# Selection of a PCM for a Vehicle's Rooftop by Multicriteria Decision Methods and Simulation
## 2 Materials and Methods
### Method VIKOR  
Following the method used by [PERSON] and [PERSON] [27], the VIKOR method solves selection problems looking for a ranking where the alternative and criteria that will be used is the solution closest to the ideal [28]. This method requires that the criteria described before have the following considerations:  
* T1 Higher = Better;  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Compound (M)** & \multicolumn{2}{c}{**Phase-Change Change (kg/m\({}^{3}\))**} & \begin{tabular}{c} **Heat of** \\ **Fusion** \\ **(kj/kg)** \\ \end{tabular} & \
\begin{tabular}{c} **Specific Heat** \\ **Capacity** \\ **(kj/kgK)** \\ \end{tabular} &
\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **(W/mK)** \\ \end{tabular} \\ \hline RUBITHERM GmbH, PCM SP 24 E & M1 & 24–35 & 1500 & 190 & 2 & 0.6 \\ PlusICE PCM, S23 & M2 & 23 & 1530 & 175 & 2.2 & 0.54 \\ savENRG PCM-HS24P & M3 & 24 & 1820 & 185 & 2.26 & 0.5–1.09 \\ PUR-PCM, BASF Polyurethanes GmbH & M4 & 22 & 970 & 365 & 2 & 0.19 \\ PlusICE PCM, S17 & M5 & 17 & 1525 & 160 & 1.9 & 0.43 \\ CoolZONE23, Armstrong & M6 & 21–22 & 770 & 342 & 2 & 0.2 \\ savENRG PCM-HS22P & M7 & 23 & 1540 & 185 & 3.05 & 0.5–1.09 \\ ThermalCORE 23 C/ 73 F, USA & M8 & 22–24 & 770 & 342 & 2.2 & 0.2 \\ Weber.murclima 23, St. Gobain-weber & M9 & 22–24 & 950 & 170 & 2.32 & 0.38 \\ RUBITHERM GmbH, PCM RT 25 HC & M10 & 22–26 & 880 & 230 & 2 & 0.2 \\ PlusICE PCM, PCM, A25H & M11 & 25 & 810 & 226 & 2.15 & 0.18 \\ PlusICE PCM, A22H & M12 & 22 & 820 & 216 & 2.85 & 0.18 \\ PlusICE PCM, A25 & M13 & 25 & 785 & 150 & 2.26 & 0.18 \\ PlusICE PCM, A24 & M14 & 24 & 790 & 145 & 2.22 & 0.18 \\ PCM-Akustikputz 23, Schreff Gmbh\& Co. & M15 & 21–22 & 400 & 196 & 1.7 & 0.08 \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of phase-change materials and their thermo-physical properties.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Compound (M)** & \multicolumn{2}{c}{**FOM1\(\ast\)10\({}^{6}\rho\)\(\ast\)L**} & \multicolumn{2}{c}{**FOM2\(\ast\)10\({}^{-6}\)_k/\(\rho\)\(\ast\)C\({}_{p}\)_**} \\ \hline RUBITHERM GmbH, PCM SP 24 E & M1 & 285 & 0.2 \\ PlusICE PCM, S23 & M2 & 267.75 & 0.16042 \\ savENRG PCM-HS24P & M3 & 336.7 & 0.12161 \\ PUR-PCM, BASF Polyurethanes GmbH & M4 & 354.05 & 0.09793 \\ PlusICE PCM, S17 & M5 & 244 & 0.14840 \\ CoolZONE23, Armstrong & M6 & 263.34 & 0.12987013 \\ savENRG PCM-HS22P & M7 & 284.9 & 0.10631 \\ ThermalCORE 23 C/ 73 F, USA & M8 & 263.34 & 0.11806 \\ Weber.murclima 23, St. Gobain-weber & M9 & 161.5 & 0.17241 \\ RubBITHERM GmbH, PCM RT 25 HC & M10 & 202.4 & 0.11363 \\ PlusICE PCM, PCM, A25H & M11 & 183.06 & 0.10335 \\ PlusICE PCM, A22H & M12 & 177.12 & 0.07702 \\ PlusICE PCM, A25 & M13 & 117.75 & 0.101459 \\ PlusICE PCM, A24 & M14 & 114.55 & 0.10263428 \\ PCM-Akustikputz 23, Schreff Gmbh\& Co. & M15 & 78.4 & 0.11764 \\ \hline \hline \end{tabular}
\end{table}
Table 2: FOMs results.  
* T2 Lower = Better;
* T3 Higher = Better;
* T4 Higher = Better;
* T5 Higher = Better;
* T6 Higher = Better;
* T7 Lower = Better.  
With these in mind, the VIKOR method will be performed as the named previous research.