Flow Boiling in Microchannels Coupled with Surfaces Structured with Microcavities

Abstract

This study addresses the characterization of two-phase flow phenomena in a microchannel heat sink designed to cool high-concentration photovoltaic cells. Two-phase flows can introduce instabilities that affect heat exchange efficiency, a challenge intensified by the small dimensions of microchannels. A single polydimethylsiloxane (PDMS) microchannel was fixed on a stainless steel sheet, heated by the Joule effect, which was cooled by the working fluid HFE 7100 as it undergoes phase change. Experiments were performed using two microchannel widths with a fixed height and length, testing two heat fluxes and three values of the Reynolds number, within the laminar flow regime. Temperature and pressure drop data were collected alongside high-speed and time- and space-resolved thermal images, enabling the observation of flow boiling patterns and the identification of instabilities. Enhanced surfaces with microcavities depict a positive effect of a regular pattern of microcavities on the surface, increasing the heat transfer coefficient by 34–279% and promoting a more stable flow with decreased pressure losses.

1. Introduction

The amount of energy consumed worldwide has been increasing steadily in recent decades, and since the Paris Agreement the need to further develop renewable sources of energy is higher. Solar energy is one of the most widely used ones, and solar panels have the potential to be installed almost anywhere.

However, the most common solar panels have low efficiency [1]. High-concentration photovoltaics (HCPVs) address this issue with lenses and mirrors to focus sunlight onto a small area. Despite their potential to be more efficient, HCPV panels are significantly more expensive; therefore, the need to optimize efficiency must compensate for the cost. High cell temperatures can reduce efficiency and even shorten a cell’s lifespan [2], a problem intensified in HCPVs due to concentrated radiation. Therefore, cooling solutions are necessary to improve efficiency and prevent long-term damage. Most solar panels are cooled using passive systems, such as fins. However, these prove to be insufficient in cooling extreme cases such as HCPVs.

Since the earlier stages of photovoltaic technology, high temperatures have been known to impact a solar panel’s efficiency. Krauter [3] studied the effects of water flowing over the front of solar panels. This would both cool cells by up to 22 °C and increase the electrical yield by around 8 to 9%, even after taking into account the pumping power used. Kuo and Lo [4] studied the cooling of concentrator photovoltaics by circulating water and using a neural network to optimize the working schedule of this system. Similar studies have compared several cooling methods applied to photovoltaics, concluding that water cooling yields better results when compared to air cooling [5].

Active cooling requires an active force external to the system, which consumes energy. Among the most promising technologies in cooling concentrator photovoltaics, microchannel heat sinks are shown to be those with the highest potential [6].

Tuckerman and Pease [7] were pioneers in suggesting the use of micro-scale heat exchangers, achieving heat fluxes up to 790 W/cm². In 2009, Lee and Mudawar [8] studied flow boiling inside microchannels with HFE 7100 as the working fluid. In this study, Lee and Mudawar [8] projected that a system under optimized conditions could exceed a heat flux dissipation of 1000 W/cm². Here, phase change also has the potential to improve heat transfer, given the additional term associated with the latent heat transfer without raising the fluid’s temperature. However, the vapor bubbles created during flow boiling can exacerbate the pressure drop problem and cause instabilities, which may compromise the efficiency of the heat exchanger. Although the topic of these instabilities has been thoroughly studied, there are limited results, particularly under demanding experimental conditions, that focus on their impact in this context.

The geometry of microchannels has also been an object of study. Upadhye et al. [9] conducted an experimental study to optimize the geometry of rectangular microchannels for cooling a 25 mm × 25 mm area. More complex geometries have also been studied. For instance, Al-Neama et al. [10] and Chen et al. [11] studied serpentine microchannels, with both studies reporting an improvement in heat transfer due to the mixing of the flow. Lu and Pan [12] studied the use of parallel diverging microchannels as a way to stabilize flow boiling. At the micro-scale, an increase in pressure drop can become an issue. In this context, the literature review of Kandlikar [13] reports that phase change heat transfer in microchannels can underperform against single-phase cooling systems. One of the suggestions presented by the author was to intensify the research on the impact of artificially enhanced surfaces to further improve heat transfer. Furthermore, the authors of [14,15] underlined the positive impact of this approach in lowering surface temperatures and improving the heat transfer coefficient (HTC). However, the effect of these surfaces on flow boiling regimes is clear: by increasing the number of nucleation sites, slug flow and pressure drop increase. It is therefore important to optimize these structures and connect the impacts these structures may have on heat transfer. Understanding the complex relation between bubble dynamics, heat transfer, and flow in two-phase flow in microchannels and accurately describing the governing phenomena is therefore vital to produce efficient heat sinks, particularly those at the micro-scale. In this context, optical access to the channels plays a major role in more fundamental studies. The use of glass is complex, does not assure infrared transparency, and can be quite expensive and difficult to handle. Polydimethylsiloxane (PDMS) is an inexpensive and versatile material with relevant optical and mechanical properties. Its usage has been strongly explored within the past years, with relevant breakthroughs, for instance in surface treatment and the addition of nanoparticles to further improve its optical and thermal properties [16].

