1. Introduction

2. Experiments

2.1. Experimental Setup

The experimental setup is shown in Error! Reference source not found.. This setup aimed to investigate the effects of anisotropic properties on microgroove flat copper surfaces during pool boiling heat transfer. All experiments were conducted under atmospheric pressure and the working fluid was maintained at saturation temperature. The dielectric liquid (Novec-7100, 3M) was employed as the working fluid in experiments. An auxiliary heater (CCTCL) connected to an autotransformer (CCTCL) was used to maintain the saturated state of the working fluid. To supply power to the test sample, a cartridge heater (220 V/800 W, CCTCL) was used and inserted into a copper block, as shown in Error! Reference source not found.. The heat input to the cartridge heater was regulated by a DC power supply (GPR-20H50D, GW Instek). The copper block was covered by a PEEK holder (0.25 W/m·K) to ensure thermal insulation. Three T-type thermocouples (CCTCL) connected to a data logger (MX100) were inserted into the copper block to record temperature data for heat transfer analysis, as depicted in Error! Reference source not found.. To reduce heat resistance, thermal grease (SG-7650, Hasuncast) with a thermal conductivity of 0.94 W/m·K was applied to the surface of the cartridge heater and the thermocouples. The test sample with a thickness of 2 mm and a diameter of 16 mm was pasted on the top surface of the copper block (Error! Reference source not found.), and a thermal grease made of the liquid metal (Thermalright, Silver King, 79 W/m·K) was applied at the interface between the test sample and copper block.

To maintain the working fluid’s circulation and atmospheric pressure, a coil condenser (CCTCL) was installed inside the boiling chamber and connected to the cooling system. The cooling coil was able to condense the saturated vapor back to the bulk liquid pool. High-speed visualization of boiling bubbles was captured by using a high-speed camera (AOS technologies AG, Promon U800) with a fixed frame rate at 210 fps and a spatial resolution of 1280 × 1024. A white light-emitting diode was used for illumination during high-speed recording.

Figure 1. Schematic of the pool boiling experimental setup.

Figure 1. Schematic of the pool boiling experimental setup.

Figure 2. Three-dimensional computer-aided design of the boiling chamber.

Figure 2. Three-dimensional computer-aided design of the boiling chamber.

Figure 3. Design of the test section.

Figure 3. Design of the test section.

2.2. Properties of Working Fluid

To prevent electricity conduction, dielectric fluid with a high dielectric constant is widely used in immersion cooling [43]. The boiling experiment is a simple way to investigate the two-phase heat transfer performance of dielectric liquid. In some previous studies, the dielectric liquid has been employed as a working fluid for boiling experiments [44,45]. The dielectric liquid produced by 3M company consists of the FC and Novec series. The primary difference between these two series lies in their global warming potential (GWP). The Novec series offers a significantly lower GWP, making it a superior alternative to the FC series. Therefore, Novec-7100 with a lower GWP and a boiling point of 61℃ was chosen as the working fluid in this study. Unlike DI water, Novec-7100 exhibits a much lower surface tension (9.3 mN/m) and boiling point (61℃). Due to a significant reduction in surface tension, the CA of Novec-7100 on plain copper surface is ~15°, which is ~73° for DI water. The properties of DI water and Novec-7100 are listed in Error! Reference source not found..

Table 1. Properties of Novec-7100 and DI water at their boiling points.

Table 1. Properties of Novec-7100 and DI water at their boiling points.

Property	DI water	Novec-7100
Boiling point (℃)	100	61
Density (kg/m3)	957.9	1418
Thermal conductivity (W/m·K)	0.679	0.062
Heat of vaporization (kJ/kg)	2257	112
Specific heat (J/kg-K)	4217	1254
Surface tension (mN/m)	60.8	9.3
GWP	--	297
CA for plain copper surface	~73°	~15°

2.3. Surface Preparation

The flat copper samples with a thickness and diameter of 2 mm and 16 mm were used as the test surfaces in boiling experiments. The procedure for fabricating smooth copper surfaces is illustrated in Error! Reference source not found. (a). To remove the oxidation layer, the copper samples were polished by using 2000-grit sandpaper. After polishing, the samples were rinsed with deionized water and acetone. Subsequently, the copper samples were immersed in acetone and subjected to sonication for 10 min to completely remove the residue on the surface. Finally, the copper samples were dried in an oven for 10 min.

