Dynamic optimization of multi-retrofit building envelope for enhanced energy performance with a case study in hot Indian climate

Energy 197 (2020) 117263

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Dynamic optimization of multi-retrofit building envelope for enhanced energy performance with a case study in hot Indian climate Pranaynil Saikia a, Marmik Pancholi b, Divyanshu Sood c, Dibakar Rakshit a, d, * a

Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India School of Engineering and Applied Sciences, Ahmedabad University, Ahmedabad, Gujrat, 380009, India c Department of Energy and Environment, TERI School of Advanced Studies, New Delhi, 110070, India d Visiting Academic, School of Civil and Mechanical Engineering, Curtin University, Bentley Campus, Australia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 June 2019 Received in revised form 19 February 2020 Accepted 25 February 2020 Available online 28 February 2020

When multiple thermal retrofits are to be installed in a building envelope for improving its energy performance, several questions arise such as “what should be the thickness of retrofits and where they should be placed within the wall/roof”, “which retrofit should be installed towards the exterior and which one should be installed towards the interior of the envelope”. Such judgements are made in contemporary studies by comparing limited predefined configurations where either the thickness or the location of retrofit assumes only a few discrete values within the envelope. The novel approach proposed in this study utilizes spatial discretization of structural layers in a composite envelope for two fold benefit. A new version of Genetic Algorithm (GA) is developed for this purpose by modifying its key operational stages. The GA is implemented in a practical scenario to optimally configure a multi-retrofit envelope (carrying phase change material and thermal insulator) of a common residential building in hot climate of India. Analysis of a single housing unit demonstrates that up to 33.5% of heat gain reduction and 9.2 kWh/day of electricity saving are achievable with improved envelope design. © 2020 Elsevier Ltd. All rights reserved.

Keywords: Building envelope Heat gain Phase change material Insulator Genetic algorithm

1. Introduction Enhancing thermal insulation of building envelope to mitigate cooling load in hot climate is an important building design aspect. Conventional insulators such as Polystyrene, Polyurethane etc are the obvious candidates for inhibiting heat transfer in myriad engineering applications. However for building heat gain problem, a new class of materials has exhibited superior performance. Popularly known as phase change materials (PCMs), these substances operate in the phase change regime where their latent heat property deters temperature fluctuation. Technological interventions involving PCM retrofitted walls [1,2] and roofs [3,4] have become a global trend in passive building conditioning. Building envelope equipped with such materials can significantly curtail indoor heat ingress and moderate interior temperature peaks in hot climate [4]. In cold climate, PCM packed building walls hinder heat loss from building interior [5]. Several

* Corresponding author. Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India. E-mail address: [email protected] (D. Rakshit). https://doi.org/10.1016/j.energy.2020.117263 0360-5442/© 2020 Elsevier Ltd. All rights reserved.

studies navigated different materials to find the favourable conditions for synergy between PCM and traditional construction materials [6,7]. Studies on parametric analysis of material properties have also surfaced to determine the critical property values which render PCMs to be compatible in given working environment [8,9]. Researchers have further demonstrated the notable effects of building orientation and climatic parameters on PCM carrying building envelope’s performance [10,11]. Overall, the phenomenal impact of PCM in building insulation has been collectively documented by Gracia & Cabeza [12] and Song et al. [13]. Often regarded as a promising solution to the ever critical building insulation predicament, PCM did however encounter instances where it was reported to be not as effective as reckoned [14]. Numerous studies have focussed on other alternatives such as conventional insulators [15,16] and modern vacuum insulated panels (VIPs) [17,18] for improving building insulation. Several studies were conducted on the effects of building morphology on its energy performance. Sharma & Rakshit [19] optimized the orientations of naturally cooled buildings in four metrological stations in India to minimize heat gain. Jain et al. [20] considered two geometric factors namely building orientation and window to wall ratio along with cooling set point temperature and

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air flow parameters to optimize cooling economics of an academic building. A suitable zoning method was suggested by Chen & Hong [21] for estimating energy performance of a group of urban buildings. Perusal of existing literature on building envelope configuration revealed the following research gaps. 1. In envelope configuration optimization studies, the generally observed trend is biased towards comparing easily perceptible and symmetrical arrangements of retrofit layers. For example, one is almost certain to witness cases investigating a retrofitting layer (Eg. an insulator/PCM panel) placed at the outside/inside/ middle of a wall/roof [22,23]. A somewhat detailed (still not sufficiently advanced) search involves placing retrofitting layer at L/4, L/2 type of positions [24]. Fig. 1 shows a few possible roof configurations depending upon the retrofitting layer’s location and thickness. x1 and y1 indicate retrofit’s location and thickness respectively. These two variables can vary continuously throughout the entire envelope and hence can assume a large number of possible values. Further, each permutation of x1 and y1 yields a unique envelope configuration. The situation becomes more chaotic in Fig. 2 with two retrofitting layers. Each permutation of x1, x2, y1 and y2 will yield a unique configuration. One can easily anticipate that the number of possible configurations for performance evaluation will be enormous. Exhaustive search of all feasible configurations is not practical. However it should not be taken as a basis to study only a few extreme or symmetrical configurations. Such configurations may be relevant when the boundary conditions on both sides of wall/roof are identical or if the heat transfer problem is steady state. Neither is true in the present problem. An apt remedy to this issue would be an optimization methodology having universal search power to examine any feasible configuration as well as the capability to converge to an optimum solution thereby avoiding an exhaustive search. 2. When optimizing a retrofitting layer’s thickness, the layer’s location within the wall/roof is an important consideration. Previous studies concerning the optimization of layer thickness keep the location of the layer fixed while varying its thickness [14,25e28]. The reverse case is also common. When the location is to be optimized, layer thickness is fixed beforehand [22,29,30]. A holistic optimization methodology capable of varying location and thickness parameters simultaneously is yet to be reported. 3. Existing envelope configuration optimization studies focus on a particular wall eg. west wall [29], south wall [31] or only the roof [14] of a building. Depending upon the variation in incident solar radiation (insolation), heat transfer dynamics differ in walls of different orientations and also in the roof. Analysis of a single wall or only the roof does not generate a complete picture of net energy savings in a building. The present work endeavours to bridge the above mentioned

