Comparison of the Axial Fan and Synthetic Jet Cooling Systems

Featured Application

The presented investigation may be used for the design process of active cooling systems.

Abstract

Choosing the right cooling device is crucial for the proper operation of electronic equipment. A comparison of the two different cooling devices is presented in this paper: one with a standard axial fan and the other with a synthetic jet actuator. Two distinct sets of operating conditions of the fan and two different loudspeakers for the synthetic jet actuator were used. The experimental setup consisted of a radial heat sink mounted onto a round electric heater and two cooling systems: one with the axial fan and the other with a synthetic jet actuator. From the thermal balance in the specified control volume, the heat sink’s thermal resistance. as well as the coefficient of performance, were determined. The highest difference between the thermal resistance of both cooling systems occurred at a low input power of P = 0.5 W. The heat sink cooled with a synthetic jet had the thermal resistance of R = 0.39 K/W, while the same heat sink cooled with a fan achieved R = 0.23 K/W. Thus, the fan cooling exhibited almost 70% better performance than synthetic jet cooling. For a higher input power of P = 7.0 W, the relative difference in the thermal resistance decreased to the value of 42%. For the input power of P = 7.0 W, the fan-cooled heat sink dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=487 \mathrm{W}$ under the temperature difference between the heat sink base and ambient air equal to 60 K. For the same input power and temperature difference, the synthetic jet cooling of the same heat sink dissipated a thermal power of ${\dot{Q}}_{\mathrm{HS}}=339 \mathrm{W}$. Under natural convection, the heat sink dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=57 \mathrm{W}$. Thus, the heat transfer enhancement with fan cooling relative to natural convection was equal to 8.5, while the enhancement with synthetic jet cooling relative to natural convection was equal to 6.0. The modified coefficient of performance and the heat transfer rate of the heat sink per unit temperature difference and unit volume of the cooling device ε are presented. The axial fan performed better in terms of both parameters under consideration. The ε of the investigated device with a fan was around four times higher than in the case of the synthetic jet actuator and eight times higher than in the case of natural convection.

1. Introduction

Proper thermal management is crucial in order to achieve the designed lifetime and correct functioning of electronic devices. The increasing power density of modern devices often renders the classic cooling methods insufficient. However, despite the development of such passive cooling materials and devices as heat pipes [1,2], phase change materials [3,4] and thermomagnetic devices [5,6], the classic fin heat sinks are still the most common.

A synthetic jet actuator (SJA) consists of a cavity with at least one orifice and an element capable of reciprocating movements, such as a loudspeaker, piezoelectric diaphragm or mechanical piston. In order to generate a synthetic jet flow, this movable or deformable element named the actuator is embedded into one of the walls of the cavity. By the periodical change of the cavity volume, a synthetic jet (SJ) is generated [7]. In recent years SJAs have found a lot of applications, such as flow control, mixing or heat transfer enhancement [8]. The investigations of the heat transfer enhancement with the synthetic jet usually concern one of the two configurations: flat plate impingement cooling and heat sink cooling.

Pavlova and Amitay [9] presented an experimental investigation of the synthetic jet cooling mechanism based on the jet impinging onto the heated surface. The synthetic jet and continuous jet impingement cooling performance as a function of the dimensionless jet to surface distance were compared at the same Reynolds number of 445. The synthetic jets were about three times more effective in cooling than continuous jets at the same Reynolds number.

Chaudhari et al. [10] presented the heat transfer characteristic of a synthetic jet impingement cooling. The experiments were performed for a wide range of input parameters: the Reynolds number was in the range of 1500–4200, and the dimensionless jet to surface distance was in the range of 0–25. A direct comparison between the continuous axisymmetric jet and the synthetic jet for the same set of conditions was performed. The behavior of the average Nusselt number with synthetic jet cooling was found to be similar to that obtained for a continuous jet. The maximum Nusselt number was about 10% higher for the continuous jet compared to the synthetic jet at a Reynolds number of the order of 4000.