The plain copper samples were textured with microgrooves by using a femtosecond laser (Tongtai, TLFS-500). The parameters of the femtosecond laser are listed in Error! Reference source not found.. The laser system had an average power of 5.4 W, a scanning speed of 100 mm/s, and a pulse repetition rate of 1 MHz. A schematic of the laser scanning path is shown in Error! Reference source not found.. The horizontal line interval for each scanning path was 10 μm, and the diameter of the laser spot size was 15 μm. A total laser fluence of ~3 J/cm² was used to fabricate microgrooves on the plain surfaces. All the test surface conditions are listed in Error! Reference source not found.. S1 represents the plain copper surface; S2, S3, and S4 represent the microgroove surfaces under the condition of different groove spacing. The varying groove spacing was realized by changing the number of laser scanning path.

Figure 4. Surface treatment before the boiling experiments: (a) sandpaper polishing process; (b) laser texturing process.

Figure 4. Surface treatment before the boiling experiments: (a) sandpaper polishing process; (b) laser texturing process.

Figure 5. Schematic of laser scanning path and groove spacing.

Figure 5. Schematic of laser scanning path and groove spacing.

Table 2. Parameters of ultrafast femtosecond laser.

Table 2. Parameters of ultrafast femtosecond laser.

Laser parameter	Value
Fluence (J/cm2)	3
Repetition rate (MHz)	1
Scanning speed (mm/s)	100
Average power (W)	5.4
Scanning interval (μm)	10
Spot size (μm)	15

Figure 6. Schematic of test surface conditions in pool boiling experiments.

Figure 6. Schematic of test surface conditions in pool boiling experiments.

2.4. Surface Characterization

2.4.1. Surface Roughness

The images of surface morphology for all surface conditions were obtained by using a laser scanning confocal microscope (NTUME Precision Metrology Lab, Brand: Japan Keyence, Controller: VK-X1000, Measuring Head: VK-X1100). Confocal, three-dimensional, and surface profile images are shown in Error! Reference source not found. and Error! Reference source not found.. Surface roughness is a critical factor that can significantly influence boiling heat transfer performance. Many studies have focused on the roughness effect on boiling surfaces; however, very few studies have considered anisotropic surface roughness, which depends on the measurement direction in microgrooves. The measurement results in parallel and normal direction to the microgrooves are shown in Error! Reference source not found.. To provide greater detail on the morphology of microgrooves, scanning electron microscopy (SEM) images of the microgroove surfaces are presented in Error! Reference source not found..

Table 3. Surface roughness measured in parallel and normal directions on S1-S4 surfaces.

Table 3. Surface roughness measured in parallel and normal directions on S1-S4 surfaces.

Sample	Ra (parallel, μm)	Ra (normal, μm)
S1	1.31	1.73
S2	1.64	6.86
S3	1.76	6.11
S4	1.68	5.09

Figure 7. Confocal, three-dimensional (3D), and surface profile images for S1 and S2 conditions measured by using the laser confocal microscope.

Figure 7. Confocal, three-dimensional (3D), and surface profile images for S1 and S2 conditions measured by using the laser confocal microscope.

Figure 8. Confocal, three-dimensional (3D), and surface profile images for S3 and S4 conditions measured by using the laser confocal microscope.

Figure 8. Confocal, three-dimensional (3D), and surface profile images for S3 and S4 conditions measured by using the laser confocal microscope.

Figure 9. Scanning electron microscopy images for (a) S2, (b) S3, and (c) S4 surfaces.

Figure 9. Scanning electron microscopy images for (a) S2, (b) S3, and (c) S4 surfaces.

