## 2 Materials and Methods
If the heat transfer resistance of the insulation layer R\({}_{\text{in}}\) is given by the expression x/k, the thermal conductivity of the insulation material is k (W/mK), and the insulation thickness is x (m), and the total heat transfer coefficient U (W/m\({}^{2}\)K) can be written as follows:  
\[\text{U}=\frac{1}{(\text{R}_{\text{wt}}+\text{x}/\text{k})} \tag{3}\]  
\(\text{R}_{\text{wt}}\) given in Equation (3) shows the sum of all resistances except the insulation layer heat conduction resistance. Accordingly, the annual heat energy required to heat the unit area (1 m\({}^{2}\)) is calculated as follows:  
\[\text{E}_{\text{h}}=\frac{86400.\text{DD}}{(\text{R}_{\text{wt}}+\text{x}/ \text{k}).\eta} \tag{4}\]  
A variety of economic analysis techniques may be employed in the assessment of investment opportunities. The present value method is employed for the calculation of the optimal insulation thickness. The present value method is a method that determines \begin{table}
\begin{tabular}{c l c c c} \hline \hline
**Wall Type** & **Building Material** & **Thickness (m)** & \
\begin{tabular}{c} **Heat Transfer** \\ **Coefficient (W/mK)** \\ \end{tabular} &
\begin{tabular}{c} **Conduction** \\ **Resistance (m\({}^{2}\)K/W)** \\ \end{tabular} \\ \hline \multirow{4}{*}{Concrete wall} & Indoor environment & - & - & 0.130 \\  & Interior plaster (a) & 0.02 & 1.40 & 0.014 \\ \cline{1-1}  & Reinforced concrete (b) & 0.15 & 1.30 & 0.115 \\ \cline{1-1}  & Exterior plaster (c) & 0.02 & 1.40 & 0.014 \\ \cline{1-1}  & External environment & - & - & 0.040 \\ \cline{1-1}  & Total heat transfer coefficient = (1/total & & 3.195 W/m\({}^{2}\)K \\ \cline{1-1}  & conduction resistance) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._whether an investment is economical or not. It is based on the principle of making a comparison by determining the sum of the cash values of all revenues and expenses over a certain interest rate during the economic life of the investment. After all parameters related to the investment are determined, cash flows related to the investment are created. Subsequently, the economic viability of the investment is determined. The disadvantage of the method is that the interest rate initially determined is assumed to remain constant throughout the economic life of the project. The change in this interest rate in the following years affects the choice of the most appropriate investment. The primary goal of evaluating investments is to define whether the investment is economical or not. In the evaluation, first of all, all parameters related to investment throughout its economic life must be determined. These parameters are investment amount, interest rate, periodic income, periodic expense, economic life, and scrap value [17]. The interest rates are closely related to the conditions of the country and the global economy. Many factors such as the amount of domestic and foreign debt, export-import balance, and public deficits affect inflation and thus indirectly or directly affect the interest rate. When evaluating an investment, the cash flow's cash (or future) value is calculated by taking into account the interest rate of that year. In calculating the present value factor, the inflation-adjusted annual interest rate (real interest rate), r (%), is employed. \[\rm{r}=\frac{\rm{i-g}}{1+g} \tag{5}\]  
In this case, the PW value is expressed by the following:  
\[\rm{PW}=\left[\frac{1-(1+r)^{-N}}{r}\right] \tag{6}\]  
The optimal insulation thickness is contingent upon a number of factors, including the outdoor temperature, the duration of the heating period, the operational time, the efficiency of the heating system, and the properties of the insulation material (heat conduction coefficient, cost, and anticipated lifetime). Annual fuel cost \(\rm{C_{h}}\) (USD) for an insulated building is calculated with Equation (7). Here, \(\rm{C_{f}}\) represents the unit price of the fuel to be used in the heating system while H (J/kg) denotes the lower heating value of the fuel.