*2.2. Preparation of Powder Coating*

All the ingredients were blended using a single-screw extruder (PK–55, Pinying Machine Co., Kaohsiung, Taiwan) at 85–90 ◦C and a screw speed of 60 rpm. The resultant blend was pressed into sheets using roller miller and ground into powder (diameter: 0.1–2 µm) using a milling machine (SFM–22, Shehui Co., Taoyuan, Taiwan). The powder was deposited directly onto the substrate surface through electrostatic spraying using a sprayer (PEM–X1, Wagner, Markdorf, Germany) before curing at 160–200 ◦C.

#### *2.3. Measurement of Thermal Conductivity*

The thermal conductivity was determined using a thermal conductivity meter (LFA447 NanoFlash, Netzsch, Selb, Germany). Thermocouples were attached to the surface of the specimens. The coating contained 3 wt% of either multilayer graphene, boron nitride, or without additive as the control. The thermal conductivity of the coating was calculated according to the following equation:

$$\frac{L\_T}{k\_T} = \frac{L\_1}{k\_1} + \frac{L\_2}{k\_2} \tag{1}$$

where *L*1, *L*<sup>2</sup> and *L*<sup>T</sup> are the thicknesses of the coating, the substrate and the total thickness, respectively, and *k*1, *k*<sup>2</sup> and *k*<sup>T</sup> are the thermal conductivities of the coating, the substrate, and the overall thermal conductivity, respectively. The thickness of the aluminum plate was 1 mm, whereas that of the coating was measured using a coating thickness meter (Qnix Qua Nix 4200P, Automation Dr. Nix GmbH & Co. KG, Cologne, Germany). The coating thickness was 40 µm.

#### *2.4. Measurement of Thermal Emissivity*

The thermal emissivity was measured using an infrared emissivity detector (ED01, Conjutek Co., New Taipei City, Taiwan) in the wavelength range of 2 to 22 µm.

#### *2.5. Forced Convective Heat Transfer*

The forced convective heat transfer of the coated and bare plates was performed according to the standard of AMCA 210–07. Figure 1 depicts the experimental setup for conducting forced convection. The heat supply was set either 8 W or 16 W. The plate was placed horizontally under a flow rate of 2 m/s. Temperatures were measured at four points on the bottom surface of the plate.

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**Figure 1.** The experimental setup for conducting forced convection. **Figure 1.** The experimental setup for conducting forced convection.

#### *2.6. Natural Convective Heat Transfer 2.6. Natural Convective Heat Transfer 2.6. Natural Convective Heat Transfer*

The natural convective heat transfer was performed by placing the plate horizontally as illustrated in Figure 2. The temperature was monitored until reaching steady state. The natural convective heat transfer was performed by placing the plate horizontally as illustrated in Figure 2. The temperature was monitored until reaching steady state. The natural convective heat transfer was performed by placing the plate horizontally as illustrated in Figure 2. The temperature was monitored until reaching steady state.

**Figure 2.** The experimental setup for conducting natural convection. **Figure 2.** The experimental setup for conducting natural convection. **Figure 2.** The experimental setup for conducting natural convection.

#### **3. Results and Discussion 3. Results and Discussion 3. Results and Discussion**

#### *3.1. Characteristics of Graphene and Powder Coating 3.1. Characteristics of Graphene and Powder Coating 3.1. Characteristics of Graphene and Powder Coating*