2.4.2. Surface Wettability

The surface wettability data and CA measurement images of all test samples were recorded by using a contact angle goniometer (Model 100SB, Sindatek Instruments Co., Ltd.). A 3-μL water droplet was dropped on each test sample for CA measurement. The results of the static CA and receding CA for Novec-7100 in parallel (θ₁) and normal (θ₂) directions to the microgrooves are displayed in Error! Reference source not found.. The deviation between the parallel CA and normal CA is known as the degree of anisotropy (Δθ₁₂). This concept could be observed in Liu’s study [39]. The characteristic of anisotropic wettability may also appear on a surface with a unidirectional structure [21,46]. The images of static CA and dynamic CA measurements are shown in Error! Reference source not found..

Table 4. Static and receding CA results measured in parallel and normal directions on S1-S4 surfaces.

Table 4. Static and receding CA results measured in parallel and normal directions on S1-S4 surfaces.

Static contact angle
Surface condition	θ1 (Parallel)	θ2 (Normal)	Δθ12 (Anisotropy)	Schematic
S1	18° ± 0°	15° ± 0.3°	~3°
S2	26° ± 1°	12° ± 0.3°	~14°
S3	25° ± 1°	13° ± 0.3°	~12°
S4	22° ± 1°	15° ± 1°	~7°
Receding contact angle
Surface condition	θrec1 (Parallel)	θrec2 (Normal)	Δθrec12 (Anisotropy)	Schematic
S1	17 ± 0.3°	15 ± 0.3°	~2°
S2	27 ± 1°	13 ± 0.2°	~14°
S3	24 ± 1°	14 ± 0.5°	~10°
S4	23 ± 0.7°	16 ± 0.6°	~7°

Figure 10. Images of (a) static CA and (b) receding CA measured in parallel and normal directions on S1–S4 surfaces.

Figure 10. Images of (a) static CA and (b) receding CA measured in parallel and normal directions on S1–S4 surfaces.

2.5. Data Reduction and Uncertainty Analysis

The heat loss analysis for the plain copper surface under different heat flux intervals is shown in Error! Reference source not found.. As a baseline check for experimental data, the heat loss percentages were less than 10% in experiments.

Table 5. Heat loss analysis during the boiling experiments.

Table 5. Heat loss analysis during the boiling experiments.

Specific heat flux intervals (W/cm2)	Heat loss (%)
$q^{\text{'}\text{'}}$~ 4.33	9.7
$q^{\text{'}\text{'}}$~ 10.33	4.3
$q^{\text{'}\text{'}}$~ 18.33	2.5

Due to the good insulation condition during experiments, the heat transfer mode was considered as 1D heat conduction. The temperature gradient $\frac{dT}{dx}$ was calculated by using the linear property of heat conduction as defined in Equation (1):

$$\frac{dT}{dx}=\frac{T_1-T_3}{2\Delta x}$$

(1)

where $∆x$ is the distance between the $T_1$ and $T_2$ thermocouples. The heat flux $q^{\text{'}\text{'}}$ was derived by using Fourier’s heat conduction law expressed in Equation (2):

$$q\mathrm{”}=-k_{Cu}\frac{dT}{dx}$$

(2)

where $k_{Cu}$ is the thermal conductivity of copper (400 W/m·K). The surface temperature$T_w$ was estimated through back-calculation as Equation (3):

$$T_w=T_1-q”(\frac{d_{Cu}}{k_{Cu}}+\frac{d_{grease}}{k_{grease}})$$

(3)

where $k_{grease}$ is the thermal conductivity of the thermal grease (79 W/m·K), $d_{Cu}$ is the distance between the $T_1$ thermocouple and the upper surface, and $d_{grease}$ is the thickness of the applied thermal grease. The wall superheat ${∆T}_w$ was estimated by using Equation (4):

$${∆T}_w=T_w-T_{sat}$$

(4)

where $T_{sat}$ represents the saturation temperature of the working fluid. The saturation temperature for Novec-7100 is 61℃.

