## 3 Numerical Modeling of HDS
### Separated Heat Pipe  
A separate heat pipe consists of an evaporator, a condenser, a rising pipe and a falling pipe. The working fluid in the separate heat pipe is R134a [32]. The flow on the refrigerant side and the air side is evenly distributed, assuming a one-dimensional flow in the refrigerant heat exchanger. The evaporator and condenser in this system are finned tube type, and the structural parameters are shown in Table 3. The power of the working fluid cycle in the heat pipe can be calculated by Equation (17).  
\[S_{dy}=\big{(}\rho_{l}-\rho_{ctp}\big{)}gH_{e}+(\rho_{l}-\rho_{v})gH_{t}+\big{(} \rho_{ctp}-\rho_{v}\big{)}gH_{c} \tag{17}\]  
where \(\rho_{l}\) is the density of saturated liquid working fluid, \(\rho_{ctp}\) is the gas-liquid two-phase density in the evaporator, \(\rho_{ctp}\) the gas-liquid two-phase density in the condenser, \(\rho_{v}\) is the density of the saturated gaseous working fluid, \(g\) is the acceleration of gravity, and \(H_{e}\), \(H_{c}\) and \(H_{t}\) are the height of the evaporator, the height of the condenser and the height difference between the two, respectively.  
The density of the two-phase zone can be calculated by Equation (18).  
\[\rho_{tp}=(\frac{x_{tp}}{\rho_{v}}+\frac{1-x_{tp}}{\rho_{l}})^{-1} \tag{18}\]  
where \(x_{tp}\) is the dryness of the two-phase zone.  
The pressure drop of the refrigerant can be calculated by Equation (19).  
\[\Delta P=\Delta P_{e}+\Delta P_{c}+\Delta P_{s}+\Delta P_{x} \tag{19}\]  
where \(\Delta P_{e}\) and \(\Delta P_{c}\) are the pressure drop of the refrigerant in the evaporator and condenser, respectively, and can be calculated by the formula of [PERSON] [33]. \(\Delta P_{s}\) and \(\Delta P_{x}\) are the pressure drop of the refrigerant in the rising and falling pipes, respectively, and can be calculated by the formula of [PERSON] [34].  
The heat transfer between air and refrigerant can be calculated by Equation (20).  
\[Q=C_{pa}m_{a}(t_{a,i}-t_{a,o})=m_{r}(h_{r,i}-t_{r,o})=KA\Delta t \tag{20}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(A\) (m\({}^{2}\)) & 4.5 \(\times\) 10\({}^{-6}\) & C\({}_{pa}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 1009 \\ \(s\) (m) & 0.0106 & C\({}_{pp}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 2028.1 \\ \(f_{d}\) (kg m\({}^{-1}\)) & 0.005 & C\({}_{pd}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 921 \\ \(f_{m}\) (kg m\({}^{-1}\)) & 0.003 & C\({}_{pl}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 4179 \\ \(Sh\) & 2.45 & C\({}_{pm}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 900 \\ \(Nu\) & 2.45 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters used in the numerical calculation of the desiccant wheel.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Evaporator** & **Condenser** \\ \hline Outer diameter of tube & 9.7 mm & 6.5 mm \\ Tube wall thickness & 0.35 mm & 0.32 mm \\ Fin distance & 1.58 mm & 1.4 mm \\ Fin thickness & 0.12 mm & 0.115 mm \\ Tube distance & 25.4 mm & 20 mm \\ Arrangement of the tubes & Regular triangle & Regular triangle \\ Number of tube rows & 4 & 2 \\ Number of tubes per row & 12 & 10 \\ Heat transfer area & 6.14 m\({}^{2}\) & 2.87 m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Structural parameters of separated heat pipe.  
The heat transfer coefficient of the inner tube of the evaporator is calculated by the formula of [PERSON] [35], and the heat transfer coefficient in the condenser is shown in the literature [36].