Table 3 and Figure 3 show the characteristics of the graphene obtained from the supplier. From the Raman spectrum of graphene, there are three distinct absorption peaks: D peak at 1353 cm−1, G peak at 1581 cm−1, and 2D peak at 2720 cm−1. The ID/IG is about 0.05 and the I2D/IG is about 0.36, indicating that this is multilayer graphene. The AFM image shows that the horizontal dimension of the graphene sheet is between 3–25 μm. Table 3 and Figure 3 show the characteristics of the graphene obtained from the supplier. From the Raman spectrum of graphene, there are three distinct absorption peaks: D peak at 1353 cm−1, G peak at 1581 cm−1, and 2D peak at 2720 cm−1. The ID/IG is about 0.05 and the I2D/IG is about 0.36, indicating that this is multilayer graphene. The AFM image shows that the horizontal dimension of the graphene sheet is between 3–25 μm. Table 3 and Figure 3 show the characteristics of the graphene obtained from the supplier. From the Raman spectrum of graphene, there are three distinct absorption peaks: D peak at 1353 cm−<sup>1</sup> , G peak at 1581 cm−<sup>1</sup> , and 2D peak at 2720 cm−<sup>1</sup> . The ID/I<sup>G</sup> is about 0.05 and the I2D/I<sup>G</sup> is about 0.36, indicating that this is multilayer graphene. The AFM image shows that the horizontal dimension of the graphene sheet is between 3–25 µm.

**Table 3.** Characteristics of graphene nanoparticles. **Item Properties Test Method Table 3.** Characteristics of graphene nanoparticles. **Table 3.** Characteristics of graphene nanoparticles.


specific surface area (m2/g) 25–50 specific surface area tester

**Figure 3.** The characteristics of graphene nanoparticles. (**a**) SEM image; (**b**) Raman spectrum; (**c**) AFM image. **Figure 3.** The characteristics of graphene nanoparticles. (**a**) SEM image; (**b**) Raman spectrum; (**c**) AFM image.

Figure 4 shows the SEM image of the cross section of graphene-loaded coating as well as the EDS images of carbon and oxygen. These images indicated that graphene nanoparticles were well distributed in the coating matrix. Furthermore, Table 4 shows that the carbon content in the coating with graphene was slightly higher than that in the pristine coating, indicating the presence of graphene. Some micro-scale aggregates were observable in Figure 4a. Similar observation was also reported in the literature [12]. This may affect the thermal conductivity of the coating, however, it is out of scope of this study. Figure 4 shows the SEM image of the cross section of graphene-loaded coating as well as the EDS images of carbon and oxygen. These images indicated that graphene nanoparticles were well distributed in the coating matrix. Furthermore, Table 4 shows that the carbon content in the coating with graphene was slightly higher than that in the pristine coating, indicating the presence of graphene. Some micro-scale aggregates were observable in Figure 4a. Similar observation was also reported in the literature [12]. This may affect the thermal conductivity of the coating, however, it is out of scope of this study.

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**Figure 4.** The SEM image of the graphene-loaded coating. (**a**) The micrograph of cross-section; (**b**) EDS images of carbon and oxygen. **Figure 4.** The SEM image of the graphene-loaded coating. (**a**) The micrograph of cross-section; (**b**) EDS images of carbon and oxygen.


**Table 4.** Atomic compositions of the coatings with or without graphene from EDS results. **Table 4.** Atomic compositions of the coatings with or without graphene from EDS results.

Graphene loaded nanocomposites have been considered for thermal managements. There are several reviews regarding the thermal conductivity of graphene-polymer composites [13–15]. In recent years, graphene and expanded graphite have been widely studied as nanofillers for polymer composites, as thermal interface materials and heat sinks [16–19]. In addition to the extremely high thermal conductivity of single-layer graphene, two-dimensional morphology also makes graphene more conducive, thus improving heat transfer performance. The thermal conductivity of graphenepolymer composites is affected by factors including loading, graphene orientation, and interface [20]. Graphene exhibits a very high specific surface area leading to large interface with the polymer chains, and causing phonon scattering and hence ultra-high interface thermal resistance. Therefore, heat is difficult to transfer through the graphene-polymer interface. In addition, when the loading of graphene is above the percolation threshold, the thermal conductivity of this composite would be Graphene loaded nanocomposites have been considered for thermal managements. There are several reviews regarding the thermal conductivity of graphene-polymer composites [13–15]. In recent years, graphene and expanded graphite have been widely studied as nanofillers for polymer composites, as thermal interface materials and heat sinks [16–19]. In addition to the extremely high thermal conductivity of single-layer graphene, two-dimensional morphology also makes graphene more conducive, thus improving heat transfer performance. The thermal conductivity of graphene-polymer composites is affected by factors including loading, graphene orientation, and interface [20]. Graphene exhibits a very high specific surface area leading to large interface with the polymer chains, and causing phonon scattering and hence ultra-high interface thermal resistance. Therefore, heat is difficult to transfer through the graphene-polymer interface. In addition, when the loading of graphene is above the percolation threshold, the thermal conductivity of this composite