Finally, the boiling heat transfer coefficient h was evaluated by using Equation (5).

$$h=\frac{q”}{∆T_w}$$

(5)

The estimation of uncertainties within specific heat flux intervals was conducted by using Taylor’s method [47]. The uncertainty analysis of the S1 surface is presented in Error! Reference source not found.. The subsequent equations are the general forms of uncertainty calculation. Equation (6) is the general formula for determining uncertainties for various parameters, including heat flux, wall superheat, and HTC. U_p denotes the uncertainty in the derived parameter p, whereas Ua_exp represents the uncertainties associated with all the measured parameters indicated as a_exp.

$$U_p=\sqrt{\sum _{i=1}^n{\left(\frac{\partial p}{\partial a_{exp}}{U}_{a_{exp}}\right)}^2}$$

(6)

The calculation of uncertainty for heat flux was performed by using Equation (7):

$$\frac{U_{q^{\text{'}\text{'}}}}{q^{\text{'}\text{'}}}={\left[{\left(\frac{{k_{Cu}U}_{T_2-T_1}}{2∆xq}\right)}^2+{\left(\frac{{k_{Cu}U}_{T_3-T_2}}{2∆xq}\right)}^2+{\left(\frac{k_{Cu}(T_2-T_1)U_{∆x}}{2{∆x}^{2}q}\right)}^2+{\left(\frac{k_{Cu}(T_3-T_2)U_{∆x}}{2{∆x}^{2}q}\right)}^2\right]}^{\frac{1}{2}}$$

(7)

Equation (8) was applied to determine the uncertainty of wall superheat:

$$\frac{U_{T_w}}{T_w}={\left[{\left(\frac{U_{T_1}}{T_w}\right)}^2+{\left(\frac{d_{Cu}{U}_q}{k_{Cu}{T}_w}\right)}^2+{\left(\frac{q{U}_{d_{Cu}}}{k_{Cu}{T}_w}\right)}^2\right]}^{\frac{1}{2}}$$

(8)

To estimate the uncertainty of the HTC, Equation (9) was employed:

$$\frac{U_h}{h}={\left[{\left(\frac{U_q}{q}\right)}^2+{\left(\frac{U_{∆T}}{∆T}\right)}^2\right]}^{\frac{1}{2}}$$

(9)

Table 6. Uncertainty analysis for a plain copper surface (S1) using Novec-7100 as the working fluid at differing heat flux intervals.

Table 6. Uncertainty analysis for a plain copper surface (S1) using Novec-7100 as the working fluid at differing heat flux intervals.

Specific heat flux intervals (W/cm2)	Uncertainty parameter
	Tw (K)	h (W/cm2·K)
$q^{\text{'}\text{'}}$~ 2.09	0.27	0.02
$q^{\text{'}\text{'}}$~ 10.23	0.56	0.03
$q^{\text{'}\text{'}}$~ 19.14	0.87	0.05

3. Results and Discussion

3.1. Validation of Experimental Setup

To validate the experimental setup, the pool boiling curve for a plain copper surface using Novec-7100 as the working fluid was compared with the Rohsenow correlation [48] and other related literature [49,50]. The widely used correlation proposed by Rohsenow is expressed in Equation (10):

$${q^{\text{'}\text{'}}}_{nucleate}={\mu }_l{h}_{lv}{\left[\frac{g({\rho }_l-{\rho }_v)}{\sigma }\right]}^{0.5}{\left(\frac{c_{pl}{∆T}_{sat}}{C_{sf}{h}_{lv}{Pr}^n}\right)}^3$$

(10)

where ${\mu }_l$ is the dynamic viscosity of liquid, $h_{lv}$ is the latent heat,$g$ is the gravitational acceleration, ${\rho }_l$ is the density of liquid, ${\rho }_v$ is the density of vapor, σ is the surface tension, $c_{pl}$ is the specific heat of liquid, ${∆T}_{sat}$ is the wall superheat, $Pr$ is the Prandtl number, $C_{sf}$ is the surface-fluid factor, and n is the experimental constant.

In the current study, n equals to 1.7 for fluids other than water. The surface-fluid combination $C_{sf}$ equals to 0.0036 based on the experimental data for Novec-7100 [51,52]. As depicted in Error! Reference source not found., the boiling results for plain surface in the present work are almost consistent with the Rohsenow correlation and those related studies. However, due to the prediction limit of the Rohsenow correlation, the experimental data diverges at the high heat flux regime. Vapor film gradually forms from the intensified bubble aggregation at this regime, which deteriorates the heat transfer rate. Therefore, the boiling curve diverges to the right in the end. Similar phenomena can be found in the literature above [49,50].

