Pool boiling enhancement through bubble induced convective liquid flow in feeder microchannels

Boiling is as an effective heat dissipation mode and enhancement in Critical Heat Flux (CHF) and heat transfer coefficient (HTC) is desired in many applications including IC chip cooling in computers, and steam generators in power plants and process applications. The heat transfer performance is affected by the surface morphology which affects the nucleation characteristics and wicking behavior on the heater surface.^1–3 In the past decade, researchers have identified various mechanisms to enhance the nucleation characteristics on the heater surface.^4,5 The following mechanisms have led to the development of surfaces for enhancing CHF and HTC.

• Area enhancement—Although tall fins are attractive in low heat flux applications, such as with refirgerants,⁶ they introduce large conduction resistance and are not suitable when both CHF and HTC enhancements are desired. Cooke and Kandlikar⁷ developed open microchannel surfaces on copper essentially consisting of short fins to dissipate heat fluxes in the order of 240 W/cm² with water.

• Additional nucleation sites—Porous coatings on heat transfer surfaces are the most preferred augmentation technique to alter the nucleation characteristics. Min et al.⁸ and Patil and Kandlikar⁹ have shown that modifying nucleation characteristics and facilitating liquid flow through capillary pores or channels contributed significantly in enhancing the performance.

• Liquid wettability—Incorporating nanostructures, such as nanowires, or hierarchical micro-nano structures on a heat transfer surface alters the liquid wettability characteristics. Chu et al.¹ fabricated silicon nanowires with a range of roughness values and reported a maximum CHF of 208 W/cm² for a roughness of ∼6 μm. Yao and Kandlikar¹⁰ studied micro/nano hierarchical structures that resulted in microbubble emission that significantly enhanced HTC. O'Hanley et al.² studied the effect of wettability features on a wide range of roughnesses. Betz et al.⁴ used a combination of hydrophilic and hydrophobic patterns to alter the wetting angle. Rahman et al.¹¹ investigated the effect of mixed wettability on an array of biotemplated nanostructured surfaces and reported an enhancement of 70% in CHF.

• Separate liquid-vapor pathways—Uninterrupted supply of liquid and removal of vapor to and from the nucleating region (NR), respectively, are identified to be critical in enhancing CHF. Liter and Kaviany⁵ provided vapor pathways that are separated at critical wavelengths and returned liquid through porous projections. Kandlikar¹² developed contoured fin surfaces based on the evaporation momentum force. This led to deflection of bubbles in a certain direction creating separate pathways. Jaikumar and Kandlikar¹³ designed and fabricated selectively coated configurations to increase CHF and HTC.

At CHF, a vapor blankets the heated surface as a result of increased bubble frequency and lateral bubble coalescence, and inhibits liquid supply to the nucleation sites. In order to delay the formation of the vapor blanket and to facilitate continuous liquid supply, disjunctions in the fins are proposed to serve as liquid-vapor pathways as shown in Fig. 1. The bubble departure diameter is a critical parameter which governs the lateral coalescence of bubbles and formation of separate liquid-vapor pathway.^5,12,13 In this study, the Fritz equation is employed to calculate the bubble departure diameter

where β is the receding contact angle, σ is the surface tension force, g is the gravitational force, and $ρL and ρG$ are the liquid and vapor densities, respectively. It is postulated that for water boiling on a copper heater surface at atmospheric conditions the spacing between the disjunctions on the microchannel surface should approximately be equal to the departure bubble diameter given by Eq. (1) to prevent lateral coalescence. The departure bubble diameter is calculated to be equal to 2.213 mm for β = 42.5° and the surface tension is σ = 58.91 × 10⁻³ N/m for water at 100 °C.

In the current design of the enhancement structures, the liquid supply to the nucleation sites is enhanced through feeder channels (FCs) that transport liquid from the bulk toward heater surface.¹⁴ The feeder channels provide a pathway on the heater surface for the liquid to flow uninterrupted towards the nucleation regions. Fig. 1 shows a schematic of the test surface in which nucleation occurs in the NR channels which are separated by a bank of FCs. This arrangement is referred to as NRs with FCs (NRFC). The NR channels serve as the preferential vapor generation and removal pathway with liquid addition through the FCs. Nucleation is seen to occur preferentially at the intersection of nucleating region and the feeder channels. As the separate liquid vapor pathways are established at higher heat fluxes, any nucleation occurring in the feeder channels is suppressed by the flow of cooler liquid returning from the bulk.

