## 5 Heat Transfer Analysis of Internal Meshing Screw Mixer
### Effect of Structural Parameters on Heat Transfer  
Our investigation delves into the influence of eccentricity on heat transfer within the internal meshing screw mixing device. Device eccentricity, in this context, denotes the displacement between the center of the rotor section and the center of the stator section. We maintained a constant rotational speed at \(\omega\) = 60 rpm while systematically varying the eccentricity (\(e\)) to 3 mm, 4 mm, and 5 mm. Our focus was on comprehending how eccentricity impacts the heat transfer dynamics of the device during the time interval of \(t\) = 1-4 s.  
Figure 11a,b presented below depict the heat transfer comprehensive index curves for various eccentricities in both modes. Examining Figure 11a, focusing on Mode 1, it is evident that, as eccentricity increases, the comprehensive (\(CI\)) exhibits a consistent decrease. Moreover, the influence of increased eccentricity on heat transfer efficiency becomes progressively more pronounced over time. This phenomenon can be attributed to the combined effects of heat transfer surface area and distance. When the system's eccentricity is increased, the heat transfer distance likewise increases, resulting in a diminished heat flow rate. Consequently, the \(CI\) decreases with higher eccentricities. Notably, regardless of the specific eccentricity values, the \(CI\) consistently reaches its peak within the first second, demonstrating a certain periodicity. Furthermore, it is noteworthy that, as depicted in the preceding discussion concerning the impact of varying rotational speeds on system heat transfer, the \(CI\) curves in both Mode 1 and Mode 2 exhibit periodic patterns, particularly prominent in the case of \(\omega\) = 60 rpm. In Figure 11b, under Observation Mode 2, the overall trend of the heat transfer comprehensive index aligns with that observed in Mode 1. However, notable distinctions arise when comparing the \(CI\) curves for eccentricities of 3 mm, 4 mm, and 5 mm. It is evident that the \(CI\) curve for \(e\) = 3 mm is notably higher than the curves for \(e\) = 4 mm and 5 mm, with the discrepancy progressively widening. This behavior is attributed to the Mode 2 heat transfer process, where heat is transferred from the inner wall of the rotor to the outer wall of the stator. Specifically, when the eccentricity is set to 3 mm, the rotor section traverses the stator section over the shortest distance. Consequently, the minimum separation between the inner rotor wall and the outer stator wall is achieved, facilitating enhanced heat transfer communication and significantly boosting heat transfer efficiency in comparison to the other two eccentricities. Comparing the \(CI\) curves of Modes 1 and 2, it is evident that the curve for Mode 1 exhibits a steeper incline than the curve for Mode 2, particularly within the time range of \(t\) = 1-4 s. Furthermore, the heat transfer index value in Mode 1 is consistently larger than that in Mode 2, reinforcing the conclusion that the heat transfer efficiency of Mode 1 surpasses that of Mode 2. Investigating the influence of clearances on system heat transfer is essential. The term \"gap\" refers to the minimum distance between the rotor and stator sections. Excessive gap sizes can result in material leakage. Consequently, we set the gap (h) at values of 0.2 mm, 0.5 mm, and 0.8 mm to assess its effect on the heat transfer process within the system during the time frame \(t\) = 1-4 s. Upon examining the \(CI\) diagram presented in Figure 11c for Mode 1, it is evident that the curve associated with a 0.2 mm gap initially experiences a decline, followed by a subsequent increase during the \(t\) = 1 s interval. Correspondingly, the convection transfer index is at its peak at the commencement of the rotor section, diminishing when it reaches the central point of the stator section, and surging again as it approaches the lower section of the semicircle. This substantial curve fluctuation indicates that Mode 1 relies on convection heat transfer as its primary mechanism.