**3.2 Experimental setup of the thermal performance test for the ultrathin vapor chamber**

When the assembly of the ultrathin vapor chamber is completed, a certain amount of water is filled into the inner space of the vapor chamber before the experimental tests. The vapor chamber is evacuated to 1 Pa and filled with different charge ratio η, which is defined as:

$$
\eta = \frac{V\_{\text{water}}}{V\_{\text{total}}} \times \mathbf{100} \text{\%} \tag{3}
$$

Where, *V*water is the volume of water inside the vapor chamber and *V*total is the total volume of the inner space for the vapor chamber. As shown in **Figure 11(a)**, the evacuated ultrathin vapor chamber only has a less than 200 μm thickness.

The LW-9510 vapor chamber thermal performance measurement apparatus (LongWin Co., Ltd.) is adopted for evaluating the thermal performance of the vapor chamber. The vapor chamber is heated at the evaporator side by a heater with an 8 mm × 8 mm footprint and cooled on the outer surface of the condenser by an adjustable cooling fan with a 6.875 cfm flow rate at 22°C room temperature, as shown in **Figure 11(b)**. Besides, Teflon material is used as thermal insulation materials to reduce heat loss, making the maximum heat loss is only 0.41 W in the tests. One T-type thermocouple is attached to the center of the condenser outer surface (*T*1) and 4 T-type thermocouples are attached at the side of the surface (*T*2, *T*3, *T*4, and *T*5), as shown in **Figure 11(c)**. A T-type thermocouple Five is inserted into the block below the center of the evaporator with a 1 mm distance to measure the heater temperature (*T*h), which is shown in **Figure 11(d)**.

The authors examine the thermal performance of the ultrathin vapor chambers in the horizontal and vertical direction using horizontal thermal resistance (*R*hr) and vertical thermal resistance (*R*vr), respectively, which are defined as:

$$R\_{hr} = \frac{T\_1 - T\_{\text{avg}\,(2-5)}}{Q} \tag{4}$$

$$R\_{\nu\nu} = \frac{T\_b - T\_{\text{avg}(1-5)}}{Q} \tag{5}$$

*Multiscale Micro/Nanostructured Heat Spreaders for Thermal Management of Power Electronics DOI: http://dx.doi.org/10.5772/intechopen.100852*

#### **Figure 11.**

*(a) The thickness of an evacuated ultrathin vapor chamber and the schematic of the experimental setup: (b) apparatus; (c) temperature measurement points on the top of the vapor chamber; and (d) heater temperature measurement [22].*

Where, *Q* is the input power measured by a power sensor of the LW9510, *T*avg(1–5) = (*T*1 + *T*2 + *T*3 + *T*4 + *T*5)/5 and *T*avg(2–5) = (*T*2 + *T*3 + *T*4 + *T*5)/4. *T*b is the temperature at the center of the evaporator outside surface, which is calculated based on Fourier's law:

$$T\_b = T\_h - ql \not\models k\_{\text{Cu}} \tag{6}$$

where *l* is the distance from the location of *T*h to the center of the evaporator outside surface, which has a value of 0.001 m. *k*Cu is the thermal conductivity of copper with a value of 401 W/(m·K). *q* is the input heat flux, which is defined as:

$$q = \mathbb{Q} \wr A\_h \tag{7}$$

Where, *A*h is the footprint of the heater.

For characterizing the temperature uniformity of the vapor chamber and comparing it with copper, other materials, or commercial vapor chambers, the in-plane effective thermal conductivity (*K*eff) is defined as:

$$K\_{\rm eff} = k\_{\rm Cu} R\_{h\nu, Cu} \;/\; R\_{h\nu, nc} \tag{8}$$

Where, *R*hr,Cu is the measured horizontal thermal resistance of copper.

The uncertainties are calculated based on the indirect parameter uncertainty analysis: if *F Fx x x* = ( 1 2 ,,, ,,, ,,, *<sup>n</sup>* ) , the uncertainty of *F* can be calculated by:

$$\mathbf{U}\_F = \left[ \left( \frac{\partial F}{\partial \mathbf{x}\_1} \mathbf{U}\_1 \right)^2 + \left( \frac{\partial F}{\partial \mathbf{x}\_2} \mathbf{U}\_2 \right)^2 + \dots + \left( \frac{\partial F}{\partial \mathbf{x}\_n} \mathbf{U}\_n \right)^2 \right]^{1/2} \tag{9}$$

Where *U*1, *U*2, …, *U*n are the uncertainties of *x*1, *x*2, …, *x*n, respectively. The maximum uncertainty of the heat flux *q*, horizontal thermal resistance *R*hr and vertical thermal resistance *R*vr under 95% confidence level are ±0.4%, ±6.1%, and ± 2.5%, respectively.

