## Abstract

Microchannel flow boiling has shown great cooling potential with steady-state studies demonstrating the capability to dissipate heat fluxes over 1 kW cm−2. However, most microelectronic devices undergo transient heat loads involving cold startups or pulse-like power operation. Transient heating events in low thermal resistance, low thermal capacity cold plates may exacerbate boiling instabilities and result in device damage or failure due to local dryout conditions. Currently, limited studies are investigating these effects and potential mitigation strategies. In this study, step function, or pulsed, and ramped heat loads are investigated on a multimicrochannel silicon evaporator using R134a under a range of heat fluxes and ramping rates. The transient temperature response of the base heater is recorded using a calibrated infrared (IR) camera, while fluid flow visualization is captured using a video camera microscope. Pulsed heat loads resulted in a large temperature overshoot in the test section until the fluid reached the onset of nucleate boiling (ONB), while significant vapor backflow is observed despite the presence of channel inlet restrictions. Steady boiling is eventually reached and vapor backflow is suppressed. The magnitude of the temperature overshoot is observed to be strongly dependent on peak heat flux. In contrast, ramped heat loads resulted in lower peak temperature rises before ONB as well as significantly reduced vapor backflow compared to the pulsed heat loads.

## Introduction

The miniaturization of electronics has facilitated major advancements in technology [1]. For example, decreased transistor size has enabled implementation into smaller devices such as smartphones and sensors while increasing functionality and performance [2]. These higher performance and smaller footprint devices have increased power densities and subsequently resulted in higher device heat fluxes [3]. It is well known that thermal issues are the limiting factor to advancement in microelectronics, causing nearly 60% of electronic device failures [4,5]. As heat loads increase, operating temperatures increase commensurately without sufficient thermal management and can result in diminished device performance metrics, undesirable drifts in output, and device failure in extreme cases.

Microchannel two-phase cooling is an encouraging thermal management option due to its high heat transfer rates and temperature uniformity. One study successfully rejected heat fluxes as high as 1.1 kW cm−2 [6]. Two-phase cooling in microchannels is known to have reduced flowrate requirements due to high heat transfer characteristics, reduced surface area to volume ratios, lower pressure drop for smaller hydraulic diameters, and lower required fluid charge and pumping power, and thus is a more compact system than single-phase systems. Despite this promising technology, most research for two-phase cooling in microchannels has investigated steady-state boiling conditions where heating conditions are constant. Some studies focused on boiling heat transfer characteristics such as different flow boiling regimes [715], while others focused on the instabilities inherent to flow boiling systems that can result in device damage [1620]. Flow boiling heat transfer is heat flux dependent; therefore, as the heat flux is changed so are the heat transfer characteristics. Additionally, initially subcooled fluid requires a certain amount of wall superheat to initiate boiling (spatially and temporally). The onset of nucleate boiling (ONB) causes rapid changes in flow and heat transfer characteristics as the system responds to the generation of vapor.

However, microelectronics such as central processing units, power conversion electronics, and laser diodes often experience time-dependent changes in power, and thus heat load, during cold startups and pulsed or variable power operations. Sharp temporal changes in the rejected heat load may cause large perturbations to fluid dynamics, especially if the heat source is closely coupled to the fluid in a multimicrochannel evaporator. Transient device heating may lead to temperature-dependent reductions in performance metrics, induce dryout or other flow instabilities, and in extreme cases result in device damage or failure. Furthermore, while decreased packaging volume can reduce the thermal resistance pathway to the fluid, it reduces the thermal capacity of the device, exacerbating the effects of these transient excursions. These additional considerations make the study of flow boiling under transient heating in microchannel evaporators even more complex but merit study to understand how a transient heating event impacts the flow boiling process and device performance.

