## 3 Data Processing and Uncertainty Analysis
### Data Processing
The amount of heat transferred from the working fluid to the cold air stream is calculated using Equation (8). \[Q_{c}=\dot{m}_{c}\cdot c_{p}\cdot(T_{out,\ c}-T_{in,c}) \tag{8}\]  
The heat capacity rates for the evaporator \((C_{h})\) and condenser sections \((C_{c})\) are calculated by Equations (9) and (10):  
\[C_{h-}\dot{m}_{h}\cdot c_{p,h} \tag{9}\]  
\[C_{c-}\ \dot{m}_{c}\cdot c_{p,c} \tag{10}\]  
The thermal efficiency of the heat exchanger is calculated as the ratio of the energy absorbed by the cold air to the energy supplied by the hot air, as shown in Equation (11):  
\[\eta=\frac{Q_{c}}{Q_{c}} \tag{11}\]  
Thermal resistance is calculated using Equation (12) by dividing the temperature difference between the evaporator and condenser sections by the heat input to the evaporator:  
\[R=\frac{T_{evap}-T_{cond}}{Q_{c}} \tag{12}\]The Reynolds number (Re) was calculated using Equation (13) to characterize the air flow regime in the hot and cold air channels. \[Re=\frac{\rho\cdot V_{avg}\cdot D_{h}}{\mu} \tag{13}\]  
where \(D_{h}\) is the hydraulic diameter (m) of the rectangular duct, which was calculated using the standard expression \(D_{h}=4A/P\), where A is the cross-sectional area and P is the wetted perimeter of the duct. The heat transfer coefficient (h) was determined from the cold side using Equation (14):  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]0  
where \(A\) denotes the heat transfer surface area (m\({}^{2}\)) and \(\Delta T_{lm}\) is the log mean temperature difference, calculated as follows:  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]1  
The effectiveness (\(\varepsilon\)), which indicates the ratio of the actual heat transferred to the maximum possible, is a key performance indicator in heat exchanger systems, and it is calculated by Equation (16):  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]2  
\(C_{min}=\min(\dot{m}\cdot c_{p})\) is the smaller heat capacity rate between hot and cold air streams. The performance improvement rate was calculated by comparing nanofluids to deionized water using Equation (17):  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]3  
The exergy balance for a steady-state control volume is expressed as follows:  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]4  
The total exergy loss (\(E\)) in a steady-state system can be determined as follows:  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]5  
where \(E_{h}\) is the exergy change in the hot fluid, and \(E_{c}\) is the exergy change in the cold fluid. Each of these can be expressed in two different forms [54]:  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]6  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]7  
\(T_{e}\), the environmental reference temperature, is taken as 25 \({}^{\circ}\)C (298.15 K) in this study. The total exergy loss of the heat exchanger can be rewritten as follows:  
\[\mu_{nf}=\mu_{f}\cdot\frac{1}{(1-\varnothing)^{25}} \tag{5}\]8The exergy-saving efficiency (%) is calculated as follows:  
\[ \begin{split} Exergy-Saving\ Efficiency\%_{\text{e}}\ =\left(1-\frac{E_{nanofluid\ loss}}{E_{ water\ loss}}\right)\times 100\end{split}  \tag{23}\]