Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns

A high heat flux-sustaining system providing cooling in the range of 10-10⁵ W/cm² is required in the emerging fields of electronics, defense, avionics, and nuclear device development. Conventional cooling with air is insufficient for these applications due to the low heat-transfer coefficient (HTC) for both free- and forced-convection conditions. The phase change-based cooling techniques, such as pool boiling and flow boiling, are good enough to remove high heat fluxes on the order of 10 - 1,000 W/cm^{2 1}. Since the two-phase heat-transfer process is isothermal, the cooled device temperature is almost constant over its surface. Due to the negligible variation of the temperature along the surface, the thermal shock of the device can be eliminated. However, the major limiting parameter in boiling heat-transfer is the critical heat flux (CHF), which causes an abnormal rise in temperature².

In the last few decades, extensive research has been carried out to improve the CHF by using surface modification, nanofluids, and surface coatings^{3,4,5,6,7,8,9,10,11}. Among the various methods, surface coatings are found to be the best method to improve the CHF due to the substantial increase in the surface area. Surface coatings generally increase the heat transfer by fin action, porosity effects, and surface wettability¹². Surface wettability plays a significant role in boiling heat-transfer. Previous studies show that at lower heat-flux conditions, the hydrophobic surface shows better HTC due to the early nucleation. However, at higher heat flux, the detachment of the formed bubbles is slow due to the low affinity of water towards the surface. This leads to bubble coalescence and results in a lower CHF³. On the other hand, a hydrophilic surface produces a higher CHF, because of the fast detachment of the formed bubbles, but it gives a lower HTC at low heat fluxes, due to the delay in bubble nucleation¹³.

The hybrid structures show a remarkable enhancement in boiling heat-transfer for all heat fluxes due to the combined effect of hydrophobicity and hydrophilicity^14,15,16. Hsu et al. produced heterogeneous wettable surface by coating superhydrophilic Si nanoparticles on a masked copper surface. They achieved different wettability ratios by varying the coating time. The onset of boiling occurred earlier on the heterogeneous surfaces compared to the homogeneous surface, which substantially reduced the wall superheat¹⁷. Jo et al. conducted nucleate boiling heat-transfer studies on hydrophilic, hydrophobic, and heterogeneous wetting surfaces. The heterogeneous wetting surface was composed of hydrophobic patterned dots on the hydrophilic surface. They got higher HTCs and the same CHF for the heterogeneous surface as compared to the hydrophilic surface. An improvement in boiling heat-transfer directly depends upon the number of dots on the surface and upon the boiling conditions¹⁸.

In this study, axial hybrid wettable patterns were produced on a cylindrical copper surface using the dip coating technique. Pool-boiling heat-transfer studies were conducted to determine the effects of the number of interlines and of the orientation of the hybrid wettable pattern. Boiling heat flux, HTC, and bubble dynamics were analyzed for the all coated substrates and were compared with the copper substrate.

