## Materials and Methods
### Model Description
#### 2.1.1 External Node  
According to the thermal network shown in Figure 1, energy balance at the external node can be expressed as:  
\[m_{t}c_{pa}\frac{dT_{pa}}{dt}=(1-\alpha_{pa})\cdot G_{up}\cdot A-h_{rc,pu-ac} \Big{(}T_{pa}-T_{ac}\Big{)}A-Q_{ev}\cdot A-K_{pa}\Big{(}T_{pa}-T_{bottom}\Big{)}A \tag{1}\]  
where \(m_{t}\) (kg) is the instantaneous mass of the paddy, \(\alpha_{pa}\) (-) is the albedo of paddy rice, \(G_{up}\) (W m\({}^{-2}\)) is the total solar radiation, \(A\) (m\({}^{-2}\)) is the area of the crop exposed to the sun, \(h_{rc,pa-ac}\) (W m\({}^{-2}\) K\({}^{-1}\)) is the combined radiative and convective heat transfer coefficient from the paddy rice surface to the air, \(T_{ac}\) (\({}^{\circ}\)C) is the temperature of the air exiting the paddy rice surface--henceforth called exit temperature--\(T_{pa}\) (\({}^{\circ}\)C) is the temperature of the paddy rice, and \(Q_{ev}\) (k) m\({}^{-2}\) s\({}^{-1}\)) is the rate of heat utilized to evaporate moisture. \(Q_{ev}\) is calculated as [38]:  
\[Q_{ev}=0.016\cdot h_{c,pa-ac}\cdot\Big{[}\mathrm{P}_{T_{pa}}-rh_{lam}\cdot \mathrm{P}_{T_{ac}}\Big{]} \tag{2}\]  
where \(h_{c,pa-ac}\) (W m\({}^{-2}\) K\({}^{-1}\)) is the convective heat transfer coefficient from the paddy rice surface to the air, \(rh_{lam}\) (-) is the ambient relative humidity, and \(P_{Tpa}\) and \(P_{Tae}\) (N m\({}^{-2}\)) are the saturated vapor pressure at the respective temperatures. The values of \(\mathrm{P}_{T}\) were extracted from the temperature range from 25 to 55 \({}^{\circ}\)C [39], which corresponds to the operating condition of the sun drying experiments. A 1D lookup table block built in Simulink was used to retrieve the saturated vapor pressure at the respective temperatures [40].  
The energy balance of moist air above the paddy rice is calculated as:  
\[h_{r,pa-ac}\Big{(}T_{pa}-T_{ac}\Big{)}A+Q_{ev}\cdot A=h_{w}\cdot(T_{ac}-T_{am} )\cdot A \tag{3}\]  
where \(T_{am}\) (\({}^{\circ}\)C) is the ambient temperature and \(h_{w}\) (W m\({}^{-2}\) K\({}^{1}\)) is the convective heat transfer coefficient for wind. \(h_{w}\) is computed according to [PERSON] and Beckmann [41]:  
\[h_{w}=5.7+3.8\cdot V_{w} \tag{4}\]  
Figure 1: Thermal network of a one-dimensional model for the sun drying of paddy rice with layer thickness z and temperatures of ambient air, \(T_{am}\), air exiting from the surface, \(T_{ae}\), paddy rice, \(T_{pu}\), polyvinyl chloride (PVC) tarpaulin, \(T_{ta}\), asphalt, \(T_{as}\), and soil, \(T_{so}\).  
where \(V_{w}\) (m s\({}^{-1}\)) is the wind velocity.  
The radiative heat transfer coefficient \(h_{r,pa-ae}\) is written as:  
\[h_{r,pa-ae}=\varepsilon\cdot\sigma\Big{(}T_{pa}^{2}+T_{ae}^{2}\ \Big{)}\Big{(}T_{pa}+T_{ae} \Big{)} \tag{5}\]  
where the emissivity \(\varepsilon\) of a solid body is equal to the absorbance (1-\(\alpha\)) measured at the same wavelengths according to [PERSON]'s law [32; 42] and \(\sigma\) is the Boltzmann constant (5.6696 \(\times\) 10\({}^{-8}\) W m\({}^{-2}\) K\({}^{-4}\)).  
The calculation of the mass of paddy rice \(m_{t}\) during drying is done by subtracting the evaporated water from the initial mass \(m_{0}\). The evaporated mass of water \(m_{ev}\) is obtained as:  
\[m_{ev}=\frac{Q_{ev}}{L_{T_{pa}}}\cdot A\cdot t \tag{6}\]  
where \(t\) (h) is the time of the sampling interval and \(L\) (kJ kg\({}^{-1}\)) is the latent heat of vaporization, which is calculated as [43]:  
\[L=2502.535-2.386\cdot T_{pa} \tag{7}\]