Previous studies investigating microchannel flow boiling under transient heating are divided between single channel and multimicrochannel cold plates. Table 1 lists relevant experimental studies and their testing conditions to date. Basu et al., Chen and Cheng, and Kingston et al. studied flow boiling under stepped or pulsed heat loads in single microchannel devices without inlet restrictions [2123]. Basu et al. and Kingston et al. noted temperature overshoots at the ONB followed by a drop to steady-state boiling at lower heat fluxes [21,23]. Both studies observed a transitional boiling regime between the ONB and steady-state, while Kingston et al. observed a time-periodic steady-state characterized by vapor backflow and pressure drop instabilities characteristic of microchannel evaporators without inlet orifices [21,23]. At higher heat fluxes, Basu et al. and Chen and Cheng commented on a transition to film boiling with a continuously increasing heater temperature even after the ONB as the vapor fraction increased and insulated the wall from the liquid [21,22]. Time to boiling inception (defined as the growth and detachment of a vapor bubble) also decreased as heat flux increased due to more active nucleation sites which increased the rate of bubble growth and departure [21,22]. The immediate shift to film boiling at the onset of boiling for these higher heat fluxes could lead to catastrophic effects on a device such as thermal runaway or dryout.

Table 1

Studies on transient flow boiling in microchannels compared with current study conditions

Microchannel cold plate parametersTesting conditions
StudyMaterialNumber of channelsInlet restrictionWch (μm)Hch (μm)Dh (μm)tbase (μm)q"max (W cm−2)Gmax (kg m−2s−1)Tsat (°C)Working fluid(s)
Basu et al. [21]Silicon1No12002003430675380034HFE-7000
Chen and Cheng [22]Silicon1No56713221407200267100Water
Kingston et al. [23]Borosilicate1No5005005001001540065HFE-7100
Hodson et al. [24]Copper100No100010001000231002.8220926.1, 28.2R134a
Huang et al. [25]Silicon67Yes10010010028030200031.5, 35, 40R236fa, R245fa
This studySilicon142Yes302005210043086320R134a
Microchannel cold plate parametersTesting conditions
StudyMaterialNumber of channelsInlet restrictionWch (μm)Hch (μm)Dh (μm)tbase (μm)q"max (W cm−2)Gmax (kg m−2s−1)Tsat (°C)Working fluid(s)
Basu et al. [21]Silicon1No12002003430675380034HFE-7000
Chen and Cheng [22]Silicon1No56713221407200267100Water
Kingston et al. [23]Borosilicate1No5005005001001540065HFE-7100
Hodson et al. [24]Copper100No100010001000231002.8220926.1, 28.2R134a
Huang et al. [25]Silicon67Yes10010010028030200031.5, 35, 40R236fa, R245fa
This studySilicon142Yes302005210043086320R134a

These previous observations indicate the presence of flow instabilities and temperature excursions at the ONB, particularly for higher heat fluxes and no inlet orifices, but were performed on single channel devices. Multichannel devices have additional considerations due to cross-channel interactions such as parallel channel instability [1620]. Hodson et al. tested a 100 multichannel heat sink without an inlet restriction. The authors commented on a peak temperature rise before ONB; however, the effects of the ONB were not studied in detail and the overshoot was attributed to the large increase in heat transfer coefficient with a nearly constant fluid temperature during boiling [24]. Huang et al. also investigated a multimicrochannel (67 channels) evaporator with two different sizes of channel inlet restrictions [25]. Large temperature overshoots before the ONB were seen before a sharp drop to steady-state occurred. Like in Kingston et al., vapor backflow out of the channel was seen at the ONB but only with the larger inlet restrictions and only occurred during the transition to steady-state [25]. Reductions in heat flux, inlet restriction dimensions, subcooling, saturation temperature, and increasing mass flux all reduced peak temperatures, while nucleation time was inversely proportional to heat flux as observed by the single channel studies [25].

It is clear from these previous studies that boiling phenomena under transient heating in low thermal resistance and capacity microchannel evaporators result in exacerbated flow instabilities and temperature excursions which could result in drastic device damage or failure. In these studies, only a step or pulsating function in heat load was investigated. Only one study used an inlet restriction which partially mitigated peak temperatures and reduced the occurrence of flow instabilities. No, this study investigated hydraulic diameters smaller than 100 μm or a nonuniform heat distribution under the channels (a common occurrence in real devices). Furthermore, no study investigated active measures, such as modulating how quickly heat flux is applied to the fluid, to mitigate the peak temperature before the ONB or the transient vapor backflow with a given set of fluid conditions.