increased significantly. When the orientation of graphene is in the direction of heat flow, facilitating the formation of thermal conductive channel and hence improve the thermal conductivity. However, would be increased significantly. When the orientation of graphene is in the direction of heat flow, facilitating the formation of thermal conductive channel and hence improve the thermal conductivity. However, in this study, the powder was deposited onto the substrate through electrostatic spraying, thus these graphene nanosheets were randomly oriented.

This study chose thermoset powder coating as the research object. A thermoset resin is used as the film forming material, and a hardener with a crosslinking reaction is added to form an insoluble, non-melting hard coating after heating. Such a coating would not soften like thermoplastic coating even at elevated temperatures; it can only fracture. Since the resin used in the thermoset powder coating is a low molecular weight pre-polymer with a low degree of polymerization, it has good leveling and decorative properties. Moreover, this low molecular weight pre-polymer can be crosslinked into 3D network after curing, endowing the coating good corrosion resistance and mechanical properties. This has led to rapid development of the thermoset powder coating.

### *3.2. Thermal Conductivity*

Table 5 shows the thermal conductivities of the coated and uncoated aluminum plates. The overall thermal conductivity was reduced from 196.7 W/m-K of the bare aluminum to 88.2 W/m-K of the epoxy/BN coated aluminum plate. This indicates that the coating on the surface can impair the heat conduction. This may appear to violate the purpose of improving thermal dissipation. However, the heat generated from the electronic elements dissipates to the ambient through not only conduction but also convection and radiation. In the subsequent sections, the coating actually did facilitate the dissipation of the heat.


**Table 5.** Thermal conductivity of the aluminum plates with or without coating \*.

\* *T* = 25 ◦C, Light voltage = 250 V, pulse width = 0.02 ms, model = Cowan.

The thermal conductivity of the coating in Table 5 was calculated from the overall thermal conductivity according to Equation (1). Three types of coating were measured: pristine epoxy-polyester coating (EPC), BN-loaded (EBN) and graphene-loaded (EGR) epoxy-polyester coating. The thermal conductivity of the BN-loaded coating was slightly higher than that of the pristine epoxy coating. On the other hand, the loading of graphene improved the thermal conductivity of the coating to above 6 folds. This is reasonable since graphene is well-known for high thermal conductivity. Because the pristine epoxy-polyester coating exhibited low thermal conductivity, this coating was not studied further in the subsequent heat transfer experiments. Only Al, EBN and EGR were employed in the heat transfer tests.

#### *3.3. Thermal Emissivity*

Table 6 shows the emissivity of the samples in the wavelength range from 2 to 22 µm. In general, the emissivity values of metals are low while those of polymers are much higher. In this study, EBN coating appears white, whereas EGR coating appears black.

**Table 6.** The emissivities of aluminum plate and two types of coatings \*.


#### *3.4. Forced Convective Heat Transfer*

and forced convection.

In order to investigate the role of radiation heat transfer in the thermal dissipation performance of coating, the aluminum plates were subject to heat transfer experiments under natural convection and forced convection. *Polymers* **2020**, 4, x FOR PEER REVIEW 8 of 15

Table 7 summarizes the results of heat transfer under forced convection. For a small object in a big room, the radiative heat flux was calculated according to the Stefan-Boltzmann Law: [21] In order to investigate the role of radiation heat transfer in the thermal dissipation performance

of coating, the aluminum plates were subject to heat transfer experiments under natural convection