### **3.3 Effect of the wettability patterned surface on the thermal performance of the ultrathin vapor chamber**

**Figure 12** presents the experimental results of the thermal performance of the ultrathin vapor chambers. In this section, the thermal performance of the vapor chamber case 2 and case 3 are compared with each other to investigate the effect of wettability patterned surface as the only difference between them is whether a wettability pattern is integrated into the evaporator or not.

**Figure 12(c)** and **(e)** show the horizontal thermal resistance of the vapor chamber case 2 and case 3, respectively. The horizontal thermal resistance of case 2 for all the charge ratios first quickly decreases with the increase of the heat flux from 8.59 W/cm2 to 14.53 W/cm2 . Then it gradually decreases when the heat flux increases from 14.53 W/cm2 to 23.91 W/cm2 . On the other hand, the horizontal thermal resistance always decreases with the decrease of the charge ratio at a certain heat flux. Thus, the minimum horizontal thermal resistance exists at the 23.91 W/cm2 heat flux of 60.4% charge ratio, which is 0.170°C/W. Compared with case 2, case 3 shows a similar trend but a lower horizontal thermal resistance under the same test conditions. For example, the horizontal thermal resistance at the 8.59 W/cm2 of 60.4% charge ratio is 0.666°C/W for case 2 while it is only 0.295°C/W for case 3, which is only 44.3% of the previous. The minimum horizontal thermal resistance of case 2 is only 0.055°C/W occurring at 23.91 W/cm2 heat flux of 60.4% charge ratio. The comparison proves integrating a wettability pattern to the inner surface of the evaporator of the ultrathin vapor chamber can greatly enhance the horizontal thermal performance of the ultrathin vapor chamber.

**Figure 12(d)** and **(f )** present the vertical thermal resistance of the vapor chamber case 2 and case 3, respectively. The vertical thermal resistance of case 2 for large charge ratio (65.2, 67.6, and 70.1%) gradually decreases with the increases of the heat flux, proving case 2 with large charge ratios does not reach the partial dryout condition. When the charge ratio is less than 65.2%, case 2 starts partial dry-out at the heat flux of 23.91 W/cm2 , due to an insufficient amount of water returning to the evaporator. Though a small charge ratio gives a lower vertical thermal resistance if partial dry-out does not happen, the minimum thermal resistance for large charge ratios is close to that for the small charge ratio. This is because case 2 with a large charge ratio can work at a higher heat flux, leading to a further decrease of the vertical thermal resistance. The minimum vertical thermal resistance of case 2 is 1.37°C/W, happening at the heat flux of 19.84 W/cm<sup>2</sup> of 62.8% charge ratio. However, though the trend of the vertical thermal resistance of case 3 is similar to case 2, case 3 does not shows an improvement of the vertical thermal performance. When the charge ratio is small (60.4% and 62.8%), case 3 starts partial dry-out at a lower heat flux which is 19.84 W/cm2 . Besides, the vertical thermal resistance for all the charge ratios at a certain heat flux of case 3 is larger than that of case 2. The minimum thermal resistance for case 3 is just 1.54°C/W at 23.91 W/cm<sup>2</sup> heat flux of 70.1% charge ratio. Therefore, the evaporator integrated with the wettability

*Multiscale Micro/Nanostructured Heat Spreaders for Thermal Management of Power Electronics DOI: http://dx.doi.org/10.5772/intechopen.100852*

**Figure 12.**

*Thermal performance of the ultrathin vapor chambers: Horizontal thermal resistance (a), (c), and (e); vertical thermal resistance (b), (d), and (f) [22].*

pattern does not enhance the vertical thermal performance in this study. One possible reason is the large area of hydrophobic islands deteriorates the backflow ability of the wick structure. The capillary pressure determined the backflow ability of the wick structure, which can be calculated by [22]:

$$P\_{\rm Cap.} = \frac{2\sigma\cos\theta}{r\_{\rm eff}}\tag{10}$$

where *σ* is the surface tension of the working fluid, *r*eff is the effective radius of the wick structure and *θ* is the working fluid contact angle on the wick structure. Since part of the working fluid returns to the evaporator through the interface between the wick structure and the wettability patterned surface, the contact angle may be larger considered the effect of hydrophobic islands. Moreover, the area fraction of hydrophobic islands in this study reaches 47.9%, giving that cosθ in Eq. (10) for case 3 may be much smaller than that for case 2. Thus, the backflow ability of the wick structure for case 3 is poorer than that of case 2, leading to lower cooling performance. Another possible reason is the photoresist, which may be left on the surface after the fabrication, releases non-condensable gas during the tests and deteriorate the backflow ability due to its hydrophobicity. Therefore, optimizing the design of the fabrication process may improve the vertical thermal performance of the ultrathin vapor chambers.

Generally, a wettability pattern can greatly enhance the temperature uniformity and is also promising to lower the vertical thermal resistance of a vapor chamber. In the next section, the authors will present that only changing the wettability of the condenser can also improve the temperature uniformity of a vapor chamber.
