## Theory and Model Derivation  
### Effective Drying Accumulated Temperature Theory  
Previous studies have fully proven that the temperature, especially the accumulated temperature, plays a vital role in ensuring seed germination [24; 25; 26], ensuring vegetation growth and distribution [27], increasing crop yield [28], and reducing insect pests [29]. Agronomists and meteorologists began to use an integral method to calculate the accumulated temperature in the 1950s. The temperature changes with time were plotted, and the following formulae were respectively proposed to calculate the active accumulated temperature and effective accumulated temperature [30]:  
\[A_{n}\ =\ \int_{t_{0}}^{t_{n}}T(t)dt\quad T(t)\geq T_{0};\ \text{if}\ T(t)<T_{0},T(t)\ =\ 0, \tag{1}\]  
\[A_{e}\ =\ \int_{t_{0}}^{t_{n}}[T(t)-T_{0}]dt\quad T(t)\geq T_{0};\ \text{if}\ T(t)<T_{0},T(t)-T_{0}\ =\ 0, \tag{2}\]  
where \(A_{n}\) is the active accumulated temperature (\({}^{\circ}\)C-d), \(A_{e}\) is the effective accumulated temperature (\({}^{\circ}\)C-d), \(t_{0}\) is the initial time, \(t_{n}\) is the final time, and \(T_{0}\) is the biological zero degree (\({}^{\circ}\)C). The biological zero degree is defined as the lower temperature limit for plant growth and development under suitable conditions. Correspondingly, there is an equilibrium temperature in the grain drying process; that is, drying will begin only when the temperature is higher than the equilibrium temperature without considering other environmental factors. In this paper, the effective drying accumulated temperature of the grain (hereinafter referred to as drying accumulated temperature) is defined as the sum of the temperatures higher than the equilibrium temperature of the grain in the drying process, expressed as follows:  
\[AT\ =\ \int_{0}^{t_{n}}[T-T_{e}]dt, \tag{3}\]  
where \(AT\) is the accumulated effective drying temperature of the grain (\({}^{\circ}\)C-h), \(T\) is the temperature of the grain at time \(t\) (\({}^{\circ}\)C), \(T_{e}\) is the desorption equilibrium temperature of grain at time \(t\) (\({}^{\circ}\)C), and \(t_{n}\) is the drying time (h). \(T_{e}\) can be derived from the modified Chung-Pfost equation (MCPE) [31; 32]:  
\[RH\ =\ \exp\biggl{[}-\frac{C_{1}}{T_{e}+C_{2}}\exp(-C_{3}\times M_{e}) \biggr{]}. \tag{4}\]  
The equilibrium temperature is expressed as follows:  
\[T_{e}\ =\ -\frac{C_{1}}{\ln(RH)}\exp(-C_{3}\times M_{e})-C_{2}. \tag{5}\]  
In these equations, \(RH\) is the relative humidity (decimal), \(M_{e}\) is the equilibrium moisture content (\(\%\), dry basis), and \(C_{1}\), \(C_{2}\), and \(C_{3}\) are constants that depend on the crop variety. The research object of this paper was rice, and the corresponding constants are as follows: \(C_{1}=529.276\), \(C_{2}=52.725\), and \(C_{3}=0.177\)[32]. The formula of the equilibrium moisture content of the grain is as follows:  
\[M_{e}\ =\ -\frac{1}{N_{3}}\times\ln\biggl{[}-\frac{(T_{r}+N_{2})\times\ln( RH)}{N_{1}}\biggr{]}, \tag{6}\]where \(T_{r}\) is the relative temperature (\({}^{\circ}\)C), and \(N_{1}\), \(N_{2}\), and \(N_{3}\) are constants that depend on the crop variety. The constants for rice are as follows: \(N_{1}=588.376\), \(N_{2}=59.026\), and \(N_{3}=0.18\)[32]. The equilibrium temperature as a function of the moisture content and environmental relative humidity can obtained using Equation (5), and the obtained equilibrium temperatures are plotted in Figure 1. The higher the moisture content of the rice is, the lower the desorption equilibrium temperature of the rice is. The higher the environmental relative humidity is, the higher the desorption equilibrium temperature of the rice is. For a fixed moisture content of the rice, the desorption temperature increases significantly with the increase in the relative humidity of the environment. For a fixed environmental relative humidity, the moisture content of rice is negatively correlated with the desorption equilibrium temperature.