The literature review presented so far evidences a diverse number of studies on various parameters, without a consensual description of their effects and particularly of the physics underlying the observed trends. There are also numerous studies on the use of microstructured surfaces, but in most cases the structures are quite large and the working conditions are closer to pool than to flow boiling conditions.

Hence, the present work addresses these challenges and knowledge gaps by simplifying a microchannel heat sink to a single channel where a refrigerant fluid, HFE 7100, undergoes phase change. This fluid, with a saturation temperature of 61 °C at ambient pressure, suits the solar cell’s operating temperature. This study aims to characterize the flow, identifying potential instabilities and the conditions at which they occur. The use of PDMS to produce microchannels allows optical access to its interior. To connect flow dynamics and thermal behaviors, a high-speed camera is paired with a thermal camera, providing complementary and unique synchronized analysis of both bubble dynamics and corresponding heat transfer mechanisms. Previous studies paired these techniques in order to better define the heat transfer mechanisms in pool boiling and flow boiling heat transfer [17,18]. In this work, the same techniques will be applied to microchannel flow boiling. Surfaces with and without structured artificial nucleation regions are also compared, to infer the effect of the cavities at the microscale level.

2. Materials and Methods

2.1. Experimental Arrangement

A schematic of the experimental setup can be seen in Figure 1. A polydimethylsiloxane (PDMS) microchannel was placed on top of an AISI 304 stainless steel sheet, which, in turn, was placed on top of a wooden plate. PDMS was chosen to ensure good optical access, amongst other advantages, as discussed in the Introduction. Although it does not have the best thermal properties, the optical properties, ease of usage, and cost, among other aspects, overcome that limitation, especially since the heat fluxes used here are low.

To ensure that there are no leaks, an acrylic plate presses the PDMS against the stainless steel sheet and the wooden plate by using four sets of screws and bolts. Since PDMS is a self-sealant, the liquid should be contained within the microchannel during testing. A TDK-LAMBDA GEN 750W DC power supply (TDK-Lambda Corporation, Tokyo, Japan) generates the current that heats the stainless steel sheet via the Joule effect. The working fluid, HFE 7100 (3M™ Novec™ 7100 Engineered Fluid, 3M Company, St. Paul, MN, USA), contains 53% air by volume, according to Wang et al. [19], which causes bubbles to form at temperatures below its boiling point. Therefore, HFE 7100 is degassed before testing. For this, a degasification station was built, consisting of a syringe with a heating pad wrapped around it, which heats the fluid, increasing the pressure inside the syringe. The fluid is then transferred from the bottom to a separate syringe, and the air on top is removed, repeating the process until no air remains. The degassed fluid is then loaded into a syringe on an NE-1010 Syringe Pump (New Era Pump Systems Inc., Farmingdale, NY, USA), which regulates the flow rate for testing. This syringe pump has an accuracy of ±1%.

To bring the fluid near its saturation temperature, it passes through a thermal bath before entering the microchannel, where it undergoes phase change and is then collected in a reservoir for reuse.

The pressure difference between the inlet and outlet of the microchannel is measured by connecting an Omega PX409-001DWUV (Omega Engineering Inc., Norwalk, CT, USA) differential pressure to the setup. The temperature is measured at the inlet and outlet with a type-K thermocouple. A type-K contact thermocouple is placed between the PDMS and the stainless steel sheet to measure the sheet’s temperature. Two additional type-K thermocouples are placed inside the thermal bath, one connecting to the PID controller used to control the thermal bath, while the other is used to gather data. Finally, another type-K thermocouple is placed near the setup to monitor ambient temperature. Temperature and pressure signals are sent to an acquisition system (DT9828, Data Translation Inc., Marlboro, MA, USA). A Phantom v4.2 Vision Research high-speed camera with a 506285 Leica Germany 10× microscopic lens was used to capture bubble dynamics and flow regimes. The image resolution is 512 × 512 px, with the size of the pixel being approximately 22 μm. The images are captured with a sample rate of 2200 pps (pixels per second) and an exposure time of 50 μs. The experiments intending to address the effects of surface microcavities on flow boiling heat transfer and stabilization used an Onca MWIR-InSb-320 high-speed infrared (IR) thermographic camera (Xenics nv, Leuven, Belgium), aligned on the bottom of the stainless steel surface, which records the evolution of the temperature distribution of the stainless steel sheet at 1000 fps. The surface back was coated with black paint with high emissivity (0.95 according to the manufacturer). The uniformity of the coating was checked using a Dektak 3 profile meter (Veeco Instruments Inc., Plainview, NY, USA) with a vertical resolution of 20 nm. A small sapphire window also assures the best optical access and infrared transparency to the stainless steel surface. The videos from the infrared thermographic camera were extracted with raw data from the software, and a custom-made calibration was applied to transform the data into °C. This calibration was made using a type-K thermocouple reading on a small water container. The bottom of this container is put in direct contact with the stainless steel surface and sapphire window. After this, boiling water is poured into the container, and the surface temperature is measured with the thermocouple until it reaches ambient temperature, comparing it to the IR camera’s measurements. This ensures that any effect from the window transmissivity and the foil’s emissivity is nullified. Further details on the calibration procedures can be found in [20].

