## 4 Conclusions  
The design of shell-and-tube LHTES is a complicated process encompassing a wide range of issues such as material selection, geometric design, and numerical and experimental study. So far, limited all-inclusive design methodology has been found in the literature to guide design engineers step by step from the material selection to a valid geometrical design and at the same time optimize the design with cost minimization. This study proposes a comprehensive design methodology that aims to overcome this issue.  
The methodology proposed comprises a material assessment step to examine the competencies of the PCM choices and a geometrical assessment step to produce the geometric parameters that minimize the storage unit's purchase cost with user-specified boundaries and constraints. The material assessment step adopts the multi-criteria decision-making tools to evaluate the database of PCMs based on their properties and collective competencies and suggests the best choices. The LHTES unit is evaluated by the \(\epsilon\)-NUTU method for quick and accurate performance approximation. The optimization step employs the Genetic Algorithm, which varies all open parameters with user-specified constraints, and compares the costs from each step with the parent step until the minimum cost is found.  
Two case studies have been presented to explain the applicability of the methodology. The first case uses real storage units produced and reported in the literature to validate the \(\epsilon\)-NTU method. In the second case study, design optimizations based on cost minimization are realized for the solar absorption chilling application. The minimized costs for different scenarios such as different PCMs and different geometric variables are presented. The total purchase cost of as low as USD 8396 per unit is reported for a 1.42 kW shell-and-tube LHTES unit.  
The methodology is a systematic and flexible procedure to generate a reliable preliminary design of the storage unit without occupying too many numerical resources such as the computational fluid dynamics tools. It can also be used for parametric studies when the engineers are in search of the parameters that influence the performance or the cost of the storage unit the most.  
Figure 6: Comparison of the 1.42 kW LHTES unit using different shell and tube materials.  
To make the design methodology more accurate, future research can consider natural convection for LHTES performance approximation. The methodology can also include other storage types and the interaction between the storage unit to the downstream energy system.  
Conceptualization, H.X., F.C., L.Y., B.A. and A.R.; methodology, H.X., L.Y., F.C., B.A. and A.G.; software, L.Y. and H.X.; validation, L.Y. and A.G.; writing--original draft preparation, H.X.; writing--review and editing, L.Y., L.F.C. and A.R.; supervision, L.F.C. and A.R.; project administration, L.F.C. and A.R.; funding acquisition, L.F.C. and A.R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by SJ-NTU Corporate Lab. This research was partially funded by the Ministerio de Ciencia Innovacion y Universidades de Espana (RTI2018-093849-B-C31--MCIU/AEI/FEDER, UE), and the Ministerio de Ciencia, Innovacion y Universidades--Agencia Estatal de Investigacion (AEI) (RED2018- 102431-T). This work is partially supported by ICREA under the ICREA Academia programme.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors