## 2 Mathematical Model of the Hydrocooler
### Mathematical Model of Refrigeration System
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Parameters** & **Property** & **Values** \\ \hline \(A_{cap}\) & Area of contact surface between circulating water pipe and air & 1.1 m\({}^{2}\) (Calculated) \\ \(A_{spb}\) & Area of contact surface between spray precooling box and air & 4 m\({}^{2}\) (Assumed) \\ \(A_{st}\) & Area of contact surface between thermal storage tank and air & 10 m\({}^{2}\) (Assumed) \\ \(c_{int}\) & Specific heat of litchi & 3.704 \(\times\) 10\({}^{3}\) J kg\({}^{-1}\) K\({}^{-1}\)[35] \\ \(c_{sur}\) & Specific heat of water & 4.2 \(\times\) 10\({}^{3}\) J kg\({}^{-1}\) K\({}^{-1}\)[36] \\ \(c_{ice}\) & Latent heat of water freezing & 3.35 \(\times\) 10\({}^{5}\) J kg\({}^{-1}\)[36] \\ \(h_{icic}\) & Thermal conductivity coefficient between the ice and coil & 2300 W m\({}^{-2}\) K\({}^{-1}\)[36] \\ \(h_{icic}\) & Boiling coefficient of heat transfer on the refrigerant in the coil & 4000 W m\({}^{-2}\) K\({}^{-1}\)[36] \\ \(h_{isi}\) & Convective heat transfer coefficient between ice and water & 4000 W m\({}^{-2}\) K\({}^{-1}\)[36] \\ \(h_{isiu}\) & Convection heat transfer coefficient of water and thermal storage tank & 100 W m\({}^{-2}\) K\({}^{-1}\)[36] \\ \(h_{pqu}\) & Convection heat transfer coefficient of spray precooling box and air & 20 W m\({}^{-2}\) K\({}^{-1}\) (Measured) \\ \(h_{sta}\) & Convection heat transfer coefficient of thermal storage tank and air & 6 W m\({}^{-2}\) K\({}^{-1}\) (Measured) \\ \(m_{lin}\) & The mass of litchi precooling & 1000 kg (Assumed) \\ \(m_{start}\) & The mass of water in thermal storage tank & 1200 kg (Assumed) \\ \(P_{bal}\) & Cooling loss rate caused by opening the door & 300 W (Assumed) \\ \(P_{ribb}\) & Power of heat bridge heat transfer & 200 W (Assumed) \\ \(P_{app}\) & Water pump power in precooling & 280 W (Calculated) \\ \(q_{am}\) & Heat load per unit area of the condenser & 260 W m\({}^{-2}\)[34] \\ \(q_{eu}\) & Heat load per unit area of the evaporator & 3500 W m\({}^{-2}\)[34] \\ \(\tau_{ori}\) & Radius of evaporation coil & 0.008 m (Assumed) \\ \(r_{ic}\) & Radius of circulating water pipe & 0.032 m (Assumed) \\ \(r_{ic}\) & Inner radius of evaporation coil & 0.007 m (Follow determination) \\ \(r_{icic}\) & Radius of circulating water pipe insulation layer & 0.072 m (Follow determination) \\ \(t_{dr}\) & Charging time of thermal storage & 12 h (Assumed) \\ \(t_{trp}\) & Time from the end of charging to the end of precooling & 12 h (Assumed) \\ \(t_{eqp}\) & Operation time of water pump & 8 h (Assumed) \\ \(T_{amb}\) & The ambient temperature & 30 \({}^{\circ}\)C (Measured) \\ \(T_{dt}\) & The initial temperature of litchi precooling & 29 \({}^{\circ}\)C (Measured) \\ \(T_{raw}\) & The initial temperature of water & 31 \({}^{\circ}\)C (Measured) \\ \(T_{soil}\) & Outer surface temperature of ice & 0 \({}^{\circ}\)C (Assumed) \\ \(T_{ttl}\) & The termination temperature of litchi precooling & 8 \({}^{\circ}\)C (Assumed) \\ \(T_{ttu}\) & The termination precooling temperature of water & 7 \({}^{\circ}\)C (Assumed) \\ \(T_{nut}\) & The water temperature of thermal storage tank & 15 \({}^{\circ}\)C charging (Assumed) \\ \(\alpha\) & The power coefficient of water pump & 0.57 (Measured) \\ \(\delta_{hs}\) & Insulation layer thickness of spray hydrocooling box & 0.01 m (Assumed) \\ \(\delta_{it}\) & Insulation layer thickness of thermal storage tank & 0.05 m (Assumed) \\ \(\lambda_{coil}\) & Coil’s thermal conductivity & 377 W m\({}^{-1}\) K\({}^{-1}\)[36] \\ \(\lambda_{ice}\) & Ice layer’s thermal conductivity & 2.22 W m\({}^{-1}\) K\({}^{-1}\)[36] \\ \(\lambda_{ic}\) & Insulation layer’s thermal conductivity & 0.038 W m\({}^{-1}\) K\({}^{-1}\)[36] \\ \(\lambda_{sls}\) & Insulation layer’s thermal conductivity & 0.038 W m\({}^{-1}\) K\({}^{-1}\)[36] \\ \(\lambda_{lat}\) & Density of ice & 920 kg m\({}^{-3}\)[36] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of equation parameters.