1. Preparation of the Modified Surfaces

1. Manually polish the test piece (hollow copper cylinder with a 40-mm length (l), a 25-mm outer diameter (d_o), and an 18-mm inner diameter (d_i)) for 15 min using a ＃2,000 emery paper. Clean the polished surface by rinsing it with acetone followed by DI water.
2. Place the polished test piece in an oven for 2 h at a constant temperature of 120 °C.
3. Prepare a superhydrophilic SiO₂ nanoparticle solution using the following steps.
   1. Prepare solution A by mixing 1:4 molar ratios of tetraethoxy silane and DI water. Add 2 drops of 37% concentrated HCl to solution A and stir for 2 h.
   2. Make solution B by mixing a 1:3 molar ratio of ethanol and DI water.
   3. Mix 1 mL of solution A to 80 mL of solution B and stir for 2 h.
   4. Add 32 g of SiO₂ nanoparticles (40-nm diameter) to the prepared solution and stir for 1 h.
4. Immerse the test piece in the prepared solution by using the dip-coating apparatus at a velocity of 5 mm/min. Keep the coated test piece in an oven at 120 °C for 1 h.
5. Prepare 2, 4, and 8 interlined hybrid patterns with different orientations along the axial direction (as shown in Figure 1) using the following steps.
   1. Mask the area to be uncoated using the insulation tape according to the required number of interlines with the proper orientation (For the 2-interline surface at a 0° orientation, adjust interlines at the center and the superhydrophilic area (area to be coated )on the top side. On the other hand, for the 90° orientation, adjust one interline at the top and another at the bottom and for the 180° orientation, adjust superhydrophilic area at the bottom and the interlines at the center. Similarly, adjust the position of the 4, 8 interlined surfaces with the different orientation as shown in Figure 1).
   2. Immerse the masked test piece in the prepared solution by using a dip-coating apparatus, dip at a high dipping velocity and rise at a slow velocity of 5 mm/min.  Keep the coated test piece in an oven at 120 °C for 1 h.
   3. Remove the insulation tape from the masked area to obtain the required number of interlines with the proper orientation.

Figure 1. Selection of Various Interlined Surfaces. (a) Schematic of various interlined surfaces with different orientations. The area ratio of a plain copper surface and a superhydrophilic surface is 1:1 in all conditions. (b) Orientation selection criteria. (c) Isometric view of the 2 interline 0° angle oriented surface. Orientation is selected as the angle between the baseline and coating center line of the first hydrophilic pattern from the top side and it is measured in a clockwise direction. Please click here to view a larger version of this figure.

2. Experimental Procedure

1. Using the insulation tape, fix one glass tube at each circular base of the coated test piece.
2. Horizontally fix this assembly to the 140- x 140- x 160-mm chamber (as shown in Figure 2) using silicon paste according the required position of interlines.
3. Place a 550-W, 18-mm diameter, and 40 mm-long cartridge heater with a thin film of thermal paste on the circumferential area into the hole of the test piece.
4. Connect the cartridge heater to a direct current (DC) power supply unit.
5. Place T-type thermocouples into the 8 equally-spaced 1-mm holes, with alternate depths of 5 mm and 7 mm as shown in Figure 3 Connect them to the data logger.
6. Insert and fix resistance temperature detectors (RTD), a reflux condenser, and an auxiliary heater in the spaces provided on the top cover. Fix them over the boiling chamber.
7. Fill 1,400 mL of DI water into the pool-boiling chamber.
8. Connect the reflux condenser to a cooling chamber that is maintained at 5 °C.
9. Prior to the experiment, vigorously boil the DI water in the pool-boiling chamber for 30 min using the auxiliary heater.
10. Keep the DI water at the saturated boiling condition by using the auxiliary heater. Subsequently, switch on the power supply and give an initial current of 0.1 A.
11. Wait for 2 min in order to reach a steady state. Then, increase the electric current with increments of 0.3 A.
12. Record the temperature at each power input by using the data logger. Continue the experiment until a maximum current of 4 A is reached. Meanwhile, record the bubble dynamics for each power input by using a CCD camera placed in front of the pool-boiling chamber, which is focused on the test piece.

Figure 2. Schematic of the Pool-boiling Chamber. Glass tubes are connected to both sides of the hollow copper cylinder with silicon paste. This is fixed to the pool-boiling chamber with silicon paste. Please click here to view a larger version of this figure.

Figure 3. Thermocouple Positioning. 8 thermocouples are placed inside the 1 mm diameter holes circumferentially in the test piece place at a diameter of 20 mm. The depths of alternate 1mm diameter holes are fixed at 5 mm and 7 mm respectively. Please click here to view a larger version of this figure.