The spacing between the NR channels was derived from the departure bubble diameter information using Fritz equation (Eq. (1)). However, this was used as a guidance. The optimum spacing may be different because of deviations in departure bubble diameter due to the effects arising from localized geometry and heat flux levels. An optimum spacing for specific heater surface and fluid may be obtained through experiments. Therefore, four chips with NRs separated by 4.75 mm, 3 mm, 2.125 mm, and 1.6 mm, respectively, were fabricated as shown in Fig. 2. A detailed explanation of the test section geometry including the NR channel and FC dimensions, heat flux and surface temperature computation, and uncertainty analysis is provided in the supplementary material.¹⁵ 

The results are presented in a pool boiling curve which relates the heat flux and the wall superheat. The wall superheat is defined as the difference between the surface temperature of the chip and the saturation temperature of the fluid. The surface temperature is calculated as the temperature at the top of each microchannel chip. Also, a heat transfer performance plot showing the heat transfer coefficient versus the heat flux provided a clear comparison with a plain chip.

First, distilled water was boiled on a plain chip to serve as the baseline for all enhancement comparisons. This chip reached a CHF of 128 W/cm² at a wall superheat of 20 °C with an HTC of 65 kW/m² °C. Figure 3 shows a comparison of pool boiling curves for four NRFC chips (see Fig. 2) with 1–4 NR channels. All the test chips were tested until they reached CHF. The CHF and wall superheat values are tabulated in Table I. It is seen that NRFC-3 was the best performing chip with a CHF of 394 W/cm² at a wall superheat of 5.5 °C which translated to an enhancement of 209% in CHF compared to a plain chip. NRFC-1, 2, and 4 had CHFs of 350 W/cm², 285 W/cm², and 252 W/cm² at wall superheats of 13.1 °C, 11 °C, and 14.9 °C, respectively. The corresponding performance with open microchannels as reported by Cooke and Kandlikar⁷ was 244 W/cm². From a simplistic approach, although the area enhancement was reduced in the NRFC configurations compared to the open microchannels, the performance was enhanced which suggested that separate-liquid vapor pathways assisted with liquid feed channels were the driving mechanism for the enhancement as against the area augmentation.

Figure 4 shows the variation of the HTC plotted against heat flux. At CHF, HTCs of 267 kW/m² °C, 257 kW/m² °C, and 168 kW/m² °C were observed for NRFC-1, 2, and 4, respectively. NRFC-3 had the best performance with an HTC of 713 kW/m² °C representing an exceptional enhancement of 996% in the HTC at CHF over a plain chip.

Of particular interest is the trend showing lower wall superheats at higher heat fluxes with NRFC-3. This trend is similar to the trend in the boiling curve seen for the contoured fin,¹² where the reduction in wall superheat at higher heat fluxes was attributed to the evaporation momentum force. This force increases with heat flux and dictates the bubble motion toward the center of the nucleating region. As the heat flux increases, the bubbles are driven toward the center of the nucleating region as they depart, and a strong liquid circulation pattern is established that prevents any nucleation in the feeder channels. The liquid transport in the FCs is governed by the liquid circulation set by departing bubbles. The feeder channel geometry affects the flow resistance, heat transfer coefficient to the impinging liquid and surface area available for heat transfer to the liquid. Further optimization can be achieved by varying the feeder channel dimensions. These bubble induced separate liquid-vapor pathways result in a highly efficient mechanism that is responsible for the large rise in the heat transfer coefficient to an unprecedented value of 713 kW/m² °C, which is about 11 times the plain chip HTC and 2.7–4.2 times the HTC value compared with the NRFC 1, 2 and 4 configurations.