The present study investigates the transient temperature response of a closely thermally coupled multichannel evaporator with inlet orifices under two types of transient heating modes. Key differences from previous studies include the smallest reported hydraulic diameter (52 μm), more microchannels (142), a nonuniform heat load to the channels, and the investigation of a ramped heating profile. Pulsed or stepped heat load changes at different heat flux magnitudes are investigated to compare with previous studies. Heat load ramping at different rates was studied to approximate the performance of added thermal capacity and to understand the differences between pulsing and ramping on the transient heater temperature as measured from infrared (IR) thermography. Flow visualization synchronized with the IR temperature measurements allows comparison of boiling fluid dynamics with heater temperature response.

## Experimental Setup

### Test Section.

The microchannel evaporator used in this study was etched out of a 300 $μ$m thick silicon wafer, with the details of the etching process and evaporator design described in previous work [8]. Extensive steady-state testing of similar evaporators with different channel geometries operating under different mass fluxes and saturation pressures was performed in a previous study and influenced the choice of fluid, test conditions, and test section geometry in this study. While more environmentally friendly refrigerants have since been developed, R134a was chosen as the test fluid in the steady-state tests since it is commonly used on naval vessels, is readily available, and has well-characterized thermophysical properties. The refrigerant enters the device and is distributed throughout an inlet manifold by supporting silicon features. The silicon test section can be seen in Fig. 1. Before entering the channels, the refrigerant flows through restrictions etched at the inlet of each channel. It is well-documented that inlet restrictions mitigate flow instabilities in two-phase systems at steady-state, and this was the case for steady-state testing of this device [19,2629]. The inlet orifices are nominally 15 μm wide, 200 μm deep, and 150 μm long. Upon exiting the inlet restrictions, the fluid flows through the 142 channels which are 2 mm long, 30 μm wide, and 200 μm deep. The channel hydraulic diameter is 52 μm. The fins separating the channels are 40 μm wide. A 500 $μ$m-thick sheet of borosilicate glass is anodically bonded to the top of the silicon channels to provide a hermetic fluid seal. A 10 mm-by-1 mm thin film platinum resistive heater was deposited over the center of the channels on the backside of the test section to act as a surrogate laser diode bar. Current is passed through the heater to produce Joule heating. The base thickness between the heater and the bottom of the channels is 100 $μ$m. Since the heater spans only the center millimeter of the channels, axial conduction, or heat spreading, is expected to play a larger role than previous transient boiling studies with uniform heat distribution. Previous steady-state studies using finite element analysis models on these evaporators found that local heat fluxes were highly nonuniform, with up to 70% of heat transfer occurring outside the heater footprint [8,30,31].

Fig. 1
Fig. 1

### Test Facility.

Transient flow boiling experiments were conducted in a two-phase pumped loop which was originally constructed for the prior steady-state testing, and details on sensor calibration and system components can be found elsewhere [8]. Several changes to the system were implemented to prepare the system for transient measurements. A simplified schematic of the system configuration used in this study is presented in Fig. 2. Before testing, the facility is evacuated to remove air bubbles and then is filled with liquid R134a. A positive displacement gear pump circulates the fluid while the mass flow rate is monitored by a Coriolis meter (Rheonik, Pleasanton, CA, RHM015) just upstream of the test section. The degree of inlet subcooling (how much the fluid temperature is below the saturation temperature) is set using a plate and plate heat exchanger upstream of the test section and monitored using a calibrated K-type thermocouple. The inlet pressure is set using an accumulator by adjusting the compressed inert gas (nitrogen) side and is monitored by an upstream pressure transducer. The heat load is applied by varying the current flow to the heater with a programmable power supply (Agilent, now Keysight Technologies, Santa Rosa, CA, N8735A). The test section temperature is monitored at a frame rate of 120 Hz using a calibrated infrared (IR) camera (Micro-Epsilon, Raleigh, NC, TIM 160). To monitor flow conditions, a microscopic camera (Dino-Lite, Torrance, CA, AM7915MZTL), synchronized to start simultaneously with the IR camera, is used to view the channels through the borosilicate glass at a rate of 20 Hz and a resolution of 640 × 480 pixels with an on-axis light-emitting diode ring light.