Mangate and Chaudhari [11] performed an experimental investigation on the heat sink cooling performance with the use of a synthetic jet for various sets of geometrical configurations. The authors also presented a direct comparison between active cooling methods with a fan and synthetic jet at the same input power levels. The heat sink’s thermal resistance with the synthetic jet cooling strongly decreased with the increased input power, while for the fan-cooled heat sink, the thermal resistance above 1 W was found to be almost constant. The heat sink’s thermal resistance with a synthetic jet actuator and a fan at the same input power of 1.35 W was 0.90 and 0.54 K/W, respectively, which means that the fan’s cooling performance was 67% higher than the performance of the synthetic jet’s cooling. With the input power increased to 5.5 W, the heat sink thermal resistance was comparable for both cooling systems, but the fan-cooled heat sink still overperformed synthetic jet cooling by 6%.

Yu et al. [12] investigated the impact of the geometric parameters (the number of fins, the fin length and the fin height) on the heat flux of the radial heat sink under natural convection conditions. They showed that the optimal values for the fin number and fin length exist that result in the lowest effective heat sink temperature. In [13], the same group of researchers simultaneously optimized the thermal performance and mass of the three types of radial heat sinks. They showed that the optimization of mass deteriorates the values of the thermal parameters and vice versa; therefore, they used the Pareto optima to indicate the overall best solution. Similar optimization was conducted for the pin-fin radial heat sink by Jang et al. [14]. The effect of the radiation of the heat sink acting simultaneously with natural convection was investigated by Yu et al. [15]. The radiation turned out to account for as much as 27% of the total heat transfer.

Xu [16] optimized the thermosyphon heat sinks with rectangular radial fins dedicated to the LED lamp cooling, which was operated by natural convection. The measured radiation of the heat sink was negligible, and the numerical simulation was used to calculate the heat transfer parameters. The number and length of the fins varied, and the Pareto optimal solution was used to balance the heat sink mass and the thermal performance.

Saini and Webb [17] investigated the heat sink with active cooling. The impinging jet and the duct flow were generated by the fan. The impinging jet exhibited higher thermal performance in comparison with the ducted flow. Lasance et al. [18] compared fan and impinging synthetic jet (SJ) active cooling methods. The synthetic jet actuator (SJA) achieved a higher heat transfer coefficient than the fan at the same or lower driving power. Additionally, the operation of the SJA caused less noise than the fan. Arik et al. [19] proposed the heat sink with SJA contained within the volume not exceeding that of a regular heat sink. The use of the SJ increased the heat transfer by a factor of 2.2 compared to natural convection. The benefits of using SJ to cool electronics have been demonstrated many times over [20,21].

Tan et al. [22] compared the SJ and continuous jet in impingement heat transfer. The SJ heat transfer parameters were better than in the case of the continuous jet but depended strongly on the Reynolds number of SJ.

The SJ actuators are usually used to produce an impinging jet [22,23,24]; however, other configurations also exist, such as that proposed by Gil [25] for the purpose of heat-sink cooling. In [25], the cylindrical SJA with orifices located at the curvilinear surface was used. The actuator was closed on one side by the loudspeaker, and on the other side, the heat sink was positioned in such a way that the fins were inside the actuator cavity. The heat sink was milled out of a single aluminum block. The amount of heat dissipated by the SJA reached values 3.7 times higher than those observed when the synthetic jet was turned off. This type of heat sink with an integrated SJA was also investigated in [26,27,28,29].

Gil et al. [27] investigated the SJA with different numbers and diameters of the orifices; there was a total of 11 cases. They showed that the heat performance of the device and the noise generated by the synthetic jet actuator depend on the ratio of the total cross-sectional area of the orifices and the effective area of the actuator diaphragm. These results may be seen as the more general form of the observations made by Kordík and Trávníček [30], who had indicated that the ratio of an orifice to diaphragm diameter is related to the efficiency of the actuator. However, the investigation of Kordík and Trávníček [30] was concerned with the SJ velocity and the efficiency of a single-orifice actuator, while the results of Gil et al. [27] indicated this dependence on the heat performance and multi-orifice SJA. The flow parameters and the heat performance are directly related to each other in the case of the synthetic jet [8,24,31].

Gil and Wilk [28] investigated the SJA with a heat sink inside a cavity for four different loudspeakers. The loudspeaker had a significant impact on the flow and heat transfer enhancement. The disparity of the thermal resistance between the different loudspeakers reached as much as 18%, while the sound pressure level was comparable for all investigated loudspeakers for the same electric power delivered to the SJA.