$$q\_r = \varepsilon \sigma (T\_s^4 - T\_a^4) \tag{2}$$

where *q<sup>r</sup>* is the radiative heat flux from the sample to the ambient, ε is the emissivity of the surface, <sup>σ</sup> is the Stefan-Boltzmann constant (5.67 <sup>×</sup> <sup>10</sup><sup>8</sup> <sup>W</sup>/m/<sup>K</sup> 4 ), and *T<sup>s</sup>* and *T<sup>a</sup>* are respectively the surface temperature and ambient temperature (in K). The convective heat flux (*qc*) equals the total heat flux (*qt*) minuses the radiative heat flux. The radiative heat transfer ratio is *q<sup>r</sup>* /*qt* . For bare aluminum plate, because of low emissivity, the radiative heat transfer ratio was 1.7–1.9%. However, for aluminum plates coated with epoxy-polyester resin loaded with BN or graphene, the radiative heat transfer ratio increased to 8.9–9.4% and 15.9–16.6%, respectively. These additional heat flux would improve the heat dissipation, making the surface temperature lower, thus the heating source (e.g., IC or LED) would be cooler. Indeed, the surface temperature for EGR were 7 ◦C and 13 ◦C lower than those for bare aluminum when the heat flux was respectively 800 and 1600 W/m<sup>2</sup> . big room, the radiative heat flux was calculated according to the Stefan-Boltzmann Law:[21] 4 4 ( ) *r sa q TT* = − εσ (2) where *qr* is the radiative heat flux from the sample to the ambient, *ε* is the emissivity of the surface, σ is the Stefan-Boltzmann constant (5.67 × 108 W/m/K4), and *Ts* and *Ta* are respectively the surface temperature and ambient temperature (in K). The convective heat flux (*qc*) equals the total heat flux (*qt*) minuses the radiative heat flux. The radiative heat transfer ratio is *qr*/*qt*. For bare aluminum plate, because of low emissivity, the radiative heat transfer ratio was 1.7–1.9%. However, for aluminum plates coated with epoxy-polyester resin loaded with BN or graphene, the radiative heat transfer ratio increased to 8.9–9.4% and 15.9–16.6%, respectively. These additional heat flux would improve the heat dissipation, making the surface temperature lower, thus the heating source (e.g., IC or LED) would be cooler. Indeed, the surface temperature for EGR were 7 °C and 13 °C lower than those for

Figure 5 shows that the convective heat flux depends linearly with the temperature difference. The slope (28.456 W/m2K) is the convective heat transfer coefficient under this specific test condition. The coefficient of determination (R<sup>2</sup> ) was 0.996, indicating that this correlation fits very well to the experimental results. We can use this value to predict the heat dissipation rate at other heat flux at the same air flow speed. Furthermore, the heat transfer coefficient is independent on the substrate, whether it is bare aluminum or coated with a layer of polymer coating. bare aluminum when the heat flux was respectively 800 and 1600 W/m2. Figure 5 shows that the convective heat flux depends linearly with the temperature difference. The slope (28.456 W/m2K) is the convective heat transfer coefficient under this specific test condition. The coefficient of determination (R2) was 0.996, indicating that this correlation fits very well to the experimental results. We can use this value to predict the heat dissipation rate at other heat flux at the same air flow speed. Furthermore, the heat transfer coefficient is independent on the substrate, whether it is bare aluminum or coated with a layer of polymer coating.

**Figure 5.** The linear correlation between convective heat flux and temperature difference. **Figure 5.** The linear correlation between convective heat flux and temperature difference.

The Reynolds number Re (= *uL*/*ν*) for this test condition was around 1.2 × 104, less than 5 × 105, suggesting the air flow was laminar. For laminar forced convection, the heat transfer coefficient based on boundary layer model is as follows The Reynolds number Re (<sup>=</sup> *uL*/ν) for this test condition was around 1.2 <sup>×</sup> <sup>10</sup><sup>4</sup> , less than 5 <sup>×</sup> <sup>10</sup><sup>5</sup> , suggesting the air flow was laminar. For laminar forced convection, the heat transfer coefficient based on boundary layer model is as follows

$$h\_L = 0.664 Pr^{1/3} Re\_L^{1/2} \left(\frac{k}{L}\right) \tag{3}$$

where *L* is the length of the plate, *k* is the thermal conductivity of air, *Pr* is the Prandtl number of the air, *Re* is the Reynolds number of the air stream, *u* is the speed of the air stream, and ν is the kinematic viscosity the air. The resultant convective heat flux was then calculated as

$$q\_{fc} = h\_L(T\_s - T\_a) \tag{4}$$

The calculated results were presented in Figure 5 as well. However, the heat transfer coefficient (the slope) was only 60% of the experimental results. This probably is due to the turbulence in the actual measuring environment, which would accelerate heat transfer.