Fig. 2
Fig. 2

### Testing Conditions and Measurement Uncertainties.

To perform the transient experiments, the fluid is conditioned before a heat load. Table 2 details the testing and initial inlet conditions used in the current study. The nominal initial inlet conditions used in this study are: mass flux G of 863 kg m−2s−1, inlet pressure Pin of 572 kPa (Tsat,in = 20 °C), and Tin =15 °C (ΔTsub = 5 °C). Once the system has reached steady-state at the desired inlet conditions, determined when inlet temperature and pressure change by <0.1 °C or <0.7 kPa, respectively, over a 1-min period, a heat load is applied. Fluid flow conditions (5 Hz), test section temperature (120 Hz), and flow visualization (20 Hz) data are collected prior, during, and after a heat load is applied and are synchronized at their starting time. Hardware limitations prevented higher data collection rates for fluid flow conditions and visualization; however, 20 Hz was sufficient to capture the transient flow response, and 5 Hz was sufficient to capture the mass flow and pressure dynamics which changed much more slowly than the test section temperature.

Table 2

Initial fluid flow and testing conditions with corresponding measurement uncertainties

ConditionValueAbsolute uncertainty
Pin (kPa)572.30.6
Tsat,in (°C)20.010.03
Tin (°C)15.00.5
G (kg m−2s−1)8632
q″ (W cm−2)1486
2498
36010
39010
43011
Ramp rate (W s−1)4
9.5
29
50
ConditionValueAbsolute uncertainty
Pin (kPa)572.30.6
Tsat,in (°C)20.010.03
Tin (°C)15.00.5
G (kg m−2s−1)8632
q″ (W cm−2)1486
2498
36010
39010
43011
Ramp rate (W s−1)4
9.5
29
50

Heat is applied using two different modes: pulsed and ramped. In a pulsed test, the heat load is changed in a step function from zero to peak load for the particular test. During a ramped test, the heat load is applied incrementally over a step-time interval. Fluid conditions and heat duty are monitored and measured with a National Instruments cDAQ-9174 (National Instruments, Austin, TX) and then recorded using a custom labview program. Multiple trials were performed to access repeatability in testing. Between trials, the system was given time for the inlet conditions to return to their nominal values. 430 W cm−2 was chosen as the peak heat flux in this study since the peak temperature was close to that found in the steady-state studies to result in R134a decomposition and evaporator fouling [8].

To determine the uncertainty of the initial inlet fluid conditions, steady-state data was collected before a heat load. Since the data is transient, multiple readings at a particular condition were not possible. Therefore, the precision error was estimated from steady-state data before the heat load [32]. Combined statistical (95% confidence interval) and instrument bias uncertainties in testing conditions are also presented in Table 2. Instrument bias uncertainties for pressure transducers were ±0.1% of reading, for calibrated K- or J-types thermocouples were ±0.4–0.5 °C, and for the flowmeter ±0.2% of reading. Heat losses were estimated from an extensive steady-state investigation presented in Ref. [8] to be nominally 3% and dependent on a variety of factors; however, the average uncertainty in the applied heat duty was ±3%, and, due to the transient process, incorporating an estimate of ambient heat loss does not yield any additional insights nor introduce substantial errors in the results.

To ensure temperature measurements collected by the infrared camera are accurate, a calibration was performed relative to a high accuracy reference standard. A thin layer of high emissivity matte black paint (emissivity of ∼0.95), used in the experiments on the heater, was painted onto a block of copper. A surface thermocouple, calibrated using a high accuracy Fluke reference resistance temperature device to ±0.1 °C, was placed next to the high emissivity paint on the copper block. A resistive heater was placed on the back of the surrogate test section to increase its temperature. The average temperature readings by the IR camera over the high emissivity paint and thermocouple were recorded over two trials with greater than 100 data points for each trial for temperatures ranging from 15 to 70 °C. After calibration, the uncertainty of the average IR camera temperature measurement decreased from the manufacturer specified ±2 °C to ±0.3 °C over the measured heater area. The temperatures reported are the average temperatures over the platinum resistive heater (maximum local variations of up to 5 °C on the heater surface were seen but were not considered due to the larger uncertainty of ±2 °C for local measurements).

## Results and Discussion

Results of the pulsed heat load will be discussed first followed by a comparison to the results of the ramped heat load at a selected heat flux. In addition, observed system dynamics will also be discussed in reference to the evaporator transient temperature.

