## 1 Introduction  
In the present day, there is a growing demand for processing polymer materials [1; 2; 3]. However, conventional screw mixers exhibit certain limitations in achieving optimal material mixing [4; 5; 6]. To address this challenge, recent advancements have seen the emergence of a piece of novel high-viscosity material-processing equipment known as the eccentric rotor extruder [7]. Whether it is a traditional screw extruder relying on shear rheology [8; 9] or a modern internal meshing screw mixer grounded in extensional rheology [10; 11], comprehensive research into the convective heat transfer within these devices is of paramount importance [12; 13]. In order to mix the obtained materials smoothly, it is necessary not only to improve the operating efficiency within the device, but also to improve the heat transfer efficiency between the device components [14; 15; 16]. As an illustrative instance, conventional screw extruders offer an insightful context for the examination of convective heat transfer efficiency [17; 18; 19]. The extrusion process in screw extruders necessitates the transfer of heat from a heater to the material via heat exchange within the extruder barrel, a fundamental step in achieving successful melt processing [20; 21; 22]. Furthermore, the airflow around the extrusion port during screw extrusion processes can significantly enhance the heat dissipation on the material surface, playing a pivotal role in convective heat transfer mechanisms [23; 24; 25]. These intricacies of heat transfer within screw extruders are integral to the broader field of polymer engineering and science, offering valuable insights into material-processing efficiency and product quality. This aspect has garnered attention both domestically and internationally, exemplified by notable contributions. For instance, [PERSON] [26] introduced a novel screw design aimed at optimizing the flow characteristics of liquid materials and mitigating temperature differentials. This inventive device incorporates variably pitched spiral edges to enhance energy transfer, resulting in a more uniform temperature distribution within the heated liquid. In a similar vein, [PERSON] [27] leveraged the principles of liquid heat transfer in polymer materials to delve into the intricate interplay between the screw structure and the process parameters, particularly concerning the cooling of liquid materials within the screw extruders. Moreover, [PERSON] [28] employed advanced fluid simulation software to refine specific components within the collaborative screw-metering section, exploring the profound influence of the structural and process parameters on the heat and mass transfer dynamics in the final product. These studies underscore the significance of optimizing the polymer-processing equipment and techniques to advance our understanding of heat transfer, with implications for enhanced material quality and processing efficiency in polymer engineering and science. [PERSON] [29] introduced an innovative approach for the prediction of the temperature distribution within a liquid in a twin-screw extruder. The findings underscore the minimal heat conduction through the screw in high-speed twin-screw extruders. By harnessing our knowledge of viscosity and heat transfer properties, it becomes feasible to calculate the melt temperature with a high degree of precision. Drawing upon insights from international research, it becomes evident that a comprehensive examination of the heat transfer mechanisms within internal meshing screw devices holds paramount significance [30; 31; 32]. Nonetheless, the investigation into heat transfer within volumetric-stretching-dominated internal meshing screw mixers remains an uncharted territory. An insightful approach would involve drawing from the research methodologies established in traditional screw extruder heat transfer studies and adapting them to explore the heat transfer efficiency of internal meshing screw mixers using numerical simulations and actual experimental verification methods.