Separate tests were performed with the camera observing the channels sideways, to better detail the 3D behavior of the flow.

Two microchannel geometries were used in this work. Both have a cross-section with a height of 1 mm. The length of the microchannels was 40 mm. The widths were varied, with widths of 0.5 mm and 0.75 mm selected. These dimensions are in line with previous works but were selected due to manufacturing constraints.

A TDK-LAMBDA GEN 750W DC power supply generates the current that heats the stainless steel sheet via the Joule effect. The sheet has a cross-sectional area, Ac, of 3.8 × 10⁻⁷ m²; a horizontal area, Ah, of 1.121 × 10⁻³ m²; a length, L, of 59 × 10⁻³ m; and a resistivity of 7.5 × 10⁻⁷ Ω·m. Adjusting the electrical power fed to the sheet, the imposed heat fluxes were varied between 1580 W/m² and 2104 W/m². Finally, stainless steel sheets were modified with a pattern of microcavities. The fabrication, preparation, and characterization of these surfaces are detailed in Section 2.3.

2.2. Working Conditions

The working fluid is HFE 7100. The target inlet temperature of the fluid is 50 °C. At this temperature HFE 7100 has a liquid density of 1424.85 kg/m³, a kinematic viscosity of 2.6525 × 10⁻⁷ m²/s, a thermal conductivity of 0.06394 W/m·k, a liquid specific heat of 1233 J/kg·K, and a heat of vaporization of 111.6 J/kg.

The volumetric flow rates were selected to match three values of the Reynolds number: 70, 95, and 120, corresponding to low, medium, and high flow rates for this kind of channel, within the laminar flow regime.

2.3. Surface Characterization

The stainless steel foil was previously characterized in terms of wettability and roughness. The wettability was quantified in terms of contact angles, using a THETA optical tensiometer from Attension. A water droplet was deposited on top of the surface and the static contact angles were evaluated using OneAttension v1.8 software, using a Young–Laplace fit. The surface showed hydrophilic behavior with a 64.2 ± 0.7° static contact angle. The roughness was quantified using a Dektak 3 profile meter (Veeco). The untreated surfaces were considered smooth within the vertical resolution of the equipment (20 nm).

The structured surfaces have 333 cavities with a diameter of 0.1 mm, disposed in a square grid of 0.4 mm. This pattern is repeated in a circular area with a 10 mm diameter. This structure can be seen in Figure 2. The microchannel was placed on top of this surface, so that the area inside the microchannel had 2 rows of 21 cavities each. These cavities were produced by laser etching, following the procedure detailed in [21].

It is worth noting that the ageing of the surfaces under boiling conditions was extensively investigated in all the experimental campaigns by controlling the surface topography and wettability before and after the experiments. In the current work, no significant changes were found in the surfaces’ wettability or topography after the experiments.

2.4. Manufacturing the PDMS Microchannels

The mold of the microchannel was constructed via addictive manufacturing, namely through SLS 3D printing. Then, aluminum tape was used to prepare a small parallelepiped shape around the mold. The adhesive side of the tape only comes into contact with the bottom side of the mold. Additional tape might be added to reduce the probability of any leakage. The PDMS was mixed with a curing agent in a 1:10 ratio. More specifically, 4 g of PDMS was mixed with 0.4 g of the curing agent, which was then poured on top of the mold. The curing process took two days. The microchannel was then demolded and cut to the right dimension.

2.5. Experimental Procedure

2.5.1. Experimental Routine

The typical experimental routine occurred as follows: The power supply and the thermal bath were turned on. The working fluid started the degassing process. When the working fluid was degassed and cooled down to ambient temperature, and the sheet and thermal bath reached the desired temperatures for testing, the syringe pump started pumping the fluid at the highest flow rate. When the temperature and pressure drop were stabilized, a note of the remaining fluid in the syringe was taken so that the remaining time of the test could be equally divided by all the flow rates. While conditions were stable, high-speed and thermal images were recorded. After the time calculated had passed and images were recorded, the flow rate was changed to the next highest flow rate to be tested.