research gaps with following novel contributions: 1. In context of building envelopes carrying multiple thermal retrofits, the present work reports for the first time a continuous optimization strategy, where the location (x1, x2 etc) and thickness (y1, y2 etc) parameters of retrofits can take any floating value in the feasible domain, rather than assuming a limited set of discrete values. 2. Location and thickness of different material layers in a building envelope were treated as separate independent variables in previous optimization studies. The present work demonstrates how these two variables are actually different manifestations of the same entity-the number of elementary units of material layer (explained in subsequent sections). This novel concept enables the simultaneous variation of both parameters (location and thickness) in contrast to previous studies where one parameter is kept fixed while varying the other. 3. The proposed optimization strategy is capable of performing a universal search, however the exhaustive search of all feasible candidates is circumvented with the help of GA which drives the search towards optimality. 4. New modifications are introduced in GA for swift handling of complex thermal objective function. These modifications can be adopted in GAs employed for optimizing intricate multivariable constrained problems with enhanced performance. 5. The present study also furnishes insight into relative thermal performances of different retrofitting materials. It illustrates how the optimum configuration varies with the orientation of wall and emphasizes the idea that optimization analysis should be performed for the entire envelope rather than one particular wall or the roof. Pradhan Mantri Awas Yojana (PMAY), the flagship urban housing scheme recently launched by the Government of India is envisaged for large scale implementation to provide affordable residence to its citizens. Most of the urban area targeted for housing fall in the typical hot climatic zone prevailing in the country. Therefore an optimal building design to minimize cooling load through passive means in the houses covered in this incentive will aid in nationwide energy savings. Delhi being the national capital bears suitable landscape for urban housing. The indoor thermal comfort in Delhi is ailed by hot weather conditions during summer. Substantial electricity tariff is accrued to its inhabitants for maintaining thermal comfort. Under these circumstances, PMAY house (Fig. 3 [32]) in hot Delhi climate presents an ideal platform for application of the current research. 2. Mathematical modelling Heat gain reduction through wall/roof is a function of the size and position of retrofits such as insulator, PCM etc. Added to the concrete structures. Numerous wall/roof configurations are feasible to construct by varying the size and position of retrofits, one of which is likely to result in minimum heat gain. It is not practical

Fig. 1. Different configurations of a roof section depending upon the location and thickness of single retrofitting layer.

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Fig. 2. Different configurations of a roof section depending upon the location and thickness of two retrofitting layers.

Fig. 3. PMAY house schematic (a) Top view (b) Side A view (c) Side B view (d) Side C view (e) Side D view (All dimensions are in mm).

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however to find out the optimum configuration experimentally by varying the size and position of each structural component in minute increments. This necessitates a numerical model for overcoming experimental limitations. Consequently a mathematical model is developed for assessing the thermal performance of walls/ roof carrying PCM and insulator for passive enhancement of building HVAC system. The mathematical formulation is divided into two major segments namely Thermal modelling and Optimization using Genetic Algorithm. Following are the assumptions considered in the present discourse. i. One-dimensional heat transfer takes place through the thickness direction of the envelope. ii. Thermophysical properties of materials do not change with temperature and time. This is an approximation which holds reasonably for the materials considered in the present study. For testing new materials, it is advisable to use variable material properties with respect to time and temperature (based on availability and quality of data) to reduce the approximation. iii. 25% volumetric clearance is given to the PCM panel to accommodate any volumetric change during phase transition and possible superheating or subcooling of PCM [6]. iv. Building interior temperature (Tinterior) is kept constant at 24
C following the recent guidelines from the Government of India as an energy saving initiative [33]. Also, the constant indoor temperature ensures that the thermal comfort of the occupants is not compromised at any time. Incorporation of thermal retrofits reduces the temperature of envelope’s inner surface so that convective heat transfer from the inner surface to the indoor air is reduced which in turn reduces the cooling load.

2.1. Thermal modelling The diurnal variation of solar radiation and ambient temperature introduce variable thermal loading on building wall and roof thereby making the heat transfer phenomenon a transient one. Transient heat transfer formulation for a slab of finite thickness described in Ref. [34] with a few modifications is adopted for the present model. 2.1.1. Modelling concrete-PCM-insulator composite wall and roof The mathematical model developed and validated in Ref. [10] is appended with minor modification to account for an additional insulator layer present in the composite wall/roof. The model in Ref. [10] is capable of computing temperature distribution and heat gain through a PCM packed concrete wall. In the Concrete-PCMConcrete configuration, if a layer of insulator is inserted in the outer or inner concrete layer (Fig. 4 (a)&(b)), the equations in the respective concrete layer in the vicinity of the insulator need to be

second order space derivate of temperature can be computed with following nodal equations [34].

dT Ti;jþ1  Ti;j ¼ dt Dt

(1)

v2 T Tðx  Dx; tÞ  2Tðx; tÞ þ Tðx þ Dx; tÞ ¼ vx2 Dx2

(2)

Combining Eq (1)&(2) we get Eq (3)

  Ti;jþ1 ¼ F Ti1;j þ Tiþ1;j þ ½1  2FTi;j

where subscript ‘i’ represents element number and subscript ‘j’ represents time step in the equations. Elemental Fourier number (F) is defined by Eq (4).

F¼

aDt Dx2

(4)

The computational model’s execution sequence proceeds from top concrete surface to the bottom concrete surface by solving the above equations in each differential layer. When the execution sequence approaches the insulator after computing the last differential layer of the upper concrete, the value of F changes due to different material properties (a). Suppose there are N1 differential layers in upper concrete, N2 layers in insulator and N3 layers in lower concrete. The following equations adopted in the present study are then used to calculate temperature for different layers.

  Ti;jþ1 ¼ F1 Ti1;j þ Tiþ1;j þ ½1  2F1 Ti;j

(5)

for i ¼ 2 to N1

  Ti;jþ1 ¼ F2 Ti1;j þ Tiþ1;j þ ½1  2F2 Ti;j

(6)

for i ¼ N1þ1 to N1þN2

  Ti;jþ1 ¼ F3 Ti1;j þ Tiþ1;j þ ½1  2F3 Ti;j

(7)

for i ¼ N1þN2þ1 to N1þN2þN3-1. F1, F2, F3 are the elemental Fourier numbers for upper concrete, insulator and lower concrete respectively. The material properties of upper and lower concrete are same. Also, differential layer sizes and time step are equal for all material layers. Therefore F1 ¼ F3. The first layer of the upper concrete (i ¼ 1) and/or the last layer of the lower concrete (i ¼ N1þN2þN3) can interact with the surrounding through heat convection. Temperature change for such a layer with convective boundary condition is computed using following equations [34].

T1;jþ1 ¼ T1;j ½1  2F1 ð1 þ Bi1 Þ þ 2F1 Bi1 To þ 2F1 T2;j ðFirst layer of upper concrete exposed to surroundingÞ

TN1þN2þN3;jþ1 ¼ TN1þN2þN3;j ½1  2F3 ð1 þ Bi2 Þ þ 2F3 Bi2 Ti þ 2F3 TN1þN2þN31;j ðLast layer of lower concrete exposed to surroundingÞ

modified. Consider an insulator panel sandwiched between two layers of concrete as shown in Fig. 4(c). This setup is divided into differential layers or elementary units where first order time derivative and

(3)

(8)

(9)

Elemental Biot number (Bi) is defined by following equations.