3. Data Reduction

1. Calculate the heat input (Q) by using the following equation¹⁹
   Q = IV     (1)
   NOTE: I and V are the input current in amps and the voltage in volts, respectively.
2. Estimate the heat loss (Q_loss) from the two side surfaces by using the formula¹⁹:
        (2)
   NOTE: k is the thermal conductivity of copper; T_{7 mm} and T_{5 mm} are the average values of the temperature at depths of 7 mm and 5 mm, respectively; Δx (2 mm) is the difference between the depths; and
   is the cross-sectional area of the test piece.
3. Determine the heat flux (q'') by using the following formula¹⁹:
        (3)
   NOTE: A = πd_ol is the circumferential area of the test piece.
4. Calculate the wall superheat (using the following equation¹⁹:
        (4)
   NOTE: T_m is the average of T_{7 mm} and T_{5 mm}, is the length of the test piece, r_o (12.5 mm) outer radius of the test piece, r_m (10 mm) radius of the test piece at the measuring holes, and T_sat is the saturation temperature of DI water as shown in Figure 4.
5. Calculate the HTC (α) using the following formula¹⁹:
        (5)

Figure 4. Schematic of Wall Temperature Analysis. Wall temperature is calculated using the measured average temperature and known cylindrical thermal resistance. Please click here to view a larger version of this figure.

Pool-boiling heat-transfer experiments were conducted on a hybrid wettable cylindrical surface using the experimental setup whose schematic is shown in Figure 5. The pool-boiling experimental procedure explained in step 2 of the protocol section was successfully carried out while investigating the effect of the number of interlines and of the orientation of the hybrid wettable pattern on the pool-boiling performance. The pool-boiling performances of the different-treated surfaces were represented in terms of graphs: the heat flux versus the wall superheat and the HTC versus the heat flux.

In order to validate the experimental setup, pool boiling experimental heat transfer results of the plain copper surface were compared with the theoretical correlation predicted by Cornwell and Houston in 1994²⁰, as shown in the following equation:

     (6)

where N_u is the Nusselt number; A = 9.7p_c^0.5, with p_c = 221.2 bar; F(p) = 1.8p_r^0.17 + 4p_r^1.2 + 10p_r¹⁰, with p_r = p/p_c and p = 1.013 bar; Re_b is the boiling Reynolds number calculated by using Equation 7, and Pr is the Prandtl number.

     (7)

where q'' is the heat flux, D is the outer diameter of the test piece, μ_f is the dynamic viscosity, and h_fg is the latent heat of vaporization at saturation temperature.
The experimental Nusselt number is calculated by using the following equation:

     (8)

where α is the HTC and k_f is the thermal conductivity of the working fluid.

Figure 6 shows the validation graph. The experimental Nusselt number is almost the same as the theoretical correlation Nusselt number for a particular Reynolds number.

Experimental uncertainty in the calculated heat flux, the wall super heat and the HTC were calculated using Kline and McClintn method²¹. Uncertainty in heat flux, the wall super heat and the HTC were estimated in the range ±15.3%, ± 1.7%, ± 15.5% respectively.

Figure 5. Schematic of the experimental setup. The experimental setup used to investigate the pool-boiling performances. Please click here to view a larger version of this figure.

Figure 6. Validation of the experimental setup. A comparison between the present results and the correlation reported by Cornwell and Houston¹⁶ in a logarithmic scale. Please click here to view a larger version of this figure.

Figure 7 (a) shows pool-boiling curves of the plain copper surface, a fully superhydrophilic surface, and hybrid surfaces with different numbers of interlines at a 0^o orientation. The pool-boiling curve was obtained by plotting the graph of the heat flux versus the wall superheat. The heat flux and wall superheat were calculated by using Equations 3 and 4, respectively. A leftward shift in the pool-boiling curve was obtained for the 8-interline surface, whereas the 2- and 4-interline surfaces showed almost similar values. Figure 7 (b) shows the graph of the HTC versus the heat flux of different surfaces. The HTC is calculated by using Equation 5. The HTCs of different surfaces were compared, and the 8-interline surface showed the highest value, whereas the homogeneous superhydrophilic surface showed the lowest value.

Bubble nucleation sites of the different surfaces were recorded using a CCD camera. Figure 8 indicates that the number of bubbles on the fully superhydrophilic surface is the lowest, and with an increase in the number of interlines, the bubbles were also found to increase.