The results from the literature survey are contradictory: in some conditions, the synthetic jet cooling outperforms the standard active cooling systems, such as continuous jets and fans, while in other conditions, it does not. Therefore, in the present paper, the comparison between two active cooling methods, synthetic jet and axial fan, is investigated experimentally for the purpose of extending the available database. Both devices were used to cool the radial heat sink and were operated at the same input power. The results are presented in the form of the thermal resistance, dissipated thermal power and coefficient of performance.

2. Materials and Methods

The investigated synthetic jet actuator consisted of cylindrical housing, a heat sink inside the cavity and a loudspeaker (Figure 1). A radial heat sink with an outer diameter of 180 mm was used. The heat sink had 32 rectangular fins of 2 mm thickness and 25 mm height. Half of the fins were of a length of 57 mm, and the other half of a length of 42 mm. The fins were arranged alternately and axisymmetrically. The heat transfer area of the heat sink was $S$ = 0.10 m². The heat sink was mounted on the round heater plate with a thin layer of thermal grease. The heater was insulated with a 100 mm thick layer of mineral wool (Figure 2).

The heater plate was powered with a GW INSTEK PSB-1400 direct current power supply. A Keithley 2700 multimeter was used for the measurements of the voltage and current that supplied the heater. The accuracy of the DC voltage measurement was ±0.05%, and the accuracy of the DC current measurement was ±0.1%.

The temperature was measured with nine K-type thermocouples with the reference junction temperature stabilized by the Kaye 170 Ice Point Reference. The signal of the thermocouples was recorded with a Keithley 2700 multimeter, which enabled the temperature measurement with a resolution of 0.001 K. Four of the thermocouples were used to measure the ambient temperature (T_∞), another two thermocouples for the measurements of the insulation temperature (T_HD, T_D) and the last three of them were fixed inside the grooves milled in the heat sink base at different radial distances in order to measure the average heat sink base temperature (T_B) (see Figure 2). Each thermocouple was calibrated, and the accuracy of the temperature measurement has been estimated to be better than ±0.07 K in the considered temperature range.

The air at atmospheric pressure was used as a working fluid. The ambient temperature in the laboratory was controlled with an air conditioning system. During the measurements, the ambient temperature was kept within 295 ± 1.5 K.

Three different cases of heat sink cooling were investigated: natural convection (passive method), active cooling with SJA when the heat sink was located inside the actuator cavity (Figure 3a) and active cooling with the fan (Figure 3b). Data on the heat transfer characteristics with the SJ at the resonant frequency was taken from [27,28] for the actuator with 16 orifices of a diameter of 10 mm each. The results included data for two different loudspeakers: W.18.200.8.FGX [27] and W.18.180.8.FCX_v2 [28]. In the present work, these actuators are referred to as “SJ (Gil et al. [27])” and “SJ (Gil and Wilk [28])”, respectively.

For the case with an airflow forced by an axial fan, the AABCOOLING Black Jet Fan 12 V with a diameter of 120 mm was used. The fan’s maximum flow rate is equal to 170 m³/h. The fan was mounted on a disk with a diameter of 180 mm and located directly over the heat sink (Figure 3b). The fan was powered with a Teledyne T3PS3000 direct-current power supply. The measurements of the voltage and current supplying the heater were arranged in the way described above for the experiment with a synthetic jet actuator.

The setup with an axial fan was investigated in two different configurations. In the first, the hot air was sucked from the heat sink; therefore, the direction of the hot airstream was consistent with the direction of the natural convection. This setup is referred to as “upward flow”. In the second configuration, the impinging jet was created by the fan that blew cold air at the surface of the heat sink. This condition is referred to as “downward flow”. The direction of airflow is presented in Figure 4.

The typical values of standard uncertainty are presented in

Table 1. Typical uncertainty of measured values.

Name	Relative Uncertainty	Absolute Uncertainty
T∞	-	±0.25 K
Tb	-	±0.15 K
P	±0.55%	-
R	±3.4%	-

. The estimation of the uncertainty was performed according to the GUM (Guide to the Expression of Uncertainty in Measurement) [32]. For each directly measured parameter, the Type A standard uncertainty was calculated as a standard deviation of the mean. Each measurement was repeated 100 times. Type B standard uncertainty was calculated from the accuracy data provided by the equipment manufacturers presented afore. The expanded uncertainty was calculated from the combined standard uncertainty by multiplying it with a coverage factor of k = 2.

Data Reduction

The electric power of the fan and the SJA was calculated as:

$$P=E_A{I}_A·\cos \left(\phi \right)$$

(1)

where $E_A$ is an effective voltage (V), $I_A$ is an effective current (A) and $\cos \left(\phi \right)$ is a power factor.