Figure 11. Pool boiling curves of a plain copper surface using Novec-7100 as the working fluid compared with Rohsenow correlation [48] and related literature [49,50].

Figure 11. Pool boiling curves of a plain copper surface using Novec-7100 as the working fluid compared with Rohsenow correlation [48] and related literature [49,50].

3.2. Evaluations of Boiling Heat Transfer Data

Error! Reference source not found. illustrates the boiling curves (a) and HTC curves (b) for all test conditions. Error! Reference source not found. presents the increment in HTCs relative to the plain surface (S1) at the highest heat flux of S4 (22.44 W/cm²). S2 exhibited the greatest leftward-shifted boiling curve, with an HTC enhancement by a factor of 1.37 compared with that of S1. Although the HTCs of S3 and S4 were lower than that of S2, theirs still increased by a factor of 1.18 and 1.05, respectively, relative to the reference condition (S1). For CHF values, the boiling tests conducted using microgroove surfaces as test surfaces exhibited slightly lower CHF than the plain surface. A minor decrease in CHF was attributed to the earlier bubble aggregation on microgroove surfaces, which led to a large vapor slug hindering the heat transfer between surface and liquid. As a result, the highest HTC improvement between all test surfaces was increased by a factor of 37% due to the enhanced bubble nucleation facilitated by characteristics of anisotropic wettability and roughness. More details of bubble dynamics supported by the high-speed visual study will be introduced in the following section.

Figure 12. (a) Pool boiling curves of test conditions using Novec-7100 as the working fluid; (b) HTCs of test conditions using Novec-7100 as the working fluid.

Figure 12. (a) Pool boiling curves of test conditions using Novec-7100 as the working fluid; (b) HTCs of test conditions using Novec-7100 as the working fluid.

Table 7. Boiling results under S1–S4 conditions.

Table 7. Boiling results under S1–S4 conditions.

Surface condition	ΔTw,ONB (K)	CHF (W/cm2)	HTC (W/cm2K)	hSN / hS1
S1	10.29	25.08	1.10	--
S2	5.56	24.09	1.51	1.37
S3	5.85	23.32	1.30	1.18
S4	6.43	22.44	1.16	1.05

1.3. Effect of Anisotropic Wettability and Roughness

Error! Reference source not found. (a)(b) illustrates the mechanism of bubble nucleation and liquid rewetting ability on microgroove surfaces. As depicted in the figure, more bubble nucleation sites were activated when the wettability in the parallel direction was lower. In addition, higher wettability in the normal direction provided good rewetting ability because it facilitated liquid spreading [40]. Therefore, a superior heat transfer performance was achieved with a larger CA difference between parallel and normal directions, denoted as a higher anisotropy. The experimental results showed that the S2, S3, and S4 surfaces demonstrated greater heat transfer performance than the S1 surface due to their increased anisotropy observed in Error! Reference source not found.. Supported by slightly increased anisotropy, the S2 surface with the smallest groove spacing exhibited higher HTC and a similar CHF than the S3 and S4 surfaces.

The effects of anisotropic roughness can be observed in Error! Reference source not found. and Error! Reference source not found. (c)(d). In the normal direction, S2, S3, and S4 surfaces exhibited more significant surface roughness compared with that of the plain surface (S1). For the S1 condition, the surface was relatively smooth, leading to limited space for nucleation. On the contrary, the microgroove surfaces with sufficient space on the grooves could provide more nucleation sites. The strengthened nucleation ability achieved superior HTC on the microgroove surfaces. Similar boiling experiment results could be observed in previous studies [23,53]. In the end, the average roughness factors are shown in Error! Reference source not found. (d). These roughness factors were mainly affected by the groove spacing, suggesting that the smaller the groove spacing was selected, the larger the roughness factor was derived. This was because more numbers of microgrooves could be presented on the test surface with a shorter spacing. With a larger space for bubble nucleation, the S2 surface could exhibit a superior HTC than that of the S3 and S4 surfaces.

