## 2 Materials and Methods
### Design of Heat Seal Experimental Device
#### 2.3.3 Design of Heat Sealing Jaw  
The heat sealing jaw requires excellent thermal conductivity; therefore, to ensure effective heat transfer to the film to be sealed, the jaw is made from 6061 aluminum alloy [22; 23]. 6061 aluminum alloy is a commonly used material known for its excellent machinability and thermal conductivity, with 6061-T6 alloy having a density of \(\rho=2700\) kg/m\({}^{3}\), specific heat capacity \(C=900\) J/ (kg\(\cdot\)K), and thermal conductivity \(\lambda=896\) W/ (m\(\cdot\)oC), ensuring high uniformity in temperature distribution. The structural parameters of the heat sealing jaw are shown in Figure 7, with the bonding point designed as a 6 mm diameter circular protrusion. The distribution of bonding points is designed in a \"bell-mouth\" shape, narrower in the middle and wider at the outer opening. This \"bell-mouth\" arrangement facilitates the peeling of the seedling belt. Compared to a linear arrangement, during belt peeling, the peeling mechanism will only tear two bonding points at a time, requiring less force to separate the belt under the same heat seal strength conditions. The heat sealing jaw is heated by an electric heating tube, with the melting point of LDPE film being about 135 \({}^{\circ}\)C; thus, the maximum temperature of the jaw can reach up to 200 \({}^{\circ}\)C. To determine the power rating of the heating tube, one can calculate the sum of the energy required to heat the jaw to the target temperature and the heat losses during the heating process. The heating power of the electric tube can be calculated using Formula (4):  
\[\left\{ \begin{aligned} Q=m\cdot C(T_{2}-T_{1})\\ P_{h}=\frac{Q}{t}+P_{l}\end{aligned} \right. \tag{4}\]  
In this formula, \(Q\) is the energy required to heat the heat sealing jaw to the target temperature, in joules (J); \(m\) is the mass of the heat sealing jaw, in Kg; \(T_{1}\) and \(T_{2}\) are the initial and target temperatures, in \({}^{\circ}\)C; C is the specific heat capacity of 6061 aluminum alloy;  
Figure 6: Schematic diagram of working principle. \(P_{h}\) and \(P_{l}\) are the total power and power loss during heating, respectively, in W; \(t\) is the heating time, in s.  
During the heating process of the heat sealing jaw, heat is continuously lost to the environment as the temperature increases. According to thermodynamic principles, the main modes of heat loss are convection and radiation. Based on Newton's Law of Cooling and the Stefan-Boltzmann Law, the heat losses due to convection and radiation are calculated separately. The sum of these losses constitutes the total heat loss during the heating process. The calculation formula is as follows:  
\[\left\{ \begin{matrix}\dot{Q}_{c}=h\cdot A\left(\frac{T_{1}+T_{2}-2T_{E}}{2} \right)\\ \dot{Q}_{r}=e\sigma\cdot A\left[\left(T_{1}+T_{2}+546.3\right)^{4}-\ \left(T_{E}+546.3\right)^{4}\right]\\ P_{l}=\dot{Q}_{c}+\dot{Q}_{r}\end{matrix} \right. \tag{5}\]  
In this formula, \(\dot{Q}_{c}\) and \(\dot{Q}_{r}\) represent the heat losses due to convection and radiation, respectively, in watts (W); \(T_{1}\) and \(T_{2}\) are the initial and target temperatures, respectively, in \({}^{\circ}\)C; \(T_{E}\) is the ambient temperature in \({}^{\circ}\)C; \(h\) is the heat convection coefficient; \(A\) is the surface area of the heat sealing jaw, in m\({}^{2}\); \(e\) is the emissivity of the object's surface, a dimensionless constant; \(\sigma\) is the Stefan-Boltzmann constant, \(\sigma=5.67\times 10^{-8}\) W/m\({}^{2}\)K\({}^{4}\). In the actual heat sealing process, the ambient temperature is 25 \({}^{\circ}\)C, and the initial temperature of the heat sealing jaw is consistent with the ambient temperature. The emissivity of the object's surface depends on the material, surface roughness, and treatment method; this paper assumes \(\epsilon=0.1\).