## 3 Results and Discussion
\[S_{c}=W/W_{w},\]  
where \(W=G_{\rm H}\cdot c_{p\rm H}\); \(W_{w}=G_{w}\cdot c_{pw}\)--the energy capacities being referred to are those of the charge air and internal circuit coolant, respectively; \(c_{p\rm H}\)--the isobaric heat capacity of air; \(c_{pw}\)--the heat capacity of internal circuit coolant. The position of the minimum point \(M_{\Sigma}\) for various values of \(\eta_{0}\) and \(G_{ww}\) was determined by analyzing the initial sections of the curves \(M_{\Sigma}=f\) (\(S_{c}\)). Examples of such regions are shown in Figures 5 and 6. Figure 5: The initial sections of the curves \(M_{\Sigma}=f\) (\(S_{c}\)) at different \(\eta_{0}\) and constant consumption of ECC, \(G_{uw}=5.5\) kg s\({}^{-1}\). The position of the minimum points allows for some deviations associated with the shape of the curves and the specifics of the systems and heat exchangers under consideration. Based on the comprehensive analysis, it is evident that the value of \(S_{c}\), corresponding to the minimum value of \(M_{\Sigma}\), practically depends only on \(\eta_{0}\) and can be reasonably approximated by the expression  
\[S_{c}=6.0263\eta_{0}-5.0311.\]  
It has also been established that for the range \(\eta_{0}=0.90\ldots 0.95\) with rational \(S_{c}\) (corresponding to the minimum value of \(M_{\Sigma}\)), the charge air cooler efficiency value is approximately constant and corresponds to \(t_{0}\)  
\[\eta_{c}\approx 0.97.\]  
With an irrational value of \(S_{c}\), the efficiency of the charge air cooler, \(\eta_{c}\), significantly affects \(M_{\Sigma}\). The value of \(M_{\Sigma}\) decreases monotonically with increasing \(\eta_{c}\). If in the simplest cooling system, the flow rate of ICC, \(G_{w}\), is increased to the possible limit (up to the consumption through the engine), then the value of \(M_{\Sigma}\) will increase. The value of \(M_{c}\) can either increase or decrease. For example, for an engine whose parameters correspond to Table 1, at \(\eta_{0}=0.9\) and \(G_{w}=4.0\) kg s\({}^{-1}\) (optimal \(S_{c}\)), the value of \(M_{\Sigma}=281.5\) kg, \(M_{c}=126\) kg at \(\eta_{c}=0.97\). At \(\eta_{0}=0.9\), \(G_{w}=22.2\) kg s\({}^{-1}\) (maximum \(G_{w}\)), then \(M_{\Sigma}=416.9\) kg, \(M_{c}=136.2\) kg, \(\eta_{c}=0.99\). At \(\eta_{0}=0.953\) (for optimal \(S_{c}\)), the value is \(M_{\Sigma}=394\) kg, \(M_{c}=211\) kg (optimum \(G_{w}=2.0\) kg s\({}^{-1}\), \(\eta_{c}=0.97\)). At \(\eta_{0}=0.953\), \(G_{w}=22.2\) kg s\({}^{-1}\) (maximum \(G_{w}\)), the value is \(M_{\Sigma}=1201\) kg, \(M_{c}=135\) kg (\(\eta_{c}=0.99\)). As can be seen from the provided data, the variation in \(M_{\Sigma}\) is contingent on \(\eta_{0}\) and exhibits a substantial increase with its growth, aligning with one of the conclusions drawn. Figure 6: The initial sections of the curves \(M_{\Sigma}=\)\(f\) (\(S_{c}\)) at different \(\eta_{0}\) and a constant consumption of ECC, \(G_{uw}=6.9\) kg s\({}^{-1}\). The efficiency of the second heat exchanger, \(\eta_{w}\), contingent on \(\eta_{0}\), and for the same range of \(\eta_{0}\), can be approximated by the expression  
\[\eta_{w}=0.2941\eta_{0}+0.667.\]  
The accuracy of cooling system calculations and potential errors primarily depend on the precision of heat exchanger calculations. This work employs widely accepted methods for calculating heat exchangers, and system calculations are carried out based on established mathematical and thermal engineering principles. The objectives of this work preclude the possibility of experimental verification for all the presented material. Nevertheless, the key results of experimental checks related to the accuracy of heat exchanger calculations and the validity of calculation methods for the cooling system can be provided. These checks were conducted to validate the calculations of the simplest cooling system, serving as the foundation for all subsequent calculations. Specifically, the elements of boundary conditions for heat exchangers were scrutinized, and the correctness of the chosen methods for cooling system calculations was verified.