The heat sink thermal resistance was calculated as [26]:

$$R=\frac{T_{\mathrm{b}}-T_{\infty }}{{\dot{Q}}_{\mathrm{HS}}}$$

(2)

where $T_{\mathrm{b}}$ is a heat sink base temperature (K), $T_{\infty }$ is an ambient temperature (K) and ${\dot{Q}}_{\mathrm{HS}}$ is a thermal power dissipated by the heat sink and was calculated as [26]:

$${\dot{Q}}_{\mathrm{HS}}=E_{\mathrm{H}}{I}_{\mathrm{H}}-\lambda S_{\mathrm{H}}\left(\frac{T_{\mathrm{HD}}-T_{\mathrm{D}}}{H_{\mathrm{INS}}}\right)+E_A{I}_A$$

(3)

where $\lambda$ is a thermal conductivity of the mineral wool (W/(m·K)), $S_{\mathrm{H}}$ is an area of the heater plate (m²), $T_{\mathrm{HD}}$ is the temperature of the heater (K), $T_{\mathrm{D}}$ is the temperature at the bottom of the mineral wool layer (K), $H_{\mathrm{INS}}$ is the thickness of the mineral wool, $E_H$ is the voltage supplied to the heater (V) and $I_H$ is the current supplied to the heater (A).

The average heat transfer coefficient was defined as [13]:

$$h_{\mathrm{avg}}=\frac{1}{R·S}$$

(4)

where $S$ is the heat transfer area of the heat sink (m²).

The coefficient of performance (COP) may be defined as the ratio of the dissipated thermal power to the actuator input power:

$$\mathrm{COP}=\frac{{\dot{Q}}_{\mathrm{HS}}}{P}$$

(5)

The value of the COP alone is insufficient for describing the heat transfer characteristics of the cooling device because it does not include the temperature difference between the surroundings and the cooled object. Increasing temperature difference increases the amount of dissipated heat; therefore, it is better to investigate the modified coefficient of performance COP*, defined as [27]:

$${\mathrm{COP}}^{*}=\frac{{\dot{Q}}_{\mathrm{HS}}}{P·\mathsf{\Delta }T}=\frac{\mathrm{COP}}{\mathsf{\Delta }T}=\frac{1}{R·P}$$

(6)

where $\mathsf{\Delta }T=\left(T_{\mathrm{b}}-T_{\infty }\right)$.

The heat transfer rate of the heat sink per unit temperature difference and unit volume of the cooling device (including the heat sink and the actuator forcing the flow) may be defined as:

$$\epsilon =\frac{{\dot{Q}}_{\mathrm{HS}}}{\mathsf{\Delta }T·V}=\frac{1}{R·V}$$

(7)

where $V$ is the volume of the cooling device (dm³).

3. Results and Discussion

3.1. Validation

The experimental setup and method were validated by the measurements of the average heat transfer coefficient of the radial heat sink under natural convection conditions. Due to the novelty of the investigated device, there are no heat transfer data in the literature for devices of similar working principles and geometry under forced convection conditions. There are, however, reports of the values of the average heat transfer coefficients for radial heat sinks under natural convection, and those data were chosen for comparison. The results for the radial heat sink presented in Figure 5 agree well with those reported by Gil et al. [27]. It confirms that the measurement setup is able to give repeatable results, and the methodology is correct. The average heat transfer coefficient under natural convection conditions for the radial heat sinks investigated by Yu et al. [15] and Jang et al. [14] is additionally shown in Figure 5, and its values are comparable with the present results.

With the increased heat flux, the temperature difference between the heat sink base and ambient air also increases. Consequently, for higher temperature differences, the heat transfer by natural convection is enhanced as the Grashof number increases. For the higher temperature difference, the part of heat transferred by radiation also increases.