This routine was repeated until all three flow rates were tested and no fluid remained in the syringe. Experiments were repeated to ensure the repeatability of five valid tests for each working condition.

2.5.2. Temperature and Pressure Data

The temperature and pressure data acquired is exported to a Microsoft Excel Workbook file. The parameters acquired are the internal temperature of the thermal bath (Tbt), the ambient temperature (Ta), the inlet temperature (Ti), the outlet temperature (To), the temperature of the stainless steel sheet (Ts), and the pressure drop (dP). Additional parameters are calculated, such as the temperature difference between the outlet and inlet (ΔT) and a dimensionless temperature difference (dT*), given by Equation (1):

$$d{T}^{*}={\displaystyle \frac{∆T}{T_s-T_i}}={\displaystyle \frac{T_0-T_i}{T_s-T_i}}$$

(1)

Each of the different volumetric flow rate changes are noticeable by a variation in the pressure drop. The values for each test condition (volumetric flow rate, heat flux, and microchannel geometry) are then compiled and compared.

2.6. Uncertainty Analysis

The equipment used to measure the various parameters has an uncertainty associated with it and is compiled in

Table 1. Uncertainties of the equipment used.

Equipment	Uncertainty
NE-100 Syringe pump	±1%
Type K thermocouple	±0.75%/±2.2 °C
Omega PX409-001DWUV	±01%/±0.069 kPa

, with total uncertainty calculated according to Moffat [22].

According to Moffat [22], for multiple-sample uncertainty analysis, random errors need to be taken into consideration. This way, the total uncertainty in a result, at a 95% confidence level, is calculated according to the following equation:

$${{(U}_R)}_{95} = \sqrt{{{(B}_R)}^2+{\left(2S_R\right)}^2}$$

(2)

where BR represents the overall bias limit (associated with fixed errors) and SR is the precision index, which is equal to the standard deviation of a set of 5 measurements minimum. Regarding pressure losses, the overall bias limit is influenced by not only the pressure sensor but the syringe pump as well.

3. Results

The results presented and discussed here aim to characterize the thermal and fluid dynamics behavior of the flow inside the microchannels, focusing on the effect of the geometry and identifying the boiling regimes that are observed for the chosen experimental conditions (related to the cooling of the solar panels). This part of the results is discussed in Section 3.1. Several oscillations are clearly related to flow instabilities, which are analyzed in Section 3.2. A third sub-section relates the quantitative analysis performed in the previous sub-sections with a qualitative analysis based on extensive image post-processing (Section 3.3). Finally, the use of surfaces structured with microcavities is discussed to infer their potential to improve heat transfer and aid in flow stabilization (Section 3.4).

3.1. Thermal Analysis

The test section is not completely insulated thermally. Therefore, some of the heat generated by the stainless steel sheet is dissipated to the surrounding environment. To estimate these heat losses, two separate paths were considered, namely the heat dissipation to the wood panel and the air below and the heat dissipation to the PDMS microchannel, to the acrylic plate on top of it, and to the air above. Once the heat losses are estimated, it is considered that the remainder is supplied to the fluid inside the microchannel. This analysis allows the calculation of an effective and more realistic heat flux. Figure 3 depicts the equivalent circuit of the thermal resistances that were taken into consideration while calculating the heat losses.

An estimated thermal conductivity of these materials and respective thermal resistances is depicted in

Table 2. Estimated thermal conductivity, k, and thermal resistance, R_t,cond, of the material involved in conduction heat loss. The properties were taken from [23,24,25] to characterize acrylic, wood, and PDMS.

Material	k (W/mK)	Rt,cond (K/W)
Acrylic	0.19	14.62
Wood	0.095	22.02
PDMS channel 0.5 mm	0.2	27.42
PDMS channel 0.75 mm	0.2	27.67

.

To calculate convection heat loss, an iterative process determines the surface temperature of each air-exposed surface.