#### *3.5. Natural Convective Heat Transfer*

In addition to forced convection, natural convection is the other path for heat dissipation. Table 8 summarizes the results of heat transfer under natural convection. All the conditions were the same as in Section 3.4, except there was no air flowing on the surface. The temperature difference was higher that its counterpart in Table 7, suggesting that natural convection is slower than forced convection in heat dissipation. Furthermore, because of higher surface temperature, the radiative heat flux in natural convection was higher than in forced convection. Consequently, the convective heat flux in natural convection was lower than in forced convection, reflecting the slower heat dissipation in natural convection. The order of the radiative heat transfer ratio was the same as in Table 7, that is, EGR > EBN > Al. This order is the same as that of the emissivity, suggesting that graphene-loaded coating can enhance heat dissipation.

**Table 7.** The heat transfer rates by convection and radiation under forced convection \*.


\* RH = 76.2%, *P*amb = 747.5 mm Hg, air flow rate = 2 m/s.



Natural convection is a result of the motion of the fluid due to density changes arising from the heating. In this study, the heated plate was placed horizontally, inducing an upward air stream. The flow pattern is complicate. No reliable empirical correlation is capable to predict the heat transfer. Therefore, we construct an empirical correlation of convective heat flux vs temperature difference. Because the aluminum plate has a low emissivity, the aluminum plate was used to measure the surface temperature for a series of total heat fluxes. The convective heat flux was obtained by subtracting the

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radiative heat flux from the total heating flux. Figure 6 shows that the convective heat flux depends on the temperature difference. Linear regression yielded a quadratic correlation with R<sup>2</sup> equals to 0.981.

$$q\_{\mathbb{C}} = 0.0369(\Delta T)^2 + 12.27\Delta T \tag{5}$$

**Figure 6.** The convective heat fluxes of coated and uncoated aluminum plates under natural **Figure 6.** The convective heat fluxes of coated and uncoated aluminum plates under natural convection.

#### convection. *3.6. Heat Transfer Coe*ffi*cients*

hT (W/m2K) 26.8 ±

hc (W/m2K) 26.4 ±

hr (W/m2K) 0.46 ±

hr/hT (%) 1.7 ±

2.1

2.1

0.02

0.2

29.4 ± 0.8

26.8 ± 0.9

2.62 ± 0.09

8.9 ± 0.6

35.4 ± 0.6

29.7 ± 0.4

5.63 ± 0.17

15.9 ± 0.2

28.5 ± 2.0

28.0 ± 2.0

0.53 ± 0.02

1.9 ± 0.2

*3.6. Heat Transfer Coefficients*  Table 9 summarizes heat transfer coefficients calculated from the experimental results in Tables 7 and 8. Heat transfer coefficient is the measure of heat dissipation. Among these heat transfer Table 9 summarizes heat transfer coefficients calculated from the experimental results in Tables 7 and 8. Heat transfer coefficient is the measure of heat dissipation. Among these heat transfer coefficients, the total heat transfer coefficient (*h*T) was calculated as follows:

coefficients, the total heat transfer coefficient (*h*T) was calculated as follows:

$$h\_{\rm T} = q\_{\rm T} / \Delta T \tag{6}$$

and the convective heat transfer coefficient (*h*c) and the radiative heat transfer coefficient (*h*r) were calculated respectively as follows: and the convective heat transfer coefficient (*h*c) and the radiative heat transfer coefficient (*h*r) were calculated respectively as follows:

$$
\Delta h\_{\odot} = q\_{\odot} / \Delta T \tag{7}
$$

$$h\_{\mathbf{r}} = q\_{\mathbf{r}} / \Delta T \tag{8}$$

19.6 ± 1.3

13.2 ± 1.3

6.41 ± 0.03

32.8 ± 2.3

16.3 ± 0.2

15.6 ± 0.2

0.68 ± 0.00

4.1 ± 0.1

20.2 ± 0.5

16.7 ± 0.5

3.52 ± 0.01

17.4 ± 0.5

23.0 ± 1.0

15.6 ± 1.0

7.40 ± 0.07

32.2 ± 1.7

where Δ*T* is the temperature difference between the surface temperature and the ambient temperature. where ∆*T* is the temperature difference between the surface temperature and the ambient temperature.