#### Transient Temperature Profile and Flow Visualization.

Stepped or “pulsed” heat load tests were conducted to represent a cold start up on an electronic device. A typical time series of the time-dependent temperature of the heater exposed to a pulsed heat load is shown in Fig. 3. The heat load is applied as a step function at time 0.5 s to a maximum value of 430 W cm−2. The heater temperature rises rapidly due to the step as the liquid R134a undergoes sensible heating and reaches a maximum of 70.6 °C approximately 117 ms later. At this peak, there is a point of inflection, represented by the onset of nucleate boiling (ONB), where the temperature decreases sharply as the heat transfer coefficient increases drastically due to boiling heat transfer in a developing boiling dynamics region. Finally, a steady-state boiling profile is reached at 36.4 °C around 1.5 s after heat is initiated.

Fig. 3
Fig. 3

Flow visualization in the channels was investigated to understand the two-phase flow dynamics and is chronicled in Fig. 4 relative to the time-dependent temperature is shown in Fig. 3 at selected times of interest. For reference, adiabatic single-phase steady-state flow is shown before a heat load (state 1). At the ONB (state 2), rapid generation of vapor results in vapor expansion both downstream and upstream. Vaporization in the inlet plenum, marked by the white dotted lines in Fig. 4, was unexpected considering the inlet restrictions but can be explained by the increase in pressure at the ONB. The large superheat temperature (∼50 °C) before the ONB provokes extremely rapid bubble growth at the ONB, producing a large, localized pressure in the channels which overcomes the pressure drop due to the inlet orifice.

Fig. 4
Fig. 4

From states 3–4, the inlet flow begins to overcome the large pressure gradient from the ONB and vapor is pushed downstream through the channels which precipitate a gradual reduction in test section temperature. At state 5, the majority of vapor has been pushed downstream, and more two-phase flow is entering the outlet. At this point, the flow approaches steady-state boiling and the rate of change in temperature decreases. Finally, at point 6, no more vapor is present at the inlet, and steady-state boiling has been reached.

The transient temperature due to a pulsed heat load can be broken down into three distinct zones. The time between states 1 and 2 is sensible heating before nucleate boiling. Between states 2 and 6, a transitional zone of boiling occurs in response to the rapid generation of vapor. In this zone, vapor backflow instability occurs, partially suppressing the high heat transfer characteristics of boiling flow and resulting in a somewhat gradual heater temperature decay. After state 6, flow instabilities are completely suppressed, and steady-state two-phase flow has been attained.

The large temperature overshoot and subsequent vapor backflow are thought to be attributed to two factors. Steady-state correlations developed for ONB superheat temperatures give a “required” wall superheat for a given heat flux [3335]. However, there may be a limit on the amount of “available” superheat the fluid can accept at any given time due to the thermal boundary layer growth. Hsu's work showed that an underdeveloped thermal boundary layer impedes nucleation site activation due to the suppression of bubble growth by the subcooled bulk liquid [36]. During a pulsed heat load, the heat is applied rapidly and the thermal boundary layer may not develop quickly enough to allow bubble growth and detachment, leading to increased wall superheats relative to steady-state developed flow boiling. Then, the liquid near the vicinity of the wall may become superheated. Once the “available” superheat increases as the boundary layer grows, the bulk fluid temperature increases and nucleation sites begin to activate. This superheated liquid combined with the now larger than “required” wall superheat leads to rapid vapor generation, large, localized pressure gradients, and vapor backflow into the inlet [37]. While Hsu studied steady subcooled boiling development down the length of a channel, it is plausible this hypothesis holds true for the transient boundary layer growth at a specific axial location as wall temperature increases in time. The vapor backflow may be exacerbated due to larger bubble confinement given the small hydraulic diameters of the channels in this study [37].

#### Impact of Heat Pulse Magnitude.

Figure 5 compares the transient temperature profiles from the trial with the largest peak temperature for the five pulsed heat fluxes investigated in this study. Increasing the heat flux trends with an increase in both transient peak temperature as well as steady-state temperature. However, at 148 W cm−2, the qualitative behavior of the transient temperature profile differs starkly from that of the other heat fluxes. In this scenario, the heat flux is low enough that the subcooled liquid convection likely suppresses vapor generation, which causes the evaporator to reach steady-state in a single-phase before the ONB triggers a sharp drop in temperature nearly 0.9 s after heat is applied.

