vari-ation in the incident solar radiation as the sun movesfrom east to west. In the experimental rooms II and III,south and east shows higher heat gains, and the peakon the west wall that occurs at a later duration wouldhave been attenuated due to the high thermal lag byinsulation provided in these rooms and drop in exter-nal solar radiation in the night. The results from Fig. 6suggest that room III performs better in terms of en-ergy consumption consistently over the period of datacollection. A correlation is made between U-value andaverage daily energy consumption in Table 2.

Table 2: Correlating U-value and average daily en-ergy consumption.

RoomI

RoomII

RoomIII

U-Value(W/m2-K) 2.346 0.374 0.244

Energy consumed(kWh) 10.35 4.2 3.19

Energy Savings 59.4% 69.1%

Table 2 demonstrates that U-value is a key parameterfor comparative evaluation of energy consumption inrooms with different insulation materials. To investi-gate the reasons for better performance and the trendsobserved in surface temperatures, we have adoptedtwo modeling approaches as described below.

DesignBuilder (DB) modelling softwareThe energy modeling software DesignBuilder is usedto compare the performance of the rooms in the study.This software is powered by EnergyPlus simulationengine and we used weather data obtained from ener-gyplus website for our site location for the simulations(UIUC and LBNL, 2012). Detailed inputs on con-struction details, HVAC, usage and activity data arefacilitated through the DesignBuilder interface. Thesoftware allows specifying each construction com-ponent of the room using the materials informationlisted in Table 1. Overall U-value is evaluated com-bining the thermal conductivity and the convectiveheat transfer co-efficient (Table 2; the U-values for theroof of Room I was calcualted to be 4.5 W/m2-K andthat in Room II & III to be 0.21 W/m2-K). The air-conditioner is modeled using its COP value of 3.53and cooling capacity (1 tonne, 3.51 KW). The opera-tion schedule of the electrical equipment like HVAChas been used to improve the accuracy of the sim-ulation results. Surface temperatures and indoor airtemperatures as well as overall thermal performancesuch as heat gain behavior through each componentwall and roof have been obtained through these simu-lations (A discussion of these results is deferred to themodel validation section, Fig. 14, 15). Though De-signBuilder software enables quick and user-friendlythermal analysis of buildings, it is difficult to ob-tain higher granular features of the heat transfer in astraight-forward manner.

Thermal modeling using electrical analogy (EA)We now discuss a technique to analyze heat flow inbuildings using an electrical equivalent circuit model.Table 3 shows the equivalence between the thermody-namic and the corresponding electrical quantity. Theproposed technique gives fine-grained insights into thevarious aspects of heat transfer in the room, in reason-able simulation times as complex building models arereduced to simple lumped electrical networks. Empir-ical data from the controlled experiment is used forrefining the model which is simulated through an elec-trical circuit simulator software NGSPICE. In this ap-proach, the total heat balance in the analysis zone asshown in Fig. 7 (ASHRAE) is reduced to a simplifiedone as shown in Fig. 8. Modeling of each mode of heattransfer in Fig. 8 is explained in the subsections below.

Table 3: Correlation between heat flow terminologieselectrical circuit parameters.

Thermodynamic quan-tity

Electrical equiva-lent quantity

Heat flow (W) Current (A)Temperature (K) Voltage (V)Thermal Resistance (K/W) Resistance (Ω)Thermal mass (J/K) Capacitance (Farad)

Figure 7: Heat exchange by different modes for theroom being analyzed.

Figure 8: Simplified model for heat exchange in oursystem.

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The proposed electrical equivalent model is based onthe following assumptions:

1. Inside the wall, heat flows only in one direction i.eacross the wall’s outer and inner surface.

2. Properties of all the materials and fluid remainsconstant irrespective of temperature.

3. All layers of the wall are isothermal.

4. Heat exchange between wall and inside air is onlyby convection.

5. Floor is completely insulated.

6. Each wall is exactly oriented in one of the four di-rections.

Conduction through the wall

The selection of envelope insulation mainly affects theconduction through the wall and is the limiting param-eter in total heat gain of the zone. Fig. 9 shows theelectrical equivalent circuit of heat conduction througha layer of the wall (Mathews et al., 1994).

Figure 9: Heat conduction through a wall is repre-sented by two resistors R1 and R2 and a capacitor C.

