Thermal insulation performance curves for exterior walls in heating and cooling seasons
Journal of Thermal Engineering 2023, Vol. 9, Issue 4, pp. 1053-1069; doi.org/10.18186/thermal.1337469
Abstract
Keywords: Degree-day; Energy Saving; Insulation Characteristic Curves; LCCA Method; Payback Period
Introduction
Despite the availability of many mega projects globally to produce electricity from renewable energy, the use of petroleum products, natural gas and coal still accounts for approximately 70% of the total electricity generated worldwide. Space heating and cooling of buildings are considered
as one of the most important sectors of electricity consumption, which in 2016 accounted for approximately 40% of the total electricity generated [1, 2]. To reduce the energy requirement for space heating and cooling, an appropriate engineering design should be made for the building envelope; by selecting proper type of construction and insulation materials that would minimize heat loss/gain
*Corresponding author. *E-mail address: mabatiha@yahoo.com This paper was recommended for publication in revised form by Editor in Chief Chandramohan VP Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
from buildings envelope and reduce loads for space heating-cooling and thus achieving energy conservation [3]. Hence, extensive scientific studies have been conducted on the development and testing of new materials of insulation. In the literature, there is over 40 types of thermal insulation materials have been developed, many of them are now available in the market and used in buildings. They have a wide range of thermal conductivities, ranging from 0.004 W/m K for vacuum insulation panel [4] to 0.485 W/m K for cement-based lightweight composites [5]. Al-Homoud [6] classified the available insulation materials into six categories, namely; organic, inorganic, metallic, aerogel, insulations made from waste materials and composites. These materials have been used for floor, wall, ceiling and roof insulation. For the external walls of building, the most widely used insulation materials are polyurethane (0.0200.030 W/m K), extruded polystyrene (0.025-0.035 W/m K), expanded polystyrene foam (0.030-0.040 W/m K), glass wool (0.030-0.046 W/m K), rock wool (0.033-0.046 W/m K), fiberglass (0.033-0.040 W/m K), and cellulose (0.0460.054 W/m K) [4, 6–8]. The thermal conductivities of these materials range from 0.020 to 0.054 W/m K. Insulation thickness is directly proportional to the investment cost and is inversely proportional to the heating and cooling transmission loads (i.e. operating costs). The economic thermal insulation thickness at which these costs are optimized (i.e. minimum thickness in relation with the total cost) is called as the “optimum insulation thickness” (OIT) [9]. For external walls, the OIT has been estimated for different climate conditions based on cooling [9–14] and heating loads [15–21]. Most of the available studies on OIT were performed under static conditions in which heating and cooling energy requirements were estimated using a common method called the degree-day method (heating degree-day (HDD) or cooling degree-day (CDD)). On the other hand, few studies have been analytically analyzed the dynamic behavior of multilayer envelopes [22–24]. The most commonly used financial method to optimize the thermal insulation thickness of external walls is the life cycle cost analysis (LCCA) method [9, 25, 26]. LCCA considers energy uses during the lifetime of the building, which can be taken as 10 years [26], 20 years [27], 25 years [28], 30 years [29], or 50 years [30]. Using the present worth factor (PWF), the net energy savings due to the use of insulation material during the lifetime of the building is estimated in its present value. For decision making purposes, design engineers used to rely on performance curves rather than conducting a comprehensive study for each specific case. For example, engineers would not conduct LCCA study for selecting the optimum insulation type and thickness. Instead, they will select the cheapest available insulation material in the market with rough thickness, although mostly this could not be the optimum and economic choice. Up to the best of our knowledge, however, there were no thermal insulation performance curves (TIPCs) have been reported in
the literature. Therefore, the goal of this work is to develop TIPCs from which the insulation performance characteristics can easily be found for any climate condition and all economic factors related to energy and insulation. These curves are generated based on LCCA method coupled with DD method for heating and cooling processes. TIPCs are constructed to cover commonly used insulation materials for building walls with thermal conductivities reported above, i.e. 0.020-0.055 W/m K. Unlike the current literature, this study is the first that focus on, f-factor curves in cooling and heating period for different insulation materials and OIT. In addition, curves for the payback period and energy saving values for different thermal resistances (between 0.4 to 0.8 m2 K/W) are shown. Moreover, the results of this research not only point to the need to change energy policies, but also benefit from the selection of the most suitable insulation material by providing useful and practical results in the construction process of buildings.
