# Numerical Design and Laboratory Testing of Encapsulated PCM Panels for PCM-Air Heat Exchangers
## 3 Results and Analysis
### Numerical Design
#### 3.1.2 2D Simulations  
The design of Shape 9 allows the simulations to be conducted in 2D as it is uniform along its width. Thirteen variations (Table 4, Shapes 11 to 23) were generated and stacked in 7 sevenpanels per module to perform a parametric analysis of the spacing between ridges, ridge height and radius for Reynolds number varying from 7200 to 21,600. Figure 9 shows the temperature distribution of Shape 11, where the outlet temperature and inlet pressure were averaged and used to calculate the Nusselt number and pressure drop.  
Figure 10 shows that shape 11 has, at most Reynolds numbers, the highest heat transfer, representing 75% more heat transfer on average when compared to a smooth panel. The efficiency of this shape is close to 1.0 on average, which reflects that the heat transfer and pressure drop increased in a similar rate while other shapes have a higher increase in pressure.  
Figure 10: Nusselt number and Nusselt number ratio from a smooth panel.  
Figure 9: Temperature distribution of Shape 11 at Re = 18,736.  
As Shape 11 was the most effective in terms of heat transfer and pressure drop, the same gap distance and surface geometry was used to generate nine additional cases (Table 4, shapes 24 to 32) by varying panel thickness, spacing between panels and total panels per module of TB.  
As a result, shape 29 had the worst performance when compared to other shapes. Conversely, shapes 26, 11 and 24 (Figure 11, upper left) have the highest Nusselt numbers at any Reynolds number. This increase allows a fast response by the PCM-Air heat exchanger when the heat load increases suddenly.  
When the Nusselt number is compared to a smooth surface \((Nu/Nu_{o})\), shapes 24, 26 and 11 present the best results, showing an average increase of 2, 1.8 and 1.75 as shown in Figure 11 (right) where the ratio is shown for all cases. The inclusion of ridges favored heat transfer by the increase of turbulence at lower Reynolds number, allowing a reduction in PCM-Air heat exchanger airflow, saving energy and reducing noise. The result also shows that the existing panel performs better than a smooth surface only at low Reynolds numbers (1.27 for 7200). For Reynolds numbers above 10,089 the existing panel have a performance similar to a smooth panel with a \(Nu/Nu_{o}\) lower or equal to 1.  
Figure 11 (bottom) shows that the efficiency of shapes 11, 24, 25, 27, 28 and 30 have values above 1, which means that the inclusion of ridges enhanced the heat transfer at a lower cost in terms of pressure drop when compared to a smooth surface. Shape 26 has the best performance in terms of Nusselt number but the higher pressure drop lowers its efficiency (0.86 on average). Values below 1 mean that the pressure drop increases in a proportion higher than the Nusselt number, leading to an increase of noise and energy cost with a small benefit on heat transfer.  
When the volume of PCM held in a panel is (Table 5) it can be seen that shape 26 holds 20.51% more PCM when compared to the existing panel while shapes 11 and 24 are able to hold 13.68 and 0.08% more, respectively.  
Figure 11: Nusselt number and smooth panel ratio and Nusselt number for refined panels.  
To ensure that a small fan can provide the required airflow for the selected shapes, the pressure drop of the panels against the fan head curve was plotted. As it can be seen in Figure 12, the air handling unit can provide sufficient pressure at the required airflow to overcome this drop for shapes 11, 24 and 25.  
Based on these results, shape 11 was selected to be fabricated.