## 2 Materials and Methods
### Theoretical Principle Used for Energy and Exergy Analyses
#### 2.4.1 Energy Analysis  
The energy balance equation on account of the first law of thermodynamics was express as Equation (1) [35]:  
\[\sum\dot{E}_{in}=\sum\dot{E}_{out} \tag{1}\]  
The energy flow in the present hot air-drying system for corn is shown in Figure 4. According to the Equation (1) and Figure 4, the following equation was obtained:  
\[\dot{Q}+\dot{P}=\dot{W}+E_{nexp}+\sum\dot{E}_{loss} \tag{2}\]  
where \(\dot{Q}\) is the energy provided by the fuel, \(\dot{P}\) is the electrical energy provided by the power source, and \(\dot{W}\) is the work done by the hoist. For the whole drying system, the total energy consuming element consists of \(\dot{Q}\), the hoist \((\dot{P}_{h})\), the discharging motor \((\dot{P}_{dm})\), the induced fan \((\dot{P}_{if})\) and the additional parts \((\dot{P}_{ap})\), as shown in Figures 3 and 4. The power values of the primary equipment using in the current drying system are listed in Table 2. The energy used for dehydration of corn \((\dot{E}_{nexp})\) and the electrical energy for lifting the corn \((\dot{W}_{h})\) are considered as the effective energy, which respectively calculated by Equations (3) and (4) [35]:  
\[\dot{E}_{nexp}=\dot{m}_{exp}h_{fg} \tag{3}\]  
\[\dot{W}_{h}=\frac{\dot{m}_{h,c}v^{2}}{2}+\dot{m}_{h,c}g_{v} \tag{4}\]  
Figure 4: Energy flow in hot air-drying system for corn. The average dehydrated moisture (\(m_{exp}\)) from corn in any period (\(\Delta t\)) is calculated using Equation (5):  
\[\dot{m}_{exp}=\frac{m_{d}}{(1-M\mathcal{C}_{t})}-\frac{m_{d}}{(1-M\mathcal{C}_{t+ \Delta t})} \tag{5}\]  
The latent heat of vaporization \(h_{fg}\) (J\(\cdot\)kg\({}^{-1}\)) is calculated using Equations (6) and (7) [20]:  
\[h_{fg}=2.503\times 10^{6}-2.386\times 10^{3}(T_{g}-273.16)^{0.5}\;273.16\leq T _{g}\leq 338.72 \tag{6}\]  
\[h_{fg}=(7.33\times 10^{12}-1.6\times 10^{7}T_{g}^{2})^{0.5}\;338.72\leq T_{g} \leq 553.16 \tag{7}\]  
In totally, the energy efficiency of the whole drying system can be obtained according to Equation (8)  
Figure 4.0  
For the DC, the overall energy consuming element consist of the inlet air (\(\dot{E}_{nai}\)), the \(\dot{P}_{if}\) and the infrared recover radiator (\(\dot{E}_{nfir}\)). The effective energy is \(\dot{E}_{nexp}\). The energy efficiency of the DC was obtained according to Equation (9):  
Figure 4.1  
From the Wien displacement law, the \(\dot{E}_{nfir}\) can be calculated using Equation (10) [36]:  
Figure 4.2  
\(\dot{E}_{nai}\) is calculated using Equation (11) [28]:  
Figure 4.3  
The mass flow rate of the inlet dry air (\(\dot{m}_{ai}\)) can be obtained according to Equation (12) [4]:  
Figure 4.4  
where \(\rho_{da}\) is the density of the dry air (kg/m\({}^{3}\)), \(V\) and \(S\) are, respectively the velocity of the inlet air (m/s) and the cross-sectional area of the inlet pipeline (m\({}^{2}\)). The enthalpies of the inlet and the outlet drying air (\(h_{a}\)) is calculated using Equation (13) [4]:  
Figure 4.5 \begin{table}
\begin{tabular}{c c} \hline \hline
**Equipment** & **Power** \\ \hline Hoist & 5.5 kW \\ Discharging motor & 3.75 kW \\ Induced fan & 37 kW \\ Additional parts & 1.5 kW \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power parameters of the primary equipment. For the DC, the total heat loss is chiefly consisted of the heat loss in outlet air \((\dot{E}_{nuo})\), the heat loss in outlet corn kernels \((\dot{E}_{n\alpha})\) and the heat loss in chamber wall \((\dot{E}_{mull})\), which can be calculated using Equation (14)-Equation (16) [28]:  
\[\dot{E}_{na\alpha}=\dot{m}_{\alpha a}(h_{\alpha 0}-h_{\alpha\circ}) \tag{14}\]  
\[\dot{E}_{n\alpha}=C_{c}\dot{m}_{p}(T_{po}-T_{\infty}) \tag{15}\]  
\[\dot{E}_{mull}=1.3A_{s}\frac{T_{wall}-T_{\infty}}{\frac{1}{\gamma}+\frac{1}{1. 163(6+0.5\kappa_{\circ})}} \tag{16}\]