The nucleating region channel width and the feeder channel widths have a significant bearing on the heat transfer performance. Figs. 5(a) and 5(b) show the pool boiling curves obtained for three NR and FC channel widths—300 μm, 500 μm, and 762 μm, respectively. These channel widths were chosen based on the ranges reported previously in literature.^7,9 The CHFs comparison shown in these figures suggests that an optimal channel width exists for which the performance is significantly higher. This is in agreement with the results reported by Kandlikar¹² for a contoured fin in which a channel width of 0.5 mm resulted in a performance of 300 W/cm² at a wall superheat of 4.9 °C. Furthermore, the NRFC-3 configuration resulted in an HTC that was 1.1 times that of a contoured fin surface showing that this configuration was able to sustain the mechanism efficiently at higher heat fluxes.

The architecture of the surface was such that the FCs were able to continuously supply liquid to the NR channels. The liquid supply was heavily influenced by the FC bank width. High speed images were obtained using a Photron fastcam^® at a high frame rate of 4000 fps and are shown in Figs. 6(a)–6(f) for NRFC-3.

Fig. 6(f) distinctly shows separate liquid-vapor pathways with vapor columns over the NR channel and subsequent liquid addition through the FC regions. In the videos captured at lower heat fluxes, some bubbles were seen to nucleate inside the FCs. However, these bubbles are suppressed at higher heat fluxes and provide unobstructed pathways for liquid flow. Note that the maximum wall superheat for the best performing chip was only 5.5 °C. In the NRFC-2, similar separate liquid-vapor pathway to NRFC-3 was observed as seen in Fig. 6(h) while the NRFC-4 shows bubble coalescence over the FCs blocking the liquid supply pathways.

A trend in CHF with the distance between the NRs was observed from the test surfaces investigated in this study. As mentioned previously, the bubble departure diameter obtained from Fritz equation resulted in a value of 2.21 mm which was also in close correspondence to the critical capillary length, λ_c, (2.5 mm for water at 100 °C) obtained using the following equation:

NRFC-1 and NRFC-3 have NRs separated by 4.75 mm and 2.125 mm (see Fig. 2) that are close integer multiples (∼2 and ∼1, respectively) of the bubble departure diameter (2.213 mm). These values indicate that spacing between the NR channels is dependent on the bubble departure diameter in such a way that the integer multiples of the bubble diameter enhances the pool boiling performance significantly compared to other configurations. The hydrodynamic theory using the bubble departure diameter and the capillary length explains the enhancement obtained when the FC lengths are equal to the capillary length as in the case of NRFC-3. The NRFC-1 case represents a single nucleating channel with large feeder channel lengths on its either side.

Future testing with higher integer multiples (3, 4, 5, etc.) is proposed to further validate the observed trend. However, it is demonstrated that the bubble departure diameter can be used as a guidance to develop enhanced microstructures by incorporating a network of nucleating and feeder channels. The best performance is obtained when this multiple is 1 as seen for NRFC-3. In the other two configurations, the increased flow distance in the FCs (NRFC-2) and lateral bubble coalescence (NRFC-4) makes the mechanism less efficient resulting in early CHFs.

Providing separate liquid-vapor pathways and incorporation of liquid feeder channels directing liquid flow toward the nucleating regions were seen to be very effective in enhancing the CHF and HTC. Making the distance between the two nucleating regions, a multiple of departing bubble diameter was seen to be beneficial, with a multiple of 1 providing the highest performance. The trend of decreasing wall superheat with increasing heat flux was seen to be similar to that reported in a contoured fin which benefitted from the evaporation momentum force in directing bubble motion. A record HTC of 713 kW/m² °C was obtained at a CHF of 394 W/cm² and a wall superheat of 5.5 °C with NRFC-3. High speed images clearly identified the role of nucleating channels as vapor removal pathways with liquid supply through the feeder channels.

The work was performed in the Thermal Analysis, Microfluidics and Fuel Cell Laboratory in the Mechanical Engineering Department at Rochester Institute of Technology, Rochester, NY. The authors gratefully acknowledge the financial support provided by the National Science Foundation under Award No. 1335927.