Methodology
Heat gain or loss from external walls Heat losses in buildings may occur due to poorly insulated roofs, walls, windows, doors, unused parts, garages, plumbing pipes or ventilation sections of buildings. The heat gain or loss from external walls is [31]: (1)
(3) where subscripts b, sa, 1, n and ins are denoted to indoor base, solar-air, first wall layer, pre-insulation wall layer and insulation layer, respectively, A is the wall surface area (m2), U is the overall heat transfer coefficient (W/m2 K), Ti is the temperature (K), R is the total resistance (K/W), which is the sum of the total internal resistance of wall layers and the surface resistances of convective heat transfer over the inside and outside wall surfaces, hi is the convection heat transfer coefficient (W/m2 K), ki is the thermal conductivity of the wall material (W/m K) and xi is the wall layers thickness (m). The annual heat loss/gain per unit area of external walls in terms of degree-days (DD) are calculated as: (4) (5)
where HDD and CDD are the heating and cooling degree-day numbers, respectively, which are used to estimate the buildings envelope heat transfer. For heating [20],
where CF is the fuel cost ($/kWh, $/kg or $/m3) and Ce is the cost of electricity ($/kWh). To calculate the fuel cost over a building lifetime, the present worth factor (PWF) is used. It depends on interest rate, i, (%) and the inflation rate, g, (%) [34]. For inflation, PWF is adjusted as:
(7) (14) Energy requirement and costs The cost of insulation material per unit area (CTins, $/ m2) used for external walls is [9]:
where N is insulation material lifetime, and i* is interest rate adjusted for inflation rate:
(8) where Cins is the insulation material cost per unit volume ($/m3). The annual energy requirement per unit area for heating (EAH) and cooling (EAC), in unit of J/m2 year, are estimated as [32]:
Then, the annual energy cost per unit area for heating and cooling (CE) over building lifetime is: (16)
where F is a new factor (K $/W), introduced in this paper, that has two different values for heating and cooling loads. For heating, (17)
where Rwt is the overall wall thermal resistance excluding the insulation layer (K/W), η is the efficiency of the heating system (%) and COP is the coefficient of performance. The annual fuel consumption is calculated as [33]: (11) where Hv is the fuel lower heating value (J/kWh, J/kg or J/m3). The annual energy cost per unit area for heating (CAH) and cooling (CAC), in units of $/m2 year, are calculated as [9, 32]: (12)
and for cooling, (18) The total annual cost ($/m2 year) of heating and cooling (CT) an insulated building is: (19)
Optimum insulation thickness The OIT (xopt, m) is obtained by taking: (20)
Hence, the OIT minimizing the total heating or cooling cost is calculated as: (21)
The specific annual total net energy savings (eS, m) is plotted versus OIT at different Rwt and kins. Using this curve, eS can be found at any OIT. To find ES ($/m2), eS should be multiplied by Cins. Using the f-factor, the PP is: (28)
Net energy saving and payback period The annual total net energy saving (ES, $/m2) for heating and cooling loads are calculated, as the difference between the annual energy cost of un-insulated and insulated building, as:
(22) The payback period (PP, year) for heating and cooling is calculated, as the ratio between the annual energy cost of an un-insulated building and the annual total net energy saving, as: (23)
Thermal insulation performance curves (TIPCs) The OIT curves for heating and cooling loads are prepared by grouping the terms related to energy and insulation (i.e. CF, Ce, PWF, Cins, η, COP, Hv) into one factor (f) as follows: (24) For heating, the f-factor (K m3/W) is: (25) and for cooling, the f-factor (K m3/W) is: (26) Then, the OIT is plotted versus at different Rwt and kins. Similar to the OIT curve, energy savings curves are prepared by dividing ES by Cins and grouping the same previously mentioned terms into the f-factor as:
Then, the OIT is plotted versus PP (year) at different Rwt and kins. The use of f-factor in Eqs. (24, 27-28) eliminates the spatial and temporal variations present in Eqs. (21-23), making the curves generated based on this factor valid anytime and everywhere; taking into account the variation in fuel and insulation costs and the variation in climate conditions.
Results And Discussion
Thermal insulation is done in order to minimize the heat losses caused by building elements such as walls. Regarding thermal insulation, the purpose of the developed model is to introduce a new approach in the calculation of OIT, total cost, cost savings and payback period by considering many factors. These factors are: other variables related to economic parameters and regulations such as climate conditions (degree-days), thermal conductivity and price of the insulation material, average temperature in the region, fuel price for heating, interest and inflation rates. Thus, this will provide an effective and simple guide for people working in the field to better design, analyze and operate wall thermal insulation anywhere in the world. TIPCs at different Using Eq. (24), the OIT is plotted versus kins (0.01-0.055 W/m K) and Rwt (0.4-0.8 m2 K/W), as shown in Fig. 1. Prior to use the TIPCs, the user should calculate the square root of the f-factor, using Eqs. (25) and (26) for heating and cooling loads, respectively. For any other plotted values of kins and Rwt, linear interpolation could be applied and exact results would be obtained, as shown in of Table 1. For example, for the case with Rwt, kins and
0.4. m2 K/W, 0.03 W/m K and 0.65, respectively, from Fig.
