## 5 Heat Transfer Analysis of Internal Meshing Screw Mixer
### Heat Transfer Mechanism in Two Models  
In the course of conventional screw extruder operations, as the material undergoes heating within the extruder barrel, the transmission of heat from the heating element to the material is indispensable for achieving the melt-processing phase [41]. This heat transfer process encompasses a combination of diffusion, convection, and radiation [42; 43; 44]. Within the screw extruder, heat primarily propagates to the material via diffusion and convection mechanisms. More specifically, heat generated by the heating element initially diffuses to the screw and barrel, and, subsequently, propelled by the rotation and pressure exerted by the screw, the heated material undergoes convection between the screw and barrel, thereby facilitating the transfer of heat. One can draw upon the heat transfer research methodologies established for traditional screw extruders and employ them in the investigation of convective heat transfer efficiency within the realm of internal meshing screw mixers. Heat transfer mechanisms within the internal meshing screw mixer can be categorized into two primary modes. Mode 1 entails the transfer of high temperatures from the outer wall of the stator to the interior, while Mode 2 involves the conveyance of elevated temperatures from the inner rotor wall to the external surroundings. An in-depth analysis of the heat transfer mechanisms within the internal meshing screw mixing conveyor section, operating under these two modes, is conducted through the comparison of temperature cloud diagrams at various time intervals and a thorough exploration of the dynamic trends in heat transfer efficiency, taking into account varying process and structural parameters. As depicted in the Figure 8, the temperature trend cloud diagram showcases the movement of the rotor to the midpoint of the stator in each cycle of the internal meshing screw mixing and conveying section within the time frame of \(t=1\)-\(4\) s. Figure 8a clearly illustrates the transfer of heat to the fluid domain through the stator wall. At \(t=0.25\) s (corresponding to the first cycle as the rotor moves from its initial position to the midpoint of the stator), a thin layer of thermally activated fluid becomes evident within the stator wall. Within this region, there is a pronounced temperature gradient. By \(t=1.25\) s, the heated fluid residing on the stator's heat transfer wall has traversed to the rotor wall and further dispersed, giving rise to a heat fluid wake where temperature gradients are notably high. At \(t=3.25\) s, the stator's heat transfer wall still exhibits a trail of thermally activated fluid streaming toward the rotor wall, while the thermal fluid on the stator wall continues its diffusion toward the rotor wall. As time progresses, both the fluid temperature and the temperature gradient expand. Hence, based on the evolving fluid temperature trends and the flow direction of heated fluid as observed in the temperature cloud diagram, it can be deduced that Mode 1 primarily involves convective heat transfer. Figure 8b illustrates the heat transfer mechanism through the rotor wall to the fluid domain. At \(t=0.25\) s, a layer of thermally activated fluid is also observed on the rotor wall's surface, with the thermal fluid's presence on the upper wall of the rotor being more pronounced compared to the lower wall. This disparity arises from the rotor's recent movement from its initial position to the midpoint of the stator, facilitating greater heat dispersion on the rotor wall during its motion. By \(t=1.25\) s, the heated fluid on the rotor wall continues to diffuse outward, displaying a divergent trend. At \(t=3.25\) s, the diffusion pattern of thermal fluid remains relatively consistent with the earlier observations; however, the rate of temperature change becomes less pronounced, signifying that heat transfer in Mode 2 predominantly occurs through diffusion.