## 4 Conclusions  
1. The dynamic model could predict all sizes for the two-stage chiller using an activated carbon/methanol pair, and easily could be adapted for any working pairs at variable operating conditions. 2. The two-stage chiller could be operated by using low-grade waste heat at low COP or at a high temperature heat source with moderate to high COP. 3. The proposed model could predict the COP for any chiller size with 90-95% of a Carnot cycle chiller working the same as an operating chiller at temperatures as low as 60 \({}^{\circ}\)C with heat recovery between beds. 4. The model is a useful tool to predict the effect of the changing of mass of activated carbon mass and the heat transfer coefficient of beds, evaporator and condenser. 5. The model is a useful tool to predict the effect of the flow rate of cooling and heating water in addition to the effect of chiller and condenser flow rates on chiller cooling capacity and COP. 6. The model is a useful tool to predict the effect of inlet temperature of cooling and heating water on chiller cooling capacity and COP. 7. The two-stage air-cooled adsorption chiller has a significant market potential, and the model used in this study could be used as a base for prototype scaling or series production. Figure 14: Average cooling capacity for double-sized chiller (results are at chiller nominal operating conditions, shown in Appendix B). **Subscript**  
ac **activated carbon**  
ad **adsorption**  
Al **Aluminum**  
b **bed**  
ci **cooling inlet**  
co **cooling outlet**  
c\({}_{w}\) **cold water**  
ch\({}_{w}\) **chilled water**  
con\({}_{w}\) **condenser water**  
con **condenser**  
des **desorption**  
eva **evaporator**  
fg **vaporization**  
g **gas**  
h\({}_{w}\) **hot water**  
i **inlet**  
o **outlet**  
rec\({}_{w}\) **recalculated water**  
s **solid**  
sat **saturation**  
st **storage**  
**Author Contributions:** Data curation, F.M.M. and A.A.A.-M.; Investigation, A.A.B. and A.A.; Methodology, F.M.M. and A.A.B. ; Resources, A.A.; Supervision, H.A. ; Writing--original draft, A.A.B. ; Writing--review & editing, H.A. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Table A1. **_Cont._ \begin{tabular}{c c c} \hline
**Symbol** & **Value** & **Unit** \\ \hline h\({}_{\rm fg}\) & 1200 & kJ\(\cdot\)kg\({}^{-1}\) \\ M\({}_{\rm ac}\) & 40 & kg \\ M\({}_{\rm eva,m}\) & 20 at time = 0 & kg \\ M\({}_{\rm con,m}\) & 5 & kg \\ (E/R) Methanol & 978 & K \\ (15 D\({}_{\rm so}\)/R) Methanol & 7.35 \(\times\) 10\({}^{-2}\) & S\({}^{-1}\) \\ \(x_{\rm o}\) & 0.284 & kg\(\cdot\)kg\({}^{-1}\) \\ n & 1.39 & Non Dimensional \\ K & 10.21 & Non Dimensional \\ R\({}_{1}\) & 260 & Non Dimensional \\ Q & 4.666 & Non Dimensional \\ A & 20.84 & Non Dimensional \\ B & 4696 & Non Dimensional \\ \hline \end{tabular}   
**Appendix C**  
\begin{tabular}{c c c} \hline
**Symbol** & **Value** & **Unit** \\ \hline T\({}_{\rm hi}\) & 95 & \({}^{\circ}\)C \\ T\({}_{\rm ci}\) & 30 & \({}^{\circ}\)C \\ T\({}_{\rm coni}\) & 30 & \({}^{\circ}\)C \\  
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