1(a), the OIT is 0.1 m. If kins is 0.033 instead of 0.03 W/m K, then applying linear interpolation between OITs at kins of 0.03 and 0.035 W/m K, as shown in Table 1, to get the OIT of 0.1048 m at kins of 0.033 W/m K, compared to the true value of 0.1049 m. Again, if Rwt is 0.45 instead of 0.4 m2 K/W, then applying linear interpolation between OITs at Rwt of 0.4 and 0.5 m2 K/W, as shown in Table 1, to get the OIT of 0.106 m at Rwt of 0.45 m2 K/W, compared to the true value of 0.10585 m. From Table 1, it can be noticed that the TICC reading values are very close to true values (i.e. calculated) with percent error of less than 0.6 %. When kins falls between any two plotted curves in Fig. 1, the user can
simply read the closest curve to his value with a maximum error in OIT of less than 5 mm. Using Eqs. (27 and 28), the PP and eS were plotted versus OITs at different f-factors of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6,
0.7. K m3/W and 0.8, kins of 0.02, 0.03, 0.04 and 0.05 W/m
K, and Rwt of 0.4, 0.5, 0.6, 0.7 and 0.8 m2 K/W, as shown in Figs. (2-6). Using these figures, eS and PP can be only found after the OIT has been determined from Fig. (1). The eS value determined using Figs. (2-6) must be multiplied by the current insulation material cost (Cins, $/m3) to obtain the annual total net energy saving, ES, in units of $/m2. An example of TIPCs use and interpolation is shown in Table
2. This table represents the case in which the OIT is 0.1 m
with an f-factor of 0.5 K m3/W and Rwt of 0.4 m2 K/W. The PP and eS determined from Fig. (2) at kins of 0.02, 0.03, 0.04 and 0.05 W/m K were compared with calculated (i.e. true) values. To check the validity of using linear interpolations,
k = 0.010 k = 0.015 k = 0.020 k = 0.025 k = 0.030 k = 0.035 k = 0.040 k = 0.045 k = 0.050 k = 0.055
k = 0.010 k = 0.015 k = 0.020 k = 0.025 k = 0.030 k = 0.035 k = 0.040 k = 0.045 k = 0.050 k = 0.055
k = 0.010 k = 0.015 k = 0.020 k = 0.025 k = 0.030 k = 0.035 k = 0.040 k = 0.045 k = 0.050 k = 0.055
k = 0.010 k = 0.015 k = 0.020 k = 0.025 k = 0.030 k = 0.035 k = 0.040 k = 0.045 k = 0.050 k = 0.055
k = 0.010 k = 0.015 k = 0.020 k = 0.025 k = 0.030 k = 0.035 k = 0.040 k = 0.045 k = 0.050 k = 0.055
TIPCs Validation In this section, the TIPCs are validated against published articles for both heating and cooling loads. We have selected those articles in which complete input values are provided and that the output results were represented in tabulated format; making the comparison and thus validation is possible. Using EPS as an insulation material for cooling of cold storage space in Amman city with kins of 0.034 W/m K and Rwt of 0.4862 m2 K/W, Batiha et al. [9] found that the OIT is 0.147 m with annual energy savings of 111.503 $/ m2 and PP of 1.237 year. Based on the input values given by
three interpolations were made at kins of 0.025, 0.035 and 0.045 W/m K and compared with true values. Results show that liner interpolation is valid with percent error of less than 0.2%, which can be referred to human error in reading the curve values.
(d) (e) at different insulation thermal conductivities: (a) Rwt = 0.4 m2 K/W, (b) Rwt = 0.5 m2 K/W, Figure 1. OIT vs. (c) Rwt = 0.6 m2 K/W, (d) Rwt = 0.7 m2 K/W and (e) Rwt = 0.8 m2 K/W.
Table 1. TIPC reading values with examples of interpolation OIT (m)
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
(c) (d) 2 Figure 2. PP and eS vs. OIT at Rwt = 0.4 m K/W: (a) k = 0.02 W/m K, (b) k = 0.03 W/m K, (c) k = 0.04 W/m K, (d) k = 0.05 W/m K.
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
Rwt = 0.5 (m2K/W ), kins = 0.02 (W/m K) 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3
(c) (d) Figure 3. PP and eS vs. OIT at Rwt = 0.5 m2 K/W: (a) k = 0.02 W/m K, (b) k = 0.03 W/m K, (c) k = 0.04 W/m K, (d) k = 0.05 W/m K.
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
(c) (d) Figure 4. PP and eS vs. OIT at Rwt = 0.6 m2 K/W: (a) k = 0.02 W/m K, (b) k = 0.03 W/m K, (c) k = 0.04 W/m K, (d) k = 0.05 W/m K.