Fig. 5
Fig. 5

Basu et al. observed similar qualitative behavior at their lowest base heat fluxes (<75 W cm−2), where the system first reached steady-state in single-phase before boiling appeared to trigger in a stochastic manner across several trials [21]. They observed few active nucleation sites after boiling initiated at these lower heat fluxes and posited that activation of nucleation sites tends to be stochastic, particularly if the wall superheat is near the minimum threshold necessary to trigger boiling [21]. It is likely that the delay in boiling for the lowest heat flux in this study results from similar behavior where the wall superheat was close to the minimum threshold required to trigger boiling and local variations in fluid properties and heater temperature eventually triggered nucleation sites.

As the applied peak heat flux increases, the temperature overshoot also rises. However, the increase in temperature overshoot is not equal to the shift in steady-state temperature. For example, the shift in steady-state temperature between 360 and 390 W cm−2 is ∼1 °C, but the transient temperature differences are 15 °C apart. It is possible that these results represent a transition in required and available superheat, which, with the still increasing heat load for the higher heat flux at 390 W cm−2, suppresses nucleation site activation for longer. This longer duration of single-phase cooling, along with the fact that higher heat fluxes result in higher boiling heat transfer coefficients [38], results in disproportionate shifts in transient peak temperature relative to steady-state temperature.

These noncommensurate shifts between transient and steady operating temperatures require extra attention because knowledge of the steady-state temperature difference between two different applied heat flux levels on a similar evaporator is insufficient to predict the difference in peak transient temperatures. This could have drastic consequences if a similar microchannel evaporator operating under a high heat flux maintains an adequate steady-state temperature but results in thermal runaway or a device-damaging peak temperature under a transient heat pulse.

#### System Level Dynamics.

In addition to transient temperature changes, inlet flow conditions also experience transients after the ONB. The ONB generates a pressure wave that opposes the flow and causes compressibility effects upstream of the test section. After the initial ONB pressure wave subsides and the evaporator reaches steady-state, the mass flow rate increases to a higher value (Fig. 6(a)). Figure 6(b) details the transient inlet pressure and pressure drop measurements for this test. For the pressure curves, when the heat load is turned on, a sharp increase in both pressure drop and inlet pressure is seen, likely due to thermal expansion. Following the ONB, where a slight dip in pressure drop occurs due to vapor backflow, a steady increase in both inlet pressure and pressure drop is seen. The increase in pressure drop is due to an increase in frictional and accelerational losses that are inherent with two-phase flow. This changes the system demand pressure requirement and thus changes the system flow rate due to a shift in the pump supply curve. The steady increase in inlet pressure is initiated by the increased low-density vapor which is unable to expand fully in the constant volume loop. The change in inlet pressure changes the inlet saturation temperature to 22 °C and thus increases the inlet subcooling from 5 to 7 °C. While the steady temperature did not change (reflecting a weak nucleate boiling dependence on saturation properties and flow rate), larger changes in inlet pressure and flow rate at higher heat fluxes could induce longer lasting flow instabilities.

Fig. 6
Fig. 6

#### Ramped Versus Pulsed Heat Load.

The transient peak temperature overshoots, vapor backflow, and system dynamics seen in pulsed heat load testing may be harmful to a device and result in damage or failure. The large temperature overshoots and vapor generation rates were attributed to large wall superheats possibly from an underdeveloped thermal boundary layer. Therefore, a potential mitigation strategy of ramping the heat load to minimize these temperature and flow excursions was investigated. Figure 7 compares the transient temperature profiles of pulsed and ramped (50 W s−1) heat loads at the same peak magnitude of 390 W cm−2. All ramped heat loads at this rate reduced peak ONB temperature relative to a pulsed heat load, up to 32 °C in the most extreme case. In addition, unlike under pulsed heating, with ramped heating, boiling commences before reaching the maximum heat load but still results in a similar sharp drop in temperature as the pulsed case due to the increase in heat transfer coefficient. The temperature continues to increase as the heat load reaches the maximum value for the test; however, the rate of temperature increase is slower than before the ONB due to improved two-phase heat transfer. Slight differences in steady-state temperature are likely due to changes in saturation properties and flow rate which occur after the transient perturbation to the system.