3.2. Comparision of Thermal Parameters of Different Cooling Devices

Figure 6a presents the thermal resistance of the heat sink as a function of the power supplied to the cooling device. The thermal resistance in the case of SJ was higher than in the case of a fan, and the “upward flow” configuration with an axial fan exhibited lower thermal resistance than the “downward flow” fan configuration. The thermal resistance also depends on the difference between the heat sink temperature and ambient temperature; however, this dependence is weak (Figure 6b). The lowest value of the thermal resistance in the entire experiment of $R=0.12$ K/W was observed in the fan “upward flow” configuration at $P=7.0$ W. The thermal resistance R of the heat sink decreased with the increased power P delivered to the synthetic jet actuator due to the increase in the synthetic jet velocity and Reynolds number [26]. With the increased synthetic jet Reynolds number, the heat transfer enhancement occurred. Thus the thermal resistance of the radial heat sink decreased. A similar effect was observed for fan cooling: with the increased DC voltage delivered to the fan, the input power P increased, which, in turn, caused the higher rotational speed of the fan and, in consequence, higher airflow. Increased airflow through the heat sink channels enabled heat transfer enhancement, thus reducing heat sink thermal resistance. Comparing the cooling characteristic of the best synthetic jet case referred to as SJ (Gil and Wilk) [28] with upward flow fan cooling, it may be concluded that the results are similar to those presented by Mangate and Chaudhari [11]. The highest difference between the thermal resistance of both cooling systems occurred for the low input power of P = 0.5 W: the heat sink cooled with a synthetic jet had the thermal resistance of R = 0.39 K/W while the same heat sink cooled with a fan achieved R = 0.23 K/W. Thus, the fan cooling performance was almost 70% better than the performance of synthetic jet cooling. For a higher input power of P = 7.0 W, the relative difference decreased to the value of 42%. Mangate and Chaudhari [11] also observed a lower difference between synthetic jet and fan cooling performance of 6% at higher levels of input power. The main problem with such a comparison is the quality and performance of the fan used. Mangate and Chaudhari [11] used a Delta Model AFB0612E fan with external dimensions of 60 mm × 60 mm × 25.4 mm and a maximum flow rate of 65 m³/h (at input power of P = 4.56 W), while in the present paper, the AABCOOLING Black Jet Fan with external dimensions of 120 mm × 120 mm × 25 mm and a maximum flow rate of 170 m³/h (at input power P = 3.84 W) was used. Indeed, fan maximum flow rate alone is insufficient for objective comparison because it is necessary to know the fan pressure-flow rate characteristic as well as heat sink flow resistance to determine the fan-heat sink flow operating point.

Figure 7 presents the thermal power dissipated by the heat sink for natural and forced convection as a function of the temperature difference. All the results presented in Figure 7 were recorded at the power of $P=7$ W supplied to SJA/fan. As expected, the lowest value of the dissipated thermal power occurred in the case of natural convection and was much higher for the active cooling methods. The highest value was measured in the case of the fan “upward flow” configuration. In the cases of fan “downward flow” and SJ (Gil and Wilk [28]), the values of dissipated thermal power were similar. With the increasing heat sink base temperature T_b at constant ambient temperature T_∞, the dissipated thermal power for active cooling methods increased almost linearly. For the input power of P = 7.0 W, the fan-cooled (upward flow) heat sink under a temperature difference of ΔT = 60 K dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=487 \mathrm{W}$. For the same input power and temperature difference, the heat sink cooled with synthetic jet dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=339 \mathrm{W}$, while under natural convection, it dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=57 \mathrm{W}$ (Figure 7). Thus, the heat transfer enhancement with fan cooling relative to natural convection is equal to 8.5, while the enhancement with synthetic jet cooling relative to natural convection is equal to 6.0.

Figure 8a shows the average heat transfer coefficient as a function of the power supplied to the cooling device. The heat transfer coefficient increased with the power and was the highest in the case of the fan “upward flow” configuration. The value of the coefficient was the lowest for the configuration referred to as SJ (Gil et al. [27]). The highest observed value of the heat transfer coefficient was equal to $h_{avg}=86$ W/(m²K). For reference, the average heat transfer coefficient of the heat sink for natural convection conditions was approximately $h_{avg}=8$ W/(m²K) (Figure 8b). The heat transfer coefficient in the case of synthetic jet-cooling increased with the increasing input power P due to the higher values of the Reynolds number [26]. The heat transfer coefficient observed in the case of the fan cooling also increased due to higher values of the airflow with increased input power [11]. The average heat transfer coefficient under active cooling conditions was almost independent of the heat sink base temperature (and consequently temperature difference). On the contrary, the heat transfer coefficient under passive cooling conditions depended strongly on natural convection and radiation, both enhanced with increasing heat sink base temperature (Figure 8b).