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Fig. 4. An insulator layer can be inserted in two relative configurations (a) Concrete-PCM-Concrete-Insulator-Concrete or CPCIC (b) Concrete-Insulator-Concrete-PCM-Concrete or CICPC (c) Concrete-Insulator-Concrete subsection common in (a)&(b).

Bi1 ¼

Bi2 ¼

ho Dx kconcrete hi Dx kconcrete

ðFor first layer of upper concreteÞ

(10)

ðFor last layer of lower concreteÞ

(11)

Heat gain per unit area to building interior is calculated using Eq (12).


qin ¼ hi TN1þN2þN3;jþ1  Tinterior dt

(12)

Values of ho and hi are taken as 22.7 W/m2-K and 6.1 W/m2-K for the weather conditions of Delhi [35]. Fig. 5 depicts hourly insolation and ambient temperature data for Delhi averaged over the days of the summer month of May (refer to supplementary data for

tabulated values). It is the weather data input required by the thermal model (which is the fitness function of GA). The envelope design is motivated by the idea that it should withstand the maximum heat surge into the building in summer. Delhi experiences highest temperature peaks in the month of May [36]. The cycle considered thus reflects the overall weather variation in the hottest summer month. Furthermore, significant repeatability may not be observed for day to day variations of weather parameters in a season for different years. However these disparities reduce when the average climatic conditions over a month are considered. Therefore the optimal design is based on the diurnal cycle representing average weather data of the hottest month. The heat transfer by radiation and convection is consolidated by calculating sol-air temperature with Eq (13)&(14) [19]. It is the hypothetical temperature of ambient which results in same rate of

Fig. 5. Hourly insolation and ambient temperature data for Delhi for the month of May [35].

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heat transfer by only convection to a solid surface as that imparted by the combined effect of radiation and convection from the ambient to the solid surface.

Tsol ¼ To þ

abs  I ho

Tsol ¼ To þ

abs  I εDR  ho ho

ðFor vertical surfaceÞ

ðFor horizontal surfaceÞ

(13)

(14)

Values of “abs” and “ε” for concrete are taken as 0.6 and 0.9 respectively [35,37]. When sol-air temperature is used to calculate heat gain by the outer concrete surface from ambient, Eq (8) is modified to Eq (15).

T1;jþ1 ¼ T1;j ½1  2F1 ð1 þ Bi1 Þ þ 2F1 Bi1 Tsol þ 2F1 T2;j

(15)

2.1.2. Experimental validation For authenticating the modified equations adopted in the present study, an experimental setup is fabricated in a manner that it can emulate one-dimensional heat transfer solved in the mathematical model. With one-dimensional heat transfer assumption it is convenient to perform heat transfer calculation per unit cross sectional area of roof or wall normal to the heat flow direction. Subsequently the roof of a building is divided into a grid of smaller units with cross sectional dimension of 300 mm  300 mm (a commonly used tile dimension). With no lateral heat transfer among the symmetric grid units into which the roof is divided, one such unit can be analysed independently through real time experimentation. The experimental setup is shown in Fig. 6. Two concrete layers above and below a Polystyrene insulator panel are made up of multiple concrete slab units (Fig. 6(b)), each slab having a thickness of 20 mm. The slabs are fabricated in a mould with fine surface finish to have negligible effects of air gap and contact resistance between any two slabs. The Polystyrene panel is 20 mm thick. Cumulative thickness of top concrete layer comprised of 4 slabs is 80 mm. Concrete layer below the Polystyrene panel consists of 5 slabs and it is 100 mm thick. Thus the total thickness of the insulator packed concrete setup is 200 mm which is a commonly found roof thickness. All the lateral sides of this sandwich setup are insulated with thick Polystyrene. The fabrication of the experimental composite roof from smaller

slab units facilitates the insertion of thermocouples at different locations throughout the thickness of the sandwich setup (Fig. 6(b)). The data extracted from the thermocouples provides a lucid visualization of the temperature profile along the depth of the setup at different instants. The top surface of the setup is exposed to solar radiation while both the top and bottom surfaces interact with the ambient through convection. Temperature readings of the exposed surfaces along with the interfaces are noted on hourly basis for 24 h on the date of July 15, 2018 in Delhi. The insolation is measured by a pyranometer. The data extracted from the experiment is represented in Fig. 7. The experimental cycle begins from 6 a.m. in the morning. The experimentally obtained solar radiation and ambient temperature data at 6 a.m. are fed as initial conditions into the numerical model developed for insulator embedded concrete. The numerical model also requires the initial temperature distribution throughout the sandwich setup. This is again fed into the model from the experimentally measured interface temperatures at 6 a.m. With these initial and boundary conditions, the numerical model is executed for the same time period of 24 h. The numerically obtained temperature distribution throughout the thickness of the sandwich setup, when plotted against the experimentally obtained temperature at similar times of the diurnal cycle show tenable conformance (Fig. 7) and thus validates the present numerical model. In order to compute heat transfer to the interior from building envelope, it is important that the numerical model can accurately capture the bottom surface temperature of the experimental setup. Consequently, the measured temperature values at 200 mm depth (corresponding to bottom surface of the setup) are compared with the temperature values obtained numerically for different hours. The values coincide for most of the hours of the cycle. Maximum deviation of 1.86
C is observed for bottom surface temperature at 6 p.m. which is equivalent to an error of 5.33%. An elementary unit thickness of 2 mm is used in the transient numerical model to discretize all the concrete slabs and the Polystyrene panel. As the numerical model can mimic the experimental data to a close proximity with this elementary unit size, this unit dimension is used for optimization analysis. To verify the single-valued conditions of the present model, the elementary unit thickness is varied by ±10% (i.e. element sizes of 1.8 mm and 2.2 mm) and corresponding changes in the temperature profiles are noted while comparing with experimentally measured temperature profiles. While keeping the input conditions

Fig. 6. (a) Complete experimental setup (b) Layers of concrete slabs with thermocouples inserted at the interfaces.

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Fig. 7. (a),(b),(c),(d): Validation of numerical model with experimental data.

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Fig. 8. Effect of element thickness variation in temperature calculations.

unaltered, minuscule variations are observed in the numerically computed temperature values for different element sizes which verify single-valued conditions of the present model. For judicious space utilization, these variations are presented for 3 different hours in Fig. 8 where a maximum variation of 0.55
C is observed for the bottom surface of the setup at 4 p.m. The authenticity of the present model is further verified by comparing it with the work of Li et al. [38]. The reference study in this case involves the assessment of different PCMs as building wall retrofits for reducing indoor heat gain in the hot summer climate of Isfahan, Iran. Wall dimensions as well as the thermophysical properties of conventional wall materials and the PCMs investigated by Li et al. are considered for testing with the present model along with Isfahan’s month-long weather data provided in the same study. Different non-PCM layers of the wall are assigned different thermophysical properties (eg thermal conductivity, specific heat, density) in the design considered by Li et al. which is equivalent to the presence of insulator layer in the current study.

