## 4 Results and Analysis
### Maximum Temperature  
Among the four indicators, T\({}_{\rm max}\) is generally regarded as the most crucial one since it directly shows the cooling capacity of the BTMS. The T\({}_{\rm max}\) of seven designs at five flow rates are shown in Figure 5. Design 4 always exhibited the highest T\({}_{\rm max}\) at the five flow rates. The gradient vertical spacing design with a four-cell-side inlet and six-cell-side outlet had the lowest cooling efficiency in terms of the temperature rise among all designs. Design 1 had the lowest T\({}_{\rm max}\) (315.91 K and 308.78 K) at 10.56 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s and 21.12 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s, respectively, indicating the smallest cell spacing with a regular 5 \(\times\) 9 arrangement could most effectively suppress the temperature rise at lower air flow rates, as shown in Figure 6. At 10.56 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s flow rate, all three designs in the CVSG showed better cooling performances than the three designs (six-cell-side inlet) in the GVSG. When the flow rate rose to 21.12 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s, Design 5 and 6 showed lower T\({}_{\rm max}\) (309.32 K and 309.67 K) than Design 2 and 3 (310.19 K and 310.24 K), but still higher than Design 1 (308.78 K). At all five flow rates, the T\({}_{\rm max}\) of Design 3 (317.05 K, 310.24 K, 307.19 K, 305.04 K, and 303.53 K) were always larger than Design 2 (316.52 K, 310.19 K, 306.98 K, 304.82 K, and 303.33 K), indicating the ineffectiveness of increasing vertical spacing values for the constant vertical spacing designs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Inlet** & **Flow Rate** & **Flow Rate** & **Flow Rate** & **Flow Rate** & **Flow Rate** \\
**Velocities** & **(10.56 \(\times\)** & **(21.12 \(\times\)** & **(31.68 \(\times\)** & **(42.24 \(\times\)** & **(52.80 \(\times\)** \\
**(m/s)** & **10\({}^{-3}\) m\({}^{3}\)/s)** & **10\({}^{-3}\) m\({}^{3}\)/s)** & **10\({}^{-3}\) m\({}^{3}\)/s)** & **10\({}^{-3}\) m\({}^{3}\)/s)** \\ \hline Design 1 & 1.0000 m/s & 2.0000 m/s & 3.0000 m/s & 4.0000 m/s & 5.0000 m/s \\ Design 2 & 0.9639 m/s & 1.9278 m/s & 2.8917 m/s & 3.8556 m/s & 4.8195 m/s \\ Design 3 & 0.9302 m/s & 1.8604 m/s & 2.7906 m/s & 3.7208 m/s & 4.6510 m/s \\ Design 4 & 1.0000 m/s & 2.0000 m/s & 3.0000 m/s & 4.0000 m/s & 5.0000 m/s \\ Design 5 & 1.0000 m/s & 2.0000 m/s & 3.0000 m/s & 4.0000 m/s & 5.0000 m/s \\ Design 6 & 0.9639 m/s & 1.9278 m/s & 2.8917 m/s & 3.8556 m/s & 4.8195 m/s \\ Design 7 & 0.9302 m/s & 1.8604 m/s & 2.7906 m/s & 3.7208 m/s & 4.6510 m/s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Different inlet velocities for each design to deliver five input flow rates.  
Figure 5: Maximum temperatures of 7 designs at 5 flow rates.  
The turning point of better cooling performance of gradually emerged with the rise of the air flow rates. At 31.68 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s, the T\({}_{\rm max}\) of Design 5 (305.49 K) firstly became the lowest among all designs, as shown in Figure 6. When the flow rate reached the highest value (52.8 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s), the T\({}_{\rm max}\) of Design 5-7 in GVSG (301.90 K, 302.30 K, and 302.28 K) were all lower than that of Design 1 (302.40 K), which was always the lowest in CVSG. With the flow rates increased to 42.24 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s and 52.8 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s, Design 5 continued to output the lowest T\({}_{\rm max}\) values (303.33 K and 301.90 K), as shown in Figure 6. Moreover, just like the pattern in CVSG that Design 1 (30 mm spacing) delivered the lowest T\({}_{\rm max}\) among three designs (30 mm, 31.5 mm, and 33 mm spacing) at all five flow rates, the T\({}_{\rm max}\) of Design 5 (40/30/24 mm spacing) was always the lowest among three designs (40/30/24 mm, 42/31.5/25.2 mm, and 44/33/26.4 mm spacing) in GVSG at all five flow rates. Increasing the gradient vertical spacing values was proven to be useless in reducing the T\({}_{\rm max}\) of constant or gradient vertical spacing designs.