Figure 13. Mechanism of structure-induced anisotropic properties: (a)(b) surface wettability effect; (c)(d) surface roughness effect.

Figure 13. Mechanism of structure-induced anisotropic properties: (a)(b) surface wettability effect; (c)(d) surface roughness effect.

3.4. Analysis of Bubble Dynamics

Visualizations of bubble dynamics at four different heat flux intervals that were obtained by using a high-speed camera are shown in Error! Reference source not found.. Due to the increased surface roughness in the normal direction and the increased CA in the parallel direction, the number of bubble nucleation sites on the S2, S3, and S4 surfaces surpassed that of S1 at low heat flux regime. Unlike S1 surface, bubbles started to nucleate at lower wall superheats (5.56 ~ 6.43 K) on S2–S4 surface. Supported by high-speed images in Error! Reference source not found., the emerging bubbles were more pronounced on S2–S4 surfaces compared with that of S1 at the heat flux of ~1.79 W/cm². The difference in the bubble nucleation ability can be attributed to the lower wettability in the parallel direction for S2–S4 surfaces, which was induced by the more significant energy barrier of microgroove surfaces in the parallel direction. As stated by Liu [39] et al., this energy barrier prevented liquid droplets from collapsing and penetrating the microgrooves in the normal direction. Therefore, this phenomenon caused a less-wetted condition that lowered the minimum surface energy requirement to activate the bubble nuclei. A preferable bubble nucleation environment was formed with the assistance of a larger directional wettability difference and increased surface roughness in the normal direction. With an earlier onset of nucleate boiling and an increased number of nucleated bubbles, as presented in Error! Reference source not found., the S2–S4 surfaces could transfer more heat through the help of liquid–vapor phase change.

After the ONB, a large number of bubbles emerged and started to dominate the test surface at a low heat-flux interval (1.79–4.21 W/cm²). At this heat flux regime, the bubble departure frequency was noticeably increased, making it challenging to examine the bubble behavior. As the process continued, the interaction between bubbles intensified, causing smaller bubbles to merge and form larger ones at the moderate heat-flux interval (4.21–12.27 W/cm²). The rapid aggregation and coalescence of bubbles propelled boiling to the high heat-flux interval (12.27–21.59 W/cm²). When the heat flux reached ~22.44 W/cm² on the S4 surfaces, the generated bubbles no longer had sufficient time to depart from the test surface. Consequently, these numerous bubbles coalesced to form a large vapor film that covered the entire surface. As depicted in Error! Reference source not found., larger vapor columns rapidly developed on S1-S4 surfaces at the high heat flux regime because of the over-intensified bubble coalescence, resulting in a vapor film. Due to the low thermal conductivity of the vapor film, effective heat transfer was hindered, leading to the occurrence of film boiling.

Figure 14. High-speed visualization of bubble dynamics on S1–S4 surfaces at differing heat flux regimes.

Figure 14. High-speed visualization of bubble dynamics on S1–S4 surfaces at differing heat flux regimes.

The bubble evolution cycle was another critical factor affecting the boiling heat transfer performance. As shown in Error! Reference source not found., the bubble detachment rate of S2 surface was much shorter compared with S1, S3, and S4 surfaces at the low heat flux regime (~1.79 W/cm²). This is because the wettability in the normal direction for S2 was higher than other test surfaces (Error! Reference source not found.). Enhanced liquid replenishment would accelerate the bubble evolution cycle. This efficient bubble detachment rate could facilitate heat dissipation. As presented in Error! Reference source not found., S3 also demonstrated a rapid bubble departure rate. As a result, the difference in directional wettability and surface roughness played a crucial role in reducing the surface wall superheat and achieving a higher heat transfer rate compared to S1. The S2 surface with more nucleation sites, an earlier ONB, and a faster bubble evolution cycle resulted in a most significant improvement of heat transfer performance for all four test conditions.

Figure 15. Analysis of bubble evolution cycle on S1–S4 surfaces at the heat flux of ~1.79 W/cm².