Cumulative indoor heat gain through the wall, as computed by the present model under the aforementioned conditions is compared with the findings of Li et al. for 5 different PCM retrofitted walls and a conventional wall with no PCM retrofit (Fig. 9). As observed from Fig. 9, the present model could reproduce the findings of Li et al. to a close proximity with a maximum error of 5.49% when total indoor heat transfer for a month-long period is considered. This further supports the present model’s validity. 2.2. Optimization using Genetic Algorithm The present model involves an objective function of heat gain through the building envelope which is to be minimized. Transient heat transfer through a composite wall/roof involving heat storage terms makes the calculation of the gradient of the objective function quite wearisome. Moreover the optimization problem involves multiple decision variables associated with the thickness and position of retrofits. In this scenario, GA is a top choice to handle the

Fig. 9. Comparison of total indoor heat transfer (present model versus Li et al.).

P. Saikia et al. / Energy 197 (2020) 117263

current multivariable problem without gradient calculation. 2.2.1. GA setup The current objective is to minimize heat gain through building wall/roof. Therefore the objective function (y) of GA is defined as below.

y ¼ Diurnal heat gain

(16)

Diurnal heat gain through the composite wall/roof is calculated with the thermal model presented in the study. Next, the decision variables and constraints are identified. Present motive is to vary the thickness and positions of insulator and PCM panels within the envelope. The total thickness of the concrete wall/roof is kept close to the initial design values by allotting 10% tolerance (Eq (17)&(18)) so that the space requirement for housing does not change abruptly.

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layers. Two different configurations are possible for a composite wall/ roof with respect to the relative positions of PCM and insulator; one is where the PCM is towards the outside ambient and insulator is towards the building interior and vice versa in the other configuration (Fig. 4(a)&(b)). These two different configurations obtained by swapping the insulator and the PCM are simulated separately to find the overall minima. 2.2.2. GA modifications Certain modifications are made in the major operational stages (reproduction, crossover and mutation) of GA with the motive of performance improvement. For the reproduction process, a two-member tournament selection method is adopted over conventional roulette wheel mechanism to avoid premature convergence and directionless search [41]. Tournament selection is carried out through the

Louter concrete þL PCM þL middle concrete þL insulator þL inner concrete ¼ 0:25 m ± 0:025 m ðFor wallÞ

(17)

following conditions:

L outerconcreteþL PCM þ Lmiddle concrete þ Linsulator þ Linner concrete ¼ 0:1524 m ±0:01524 m ðFor roofÞ

(18)

As the total thicknesses of the wall/roof is almost fixed, varying the size and position of the envelope retrofits will cause variation in the thickness of the concrete layer as well. All the different material layers i.e. concrete, PCM and insulator are divided into elementary units of 2 mm as explained in Section 2.1.2 and shown in Fig. 4. The thickness of different material layers can be varied by changing the number of elementary units. Therefore the decision variables for optimization are the number of elementary units for each material layer. The thickness of a PCM panel is generally restricted to maximum 30 mm [39,40] to extract most of its benefit. Hence the upper bound for the number of elementary units of PCM layer is set to 15. Similarly the thickness of the insulator is limited to a maximum of 50 mm for wall and 30 mm for roof so that it does not impart any adverse effect on the sturdiness of the building. The respective upper bounds are 25 for wall and 15 for roof. The upper bound for the number of elementary units for each of the 3 concrete layers (outer, middle and inner) is set to 140 as they do not have any thickness restriction in the envelope. The total thickness of the wall/roof is regulated by Eq (17)&(18). Lower bound of the number of elementary units of all the material layers is set to 3 as the thermal objective function requires at least 3 constituent elements to be computed for any material layer to maintain mathematical continuity. If the presence of a certain layer is detrimental in terms of heat gain, the number of elementary units for that layer will shrink to the minimum lower bound assigned to eliminate the effect of that layer. Similarly, a layer which impedes heat ingress will have an augmentation in the number of constituent units in the subsequent iterations of GA. From location perspective, if either the PCM or the insulator layer is to be pushed away from the interior of the wall, the middle and inner concrete layers will be magnified by an increase in their number of elementary units while the outside concrete layer will be dwindled by a decrease in its elementary units (and vice versa). In this manner, location of the PCM and insulator layers can be shifted by varying the number of units of the different concrete

i If |Constraint violation of (X1) - Constraint violation of (X2)| Constraint violation of (X2), then select X2; else select X1. Where X1 and X2 are two individuals of a generation. Suitable value of d is determined as 0.01 by conducting multiple trials. Constraint violation is calculated as below

gðXÞ ¼ jLtotal  0:25j gðXÞ ¼ jLtotal  0:1524j

ðfor wallÞ ðfor roofÞ

(19) (20)

For wall, if g(x) > 0.025, then Constraint violation ¼ g(x)-0.025, else Constraint violation ¼ 0. For roof, if g(x) > 0.01524, then Constraint violation ¼ g(x)0.01524, else Constraint violation ¼ 0. The crossover process is performed with a crossover probability (Pcross) which is conventionally used to select 100Pcross percent of the individuals in a stochastic manner for mating process. However, in Ref. [41], Deb stated that the random selection of individuals does not guarantee a significant advantage over the deterministic selection of good individuals. Therefore, all the individuals are transferred to the mating pool and Pcross is rather used to activate/ deactivate the crossover process. When deactivated, crossover is not performed after the tournament selection operation. Such omission engenders repeated execution of tournament selection and increases the number of copies of good individuals while eliminating the unfavourable ones. The evaluation of Pcross thus shifts from individual level (for transferring to mating pool) to generation level (for activating/deactivating crossover process). The number of probability evaluations reduces drastically this way without compromising the search power. A commensurate reduction in computational time follows every step of decreasing mathematical expression evaluation. Elitist principle is executed at each iteration to preserve the best individual of a generation [42]. Elitist principle is slightly modified

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Fig. 10. Flowchart of new elitist principle.

Table 1 Stepwise decreasing Penalty parameters. Iteration 1 to 15 16 to 30 31 to 45 46 to 60

Penalty for wall 8

10 5  107 107 5  106

Penalty for roof 108 7  107 3  107 107

in the present study to serve two purposes: firstly it carries the best individual of the previous generation to the next generation and secondly this best individual from the previous generation replaces the worst individual of the next generation (Fig. 10). Replacement of the worst individual of present generation by the best individual of previous generation escalates the overall fitness of present generation. While designating an individual as the “best” candidate, two parameters are to be checked viz. The function value of the individual and the constraint violation by the same. These are checked simultaneously by formulating a penalized function as below.

Fig. 11. Mutation operation performed only in columns having all 0s or 1s.

