## 2 Materials and Methods
### Energy Calculations  
Energy and exergy analysis is important for the design aspect of the engines as it can minimize the losses when using energy and exergy balance data [42]. This analysis deals with the first and second laws of thermodynamics on the IC Engine [43]. For the analysis, the engine was considered as a control volume under steady-state conditions as shown in Figure 4; due to limitations of the engine setup, some assumptions were made, which allow the author to simplify the thermodynamic calculations, and are as follows:  
* The air-fuel mixture for combustion and exhaust gases were supposed as ideal gases.
* The total energy produced by the fuel-air mixture was considered to be the energy input to the control volume; however, some part of it leaves as exhaust and other losses.
* Kinetic and potential energies were neglected.  
For energy and exergy analysis, the chemical reaction represented in Equation (1) was used to determine the emission characteristics data at the experimental setup.  
\[a(C_{x}H_{y}O_{z})+b(O_{2}+3.76N_{2})\to cO_{2}+dCO_{2}+eCO+fNO_{2}+gNO+hN_{2}+ jH_{2}O \tag{1}\]  
In the present study, the energy-exergy analysis includes finding major losses within the system, such as water cooling losses (\(Q_{\text{w}}\)), exhaust gas losses (\(Q_{\text{exh}}\)), along with other miscellaneous losses (\(Q_{\text{un}}\)). These analyses were done based on law of conservation of mass and energy as represented in Equations (2) and (3), respectively.  
\[\sum_{i}m_{in}=\sum_{i}m_{out} \tag{2}\]  
Figure 4: Control volume for energy–exergy analysis.  
\begin{table}
\begin{tabular}{c c c} \hline
**S. No.** & **Parameters** & **Specifications** \\ \hline
**1** & Engine & 1/4, DI engine \\
**2** & Bore \(\times\) stroke & 80 \(\times\) 110 mm \(\times\) mm \\
**3** & Connecting rod length & 235 mm \\
**4** & Compression ratio & 17.5 \\
**5** & Maximum power & 3.7, kW \\
**6** & Fuel injection pressure & 220 bar \\
**7** & Injection timing & 23.5\({}^{\circ}\) b TDC \\
**8** & Dynamometer & Eddy current \\ \hline \end{tabular}
\end{table}
Table 5: Simulation test engine technical descriptions.  
\[Q-W=\sum m_{out}h_{out}-\sum m_{in}h_{in} \tag{3}\]  
where \(m_{in}\) is the mass flow rate at the inlet and \(m_{out}\) is the mass flow rate at output. \(Q\) indicates the net heat input and h the specific enthalpy, respectively. Energy balance theory states that to calculate the heat lost from the engine to cooling water and heat carried by exhaust gases, the coolant inlet and outlet temperatures were needed. The flow rate of water was measured using a rotameter [44]. Net energy flow in (\(Q_{in}\)), the power developed by the engine (BP), water cooling losses (\(Q_{w}\)), exhaust gas losses (\(Q_{exh}\)), along with other miscellaneous losses (\(Q_{un}\)) were calculated by using the following Equations (4)-(8)  
\[Q_{in}=m_{f}\times CV \tag{4}\]  
\[BP=\omega\times T \tag{5}\]  
\[Q_{w}=m_{w}\times C_{pw}\times(T_{w2}-T_{w1}) \tag{6}\]  
\[Q_{exh}=(m_{f}+m_{a})\times C_{pg}\times(T_{exh}-T_{amb}) \tag{7}\]  
\[Q_{un}=Q_{in}-(BP+Q_{w}+Q_{exh}) \tag{8}\]  
The energy analysis is governed by the second law of thermodynamics, the principle of conservation of mass and the principle of conservation of energy. So, in the second part of the analysis, we started the exergy analysis of the IC engine by defining the exergy balance. The ratio of work done (\(BP\)) produced at the output shaft to the input fuel energy(\(Q_{in}\)) is termed as the piston thermal efficiency of the engine control volume, as described in Equation (9).  
\[\eta_{th}=\frac{workdone(BP)}{Q_{in}} \tag{9}\]