The pool-boiling performance of 2-, 4-, and 8-interlined surfaces and with different orientations are shown in Figures 9 and 10. As compared to the pool-boiling curve of the 0° orientation, the 180° orientation showed a rightward shift. In the case of 2-interlined surfaces with different degrees of angular orientation, the 0° orientation showed a better boiling performance. 4- and 8-interlined surfaces gave their maximum enhancement at orientations of 90° and 45°, respectively. In these cases, the positions of the superhydrophilic surfaces were just above the lowermost interlines. Figure 11 shows the best pool-boiling performances of different interlines. With an increase in interline number, the HTCs are found to improve.

Figure 7. Pool-boiling performance at a 0° orientation. (a) Boiling curves for the various surfaces. (b) Graph of the HTC versus the heat flux. Please click here to view a larger version of this figure.

Figure 8. Photographs of bubble nucleation. (a) Plain surface. (b) Superhydrophilic surface. (c) 2-interlined surface. (d) 4-interlined surface. (e) 8-interlined surface. Please click here to view a larger version of this figure.

Figure 9. Effect of orientation on the pool-boiling curve. Pool-boiling curves of (a) a 2-interlined surface, (b) a 4-interlined surface, and (c) an 8-interlined surface with different orientations. Please click here to view a larger version of this figure.

Figure 10. Effect of orientation on the HTC versus the heat flux. The HTC versus the heat flux graph of (a) a 2-interlined surface, (b) a 4-interlined surface, and (c) an 8-interlined surface with different orientations. Please click here to view a larger version of this figure.

Figure 11. Comparison of the best pool-boiling performances. (a) Boiling curves for the various surfaces. (b) Graph of the boiling HTC versus the heat flux. Please click here to view a larger version of this figure.

The main goal of this investigation was to develop a pool-boiling heat sink for high heat dissipation applications, such as nuclear reactors, boilers, and heat pipes, by introducing the hybrid wettable surface, as described in the protocol section. These surfaces can produce better pool-boiling performances than homogeneous wettable surfaces (hydrophilic and hydrophobic). The improvement in the boiling heat-transfer performance is due to an increase in active nucleation sites and the easy detachment of the formed bubbles from the surface. In this study, we considered the effects of the number of interlines and the orientation of the hybrid wettable patterns on the pool-boiling performance. The maximum number of interlines was limited to 8 due to the manual preparation method used. The precise positioning of interlines is crucial for all experiments, as a slight misalignment in position will lead to incorrect results. Furthermore, the maximum applied-input current plays a significant role in the life of the cartridge heater. In this study, for safety purposes, the maximum input current is limited to 4 A. Due to this limitation, pool-boiling heat-transfer studies were carried out for only the lower heat flux condition. It is impossible to determine the CHF by using the present experimental setup.

Hybrid wettable patterns play a key role in boiling heat-transfer. The boiling performance of axial interlaced hybrid structures on a cylindrical copper surface depends on the number of interlines and on the orientation of the hybrid wettable pattern. With an increase in the number of interlines, the boiling performance was found to be improved. This is due to the increase in nucleation sites on the interlines. The different hybrid wettable patterns and the position of the superhydrophilic surface play an important role in boiling heat-transfer. The lowermost interlines with an upper superhydrophilic surface give better heat-transfer performances due to the easy detachment of the formed bubbles from the interlines. During the pool-boiling experiment, the formed bubbles usually try to bend towards the top surface. Because of the low affinity of bubbles to the superhydrophilic surface, they will easily detach from the interlines, which in turn improves the pool-boiling performance.

In conclusion, the pool-boiling performance of the axial interline surfaces depends on both the number of interlines and on the orientation of the hybrid wettable pattern. With an increase in number of interlines, the nucleation sites increase, so the detachment of the formed bubbles from the lowermost interlines with an upper superhydrophilic surface will be fast.