Table 2 Key GA parameters values.

Fpenalized ðXÞ ¼ FðXÞ þ Penalty  Constraint violationðXÞ (21) There is no definite rule for determining the exact value of “Penalty” in Eq (21). Hence for the given problem it is determined by hit and trial method where a stepwise decreasing penalty parameter is found to be suitable (Table 1). The best candidate for elitism is the individual with minimum Fpenalized(X) value whereas the worst candidate is the one with

Parameter

Value

Population size Number of bits per variable Crossover probability Mutation probability Iterations

50 8 0.8 0.1 60

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maximum Fpenalized(X) value in a generation. The mutation process is tailored in a partially probabilistic approach. The mutation operator upon activation searches for columns having all digits as 0 or 1 (Fig. 11) in a population. It then flips any five random bits in the column to introduce diversity. For columns having both 0 and 1, mutation is omitted as diversity is inherently present. This model eliminates the requirement of evaluating mutation probability for each bit in a population and thereby accelerates the computation. The key parameters of the GA are listed in Table 2 which are determined after conducting several trials to obtain a balance between search power and convergence tendency.

2.2.3. Testing with standard functions The reformed GA is tested with standard Rastrigin function (Eq (22)) and Rosenbrock function (Eq (23)) [42] to check its performance.

y ¼ 20 þ x21 þ x22  10ðcos2px1 þ cos2px2 Þ

(22)

2  y ¼ ð1  x1 Þ2 þ 100 x2  x21

(23)

Both functions were successfully minimized close to their true minima (Fig. 12 and Table 3). Incidental peaks in the optimization curves are triggered by the mutation operator, creating diversity in the population. The GA is modelled and executed using MATLAB R2017b [43] in a workstation equipped with 48 GB RAM and Intel Xeon processor. Simulation runtime for optimizing the envelope configuration with a conventional GA (without the modifications proposed in this study) is approximately 90 min with ±3 min variation for different runs. This execution time is brought down to about 72 ± 3 min by adopting the modifications mentioned in the previous sections.

3. Materials Based on contemporary studies featuring PCMs as building envelope additives in hot Indian climate [7,10], two common salt hydrate PCMs (Zinc Nitrate Hexahydrate and Calcium Chloride Hexahydrate) are selected for the present study. As for insulators, the abundant availability and extensive use of Polystyrene and Poly Urethane Foam (PUF) justify the selection of these two materials. The relevant material properties are listed in Table 4.

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4. Results and discussion The GA model is executed for four PCM-insulator pairs (viz. ZNH-Polystyrene, ZNH-PUF, CCH-Polystyrene, CCH-PUF) and four distinct wall orientations (viz. north, east, west, south). Additionally, the four PCM-insulator pairs are also tested for the roof. In all these cases, two relative positions of the insulator and PCM are considered as discussed in Section 2.2.1. Altogether there are 40 cases of computation. 4.1. Optimizing the envelope configuration Prior to calculating diurnal heat gain, several (more than 30) trial runs are performed with randomly selected configurations of the composite envelope. This practice is carried out to note the cyclic repetition of temperature-time curves after certain number of diurnal cycles. 12 such randomly selected configurations are presented in Table 5 along with the corresponding values of heat gain and decrement factor (defined as the ratio of temperature fluctuation amplitude on the inner surface to that on the outer surface). From the trials with several random configurations, it is observed that the temperature-time curves exhibit cyclic repetition beyond 4th diurnal cycle thus indicating that the thermal performance of the composite wall/roof becomes initial condition independent beyond 4th cycle. Two typical samples of such randomly determined configurations (one asymmetric sample and one symmetric sample with equal retrofits size and spacing in concrete) are presented in Fig. 13 with temperature-time evolution of different layers to demonstrate the cyclic repeatability. Consequently, all the heat gain calculations are performed for a diurnal cycle beyond the 4th [10]. GA optimization curves are plotted in Fig. 14. 40 cases of computation yield 40 optimization curves. Due to space limitation only 4 sample curves are presented. Mean function value (Fmean), minimum function value (Fmin) and minimum penalized function value (Fpenalized) of generations converge in the last quartile of iterations. Fmean and Fmin curves begin from a low fitness value and rise in the first few iterations. These are individuals which offer low heat gain but violate the total thickness constraint to a large extent. As the GA moves towards feasible region, such individuals are gradually eliminated. This is depicted by the receding Fpenalized curve. The optimum values of size and position of different material layers leading to minimum diurnal heat gain through the composite wall/roof are extracted for each case after the last iteration. Table 6 summarizes the optimum configurations of all the PCMinsulator pairs for different walls and roof of the envelope, as

Fig. 12. Minimization of (a) Rastrigin function (b) Rosenbrock function with the new GA.

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P. Saikia et al. / Energy 197 (2020) 117263

Table 3 Results of standard function testing. Function

Absolute Minimum

Minimum found using GA

Absolute function value at minimum

Minimum function value found using GA

Rastrigin Rosenbrock

(0,0) (1,1)

(0.0392,-0.0392) (0.9804,0.902)

0 0

0.6071 0.3509

Table 4 Relevant material properties [7,10,29,35]. Material

Melting Latent heat of point (K) fusion (kJ/kg)

Solid phase density (kg/ m3)

Liquid phase Solid phase density (kg/m3) specific heat (J/ kg-K)

Solid phase thermal Liquid phase thermal Liquid phase specific heat (J/kg- conductivity (W/m-K) conductivity (W/m-K) K)

Zinc Nitrate Hexahydrate (ZNH) Calcium Chloride Hexahydrate (CCH) Polystyrene Polyurethane foam (PUF) Concrete

309

147

1828

1828

1340

2260

0.464

0.464

303

187

1710

1530

2200

1400

1.09

0.53

e e

e e

23 30

e e

1280 1570

e e

0.034 0.026

e e

e

e

1920

e

840

e

1.1

e

Table 5 Trial simulations performed on randomly selected envelope configurations. Configuration Sample no.