**Table 9.** Comparison of heat transfer coefficients in forced and natural convection. **Forced Convection Natural Convection**  These three heat transfer coefficients are affected by three factors: type of convection, surface coating, and total heat flux. The weight of each factor on each coefficient can be evaluated statistically with analysis of variance (ANOVA).

Surface AL EBN EGR AL EBN EGR AL EBN EGR AL EBN EGR qT (W/m2) 800 800 800 1600 1600 1600 800 800 800 1600 1600 1600

> 37.5 ± 0.6

> 31.3 ± 0.4

> 6.22 ± 0.18

> 16.6 ± 0.2

14.4 ± 0.2

13.8 ± 0.2

0.55 ± 0.00

3.8 ± 0.1

17.9 ± 0.9

14.9 ± 0.9

2.98 ± 0.01

16.7 ± 0.9

31.3 ± 0.8

28.3 ± 0.9

2.95 ± 0.11

9.4 ± 0.6

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**Table 9.** Comparison of heat transfer coefficients in forced and natural convection.

#### 3.6.1. Total Heat Transfer Coefficient These three heat transfer coefficients are affected by three factors: type of convection, surface

Table 10 presents the results of ANOVA for total heat transfer coefficient. The results show that all three factors significantly affect *h*T. Among these factors, the type of convection was the most influential while *q*<sup>T</sup> was the least. coating, and total heat flux. The weight of each factor on each coefficient can be evaluated statistically with analysis of variance (ANOVA). 3.6.1. Total Heat Transfer Coefficient

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Error 55.78 31 1.8

**Table 10.** Results of ANOVA for total heat transfer coefficient. Table 10 presents the results of ANOVA for total heat transfer coefficient. The results show that all three factors significantly affect *h*T. Among these factors, the type of convection was the most

Figure 7 shows that the total heat transfer coefficient of the forced convection was about twice of that of the natural convection. This reflects the fact that forced convection can remove heat faster than natural convection. Furthermore, bare aluminum surface exhibited lower *h*<sup>T</sup> and *h*r than the other two coated surfaces. This can be attributed to the faster radiative heat transfer from coated aluminum plates, and that graphene-loaded coating exhibited higher *h*<sup>T</sup> than other surfaces, since the emissivity of EGR was much higher than others. Figure 7 also shows that higher total heat flux (*q*T) led to higher *h*<sup>T</sup> for each surface. In forced convection, the increase was at most 6%, whereas in natural convection, the increase jumped to 17%. However, the effect of *q*<sup>T</sup> was less than the effect of the surface, which is consistent with ANOVA. Total 1931.88 35 55.20 Figure 7 shows that the total heat transfer coefficient of the forced convection was about twice of that of the natural convection. This reflects the fact that forced convection can remove heat faster than natural convection. Furthermore, bare aluminum surface exhibited lower *h*T and *h*r than the other two coated surfaces. This can be attributed to the faster radiative heat transfer from coated aluminum plates, and that graphene-loaded coating exhibited higher *h*T than other surfaces, since the emissivity of EGR was much higher than others. Figure 7 also shows that higher total heat flux (*q*T) led to higher hT for each surface. In forced convection, the increase was at most 6%, whereas in natural convection, the increase jumped to 17%. However, the effect of *q*T was less than the effect of the surface, which is consistent with ANOVA.

**Figure 7.** Effect of surface type on the total heat transfer coefficient. **Figure 7.** Effect of surface type on the total heat transfer coefficient.