This process uses the equation for heat transfer across a composite wall, following the scheme depicted in Figure 3. For the free convection with air, the following correlation was considered [26]:

$$Nu=0.52R{a}_L^{1/5} ({10}^4\le Ra \le {10}^7,Pr\ge 0.7)$$

(3)

Nu, the Nusselt number, is given as follows:

$$Nu={\displaystyle \frac{h{D}_h}{k}}$$

(4)

where h is the convective heat transfer coefficient, D_h is the hydraulic diameter of the microchannel, and k is the thermal conductivity of the fluid. The Nusselt number depends on the geometry where the heat transfer occurs. For developing flows, however, Kandlikar et al. [27] presented values for the Nusselt number in rectangular microchannels, derived from Phillips [28]. Ra_L is the Rayleigh number, given as follows:

$${Ra}_L={\displaystyle \frac{g\beta (T_s-T_{\infty })L_c^3}{\alpha \nu }}$$

(5)

where g is the gravitational acceleration constant, Ts is the surface temperature, T∞ is the temperature of the free convection stream, β is the thermal expansion coefficient, calculated as the inverse of T∞, and α is the thermal diffusivity. The characteristic length for horizontal plates, Lc, is given by the plate’s area divided by its perimeter. Pr=ν/α is the Prandtl number, where ν is the kinematic viscosity (associated with the momentum diffusivity) and α is the thermal diffusivity of the fluid.

For the upper surface of a hot plate, the Nusselt number is calculated using Equations (5) and (6) [26]:

$$Nu=0.54R{a}_L^{1/4} ({10}^4\le Ra\le {10}^7, Pr\ge 0.7)$$

(6)

$$Nu=0.15R{a}_L^{1/3} ({10}^7\le Ra \le {10}^{11})$$

(7)

The average temperature of the stainless steel sheet and the ambient temperature measured for each of the heat fluxes and each channel geometry are used. With the heat loss calculated, the remainder is divided by the channel area to calculate the effective heat flux. On the smallest channel, the highest effective heat flux calculated is 2.61 × 10⁴ W/m², and the smallest is 1.57 × 10⁴ W/m². On the largest channel, the highest effective heat flux calculated is 2.98 × 10⁴ W/m², and the lowest is 1.83 × 10⁴ W/m².

The inlet temperature of the tests was measured as being between 49 °C and 55 °C. The temperature of the stainless steel sheet, Ts, varied very little for the same geometry and imposed heat flux. As expected, the outlet temperature, T0, follows the same trend as the sheet’s temperature. The difference between the outlet and inlet temperatures, ΔT, is presented in Figure 4.

The first analysis of the data in Figure 4 reveals two trends. At a higher heat flux, the temperature difference decreases with increasing values of the Reynolds number, as a lower flow rate results in a longer residence time and a larger temperature difference. However, this trend does not hold at the lowest heat flux value, possibly due to the placement of the inlet and outlet thermocouples near the three-way valves, a few millimeters from the sheet. While positioned to minimize flow interference, this may lead to some inaccuracies in measuring the temperature difference, as heat loss to the environment can affect readings. If the heat lost is comparable to the heat added by the sheet, it could explain the observed trend at a lower heat flux. There was no assessment to quantify the error introduced by these potential heat losses to the environment for this specific case. Such an assessment was performed in a previous configuration, which was slightly different, as the setup was larger, so the tubes and connections were also larger. The flow rates and imposed heat fluxes were of the same order of magnitude as those used in the present work. For that previous configuration, reported for instance in [29], the losses for the environment were associated with a relative error in the inlet and outlet temperatures of 5% for the lower imposed heat fluxes and 15% for the largest.

Given variations in the sheet’s temperature and inlet fluctuations, trends are easily observed using a normalized dimensionless temperature difference, dT*. This is calculated using Equation (1), and the results are depicted in Figure 5.

At the highest Reynolds number tested, both heat fluxes lead to a similar value of dT* in each geometry, which means that these scenarios lead to similar heat transfer efficiency. Another note is that for the imposed heat flux value of 2104 W/m², the largest channel performs better at the lowest Reynolds number, while the smallest channel performs better than the largest channel at the highest Reynolds number. Similar performance is observed in both geometries, at intermediate values of the Reynolds number. For the imposed heat flux value of 1580 W/m², the smallest channel performed better at all the Reynolds number values tested, with the intermediate being the closest in terms of dT*.

Lastly, the simplified steady-flow thermal energy equation is applied using Equation (7):

$$Q=\dot{m}{C}_p\Delta T$$

(8)

where $\dot{m}$ is the mass flow rate and Cp is the fluid specific heat to estimate the heat absorbed by the fluid. The results are presented in Figure 6.

This calculation is a simplification, as it only considers a single phase. However, it adds some perspective on how the various temperature differences presented in Figure 4 relate to the heat removed by the fluid. In this data, there is one outlier from what would be expected: for the 0.75 mm wide microchannel, with an imposed heat flux of 2104 W/m², there appears to be a reduction in heat transfer, despite no visible anomaly being detected in the bubble formation, which will be discussed in Section 3.3.

3.2. Quantitative Analysis of Flow Instabilities

In an attempt to quantify any instability found, the standard error of the data acquired throughout the tests, SE, is calculated as follows [30]:

$$SE={\displaystyle \frac{\sigma }{\surd n}}$$

(9)

where σ is the standard deviation and n is the size of the sample. From the sets of data acquired, the most interesting ones to analyze were the inlet temperature and the pressure drop.