R1 = R2 =x

2AkC = ρCmxA (1)

where x is the width of surface (m), k is conductivityof surface (W/m-K), ρ is density of material (kg/m3),A is area of surface (m2) and Cm is specific heat ca-pacity of material (J/kg-K).

Radiation from internal surfaces

According to Stefan-Boltzmann law, radiation ex-change from surface 1 to surface 2 with temperaturesT1 and T2 is given by

H = F1−2εAσ(T 41 − T 4

2 ) (2)

F1−2 is view factor of surface 2 with respect to sur-face 1, σ is Boltzmann constant 5.670 × 10−8 W/m2

K4 and ε is emissivity of surface 1. For the test room,view factors between each inner surface with everyother inner surface is approximately 0.2 (Sukhatmeand Gaitonde, 2008b). Fig. 10 shows equivalent ra-diation model for the east wall and can be replicatedsimilarly for other surfaces of the room.

Figure 10: Model of inside surface radiation from eastwall. I-ER, I-EW, I-ES & I-EN are dependent currentsources calculated using (2) and shows radiation fromeast wall to roof, west, south and north surfaces.

External surface radiation

Exterior surfaces exchange heat with ground, sky andother surfaces by long wave radiation (UIUC andLBNL, 2014). The heat radiated by external surfaceof wall qLWR is given as

qLWR =σεFg(T4su − T 4

g ) + σεFsk(T 4su − T 4

sk)

+ σεFair(T4su − T 4

air)(3)

Fg, Fsk and Fair are view factors of surface withground, sky and air respectively; Tg , Tsk and Tair arethe corresponding temperatures in K. The external sur-face radiation (qLWR) is hence modeled as a depen-dent current source.

Solar Radiation

Solar incidence is the main source of heat energy foran envelope, and is considered as the only input sourcefor each wall and roof. Solar radiations on any sur-face depends on latitude & longitude of location, sur-face orientation, day of the year and time in the day.Total solar irradiance on any surface is denoted byIiθ (W/m2) and calculated as

Iiθ = IDN cos θ + Idθ + Irθ (4)

Here, IDN , Idθ and Irθ are direct solar radiation fromsun, diffused radiations from sky and reflected radi-ations respectively. Hourly data for IDN and Idθ isobtained from the weather data file. θ is angle be-tween incident radiation and surface normal and itscalculation depends on derived angles from solar ge-ometry (Ramgopal, 2008), which we have modelledas a piece-wise linear current source using the derivedangle calculations for each surface.

Convection from inside surfaces

Convective heat exchange between wall and air obeysNewton’s law of cooling. Heat exchanged (H) betweenwall and air is given by

H = hconvA(Tw − Ta) (5)

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Here, Tw is wall temperature (K), Ta is air tempera-ture (K) and hconv is convection coefficient (W/m2K).Comparing with Ohm’s law, we get

Rconv = 1/hconvA (6)

hconv is calculated from dimensionless numberswhich are evaluated at mean film temperatures sug-gested by actual temperature sensor data (Sukhatmeand Gaitonde, 2008a). Convection coefficients and re-sistance for the surfaces are as given in Table 4 below.

Table 4: Surface convection coefficients and resistance

Surface Vertical Horizontal HorizontalHeat flow direc-tion

Inward Downward Upward

hconv (W/m2-K)

1.574 0.6 1.3

Rconv (K/W) 0.048 0.179 0.08

Convective heat flow in conditioned and uncondi-tioned room can be significantly different and hencemodeled differently as described below.Unconditioned Room: In our ‘Simple Convection’model, (Fraisse et al., 2002) convection is representedas a resistance Rconv between inside surface and in-side zone (Fig. 11), assuming the inside air as isother-mal and neglecting any vertical temperature gradients.Indoor air temperature is modeled as a single capaci-tor (Cair) with capacitance 50 kJ/K (eqn 1). However,this simple model advanced the air temperature curveby an hour when compared to actual temperature (Fig.12).To resolve this discrepancy, we propose a new ‘Re-fined Convection’ model which mimics the convectionphenomenon more accurately. During convection, airnearby the hot surface becomes warmer which leadsto decrease in its density prompting it to rise up. Thisis then replaced by the relatively cool and dense airfrom the bottom. Hot air at the top slowly diffusesits heat downward. Fig. 11 shows the electrical equiv-alent circuit of the proposed model. In this model,room air is divided into three equal horizontal zones,each having capacitance of 50/3 ∼ 17 kJ/K. Modelassumes that uppermost zone gains heat from surfacesand it is removed from the other two zones. Here,Rconv1 = Rconv = 0.0488 K/W, and parallel com-bination of Rconv2 and Rconv3 should be 0.0488 K/W.As more heat is removed from bottom zone, Rconv3 isless compared to Rconv2, values used for Rconv2 andRconv3 are 0.1 K/W and 0.094 K/W.Calculation of Rdiff1 and Rdiff2 is not straightfor-ward, as their standard correlations are not available.In our model, we have chosen a value of 0.04 K/W forRdiff1 andRdiff2 each. External surface temperatureis used as input for refining the convection at internalsurface, which neglects all external surface phenom-ena, especially the effect of solar radiation.