#### 3.6.2. Convective Heat Transfer Coefficient 3.6.2. Convective Heat Transfer Coefficient

Table 11 shows that the major factor affecting *h*<sup>c</sup> was the type of convection. Figure 8 also shows that the *h*<sup>c</sup> of forced convection was about twice of that of natural convection This is expected because *h*<sup>c</sup> is the "convective" heat transfer coefficient. The type of surface coating affects less significantly to *h*c. This is obvious because thermal radiation depends only on the temperature difference and would not affect the air flow.

The ANOVA results indicated that *q*<sup>T</sup> was the minor factor for *h*c. This is supported in Figure 8 that higher q<sup>T</sup> led to slightly higher *h*c. In forced convection, according to Equation (3), the convective heat transfer coefficient is proportional to the thermal conductivity of the air, which increases with the temperature. Because the surface temperature increased with the total heat flux, leading to higher thermal conductivity and hence higher *h*c. However, the increase in *h*<sup>c</sup> was small, thus the slope of q<sup>c</sup> in Figure 5 was a constant, suggesting a constant *h*c. heat transfer coefficient is proportional to the thermal conductivity of the air, which increases with the temperature. Because the surface temperature increased with the total heat flux, leading to higher thermal conductivity and hence higher hc. However, the increase in *h*c was small, thus the slope of qc in Figure 5 was a constant, suggesting a constant *h*c.

that higher qT led to slightly higher *h*c. In forced convection, according to Equation (3), the convective

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Table 11 shows that the major factor affecting *h*c was the type of convection. Figure 8 also shows that the hc of forced convection was about twice of that of natural convection This is expected because hc is the "convective" heat transfer coefficient. The type of surface coating affects less significantly to hc. This is obvious because thermal radiation depends only on the temperature difference and would

In natural convection, Figure 6 shows that *q*<sup>c</sup> is a quadratic function of ∆*T*, thus *h*<sup>c</sup> is a linear function of ∆*T*: In natural convection, Figure 6 shows that *q*c is a quadratic function of Δ*T*, thus *h*c is a linear function of Δ*T*:

$$h\_{\odot} = 0.0369(\Delta T) + 12.27\tag{9}$$

However, the prefactor 0.0369 was small, making a weak dependency of *h*<sup>c</sup> on ∆T. However, the prefactor 0.0369 was small, making a weak dependency of hc on ΔT.

**Table 11.** Results of ANOVA for convective heat transfer coefficient.


**Figure 8.** Effect of surface type on the convective heat transfer coefficient. **Figure 8.** Effect of surface type on the convective heat transfer coefficient.

#### 3.6.3. Radiative heat transfer coefficient 3.6.3. Radiative Heat Transfer Coefficient

Table 12 shows the ANOVA results and that for *h*r, the major factor is the surface coating and the minor factor is the type of convection. The total heat flux affected the least the radiative heat transfer. The radiative heat transfer increased with the emissivity of the surface. In this study, the emissivity varied greatly, ranging from 0.07 for aluminum, 0.4 for BN-loaded coating, to 0.88 for grapheneloaded coating. Thus, the effect of emissivity on *h*r is significant. Figure 9 also shows this effect. The type of convection affected *h*r through *T*s and *T*a, because hr can be calculated as follows: Table 12 shows the ANOVA results and that for *h*r, the major factor is the surface coating and the minor factor is the type of convection. The total heat flux affected the least the radiative heat transfer. The radiative heat transfer increased with the emissivity of the surface. In this study, the emissivity varied greatly, ranging from 0.07 for aluminum, 0.4 for BN-loaded coating, to 0.88 for graphene-loaded coating. Thus, the effect of emissivity on *h*<sup>r</sup> is significant. Figure 9 also shows this effect. The type of convection affected *h*<sup>r</sup> through *T*<sup>s</sup> and *T*a, because *h*<sup>r</sup> can be calculated as follows:

$$h\_{\mathbf{r}} = \sigma \varepsilon \left( T\_{\mathbf{s}}^{\ \ \ \ \mathbf{r}} + T\_{\mathbf{a}}^{\ \ \ \ \ \mathbf{r}} \right) \left( T\_{\mathbf{s}} + T\_{\mathbf{a}} \right) \tag{10}$$

The surface temperature was lower for forced convection because of higher *h*c.