PCM-Insulator

CICPC

ZNHPolystyrene CCHPolystyrene ZNH-PUF CCH-PUF CCHPolystyrene ZNH-PUF CCHPolystyrene ZNH-PUF CCH-PUF ZNHPolystyrene ZNHPolystyrene CCH-PUF

1 2 3 4 5

CPCIC

6 7 8 9 10 11 12

Heat gain (kWh/m2day)

Wall orientation

Thickness(m) Outer concrete

Middle concrete

Inner concrete

PCM Insulator Total

North

0.086

0.042

0.092

0.008 0.048

0.276 0.4285

0.18

East

0.072

0.072

0.072

0.03

0.276 0.5021

0.0856

South West Roof

0.006 0.08 0.034

0.084 0.048 0.056

0.132 0.088 0.04

0.02 0.034 0.024 0.036 0.026 0.012

0.276 0.4391 0.276 0.4950 0.168 0.6887

0.1337 0.0898 0.2445

Roof North

0.048 0.08

0.048 0.08

0.048 0.08

0.012 0.012 0.018 0.018

0.168 0.6744 0.276 0.3944

0.2324 0.1438

East West South

0.112 0.05 0.106

0.094 0.11 0.04

0.016 0.064 0.064

0.006 0.048 0.012 0.04 0.026 0.04

0.276 0.4879 0.276 0.4580 0.276 0.4411

0.1601 0.1299 0.1368

Roof

0.048

0.048

0.048

0.012 0.012

0.168 0.6693

0.1225

Roof

0.028

0.08

0.036

0.008 0.016

0.168 0.6448

0.3409

0.03

Fig. 13. Sample temperature-time curves (a) Sample no. 4 of Table 5 (b) Sample no. 11 of Table 5.

Decrement Factor

P. Saikia et al. / Energy 197 (2020) 117263

13

Fig. 14. Sample GA optimization curves (a) ZNH-PUF South CICPC (b) CCH-Polystyrene North CICPC (c) ZNH-PUF Roof CPCIC (d) CCH-Polystyrene East CPCIC.

Fig. 15. Case with no operation of PCM in the latent heating regime (ZNH-Polystyrene CICPC-North wall).

determined by GA. Depending upon the orientation, insolation and hence heat input to the wall vary. Different material combinations perform diversely under varied conditions of transient heat input. A default case of concrete with no retrofit is evaluated in a similar manner. The corresponding values of heat gain and decrement factors of bare concrete are tabulated against the best possible values for each case to illustrate the plausible improvements (Table 7). It is noteworthy that the PCMs themselves have lower thermal conductivity than concrete and therefore can act as additional insulator layer in the superheated or subcooled state. The hindrance offered by PCM layer to heat propagation is a combined effect of thermal resistance (sensible heating of PCM) and thermal capacitance (latent heating of PCM). There are cases where the PCM hardly operates near its melting point (Fig. 15).

It is a result of mismatch between incoming heat rate and melting point of PCM. The melting point of ZNH is too high (309 K) in this case for the incoming heat to melt it. A larger value of decrement factor is observed (0.1706) in such case where no contribution is offered by PCM’s latent heating for temperature stabilization. Table 6(a,b) make it clear that CCH-Polystyrene combination in CPCIC arrangement is the best choice for minimum heat gain in all the walls and the roof. The long duration of latent heating operation contributes to its enhanced thermal performance as demonstrated in Fig. 16. To understand the effect of optimized retrofit size and location, the results of Table 6 can be compared with the non-optimized configurations in Table 5. Bearing in mind that the prime objective is to minimize indoor heat gain, retrofit configuration selection

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P. Saikia et al. / Energy 197 (2020) 117263

Table 6a Optimum configurations for CICPC arrangement. CICPC

Wall Outer Concrete orientation thickness (m)

Insulator thickness (m)

Middle concrete thickness (m)

PCM thickness (m)

Inner concrete thickness (m)

Total thickness (m)

Heat gain (kWh/ Decrement m2-day) Factor

ZNHPolystyrene

North East West South Roof North East West South Roof North East West South Roof North East West South Roof

0.036 0.028 0.038 0.038 0.01 0.018 0.006 0.046 0.024 0.006 0.038 0.028 0.012 0.05 0.028 0.012 0.012 0.036 0.026 0.006

0.026 0.02 0.066 0.022 0.064 0.006 0.158 0.03 0.12 0.048 0.134 0.012 0.022 0.03 0.008 0.03 0.028 0.132 0.038 0.038

0.012 0.014 0.006 0.012 0.006 0.008 0.006 0.008 0.008 0.008 0.01 0.012 0.008 0.006 0.006 0.008 0.006 0.006 0.006 0.006

0.126 0.126 0.13 0.126 0.024 0.156 0.018 0.072 0.034 0.086 0.03 0.146 0.16 0.008 0.074 0.146 0.16 0.006 0.126 0.112

0.276 0.276 0.276 0.276 0.168 0.276 0.276 0.276 0.276 0.168 0.274 0.276 0.276 0.276 0.168 0.276 0.276 0.276 0.276 0.168

0.4284 0.4879 0.4848 0.4384 0.6718 0.4284 0.4879 0.4848 0.4384 0.6726 0.4296 0.4902 0.4868 0.4384 0.6737 0.4312 0.4894 0.4847 0.4404 0.6733

ZNH-PUF

CCH-PUF

CCHPolystyrene

0.076 0.088 0.036 0.078 0.064 0.088 0.088 0.12 0.09 0.02 0.062 0.078 0.074 0.182 0.052 0.08 0.07 0.096 0.08 0.006

0.1706 0.1578 0.1477 0.1513 0.3039 0.171 0.1658 0.1326 0.1466 0.1454 0.1704 0.1543 0.1378 0.1507 0.3163 0.1494 0.1676 0.1254 0.1118 0.3453

Table 6b Optimum configurations for CPCIC arrangement. CPCIC

Wall Outer Concrete orientation thickness (m)

PCM thickness (m)

Middle concrete thickness (m)

Insulator thickness (m)

Inner concrete thickness (m)

Total thickness (m)

Heat gain (kWh/ Decrement m2-day) Factor

ZNHPolystyrene

North East West South Roof North East West South Roof North East West South Roof North East West South Roof

0.014 0.01 0.006 0.014 0.006 0.008 0.01 0.02 0.012 0.006 0.01 0.01 0.006 0.006 0.006 0.01 0.01 0.01 0.006 0.006

0.016 0.054 0.194 0.038 0.062 0.028 0.128 0.01 0.038 0.042 0.034 0.028 0.03 0.074 0.062 0.034 0.024 0.026 0.056 0.01

0.036 0.044 0.008 0.016 0.024 0.036 0.048 0.046 0.016 0.028 0.016 0.022 0.032 0.05 0.024 0.016 0.012 0.026 0.022 0.018

0.024 0.158 0.042 0.106 0.04 0.128 0.078 0.038 0.108 0.058 0.106 0.106 0.106 0.03 0.01 0.108 0.104 0.096 0.076 0.02

0.276 0.276 0.276 0.276 0.168 0.276 0.274 0.276 0.276 0.168 0.274 0.274 0.278 0.276 0.168 0.276 0.276 0.276 0.276 0.168

0.4284 0.4688 0.4623 0.4384 0.6381 0.4284 0.471 0.4848 0.4384 0.6388 0.3869 0.4451 0.4389 0.3915 0.6277 0.3854 0.4388 0.4381 0.3914 0.6096