Figure 15. Analysis of bubble evolution cycle on S1–S4 surfaces at the heat flux of ~1.79 W/cm².

3.5. Discussion on CHF Correlations

In terms of CHF performance, S2, S3, and S4 surfaces exhibited slightly lower CHF values of ~24.09 W/cm², ~23.32 W/cm², and ~22.44 W/cm², respectively, compared with that of S1 surface (~25.08 W/cm²). This suggested that the higher parallel CA and higher surface roughness of microgroove surfaces may cause slightly lower CHF values, primarily due to the over-intensified interaction of bubbles on these surfaces. Error! Reference source not found. illustrates that on S2–S4 surfaces, large vapor slugs formed at the heat flux of ~21.59 W/cm², impeding heat transfer from the test surface to the working fluid. Thus, slightly lower CHFs were achieved compared with that of the plain surface (S1).

A comparison between the CHF values obtained in the present study and those predicted by existing models is presented in Error! Reference source not found.. One notable model proposed by Zuber [54], as shown in Equation (10), is based on hydrodynamic instability theory:

$${q\text{'}\text{'}}_{CHF}=K{h}_{fg}{\left[\sigma g{{\rho }_v}^2\left({\rho }_l-{\rho }_v\right)\right]}^{\frac{1}{4}}$$

(10)

where K is the dimensionless CHF ratio, which equals 0.131 in Zuber’s model, $h_{fg}$ is the latent heat, $\sigma$ is the surface tension of the working fluid, g is the gravitational acceleration constant, and ${\rho }_v$ and ${\rho }_l$ are the density of the working fluid in vapor and the liquid phase, respectively. However, this model solely accounts for the effect of pool hydrodynamics during boiling and neglects the influence of test surface characteristics. As expressed in Equation (11), Kandlikar [55] developed an extended model of Zuber’s, which incorporated the effect of surface wettability:

$${q\text{'}\text{'}}_{CHF}={\rho }_v{h}_{fg}\left(\frac{1+\cos {\theta }_{rec}}{16}\right){\left[\frac{2}{\pi }+\frac{\pi }{4}\left(1+\cos {\theta }_{rec}\right)\cos \omega \right]}^{1/2}{\left[\frac{\sigma g\left({\rho }_l-{\rho }_v\right)}{{{\rho }_v}^2}\right]}^{1/4}$$

(11)

where ${\theta }_{rec}$ is the receding CA, and $\omega$ is the incline angle. $\omega$ equals to 0 on a horizontal surface. In this correlation, CHF values increased with the increase in surface wettability. As depicted in Error! Reference source not found., deviations between our CHF results on microgroove structures and Kandlikar’s prediction model emerged due to insufficient consideration of the effects of surface morphology. Thus, a modified correlation combined both surface wettability and roughness factor was introduced by Chu [56]. Chu’s correlation is presented in Equation (12):

$${q\text{'}\text{'}}_{CHF}={\rho }_v{h}_{fg}\left(\frac{1+\cos \theta }{16}\right){\left[\frac{2(1+\alpha )}{\pi (1+\cos \theta )}+\frac{\pi }{4}\left(1+\cos \theta \right)\cos \omega \right]}^{1/2}{\left[\frac{\sigma g\left({\rho }_l-{\rho }_v\right)}{{{\rho }_v}^2}\right]}^{1/4}$$

(12)

where$\theta$ is the apparent CA. r is the roughness factor, which is defined as the ratio of the real wetted area to the projected base area.$\alpha$ equals to $\mathrm{r}\cos {\theta }_{rec}$. In Error! Reference source not found., the roughness factor r was calculated for all test surfaces in the present study. As a result, our CHF values match well with Chu’s theoretical prediction due to consideration on the effect of surface wettability and roughness factor induced by the microgroove structure. As a result, the CHF values of microgroove surfaces can be well predicted within a 10% error by using Chu’s prediction model.

Figure 16. Comparison of the CHF values in present work with related prediction models [54,55,56].

Figure 16. Comparison of the CHF values in present work with related prediction models [54,55,56].

4. Conclusions

Nomenclature

References

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