These are depicted in Figure 7:

Considering the same geometry and heat flux, the standard error is higher for the intermediate Reynolds number value. The only exception occurs at the 0.75 mm channel, subjected to an imposed heat flux of 1580 W/m², where the standard error of the pressure drop for the lowest Reynolds number value is similar to that observed at the intermediate values of the Reynolds number. Larger standard errors are typically observed for the channel with the lower hydraulic diameter (0.5 mm), which is overall consistent with the analysis of the pressure drop and heat transfer discussed so far.

3.3. Qualitative Analysis of the Observed Phenomena

The various working conditions described in the previous section led to different flow boiling regimes, which are relevant to characterize, as complementary information to the quantitative analysis performed so far. Figure 8, Figure 9 and Figure 10 address the flow over smooth (nonstructured) surfaces.

The first phenomenon to be presented is the subcooled flow boiling, shown in Figure 8.

This image shows the evolution of a vapor bubble slightly after it has detached from the wall, with the flow moving from right to left. Afterwards, the bubble moves upwards and greatly reduces in size. This is an indication of subcooled flow boiling, as the vapor bubble condenses as it moves away from the heated surface. At a heat flux of 1580 W/m² (Figure 9), the flow pattern is mainly bubbly with subcooled characteristics, where lower values of the Reynolds numbers promote the formation of larger, more frequent vapor bubbles.

At 2104 W/m² (Figure 10), vapor occupies more of the channel; bubbly and slug flows appear at Reynolds numbers of 120 and 95, while annular flow is observed at 70, with nucleation under the central vapor bubble indicating a liquid film near the channel wall.

Overall, for lower imposed heat fluxes (1580 W/m²), subcooled and bubbly flow predominate, with subcooled flow being more frequent at higher values of the Reynolds number. For higher heat flux values (2104 W/m²), transitions from slug to annular flow are observed across all working conditions. Higher values of the Reynolds number typically lead to slug flow, while lower values of the Reynolds number mostly promote the occurrence of annular flow. Backflow begins with slug formation and increases with vapor buildup, leading to occasional flow reversals. In the 0.75 mm channel, the larger hydraulic diameter seems to mitigate some issues seen in the smallest channel (Figure 9). These images show a trend similar to that observed in the 0.5 mm channel, where reduced flow rate or increased heat flux leads to the occurrence of larger and more frequent bubbles. At 1580 W/m², bubbly flow is observed across all flow rates, with variations in bubble size. At 2104 W/m², slug flow predominates, and annular flow also appears more frequently as the flow rate decreases. Notably, no backflow was observed in the 0.75 mm channel, apart from slight slowdowns, indicating that the larger cross-section enhances flow stability. Additionally, bubbles coalesce less frequently than in the smallest geometry.

3.4. Effect of Microstructured Surfaces in Flow Boiling Heat Transfer and Stabilization

The results discussed so far are clearly affected by flow instabilities that were discussed and analyzed in the previous sub-sections. Given the known effect of the use of microcavities in pool boiling to promote active nucleation sites in well-established positions, a similar strategy was tested here, using a surface patterned with several microcavities, as described in Section 2. The results are discussed in the following paragraphs, using a smooth surface as a reference. The results are discussed for flow conditions corresponding to Reynolds number values of 70 and 120, to cover two extreme flow conditions addressing “low” and “high” mass flow rates. At this stage of the work it was not possible to match the highest imposed values of the heat flux, as discussed in the previous sub-sections, so it was decided to establish a comparative analysis for the flow inside the microchannel using a smooth surface and a surface structured with a pattern of N microcavities for two values of the imposed heat flux, namely a lower imposed value of 1346 W/m² to observe the effects of the surface when bubble formation is not so active and therefore instabilities are less evident, and a higher imposed value of 1637 W/m², representative of the values imposed at the working conditions discussed in the previous paragraphs, for which instabilities are already often observed. A qualitative analysis can firstly be performed based on high-speed and thermographic images of the flow. Then, a quantitative analysis is made, evaluating the heat flux between the surface and the fluid flow, based on the temperature map taken from the surface. It is worth noting that to ensure that the images from both cameras were recorded at the same instant, Auto-Clicker v2 software was used. On top of this software, when analyzing both images, it is possible to correct small delays via the visual observation of the phenomenon occurring. This way, the images extracted from the experiments allow us to comment on the influence of different types of flow patterns on the cooling of the stainless steel sheet.