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
(c) (d) Figure 5. PP and eS vs. OIT at Rwt = 0.7 m2 K/W: (a) k = 0.02 W/m K, (b) k = 0.03 W/m K, (c) k = 0.04 W/m K, (d) k = 0.05 W/m K.
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
f = 0.1 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 f = 0.7 f = 0.8
(c) (d) Figure 6. PP and eS vs. OIT at Rwt = 0.8 m2 K/W: (a) k = 0.02 W/m K, (b) k = 0.03 W/m K, (c) k = 0.04 W/m K, (d) k = 0.05 W/m K.
Table 2. TIPC reading values compared to true values with examples of interpolation at OIT of 0.1 m, f-factor of 0.5 K m3/W, and Rwt of 0.4 m2 K/W kins (W/m K)
the authors, listed in Table 3, the calculated f-factor, using Eq. (26), for the cooling loads is 0.789 K m3/W; = 0.888. Hence, interpolating curve values between kins of 0.03 and 0.035 W/m K at Rwt of 0.4 and 0.5 m2 K/W, using Fig. (1), we found that the OIT at kins of 0.034 W/m K and Rwt of 0.4862 m2 K/W is 0.147 m, which is the same as calculated value. Instead of making interpolation, if the TICC user decided to use the closest curve to his data (e.g., kins of 0.035 W/m K and Rwt of 0.5 m2 K/W) without making interpolations, the
OIT would be 0.148 m, which is also acceptable for decision making purposes compared to the true value of 0.147 m. Based on the OIT of 0.147 m found from Fig. (1), interpolating curve values between kins of 0.03 and 0.04 W/m K at Rwt of 0.4 and 0.5 m2 K/W, using Figs. 2(b and c) and Figs. 3(b and c), we found that, at kins of 0.034 W/m K and Rwt of 0.4862 m2 K/W, the PP and eS are 1.23 year and 1.317 m, respectively. Multiplying eS by the insulation material cost of 85 $/m3 to obtain the annual energy savings of 111.945
Table 3. Results of TIPC validation against published data Reference
$/m2. It can be clearly noticed that the values found using TIPCs are very close to that calculated by Batiha et al. [9]. In a similar manner, the other data listed in Table 3 were validated. Comparing the obtained results by using the TIPCs with those calculated by authors listed in Table 3, we can conclude that TIPCs are valid and can be trusted to use with no caution.
Conclusion
In this paper, utilizing LCCA method, TIPCs were successfully introduced and validated, which can be considered as the first attempt toward developing more simple TIPCs. TIPCs are constructed to cover commonly used insulation materials for building walls with thermal conductivities between 0.020-0.055 W/m K. f-factor for the heating and cooling loads given first time in this paper. The findings of this paper can be summarized as follows:
2. Insulation performance, such as OIT, energy savings
and PP, can be easily obtained using TIPCs based on a single factor, called the f-factor.
3. TIPCs can be used for determining the performance of
insulation materials for external walls for any: (i) climate zone, (ii) loads (i.e. heating or cooling), (iii) fuel type and cost and (iv) insulation cost.
5. TIPCs are considered to be well validated and trusted
tool. 6. TIPCs’ user can use the curve with characteristics closest to his entry values without making interpolation; the percent error would be within acceptable margins.
Nomenclature
Cost ($/kg, $/m3, $/kWh) Energy (J) Specific annual total net energy (m) inflation rate (%) Convection heat transfer coefficient (W/m2 K) Fuel lower heating value (J/kWh, J/kg, or J/m3) Interest rate (%) Interest rate adjusted for inflation rate (%) Thermal conductivity of the wall material (W/m K), insulation material lifetime (year) Payback period (year) Annual heating gain per unit area (W/m2) Thermal resistance (K/W) Temperature (°C) Overall heat transfer coefficient (W/m2 K) Thickness (m) Heating system efficiency (%)
Cooling Electricity Energy Fuel Heating Insulation Optimum Outside Pre-insulation Reference Saving Solar-air Total Wall
Abbreviations
CDD Cooling degree-days COP Coefficient of performance EPS Expanded Polystyrene HDD Heating degree-days LCCA Life-cycle cost analysis OIT Optimum insulation thickness PP Payback period PWF Present worth factor TIPCs Thermal insulation performance curves
Data Availability Statement
No new data were created in this study. The published publication includes all graphics collected or developed during the study.
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Share and Cite
BATIHA, M.A.; RAWADIEH, S.; BATIHA, M.; AL-MAKHADMEH, L.; KAYFECI, M.; MARACHLI, A. Thermal insulation performance curves for exterior walls in heating and cooling seasons. Journal of Thermal Engineering 2023, Vol. 9, pp. 1053-1069. https://doi.org/10.18186/thermal.1337469