## 3 Analysis of the Cooling Mechanism of Injection Mold  
### Analysis of Temperature Field of Injection Mold  
The injection molding process is a cyclic process, which means that the whole process of mold temperature field change also belongs to the cyclic change process. At the beginning of the cycle, the transient temperature of the mold cavity surface changes periodically according to the change in the production cycle. On the other hand, the average temperature of the mold cavity surface gradually rises, and the product quality at this stage is unstable. After completion of this stage, the stable working condition is satisfied so that the plastic parts can be produced at high quality. The transient temperature of the injection mold cavity surface maintains a cyclic state, but the average temperature is maintained at a constant value during each cycle. In the plastic-forming process, the entire mold can be regarded as a heat exchange system. Most of the heat is carried to the gate of the mold-forming machine and is transferred to the cooling system by the high-temperature melt ejected from the injection molding parts, where the cooling medium takes away the heat. The remaining heat is transported to the environment using heat radiation and heat convection through the outer surface of the mold. Then, 90-95% of the heat is carried away by the melt by the cooling medium in the cooling channel. Heat transfer between the plastic melt and the mold occurs on the surface between the mold cavity and the core. Since the temperature of the plastic melt is relatively high at the initial stage of injection and the surface temperature of the mold is room temperature at the initial stage of injection, heat transfer at this stage is mainly carried out through heat. The ratio of heat conduction and heat transfer is small, and the heat transfer effect good enough such that it can be ignored at this stage. Mold heat transfer is divided into three parts: (1) After the melt body contacts the surface of the cavity, part of the heat is brought to the mold through heat conduction. (2) The coolant absorbs most of the heat from the cooling channel inside the mold and then removes the heat through convection heat exchange. (3) Heat dissipation occurs through direct contact between the outer surface of the mold and the surrounding air, and heat is carried out through the process of convective heat transfer and radiation heat transfer. From the above analysis, according to the law of conservation of energy, the heat balance equation of the mold in stable working conditions is obtained as follows:  
\[\dot{Q}_{p}+\dot{Q}_{c}+\dot{Q}_{a}\equiv 0 \tag{1}\]  
where \(\dot{Q}_{p}\) is the heat transfer between injection molded products, \(\dot{Q}_{c}\) is the convective heat exchange between the mold and the cooling system, and \(\dot{Q}_{a}\) is the convective heat exchange between the mold and the surrounding environment. In Figure 2, when the molten polymer is injected into a mold, its heat is dissipated by the cooling medium flowing through the mold's channels and the environment surrounding the mold's surface. The heat exchange between the cooling medium and the mold occurs mainly through convection, while the heat exchange between the mold and the environment happens through a combination of convection and radiation from the mold's side surfaces. In addition, some heat is conducted into the injection molding machine. To simplify the energy balance equation, we only consider the heat transfer between the mold, the cooling medium, and the plastic product through thermal conduction and convection, and we approximate the radiative heat transfer from the mold's outer surface. This approximation is justified because the heat lost through radiation from the mold's outer surface is negligible compared to the total heat, accounting for less than 5%.