Figure 11: (I) The ‘Simple Convection’ model; and(II) the ‘Refined Convection’ model with vertical gra-dient treated separately. Diodes in the circuit en-sures proper heat flow direction, Rconv1, Rconv2 andRconv3 are convection resistances attached to top,middle and bottom zones, Rdiff1 and Rdiff2 are heatdiffusion resistances.

Figure 12: The ‘Refined Convection’ model giveslesser discrepancy in the time at which temperaturepeaks during the day, compared to the ‘Simple Con-vection’ model.

Conditioned room: In a conditioned room, ideally in-side air should be maintained at set temperature. Ad-ditional heat flow into the room should be removed bythe AC. We modeled this by a capacitor with infinitecapacitance and initial voltage across it as the set-pointtemperature of AC. This will sink the extra heat with-out changing its voltage. Load at a given time is cal-culated as the current (heat) flowing into the capacitor.

Figure 13: Cair has infinite capacitance, it maintainsthe set temperature and sinks the extra heat.

External surface convection

External surface exchanges heat with the outside air byconvection. Due to large temperature difference be-tween external surface and outside air, large amountof heat is convected out, which makes external con-vection coefficient calculation crucial. Accordingto TARP algorithms (UIUC and LBNL, 2014), heat

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transfer coefficient hc is

hc = hn + hf (7)

where hf and hn are forced and natural heat transfercoefficient of surface respectively. Simplified expres-sion for hc is

hc = 25 + 28 ×√Vz (8)

where Vz is wind velocity in (m/s). External surfaceconvection is modeled as resistance Rc = (1/hcA)between outside surface and air similar to the ‘SimpleConvection’ model.

MODEL VALIDATIONIn this section, we validate the ‘DesignBuilder’(DB)model and the ‘Electrical Analogy’(EA) model withreal time data for inside surface temperatures of eachwall component, roof and air temperature. Statisticalbox plots have been plotted on the percentage errorin surface temperatures calculated by both models foreach surface of the three rooms. In addition, air tem-perature is validated with the actual data.

Figure 14: Surface temperatures of walls and roof cal-culated using DB (red) and EA (blue) matches within15% of the measured data for all the rooms withoutAC.

Surface TemperatureThe approach used in electrical analogy model is dif-ferent for conditioned and unconditioned room andhence they are validated separately. In ‘unconditioned’case, room-I and II are validated on 27 September androom-III is validated from 29th September afternoonto 30th afternoon (Fig. 14). ‘Conditioned room’ mod-els are validated with the experimental data for Au-gust when initial conditions of room temperatures areknown (Fig. 15).In this study, the input weather data is taken from atypical year weather file that is obtained from Ener-gyPlus website and does not reflect the exact weather

profile for 2014. The weather data from the station in-stalled at site could not be used directly as input dueto its non-availability for some days and not all theparameters such as diffuse radiation were monitored.However, a comparison has been made for key param-eters of outdoor environmental conditions such as dry-bulb temperature and incident solar radiation (Fig. 16).Interestingly, when the above weather plots are com-pared with the validation graph shown in Fig. 17, it canbe seen that % error in surface temperature aggravateswith difference in weather data profile by the third dayof validation.

Figure 15: Similar accuracy as in Fig. 14 is obtainedfor the rooms with the AC using the two methods.

Figure 16: The ‘dry-bulb temperature’ and ‘solar ra-diation’, values from the data obtained from Energy-Plus is close to the and actual site weather data.