Fig. 7
Fig. 7

In Fig. 7 the ONB time and peak temperature are inconsistent between trials, particularly for the ramped heat load where discrepancies of up to 17 °C in peak ONB temperature were observed as opposed to 8 °C discrepancies for the pulsed test trials. The ramped case 2, in particular, reached ONB much more quickly than the other cases (0.35 s) and at the lowest ONB temperature (32.7 °C). The discrepancy between trials is suspected to be due to differences in trapped vapor pockets within cavities—more vapor entrapment facilitates quicker bubble nucleation and thus reduces peak temperatures at ONB. Between trials when heat is off, some of this vapor may be condensed by the subcooled bulk fluid. The impact of this trapped vapor is inherently stochastic; however, a study on transient pool boiling found that “priming” the cavities with vapor by running a short heating sequence where boiling is reached resulted in much lower peak temperatures even several hours later in subsequent trials [39]. In the current study, the time between trials could act as “prime” or “unprime” cavities in the test section and thus influence peak ONB temperature. It is possible that pulsed cases 2 and 3 as well as ramped case 2 had more trapped vapor which more readily facilitated nucleation at a lower wall superheat. This effect was not studied systematically, but it should be noted that the potential for “priming” vapor cavities exists and may reduce peak ONB temperature, particularly with pulsed or quickly ramped heat loads.

#### Effect of Ramp Rate.

Four different ramp rates (4, 9.5, 29, and 50 W s−1) were compared to a pulsed heat load for their impact on reducing peak temperatures and are plotted in Fig. 8. In all cases, the heat load was initiated at 0 s and the test section was allowed to reach a steady-state. For ramp rates of 4, 9.5, and 29 W s−1 similar peak temperatures are reached at different times. The ONB temperature appears to have a superheat-heat flux threshold that is met by each of these ramp rates but which is lower than for the pulsed heat load or the 50 W s−1 ramped case. The variability seen in Fig. 7 for the pulsed and 50 W s−1 ramped cases were not seen in the slower ramp rate cases. This may be due to increased thermal boundary layer growth which facilitates higher nucleation site density in a more regular manner compared to the more stochastic response in the underdeveloped boundary layer where local variations in temperature and fluid properties likely induce boiling in a small number of sites.

Fig. 8
Fig. 8

All the tested ramped heat loads reduced peak temperature overshoots relative to a pulsed heat load at the same nominal heat flux magnitude. It is thought that the slower heat flux application allows for the thermal boundary layer to develop both spatially and temporally. As the thermal boundary layer grows and penetrates the bulk liquid, the bulk temperature is increased, more of the fluid is at saturated temperature conditions, and the bubbles can grow without suppression by the subcooled liquid. The superheat “availability” of the fluid is increased and thus the boiling initiates at a lower superheat. It is possible that the temperature overshoot reduction limit met with increasing ramp rate means that the thermal boundary layer has developed enough and the wall superheat is near the minimum which would be “required,” any “priming” of the vapor cavities excepted.

Fig. 9
Fig. 9

#### System Dynamics.

The test section pressure dynamics for the ramped test at 390 W cm−2 are shown in Fig. 10. The heating is activated at 0 s in this figure. Unlike the pulsed test, for the ramped test the pressure remains roughly constant until the ONB at around 6.2 s, where there is a sharp increase in inlet pressure and pressure drop due to vapor generation. After the ONB, the flow rate steadily drops until a lower steady-state is reached just under 483 kg m−2s−1. This trend was observed in all ramped tests. There is a delay in the flow rate drop in the ramped test due the long duration before the ONB. The small amount of backflow in the ramped case was not large enough to cause any upstream compressibility effects. The decrease in flow rate is observed due to the increase in frictional losses and the addition of accelerational pressure drop as vapor is rapidly generated. The system demand curve increases to intersect a different region on the supply curve where the gear pump (at a set rpm level) supplies a lower flow rate for the increased pressure drop.

Fig. 10
Fig. 10

## Conclusions

This study performed transient heating experiments on a multimicrochannel evaporator on a two-phase pumped loop, and corresponding heater temperature, mass flow rate, and test section pressures were recorded. Pulsed heat load experiments resulted in large peak heater temperatures followed by a rapid drop to a lower steady-state temperature after the ONB. Fluid flow visualization revealed vapor backflow into the inlet plenum at the ONB despite the presence of an inlet restriction which eliminated backflow during steady-state testing. The vapor backflow was due to the rapid bubble growth in confined channels, elevating the channel pressure to a point where the inlet restriction was ineffective. Increases in peak heat flux resulted in noncommensurate increases in peak temperature relative to steady-state temperatures. By slowly ramping the heat load to a maximum value, reduced temperature overshoots above steady-state of up to 32 °C were observed. The reduced temperature overshoots in the ramped cases are thought to result from permitting the growth of the thermal boundary layer which activates nucleation sites at lower wall superheats. Furthermore, ramped heat loads mitigated the effects of vapor backflow seen under pulsed heat loads due to the decrease in wall superheat before ONB which in turn decreased the rapid bubble growth rate within the channels. Dynamic changes in pressure and mass flow rate were also recorded and are likely system-specific.