At this stage of the work, the patterns addressed here were fixed, as detailed in Section 2.3. They were selected based on pool boiling studies performed earlier (e.g., [31]), which gave an indication of the sizes and spacing between the cavities that would provide a good compromise between quenching and induced flow convection at bubble departure and very intense coalescence and nucleation site interaction effects. It is acknowledged that even for the low flow velocities considered here, there are drag and flow effects that are not addressed in pool boiling. However, such a study will be performed in a more advanced stage of the work, considering a wider range of different cavity sizes and spacing between them.

Figure 11a,b show the heat flux map (A), high-speed image (B), and temperature map (C) for an imposed heat flux of 1346 W/m² and a flow rate corresponding to a Reynolds number of 70, on a smooth surface and on a surface with N cavities. With respect to the smooth surface, the high-speed image shows that the flow is well-organized, and bubble growth is visible along the microchannel. The region highlighted by the blue circle is an active nucleation site. The heat flux map presents increased heat transfer in this area and the temperature map denotes a reduced temperature area. Moreover, from these images it is possible to conclude the bubble’s influence with respect to its dimensions. Smaller bubbles are hardly seen in the images obtained with the infrared camera. The larger-sized bubbles, however, have a bigger influence on the cooling of the surface, which is visible further down on the microchannel in all three images. Regarding the surface with N cavities, an active nucleation site with low frequency is only visible in images B and C. The major difference between both surfaces can be noticed in the area marked by the blue dashed rectangle. Despite appearing to be an elongated bubble, from the temperature and heat flux maps, the conclusion is that a slug is being formed. The temperature map shows a reduced temperature area directly below the bubble region. However, when observing the same area in the heat flux map it corresponds to minimum heat transfer. The surface with N cavities presents increased bubble growth, transitioning from the elongated bubbles to slugs.

Analyzing the results obtained for the same imposed heat flux, but for a higher flow rate (Re = 120), as depicted in Figure 12a,b for the flow on the smooth and microstructured surfaces, respectively, there is an understandable significant decrease in bubble diameter, especially in the flow over the smooth surface. Detailed analysis of bubble dynamics (sizes and frequencies) is out of the scope of the present study, but the high-speed images together with the temperature maps clearly evidence the differences in bubble diameter, discussed here in a more qualitative manner.

The area delimited by the blue circle enlightens the active nucleation site, and the influence of the flow pattern observed is noticeable by comparing the temperature map region before and after the nucleation site. The darker region of the surface, and therefore the cooler one, that is present in the temperature map (C) is due to a small bubble growth and detachment observed during the instants recorded. The mean surface temperature during the experiments using the smooth surface is much higher than that observed on the microstructured surface. In fact, on the surface patterned with N cavities, the image corresponding to the heat flux map (A) is much less homogeneous. This is due to the impact of cavities on the temperature distribution across the stainless steel sheet, which are responsible for differences in its resistance. This phenomenon was not seen previously for the lower flow rate since the heat flux map uses a time filter to increase image quality, which cannot be applied to images where active nucleation sites appear. Once more, only the active nucleation sites are observed, which have a significantly higher heat flux when compared to the smooth surface.

Increasing the imposed heat flux to 1637 W/m², for which instabilities are more frequently observed, as discussed in the previous sub-sections, Figure 13a,b show the fluid flow (Re = 70) over the smooth and microstructured surfaces, respectively.

Comparing these with the images obtained for the lower heat flux (Figure 11a,b), a general increase in bubble dimensions can be observed. Furthermore, on the channel with the smooth surface, the flow begins to include slugs inside the microchannel. The temperature map (C) corresponding to this frame includes a colder region that could be representative of an elongated bubble; additionally, the high-speed image only shows the end of the bubble, which is why more parameters are added to the analysis. When adding a prior instant, the effect of the slugs inside the microchannel can be better explained. From the observation of both instants, the heat flux follows the slug and has its maximum value in the core region of the bubble, whereas the temperature map always shows a colder area corresponding to the region behind the slug. The area with maximum heat flux corresponds to the phase change phenomenon with a thin liquid layer surrounding the bubble. Slug growth is then described by the vapor in direct contact with the heated surface, insulating it from convection heat transfer, which corresponds to the dry area. The rewetting zone is clearer in Figure 11.

Regarding the surface with N cavities, despite slug formation already beginning for the lower heat flux (Figure 11b), with the higher heat flux there are some improvements to the flow characteristics. Figure 13 shows a significant increase in the number of nucleation sites, with three of the most visible ones marked with the blue rectangle. In these conditions, slug formation also occurs. However, the problem regarding the dry areas is not so common due to the increased number of bubbles. The fact that there is a continuity of bubbles throughout the length of the microchannel leads to a negligible dry area, with the rewetting area close to the evaporation region. The different darker and therefore colder areas in the temperature map (C) are due to the nucleation sites that are seen to be active even when the slug is passing.

