## 3 Results and Discussion
### Numerical Results
#### 3.3.2 Parametric Influences on Thermal Management  
The validated numerical model is employed to study the influence of PCM properties on the thermal management performance to identify the most optimum PCMs. Thermo-physical properties of paraffin wax (Table 4) were used as a reference to conduct the simulation with thermal energy storage capacity of 1.15 kJ. The values of thermal conductivity, density, melting range and melting points were varied to study their influence on PCM performance. Figure 13 shows the effect of PCM thermal conductivity (upper horizontal axis) and PCM density (bottom horizontal axis) on temperature rise on left vertical axis and time to melt on right vertical axis. The relationship between density and temperature rise (\(\rho-\Delta T\)), density and time to melt (\(\rho-t_{m}\)), conductivity and temperature rise (\(K-\Delta T\)) and conductivity and time to melt (\(K-t_{m}\)) is presented in Figure 13. The PCMs show a range of thermal conductivities starting from 0.14 W/m\(\cdot\)K (for fatty acids) to 0.8 W/m\(\cdot\)K (for salts hydrates), so the same range is applied in the simulations. Figure 12: Comparison between simulation and experimental Time-temperature profiles under NV for: (**A**) salt; (**B**) paraffin; and (**C**) milk fat. Figure 13 shows that as the \(K\) increases from 0.1 to 0.4 W/m\(\cdot\)K, a temperature drop of 5 \({}^{\circ}\)C and reduction in PCMs' time to melt by 2 min is observed. The temperature drop and time to melt become less affected with further increase in \(K\) and becomes unnoticeable at \(K\) = 0.8 W/m\(\cdot\)K. The limiting conductivity in this case can be caused by overwhelmingly applied metallic fins in the present HS design and may not have room for more conductivity enhancement. It can be concluded that for the HS design under investigation, the thermal conductivity of 0.8 W/m\(\cdot\)K (for salt hydrate) is the maximum impacting conductivity. It means that the addition of thermal conductivity enhancers (like nanoparticles) into salt hydrate is not expected to improve the system performance. However, since the paraffin waxes used in this study possess less thermal conductivity (0.2 W/m\(\cdot\)K), they can be improved by adding nanoparticles or other \(K\)-enhancers to moderately increase their thermal performance. In future work, the conductivity enhancement can be studied with various HS designs that have various fin densities and arrangements. In the case of PCM based cooling systems, the PCM density is an important parameter as it would dictate the size of PCM containment and would eventually affect device volume. The higher density PCM can be packed in smaller volumes with same weight and thermal energy storage capacity compared to the lower density PCM given that the other parameters are fixed thereby reducing device size and cost. The effect of changing the density values from the lowest value of 802 kg/m\({}^{3}\) (paraffin wax) to the highest value of 1700 kg/m\({}^{3}\) (salt hydrate) is addressed. It can be seen that as the material density increases, the temperature drop increases linearly reaching up to 10 \({}^{\circ}\)C. On the other hand, an increase in density will increase the time to complete melting by 10 min. Figure 14a shows the effect of different melting ranges on the temperature rise of the heat generator surface (\(T_{b}\)). The PCMs melting range has been selected to start at 37 \({}^{\circ}\)C being substantially above the room temperature (25 \({}^{\circ}\)C) and ends at 58 \({}^{\circ}\)C being well below the device safety temperature of 60 \({}^{\circ}\)C. The start is selected to assure that all PCMs are completely in the solid phase when the device is not operating and end is selected to stabilize device temperature below safety temperature. The effect of fixing the same melting start and keep increasing end of melting temperature to mark a widening melting range (Figure 14a) is compared with fixing the same narrow melting range and shifting up start of melting (Figure 14b).