## 2 Calculation Model and Method
### Thermal-Hydraulics Model
#### 2.3.3 Heat Exchanger Model  
The primary coolant flows out of the core and enters the heat exchanger through the ascending channel. The primary coolant then flows down to the lower plenum after its heat is transferred to the organic diathermic fluid on the secondary side. The schematic diagram of the primary circuit is shown in Figure 6.  
The heat transfer models of primary coolant, tube wall and secondary coolant are as follows:  
\[V_{p}\rho_{p}C_{p}\frac{dT_{p}}{dt}=G_{p}C_{p}(T_{p,in}-T_{p,out})-h_{p,up}A_{p }(T_{p}-T_{w}) \tag{12}\]  
\[V_{w}\rho_{w}C_{w}\frac{dT_{w}}{dt}=h_{p,up}A_{p}(T_{p}-T_{w})-h_{s,up}A_{s}(T _{w}-T_{s}) \tag{13}\]  
\[V_{s}\rho_{s}C_{s}\frac{dT_{s}}{dt}=h_{s,up}A_{s}(T_{w}-T_{s})-G_{s}C_{s}(T_{s, out}-T_{s,in}) \tag{14}\]  
where \(h_{p,w}\) is the heat transfer coefficient between primary coolant and tube wall, \(h_{s,up}\) denotes the heat transfer coefficient between tube wall and secondary coolant.  
\begin{table}
\begin{tabular}{l l} \hline
**Thermophysical Parameters** & **Correlation** \\ \hline Fuel density (kg\(\cdot\)m\({}^{-3}\)) & \(11080[1+2.04\times 10^{-5}(T-273)+8.7\times 10^{-9}(T-273)^{2}]^{-1}\) \\ Fuel thermal conductivity (W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) & \((0.042+2.71\times 10^{-4}T)^{-1}+6.9\times 10^{-11}T^{3}\) \\ UO\({}_{2}\) specific heat (J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)) & \(81.825+0.78695T-1.1552\times 10^{-3}T^{2}+9.9037\times 10^{-7}T^{3}-5.1982\times 10^{-10}T^{4}+1.5241\times 10^{-13}T^{5}-1.7906\times 10^{-10}T^{6}\) \\ PuO\({}_{2}\) specific heat (J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)) & \(-4.9236\times 10^{6}T^{-2}+240.89+0.32556T-3.5398\times 10^{-4}T^{2}+1.512\times 10^{-7}T^{3}-1.9707 \times 10^{-11}T^{4}\) \\ Fuel specific heat (J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)) & \(0.7944\mathcal{C}_{\text{UO}_{2}}+0.2056\mathcal{C}_{\text{PuO}_{2}}\) \\ Cladding density (kg\(\cdot\)m\({}^{-3}\)) & \(7785[1-3(-3.0942\times 10^{-3}+1.1928\times 10^{-5}T-6.7979\times 10^{-9}T^{2}+ 7.9606\times 10^{-12}T^{3}-2.546\times 10^{-15}T^{4})]\) \\ Cladding thermal conductivity (W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) & \(21.712+0.011T-9.5483\times 10^{-6}T^{2}+3.627\times 10^{-9}T^{3}\) \\ Cladding specific heat (J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)) & \(432.8+0.7038T-2.2113\times 10^{-3}T^{2}+5.316\times 10^{-6}T^{3}-3.105\times 10^{-9}T^{4}\) \\ Coolant density (kg\(\cdot\)m\({}^{-3}\)) & \(11112-1.375T\) \\ Coolant thermal conductivity (W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) & \(3.35+1.59\times 10^{-2}T-1.95\times 10^{-6}T^{2}\) \\ Coolant specific heat (J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)) & \(164-4.06\times 10^{-2}T+1.33\times 10^{-5}T^{2}\) \\ \hline \end{tabular}
\end{table}
Table 1: Thermophysical Properties of Fuel, Cladding, and Coolant.  
Figure 6: Schematic diagram of primary circuit.  
The ARTAP code has been verified by comparing its predictions for both steady-state and transient cases of the OECD/NEA benchmark [12]. The benchmark summarizes a comparative analysis of ten different codes. Three cited codes for the comparison are: TRAC-MOD, SAS4 ADS and EXCURS-M, as they represent the range of data scatter in the published results of the benchmark report. The results indicate that ARTAP is accurate and efficient when applied for the safety analysis of the LBE-cooled ADS and CNES [26].