The impact of increased volumetric flow rate for Re = 120 is depicted in Figure 14a,b for the smooth surface and for the microstructured surface, respectively.

In this case, the smooth surface is characterized by a reduction in bubble size. With respect to the surface with N cavities, the negative impact of an increased volumetric flow rate is rapidly observed in Figure 14b. Under these flow characteristics, the impact of dry areas following the slugs is clear: despite having a temperature map (C) with reduced surface temperature for the majority of the microchannel, the heat flux map (A) shows that the heat transfer between the surface and the fluid is not optimized.

From the heat flux maps presented above, a quantitative analysis can be made. For this purpose, two different heat fluxes are defined: q”mean, which corresponds to the average heat flux in a region of the flow not influenced by bubbles, and q”max, corresponding to the maximum heat flux inside the microchannel, associated with regions where there are active nucleation sites and/or bubbles.

Table 3. Average, q”mean, and maximum, q”max, heat flux on smooth and rough surfaces (effective area corresponding to the microchannel) for flow boiling of HFE 7100 depending on the Reynolds number, for different imposed heat flux values.

Imposed Heat Flux (W/m2)	Reynolds Number (Re)	Type of Surface	q”mean (W/m2)	q”max (W/m2)
1346	70	Smooth	1426	4181
1346	70	N cavities	1284	6931
1346	120	Smooth	1574	3120
1346	120	N cavities	1188	2769
1637	70	Smooth	1587	4443
1637	70	N cavities	3104	10,589
1637	120	Smooth	1735	2785
1637	120	N cavities	2340	6151

depicts the values of the surface heat fluxes extracted from the heat flux maps for an imposed heat flux on the stainless steel sheets of 1346 W/m² and 1637 W/m².

With respect to the mean heat flux, q”mean, calculated for each of the conditions tested, the N cavities surface results in a decreased q”mean. However, the maximum heat flux, especially observed for the lower volumetric flow rate (lower value of the Reynolds number, Re = 70), has significantly higher values when compared to those obtained when using the smooth surface. The reduced value of the q”mean observed when using the microstructured surface, in comparison with the smooth surface, may be due to the appearance of bubbles. There is an effect of the cavities on the thermographic images, which is worth correcting in future work, that could be affecting the average value.

IR thermography also enabled the calculation of the heat transfer coefficient by using surface temperature and heat flux measurements from the IR camera. The results can be found in Figure 15, where microstructured surfaces were compared against smooth surfaces. The presence of cavities on the surface had a clear impact on the heat transfer coefficient, increasing between 34% and 279% compared to the smooth surface.

4. Conclusions

This study addresses the characterization of two-phase flow phenomena in a microchannel heat sink towards the design of heat sinks to cool high-concentration photovoltaic cells.

HFE 7100 was the working fluid flowing in a single PDMS microchannel. Geometries were varied mainly in terms of the cross-section area of the microchannel. Imposed heat fluxes, varying between 1300 W/m² and 2100 W/m², were covered. Flow rates were also varied to cover the values of Reynolds numbers between 70 and 120 (within the laminar flow regime). Pressure drop measurements were combined with image analysis and time-resolved thermography for a detailed characterization of the fluid dynamics and heat transfer phenomena.

Temperature analysis showed that higher Reynolds numbers correspond to lower temperature differences at high heat fluxes, due to reduced residence time. Dimensionless temperature difference calculations revealed that larger cross-sectional areas lead to better heat transfer and fluid flow performance in the microchannels at low Reynolds numbers and high heat flux, while smaller cross-section geometries show superior performance at lower imposed heat fluxes.

Standard errors in the data showed an increase at intermediate Reynolds numbers, potentially indicating recurring instabilities. High-speed images captured flow patterns and specific phenomena like backflow, which became problematic in slug and worsened in annular flow. The results also suggest that channel width affects instability, with fewer instabilities in the larger channel, while lower flow rates lead to larger, more frequent bubbles. Instabilities are more likely at lower Reynolds numbers, higher heat fluxes, and in smaller channels.

In this context, the use of surfaces patterned with microcavities of the order of 0.1 mm diameter show a beneficial effect in terms of flow stability and heat transfer, based on an extensive qualitative and quantitative analysis of bubble dynamics, surface temperature maps, and surface heat flux computed from time-resolved thermographic images. This pattern is not optimized, and the size and spacing between cavities were set based on pool boiling studies, where the relation of cavity sizes and spaces shown here was observed to enhance bubble-forced liquid convection at the surface, produced by a controlled coalescence, while precluding an uncontrolled coalescence that may precipitate the formation of a vapor blanket. Thus, deeper research is required in this field to define “optimum” micro/nanostructured patterns to be used in these kind of applications.