ZNH-PUF

CCH-PUF

CCHPolystyrene

0.186 0.01 0.026 0.102 0.036 0.076 0.01 0.162 0.102 0.034 0.108 0.108 0.104 0.116 0.066 0.108 0.126 0.118 0.116 0.114

governed by GA offers better solutions for HVAC load mitigation. Here the best configuration selection criterion is taken as minimum diurnal heat gain through the wall/roof. One may emphasize on minimizing temperature modulation (smaller decrement factor) rather than minimizing heat gain. It can be observed from Table 6 that for north and south directions, the CCH-PUF (CPCIC) configuration causes comparable diurnal heat gain as CCH-Polystyrene (CPCIC) configuration but with smaller decrement factors. Certain places levy surplus electricity tariffs during peak hours and a smaller decrement factor may be equally important as net heat gain. Under such circumstances one may select a suitable configuration by assigning weightages to heat gain and decrement factor as per requirement. The results consolidated in Table 6 portray the asymmetry

0.1678 0.1783 0.1299 0.1497 0.3496 0.1714 0.1684 0.1157 0.146 0.3271 0.1 0.1418 0.1206 0.0799 0.3253 0.1027 0.1254 0.1156 0.0871 0.2374

present in the optimal design of each material combination and wall orientation. Significant variation in configuration occurs across different materials and wall orientations; as such no conspicuous pattern can be noticed in the overall results. However for the particular case of CCH-Polystyrene CPCIC, which is deemed to be the best material combination for the given weather conditions, a somewhat general trend can be discerned. Walls/roof in this case comprise of larger outer and inner concrete layers as compared to the middle concrete layer, thereby pushing the retrofits towards the envelope core. The erratic and uneven boundary conditions imposed on two sides of the envelope drives the optimal solution away from symmetry. Such asymmetry also urge for performing independent optimization analysis for any new retrofit whose HVAC load mitigation potential is to be evaluated in the given

P. Saikia et al. / Energy 197 (2020) 117263

15

Fig. 16. Sample temperature-time plots of optimized CCH-Polystyrene CPCIC configuration (a) Roof (b) South wall.

Table 7 Bare concrete envelope performance versus optimized envelope performance. Wall direction

Best configuration

Heat gain (kWh/m2-day) Bare concrete

Best configuration

Bare concrete

Best configuration

North East West South Roof

CCH-Polystyrene CCH-Polystyrene CCH-Polystyrene CCH-Polystyrene CCH-Polystyrene

0.6047 0.6885 0.6842 0.6187 0.9306

0.3854 0.4388 0.4381 0.3914 0.6096

0.2319 0.2203 0.194 0.2066 0.4343

0.1027 0.1254 0.1156 0.0871 0.2374

CPCIC CPCIC CPCIC CPCIC CPCIC

Decrement Factor

presented in Table 8.

climate. 4.2. Fixing the building orientation Total diurnal heat gain through a wall/roof is calculated by multiplying heat gain per unit area with the surface area of respective wall/roof. The surface area is different for different walls and the roof. This creates an opportunity to further minimize heat gain by selecting an appropriate orientation of the PMAY house. To calculate heat gain through windows (Qwindow), a solar heat gain coefficient (SHGC) of 0.25 is recommended by Energy Conservation Building Code (ECBC) [44] for hot climate. SHGC is defined as “the ratio of the solar heat gain that passes through the fenestration to the total incident solar radiation that falls on the fenestration” [44]. Total insolation on different walls is obtained by first calculating the diurnal average incident radiation rate on different walls (from Table (A) in supplementary data) and then multiplying it with cycle duration. Qwindow is then obtained from Eq (24). Heat infiltration through windows located on different walls is

Q window ¼ Total insolation  SHGC  Area of window

(24)

Air leakage through the envelope is another aspect to be considered in passive building conditioning. Leakage of conditioned air to ambient is accompanied by equivalent entry of outdoor air to building interior. This exerts additional thermal load through two components. First component originates from the cooling requirement of the hot outdoor air to indoor thermal comfort temperature. Second component is the latent heat released by the additional moisture content of outdoor air during dehumidification. This component is significant for warm and humid regions. Delhi’s weather remains fairly dry during the month of May [45]. Therefore only the first component of thermal load is considered in the present study. ASHRAE [46] recommends Eq (25) to be used for calculating the thermal load imposed due to outdoor air infiltration.

Table 8 Effect of orientation on diurnal heat gain. Side A Total wall heat gain (kWh/day) orientation Side A Side B

North East West South

Side C

Side D

Qwall Qwindow (Effective (Area area 1.8 m2) 16.2562 m2)

Qwall Qwindow (Effective (No area window) 15.6276 m2)

Qwall Qwindow (Effective (Area area 1.6965 m2) 18.1865 m2)

Qwall Qwindow (Effective (Area area 0.267 m2) 2 17.0878 m )

6.2645 7.1324 7.1216 6.3625

6.8462 6.0223 6.1165 6.8566

7.118 7.9672 7.9793 7.0084

7.4973 6.688 6.585 7.4859

1.0917 1.7087 1.6763 1.1948

0 0 0 0

1.1261 1.5799 1.6104 1.0289

0.2534 0.1772 0.1619 0.2486

Roof heat gain (Effective area 32.8194 m2) kWh/ day

Total heat gain Heat gain by envelope through leakages kWh/ kWh/day day

20.0062 20.0062 20.0062 20.0062

4.338 4.338 4.338 4.338

54.5414 55.6199 55.5952 54.5299

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P. Saikia et al. / Energy 197 (2020) 117263

5. Conclusions

Qs ¼ 60Vra CPa DT

(25)

All the quantities in Eq (25) are in English Engineering units commonly followed in ASHRAE. The heat gain quantity is later expressed in SI units. DT is calculated as the difference of hourly ambient temperature values and the indoor air temperature (24
C). ECBC recommends a maximum allowable leakage of 5 L/sm2 through swinging/revolving doors and 2 L/s-m2 through other fenestrations [44]. The door area (Ad) of PMAY is 2.014 m2 whereas the total area of all windows combined (Aw) is 3.764 m2. Total leakage is then calculated with Eq (26)e(28) .