Figure 17: Error in the model results is improved whenthe actual weather data is used in the calculations.

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Air TemperatureFig. 18 compares the air temperature predicted bymodels with the actual data in rooms I, II and III whenunconditioned. Temperature variation is minimal inrooms II and III as they are highly insulated. There islarger variation of air temperature in room-I, giving abetter idea of the validity of our model. Using ‘RefinedConvection’ model with solar radiation data as input,a good match is obtained between the actual air tem-perature and the one associated with the bottom zoneof the room (Fig. 19).

Figure 18: Air temperature validation

Figure 19: Temperature of three zones of model andactual air temperature.

ANALYTICSHeat Gain AnalysisThrough DesignBuilder modeling, heat gain behaviorcan be analyzed for each surface of each room. Fig. 20shows the variation of heat gain through a scheduleof switching on and off of the air-conditioner from 25-30th September. The AC was switched on till 25th andis switched off from 26th to 28th evening. It is thenstarted again till 12 pm on 29th and remains switchedoff thereafter. Fig. 20 demonstrates that the heat gainfrom walls predominantly remains negative while theAC is switched off, but becomes considerably positivewhen the AC is switched on. The heat gain value dropsby almost 80% with addition of insulation in the roofand walls on rooms II and III.Electrical analogy model is used to evaluate separatecomponents of heat gain such as convection and radi-ation (Fig. 21). While comparing the air-conditionedand non-conditioned behavior of a room, it can be ob-served that while the net heat gain from radiation issimilar, convection data shows a huge contrast. Thejump in surface convection is responsible for higherheat gain from walls during the air-conditioned daysas shown in Fig. 20. The reason for this contrast isfurther demonstrated in Fig. 22 as the set temperature

of AC helps to maintain a larger temperature gradi-ent for convection. Also, the similar magnitude of to-tal heat gain from roofs during conditioned and non-conditioned days is explained by analyzing the con-vection and radiation data in Fig. 21. Unlike walls,the jump in convection from roofs is not considerablyhigh due to its convective heat transfer coefficient be-ing three times lesser (Table 4). This increase in con-vection when AC is switched on is similar in magni-tude to the high amount of radiation from roofs in nonAC days (Fig. 21). This large amount of radiation fromroofs is attributed to lower convection coefficient andhigher solar radiation entering from it that increasessurface temperature and eventually gets radiated to thewalls which are comparatively at low temperatures.

Figure 20: Heat gain calculated from design builderfor walls (blue) and roof (red).

Figure 21: Convection and radiation in MJ for rooms

Figure 22: Convection temperature gradient for con-ditioned and non-conditioned days.

Thermal Comfort AnalysisIn the absence of air-conditioning, indoor air tem-perature reflects the performance of the three rooms(Fig. 23). Room II has a consistently higher air tem-perature than room III due to its higher heat trans-fer co-efficient (U-value). This is also supported by

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convection heat gain data (0.034 MJ in room II vs0.028 MJ in room III) in Fig. 21.

Figure 23: Variation in indoor air temperature from25-30 September.

DISCUSSION AND CONCLUSIONTwo independent modeling methods have beenadopted to model the experiment setup in our study.In addition to using energy simulation software De-signBuilder, we developed an electrical equivalent cir-cuit model using heat transfer equations to explain thesubtle differences in performance between room II andIII. The electrical analogy model agrees with the over-all trend and goes a step further to explain that thedifference in convection rates result in faster temper-ature rise in room II compared to room III. It can beconcluded from both real time data and modeling re-sults that room III with a lesser U-value than room IIperforms better in terms of energy consumption andthermal comfort throughout the year. With a U-valuedifference of 1.3 W/m2-K, heat gain of room III is re-duced by 24%. Passive technique of efficiently in-sulating the building envelope alone has the capacityof reducing the cooling load by at least 60%. Whilethe DesignBuilder software is an efficient tool to con-duct building energy modeling in a quick and user-friendly manner, our novel approach of electrical anal-ogy model using analysis of heat transfer gives greaterflexibility over design and helps to obtain a more gran-ular picture. The combined use of both the modelsforms a holistic platform to conduct building analyt-ics and aid in improvising and validating the modelsfurther for more complex building scenarios.

ACKNOWLEDGMENTSThe research at I.I.T. Bombay was supported in partby a grant from CISCO and an IBM Faculty award toone of us (MJ).

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