Figure 9 summarizes the effect of surface coating on *h*r. The difference between convection types was less than that between surfaces. The effect of *q*<sup>T</sup> was further lower than the effect of convection.


Total 214.154 35 6.119

**Table 12.** Results of ANOVA for radiative heat transfer coefficient. was less than that between surfaces. The effect of *q*T was further lower than the effect of convection.

Figure 9 summarizes the effect of surface coating on hr. The difference between convection types

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*h*r = *σ*ε (*T*s2 + *T*a2) (*T*s + *T*a) (10)

**Figure 9.** Effect of surface type on the radiative heat transfer coefficient. **Figure 9.** Effect of surface type on the radiative heat transfer coefficient.

#### **4. Conclusions 4. Conclusions**

The transfer of heat from the source (IC, LED, etc.) to the sink (ambient) involves both heat convection and heat conduction. There is another route for heat dissipation occurring in the ambient, that is, radiation, as long as the surface temperature is different to the ambient temperature. In nature and in engineering, the natural cooling or heating of objects is achieved by natural convection heat transfer. The intensity of natural convection heat transfer is weak, especially in the air environment, with radiation heat transfer of the same order of magnitude. At relatively high temperatures, the intensity of radiative heat transfer is much stronger than that of natural convective heat transfer. Therefore, in the actual calculation of natural convective heat transfer, radiative heat transfer should not be neglected. In this study, graphene nanoparticles were blended into epoxy-polyester powder. Aluminum The transfer of heat from the source (IC, LED, etc.) to the sink (ambient) involves both heat convection and heat conduction. There is another route for heat dissipation occurring in the ambient, that is, radiation, as long as the surface temperature is different to the ambient temperature. In nature and in engineering, the natural cooling or heating of objects is achieved by natural convection heat transfer. The intensity of natural convection heat transfer is weak, especially in the air environment, with radiation heat transfer of the same order of magnitude. At relatively high temperatures, the intensity of radiative heat transfer is much stronger than that of natural convective heat transfer. Therefore, in the actual calculation of natural convective heat transfer, radiative heat transfer should not be neglected.

plate was then coated with aforementioned powder blends. For comparison, BN-loaded coating plates were also prepared. The thermal conductivity of the coating was improved from 5 W/m∙K to 6 and 33.3 W/m-K for the BN- and graphene-loaded coating, respectively. The performance of heat dissipation of the resulting plates was further investigated under forced and natural convection. Under the forced convection, the radiative heat transfer coefficient (hr) of the bare Al plate took about 1.8% of the total heat transfer coefficient (hT), whereas for the graphene-loaded coating, hr took about In this study, graphene nanoparticles were blended into epoxy-polyester powder. Aluminum plate was then coated with aforementioned powder blends. For comparison, BN-loaded coating plates were also prepared. The thermal conductivity of the coating was improved from 5 W/m·K to 6 and 33.3 W/m-K for the BN- and graphene-loaded coating, respectively. The performance of heat dissipation of the resulting plates was further investigated under forced and natural convection. Under the forced convection, the radiative heat transfer coefficient (*h*r) of the bare Al plate took about 1.8% of the total heat transfer coefficient (*h*T), whereas for the graphene-loaded coating, *h*<sup>r</sup> took about 16% of *h*T. Therefore, radiative heat transfer is not negligible in heat dissipation through forced convection.

Under the natural convection, the *h*<sup>r</sup> of bare Al plate was about 4% of *h*T, while the *h*r/*h*<sup>T</sup> of graphene-loaded coating was about 33%, indicating that the thermal radiation cannot be ignored in the dissipation through natural convection.

The heat dissipation in this study showed that thermal radiation is a non-negligible route under either forced convection or natural convection. Based on this finding, a thin layer of graphene-loaded coating with a high emissivity can improve the heat dissipation performance of metal substrate.

**Author Contributions:** F.K., prepared experiments, as well as wrote the original draft; M.-C.Y., supervised the research project and finalized the manuscripts. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
