Empirical modeling between degree days and optimum insulation thickness for external wall

ABSTRACT

Insulating is the most effective method that is used to save energy in buildings. Samples from cities from different climatic zones from TS 825 (Turkey) first. Optimum insulation thickness ($x_{opt}$) analysis is based on two types of insulating and four different fuels (natural gas, coal, fuel oil and electric) of related cities. Cost accounts, payback period and CO₂-SO₂ emission calculations were performed based on these analyses. Second of all, the relationship between a number of degree day (NDD) and optimum insulation thickness ($x_{opt}$) was developed by linear, quadratic and cubic correlations. Thirty different mathematical correlations based on different fuel types by using XPS and EPS insulating materials. Twenty-four of these models that were developed were generated peculiar to the fuel type; six of them were generated based on average insulation thickness. R² values of related correlations are between 0.9989 most and 0.9952 at least as well as it is pretty close to (R ≤ 1) one value. The model among these models is the $x_{opt}=a+b\left(NDD\right)+c{\left(NDD\right)}^2+d{\left(NDD\right)}^3$ cubic mathematical model that gives the best average value. a = 0.0036, b = 5E-05, c = – 7E-09 and d = 6E-13 are the values for XPS material. Following values are for EPS material; a = 0.0028, b = 5E-13, c = – 7E-09 and d = 4E-05. R² determination coefficient of both two equations is pretty close to 0.9989 and 1; the models obtained are less-than-stellar. Optimum insulation thickness of the area can be known based on the type of material via the number of degree day without the need for long analyses. According to the R² values, the use of all models is recommended for academic and industrial users.

KEYWORDS:

• Insulation
• environmental analysis
• energy-saving
• payback period
• climate zones

Nomenclature

Bsk	=	cold semi-arid (steppe) climate
$C_{A,C}$	=	annual cooling energy cost ($/m2-year)
$C_{A,H}$	=	annual heating energy cost ($/m2-year)
$C_i$	=	cost of insulation in ($/m3)
$\mathrm{C}\mathrm{D}\mathrm{D}$	=	cooling degree-days (0C-days)
$C_f$	=	price of the fuel ($/kg; $/m3)
Csa	=	hot-summer mediterranean climate
Csb	=	warm-summer mediterranean climate
$C_T$	=	total cost ($)
CO2	=	carbon dioxide
Dbf	=	warm-summer humid continental climate
$E_A$	=	annual energy requirement (J/m2-year)
EPS	=	expanded polystyrene
$\mathrm{g}$	=	inflation rate
HDD	=	heating degree-days (0C-days)
$H_u$	=	heating value of the fuel (J/kg; J/m3; J/kwh)
i	=	interest rate
k	=	thermal conductivity of the insulation material (W/m K)
LCCA	=	life cycle cost analysis
M	=	molar weight of the fuel
$m_{fA}$	=	amount of fuel consumed per year (kg/m2-year)
N	=	lifetime (years)
NDD	=	number of (degree-days (0C-days)
$p_b$	=	payback period (years)
PWF	=	present worth factor
q	=	heat loss (MJ m2 year−1)
$q_A$	=	annual heat loss in unit area (J/m2-year)
r	=	actual interest rate
$R_i$	=	inside air-film thermal resistances (m2K/W)
$R_{izo}$	=	thermal resistance of the insulation layer (m2K/W)
$R_o$	=	outside air-film thermal resistances (m2K/W)
$R_{TW}$	=	sum of Ri,Rw,Ro (m2K/W)
$R_w$	=	total thermal resistance of the wall materials with out the insulation (m2K/W)
SA	=	annual savings ($/m2)
SO2	=	sulfur dioxide
U	=	overall heat transfer coefficient (W/m2K)
x	=	thickness of the insulation material (m)
$x_{opt}$	=	optimum insulation thickness (m)
XPS	=	extruded polystyrene
Greek letters	=
$\eta$	=	heating system efficiency
ΔT	=	temperature difference (C0)
Subscripts	=
A	=	annual
C	=	cooling
H	=	heating
i	=	inside
izo	=	insulation
o	=	outside
opt	=	optimum
t	=	total
w	=	wall

Conflicts of Interest

“The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.”

Additional information

Notes on contributors

Mehmet Ali Kallioğlu

Mehmet Ali Kallioğlu obtained his B.E. (Mechanical Engineering) and M.E. (Energy Engineering) from the Erciyes University (ERÜ), Kayseri, Turkey, in 2010  and Nigde Omer Halisdemir University (OHU), Niğde,  Turkey, in 2014 respectively. He is currently a research scholar and Ph.D. student at Technology Faculty of Batman University (BATÜ), Batman, Turkey. His major research interests are solar energy conversion, optimum insulation thickness, CFD,  renewable energy and heat transfer

Umut Ercan

Umut ERCAN graduated from High School In 2000, and enrolled at Fırat University to study mechanical engineering. He graduated with a Bachelor of Science degree in mechanical engineering from the Department of Mechanical Engineering in 2008. He began his MSc studies at the Department of Mechanical Engineering of Çukurova University in 2008 and graduated in 2012. He worked in İNSPEGO International Inspection & Certification Services Ltd. 2011 and 2012. He has been working as Research Assistant in the Automotive Engineering Department of Batman University since February, 2012. He has started Ph.D. studies since 2014.

Ali Serkan Avcı

Ali Serkan Avcı is M.Sc. in Mechanical Engineering from Batman University, at Batman University, Faculty of Engineering and Architecture. He is currently a Ph.D. student. Works as a Research Assistant at Batman University, Faculty of Technology. Major research interests are thermodynamics, solar energy, fluid mechanics and air quality.

Cihad Fidan

Cihad Fidan is M.Sc degree in Mechanical Engineering from Munzur Üniversity, Institute of Science and Technology Institute. He is currently working as a research assistant in the Department of Mechanical Engineering at Munzur University. He holds a Ph.D. in Thermodynamics from Batman University, Department of Mechanical Engineering. Major research interests are energy conversion and solar energy applications

Hakan Karakaya

Hakan Karakaya is M.Sc. and the Ph.D. degree in Mechanical Engineering from Fırat University, Institute of Science and Technology. Currently Works as an Assistant Professor at Batman University, Faculty of Engineering and Architecture. Major research interests are energy conversion, optimum insulation thickness, solar energy applications and heating and cooling load of buildings.