It is important to note that the average heat transfer coefficient measured in the present work, in the cases of both fan and SJ, was quite low compared to some results reported in the literature. It may be explained by the fact that the value reported in the present paper is an average from the entire surface area S = 0.10 m² of the heat sink, while in some papers, the value of the heat transfer coefficient corresponds to the stagnation point or some other characteristic surface area.

The coefficient of performance is one of the most important parameters of cooling devices, and the methods to increase its value are constantly being sought after [33,34]. The COP* of investigated cooling devices is presented in Figure 9.

Figure 9a shows that the highest COP* was observed in the case of the fan “upward flow” configuration and the lowest in the case of SJ (Gil et al. [27]). The highest difference between COP*’s of both cooling systems occurred for the low input power of P = 0.5W: the heat sink cooled with synthetic jet (SJ Gil & Wilk [28]) had the COP* value equal to 5.0, while the configuration with fan cooling (upward flow) achieved the COP* of 8.8. The fan cooling system thus reached almost a 76% better cooling efficiency than synthetic jet cooling. For the higher input power of P = 7.0 W, the relative difference in COP* decreased to the value of 48%.

The COP* characteristics resulted from the thermal resistance characteristics presented in Figure 6a: the highest coefficient of performance occurred for the case with the lowest thermal resistance. As may be observed in Figure 9b, for the power of 7.0 W, the value of COP* is almost independent of the temperature difference, thus the coefficient of performance may be calculated simply as the value of COP* from Figure 9a at a specific operation point multiplied by the temperature difference. For example, for fan cooling (upward flow) with the power P = 3.0 W, the COP* = 2.4. Thus, the COP = COP*·ΔT, which, for example, for the operational temperature difference of ΔT = 40 K, gives the COP as equal to 96. It means that for the input power of P = 3.0 W, the dissipated thermal power is equal to ${\dot{Q}}_{\mathrm{HS}}=3 \mathrm{W}·96=288 \mathrm{W}$.

The SJ is usually used as an impinging jet, and, therefore, it is appropriate to compare it to the continuous impinging jet at the same Reynolds number [22,35]. The parameters of SJ depend on many factors, such as the orifice or cavity shape and dimensions, the type of the actuator used and the number of orifices.

In the presented investigation, the best cooling conditions were achieved in the case with the axial fan, referred to as “upward flow”. The values of the parameters in cases SJ (Gil and Wilk [28]) and fan “downward flow” were similar, particularly at the higher power levels. The worst modified coefficient of performance was observed in the case of SJ (Gil et al. [27]). It must be noted that the SJA (Gil et al. [27]) and SJ (Gil and Wilk [28]) differed mainly in the type of loudspeaker used.

In this paper, the data are presented and compared as a function of the real power supplied to the cooling devices. Such a choice may be justified by the fact that the supply power is a quantity that is interesting from a practical point of view since it is an indicator of the real energy demand.

3.3. 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 $\epsilon$ as a function of the power supplied to the cooling devices is presented in Figure 10.

The ratio $\epsilon$ 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 $\epsilon$ values at $\mathsf{\Delta }T=10 \mathrm{K}$ and $\mathsf{\Delta }T=60 \mathrm{K}$ was approximately 12%. In other cases, the difference was lower than 10%.

The ratio $\epsilon$ is useful mainly for the comparison of different types and arrangements of cooling devices. Therefore, in Figure 11, such a comparison in terms of ε is presented. Only the devices that use air as a working fluid are included. The following cooling systems have been selected for comparison:

