# Comparison of the Axial Fan and Synthetic Jet Cooling Systems
## 3 Results and Discussion
### A Comparison of the Performance of Different Cooling Devices  
The other important decisive parameter is the space required for the operation of the device. All of the parameters discussed above describe the heat transfer but not the volume of the investigated devices. In order to take that aspect into account, the heat transfer rate of the heat sink per unit temperature difference and unit volume of the cooling device was defined (Equation (7)). The ratio \(\varepsilon\) as a function of the power supplied to the cooling devices is presented in Figure 10.  
The ratio \(\varepsilon\) increases with the power delivered to the cooling devices (Figure 10a) because the thermal resistance decreases and is almost independent of the temperature difference. For the fan \"downward flow\" configuration, the differences between the \(\varepsilon\) values at \(\Delta T=10\) K and \(\Delta T=60\) K was approximately 12%. In other cases, the difference was lower than 10%. The ratio \(\varepsilon\) is useful mainly for the comparison of different types and arrangements of cooling devices. Therefore, in Figure 11, such a comparison in terms of \(\varepsilon\) is presented. Only the devices that use air as a working fluid are included. The following cooling systems have been selected for comparison:  
Figure 10: The heat transfer rate of the heat sink per unit temperature difference and unit volume of the cooling device \(\varepsilon\) as a function of (**a**) the power supplied to the cooling device; (**b**) temperature difference \(\Delta T=(T_{\mathrm{b}}-T_{\infty})\) at the power of \(P=7.0\) W. Data from: [PERSON] et al. [27], [PERSON] [28]. * Fischerelectronik ICK S R 140 \(\times\) 70; commercial pin fins heat sink with parameters: \(R=1.7\) K/W; \(V=1.08\) dm\({}^{3}\); \(\varepsilon=0.55\) W/(K\(\cdot\)dm\({}^{3}\)). * Fischerelectronik ICK LED R 200 \(\times\) 40; commercial plane fin heat sink with parameters: \(R=1\) K/W; \(V=1.26\) dm\({}^{3}\); \(\varepsilon=0.79\) W/(K\(\cdot\)dm\({}^{3}\)). * Natural convection; investigated heat sink under natural convection conditions with parameters: \(R=1.4\) K/W; \(V=0.64\) dm\({}^{3}\); \(\varepsilon=1.11\) W/(K\(\cdot\)dm\({}^{3}\)). * [PERSON] et al. ; The heat sink optimized by [PERSON] et al. [13], with \(\varepsilon=0.85-1.2\) W/(K\(\cdot\)dm\({}^{3}\)) depending on the heat flux density applied to the heat sink base. * SJ ([PERSON] and [PERSON]); the actuator investigated by [PERSON] and [PERSON] [28] with parameters: \(R=0.17\) K/W; \(V=2.44\) dm\({}^{3}\); \(\varepsilon=1.11\) W/(K\(\cdot\)dm\({}^{3}\)), \(P=7\) W.
* SJ ([PERSON] et al. ); the actuator investigated by [PERSON] et al. [27] with parameters: \(R=0.19\) K/W; \(V=2.3\) dm\({}^{3}\); \(\varepsilon=1.11\) W/(K\(\cdot\)dm\({}^{3}\)), \(P=7\) W.
* Fan (downward flow); the investigated configuration with parameters: \(R=0.16\) K/W; \(V=1\) dm\({}^{3}\); \(\varepsilon=6.43\) W/(K\(\cdot\)dm\({}^{3}\)), \(P=7\) W.
* Fan (upward flow); the investigated configuration with parameters: \(R=0.12\) K/W; \(V=1\) dm\({}^{3}\); \(\varepsilon=8.61\) W/(K\(\cdot\)dm\({}^{3}\)), \(P=7\) W.
* Fischerelectronik LA ICK PEN 38 W 12; commercial fan-cooled heat sink with parameters: \(R=1.1\) K/W; \(V=0.13\) dm\({}^{3}\); \(\varepsilon=7.42\) W/(K\(\cdot\)dm\({}^{3}\)); \(P=0.6\) W.
* Jian-Hui and Chun-Xin; the fan-cooled heat sink optimized by [PERSON] and [PERSON] [36] with parameters: \(R=0.169\) K/W; \(V=0.381\) dm\({}^{3}\); \(\varepsilon=15.53\) W/(K\(\cdot\)dm\({}^{3}\)); \(P=6.6\) W.
* [PERSON] and [PERSON]; the fan-cooled heat sink investigated by [PERSON] and [PERSON] [17] with parameters: \(R=0.185\) K/W; \(V=0.22\) dm\({}^{3}\); \(\varepsilon=24.35\) W/(K\(\cdot\)dm\({}^{3}\)). The fan-cooled heat sinks achieve higher heat dissipation than the SJ-cooled heat sinks for the same temperature difference and the same volume in the present investigation. The SJ cooling devices increase the \(\varepsilon\) by around two times relative to the natural convection, while the fan cooling increases it by around eight times.