Vd ¼ Ad  5 ¼ 10:07 L=s

(26)

VW ¼ AW  2 ¼ 7:528 L=s

(27)

V ¼ Vd þ VW ¼ 17:598 L=s ¼ 37:288 cfm

(28)

Values of ra and Cpa are 0.075 lbm/ft and 0.24 Btu/lb℉ respectively [46]. Using Eq (25), the total daily heat infiltration due to leakage is calculated to be 4.338 kWh/day (refer to Table (B) of supplementary data for hourly values). Heat gains induced by active building utilities such as forced air ventilation system, lighting systems and other electronic appliances are minimally influenced by the envelope’s structural modifications discussed in this study. Therefore such active heat gains lie beyond the scope of the present study on envelope configuration modifications which passively enhance building energy performance. The effective area to compute Qwall for each wall is obtained by subtracting the areas of door and windows on the respective walls from the total façade area (Table 8). The orientation of “Side A” in Fig. 3 is mentioned in Table 8 to indicate the overall building orientation. As observed from Table 8, South orientation of “Side A00 results in minimum heat gain through the envelope. Total heat gain calculated in a similar manner for a non-optimized concrete envelope with the same orientation (Side A facing South) is 80.8578 kWh/day but it can be as high as 82.003 kWh/day (Side A facing East) if orientation is not optimized. The overall optimization of envelope configuration and orientation results in a total heat gain reduction of 27.4731 kWh/day which is 33.5% of the total diurnal heat gain with a non-optimized envelope with East orientation of Side A. This figure is close to one of the highest reported building heat gain reductions of 39% achieved by Alawadhi & Alqallaf [4] in the hot climate of Kuwait. With an air conditioner of COP 3, the equivalent reduction in electricity consumption is 9.2 kWh/day. It is the electricity saving attained in a single PMAY house unit. More than 1 lakh of such units have been commissioned by the Government of India in the nearby vicinity of Delhi [47] carrying a scope of prodigious energy saving by adopting the current optimization methodology. Most of the optimized configurations in Table 6 exceed the assigned maximum total thickness by 1 mm. This can be rectified by assigning larger values of penalty parameter. From building construction perspective, this minuscule tolerance can still be accommodated in the design. Saxena et al. [36] presented a practical demonstration of PCM incorporation in slots cut into bricks which constitute a building envelope. This research is complemented by the present study in a sense that the size and location of such slot can be predetermined to ensure optimal thermal performance of the house. The work of Saxena et al. is a standard example where the present study can be implemented in a practical scenario. 3

The key conclusions of the present study are summarized as below. I The proposed methodology can be instrumental in designing multi-retrofit building envelopes to minimize indoor heat gain in hot Indian climate. The model can holistically account for both sensible as well as latent heat storage materials for optimum thermal performance. II In addition to determining the best envelope configuration, the present model can also be used for comparing the relative thermal performances of different envelope additives. Out of the different PCMs and insulators investigated in the present study, CCH-Polystyrene combination results in minimum heat gain. III With an optimized design of building envelope, up to 33.5% of heat gain reduction and 9.2 kWh/day of electricity savings can be achieved with the given retrofits in a single building out of copious PMAY units. The net energy saving by replicating the optimized design in lakhs of such units envisaged to be constructed can certainly be a big leap towards energy sustainability in the country. Further improvement in the energy saving figure can be achieved by testing a wider range of materials with the same optimization methodology. The holistic optimization ensures that each of the installed retrofit is appropriately configured to deliver maximum thermal performance. IV The optimum configuration is significantly affected by the orientation of the structure. Although the material pair CCHPolystyrene dominates other materials in the optimization, its optimum configuration (thickness and locations of PCM and insulator) vary in different walls and roof. V The concept of optimality can vary according to different scenarios. One may be rather interested in finding the configuration with minimum heat gain during peak hours or minimum heat gain per unit cost of construction and maintenance. These parameters can be derived with simple arithmetic operations on the total diurnal heat gain obtained from the thermal model. Replacing the fitness function in the GA with such modified expressions will lead to respective optimum solutions.

Author statement All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript.

Acknowledgment The authors would like to thank Department of Science and Technology, Government of India for providing the necessary resources to carry out the present study under the research grants titled “Characterisation studies of Nano-enhanced Phase Change Material (NEPCM) in thermal storage devices for sustainable building designs in India” - Grant number- TMD/CERI/BEE/2016/ 84(G), “Energy Efficient Buildings: Technology with Intelligence” Grant number- TMD/CERI/BEE/2016/102(G).

P. Saikia et al. / Energy 197 (2020) 117263

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.energy.2020.117263. Nomenclature T t x F

Temperature (K) Time (s) length along wall/roof thickness (m) Fourier number a Thermal diffusivity (m2/s) Bi Biot number To Ambient temperature (K) ho Exterior convective heat transfer co-efficient (W/m2-K) hi Interior convective heat transfer co-efficient (W/m2-K) kconcrete Thermal conductivity (W/m-K) Tinterior Building interior temperature (K) qin Heat gain per unit area to building interior (J/m2) Tsol Sol-air temperature (K) I Incident solar radiation (W/m2) abs Absorptivity ε Emissivity DR Long-wavelength radiation exchange for horizontal surface (¼63 W/m2) Louter concrete Outer concrete thickness (m) LPCM PCM thickness (m) Lmiddle concrete Middle concrete thickness (m) Linsulator Insulator thickness (m) Linner concrete Inner concrete thickness (m) Pcross Crossover probability Qwall Convective heat transfer from inner wall surface to the building interior (kWh/day) Qwindow Heat gain through window (kWh/day) Qs Sensible heat gain due to air leakage (kWh/day) Vd Air flow rate through door (cfm) Vw Air flow rate through window (cfm) V Total air flow rate (cfm) ra Density of air (lbm/ft3) Cpa Specific heat of air(Btu/lb℉) References [1] Peippo K, Kauranen P, Lund PD. A multicomponent PCM wall optimized for passive solar heating. Energy Build 1991;17:259e70. https://doi.org/10.1016/ 0378-7788(91)90009-R. [2] Neeper DA. Thermal dynamics of wallboard with latent heat storage. Sol Energy 2000;68:393e403. https://doi.org/10.1016/S0038-092X(00)00012-8. [3] Alqallaf HJ, Alawadhi EM. Concrete roof with cylindrical holes containing PCM to reduce the heat gain. Energy Build 2013;61:73e80. https://doi.org/10.1016/ J.ENBUILD.2013.01.041. [4] Alawadhi EM, Alqallaf HJ. Building roof with conical holes containing PCM to reduce the cooling load: numerical study. Energy Convers Manag 2011;52: 2958e64. https://doi.org/10.1016/J.ENCONMAN.2011.04.004. [5] Guarino F, Athienitis A, Cellura M, Bastien D. PCM thermal storage design in buildings: experimental studies and applications to solaria in cold climates. Appl Energy 2017;185:95e106. https://doi.org/10.1016/ J.APENERGY.2016.10.046. [6] Saxena R, Biplab K, Rakshit D. Quantitative assessment of phase change material utilization for building cooling load abatement in composite climatic condition. J Sol Energy Eng 2017;140:011001. https://doi.org/10.1115/ 1.4038047. [7] Saikia P, Rakshit D. A comparative study and parametric analysis of phase change materials utilization for interior heat gain reduction. 2017. 2017. [8] Zhou D, Eames P. Phase Change Material Wallboard (PCMW) melting temperature optimisation for passive indoor temperature control. Renew Energy 2019;139:507e14. https://doi.org/10.1016/J.RENENE.2019.02.109.
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