• Fischerelectronik ICK S R 140 × 70; commercial pin fins heat sink with parameters: $R=1.7$ K/W; $V=1.08$ dm³; $\epsilon =0.55$ W/(K·dm³).
• Fischerelectronik ICK LED R 200 × 40; commercial plane fin heat sink with parameters: $R=1$ K/W; $V=1.26$ dm³; $\epsilon =0.79$ W/(K·dm³).
• Natural convection; investigated heat sink under natural convection conditions with parameters: $R=1.4$ K/W; $V=0.64$ dm³; $\epsilon =1.11$ W/(K·dm³).
• Yu et al.; The heat sink optimized by Yu et al. [13], with $\epsilon =0.85-1.2$ W/(K·dm³) depending on the heat flux density applied to the heat sink base.
• SJ (Gil and Wilk); the actuator investigated by Gil and Wilk [28] with parameters: $R=0.17$ K/W; $V=2.44$ dm³; $\epsilon =1.11$ W/(K·dm³), $P=7$ W.
• SJ (Gil et al.); the actuator investigated by Gil et al. [27] with parameters: $R=0.19$ K/W; $V=2.3$ dm³; $\epsilon =1.11$ W/(K·dm³), $P=7$ W.
• Fan (downward flow); the investigated configuration with parameters: $R=0.16$ K/W; $V=1$ dm³; $\epsilon =6.43$ W/(K·dm³), $P=7$ W.
• Fan (upward flow); the investigated configuration with parameters: $R=0.12$ K/W; $V=1$ dm³; $\epsilon =8.61$ W/(K·dm³), $P=7$ W.
• Fischerelectronik LA ICK PEN 38 W 12; commercial fan-cooled heat sink with parameters: $R=1.1$ K/W; $V=0.13$ dm³; $\epsilon =7.42$ W/(K·dm³); $P=0.6$ W.
• Jian-Hui and Chun-Xin; the fan-cooled heat sink optimized by Jian-Hui and Chun-Xin [36] with parameters: $R=0.169$ K/W; $V=0.381$ dm³; $\epsilon =15.53$ W/(K·dm³); $P=6.6$ W.
• Saini and Webb; the fan-cooled heat sink investigated by Saini and Webb [17] with parameters: $R=0.185$ K/W; $V=0.22$ dm³; $\epsilon =24.35$ W/(K·dm³).

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 $\epsilon$ by around two times relative to the natural convection, while the fan cooling increases it by around eight times.

As it has already been mentioned, the SJ in the impinging configuration generally exhibits a higher heat transfer coefficient than the devices presented by Gil et al. [27] and Gil and Wilk [28]. However, neither the papers describing the impinging setups specify the exact size of the entire actuator nor the methodology adopted in those papers allows the coefficient $\epsilon$ to be calculated in the same way as in the case of the present paper.

The comparison presented in Figure 11 shows that further optimization of the heat-sink cooled with SJA is required. It may be carried out by increasing the heat transfer area of the heat sink, refining the design of the SJA dedicated to cooling a specific device or by the use of more efficient loudspeakers. The basic problem of SJA in the context of ε is the size of the loudspeaker, which is approximately 40% of the total volume of the cooling device, while the fan occupies only 15% of the volume [17].

4. Conclusions

The synthetic jet actuator with the heat sink mounted inside the cavity was investigated as a cooling device and compared with the heat sink attached to the axial fan. The fan was operated in two configurations: with upward and downward flow.

The highest difference between the thermal resistance of both cooling systems occurred for a low input power of P = 0.5 W: the heat sink cooled with a synthetic jet had the thermal resistance of R = 0.39 K/W while the same heat sink cooled with a fan achieved R = 0.23 K/W. Thus, the fan cooling performance was almost 70% better than the performance of the synthetic jet cooling. For a higher input power of P = 7.0 W, the relative difference decreased to the value of 42%.

For the input power of P = 7.0 W, the fan-cooled (upward flow) heat sink under a temperature difference of ΔT = 60 K dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=487 \mathrm{W}$. For the same input power and temperature difference, the heat sink cooled with a synthetic jet dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=339 \mathrm{W}$ while under natural convection, it dissipated the thermal power of ${\dot{Q}}_{\mathrm{HS}}=57 \mathrm{W}$. Thus, the heat transfer enhancement with fan cooling relative to natural convection was equal to 8.5, while enhancement with a synthetic jet cooling relative to natural convection was equal to 6.0.

The highest difference between the COP* of both cooling systems occurred for a low input power of P = 0.5 W: the heat sink cooled with a synthetic jet had the COP* value equal to 5.0, while the configuration with fan cooling (upward flow) achieved the COP* of 8.8. The fan cooling system thus reached almost 76% better cooling efficiency than synthetic jet cooling. For a higher input power of P = 7.0 W, the relative difference in COP* decreased to the value of 48%.

The fan-cooled heat sinks achieved 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 increased the ε by around two times relative to the natural convection, while the fan cooling increased it by around eight times.

The fan with the upward flow configuration provided better heat transfer conditions than the fan with the downward flow configuration in the present investigation.

The $\epsilon$ of the SJA may be increased by the use of more efficient loudspeakers, increasing the heat transfer area of the heat sink or by improving the design of the SJA dedicated to cooling a specific device.