The extreme peak temperatures and flow instabilities shown in the current study have the potential for device damage or failure, particularly if low thermal resistance evaporators become more popular for high heat flux embedded cooling strategies. If a device cooled by such an evaporator undergoes a rapid increase in power which triggers boiling, temperature overshoots would likely be large. This could lead to device damage and thermal fatigue or burnout, particularly if the device is power cycled frequently. Due to the potential for catastrophic damage, additional testing is warranted to understand the dynamics associated with transient heat loads and provide mitigation strategies for peak ONB temperature and vapor backflow while still maintaining the low thermal resistance, high heat transfer performance of an evaporator of this form.

Different test section geometries should also be explored to mitigate or eliminate the peak ONB temperature seen in this study. For example, an increase in floor thickness between the heater and fluid could reduce the rate of heat flowing into the fluid (and thus potentially reduce the temperature overshoot) but may increase the steady-state heater temperature due to increased thermal resistance. This tradeoff should be further explored. Ramping the heat load may be desirable from a developing boiling perspective but may not be practical under typical operating requirements. The inclusion of a parallel thermal energy storage pathway may facilitate reduced peak transient temperatures similar to a ramping heat load by buffering the heat rate into the fluid without substantially increasing thermal resistance.

## Acknowledgment

The authors would like to acknowledge DEVCOM Army Research Lab (ARL) and Lawrence Livermore National Lab (LLNL) for their support in device and test facility fabrication.

## Funding Data

• U.S. Office of Naval Research (ONR) (Grant Contract No. N00014-18-1-2198; Funder ID: 10.13039/100000006).

## Nomenclature

• A =

channel area, μm2

•
• Dh =

channel hydraulic diameter, μm; $(4AcPerwet)$

•
• G =

channel mass flux, kg m−2s−1

•
• H =

height, μm

•
• L =

length, μm

•
• P =

pressure, kPa

•
• Per =

channel perimeter, μm

•
• q″ =

heat flux, W cm−2

•
• t =

thickness, μm

•
• T =

temperature, °C

•
• W =

width, μm

Greek Symbol

• Δ =

difference

### Subscripts

Subscripts

• avg =

average value

•
• base =

silicon substrate between channels and heater

•
• c =

cross-sectional

•
• ch =

channel

•
• fin =

extended silicon surface/wall between channels

•
• heater =

thin-film platinum resistive heater

•
• in =

inlet condition for evaporator

•
• max =

maximum value examined in a study

•
• orifice =

channel inlet orifice/restriction

•
• sat =

thermodynamic saturation temperature

•
• sub =

liquid subcooling below saturation temperature

•
• wet =

wetted by the fluid

### Acronyms and Abbreviations

Acronyms and Abbreviations

• ARL =

Army Research Lab

•
• DEVCOM =

Combat Capabilities Development Command

•
• HXR =

heat exchanger

•
• IR =

infrared/thermal

•
• LLNL =

Lawrence Livermore National Laboratory

•
• ONB =

onset of (nucleate) boiling

•
• ONR =

Office of Naval Research

## References

1.
Atherton
,
W. A.
,
1984
,
From Compass to Computer
, pp.
237
267
.
2.
Palm
,
P.
,
Moisala
,
J.
,
Kivikero
,
A.
,
Tuominen
,
R.
, and
Iihola
,
A.
,
2005
, “
Embedding Active Components Inside Printed Circuit Board (PCB)—A Solution for Miniaturization of Electronics
,”
Proceedings 10th International Symposium on Advanced Packaging Materials: Processes, Properties and Interfaces
, Irvine, CA, Mar. 16–18, pp.
1
4
.10.1109/ISAP M.2005.1432034
3.
Amon
,
C. H.
,
Murthy
,
J.
,
Yao
,
S. C.
,
Narumanchi
,
S.
,
Wu
,
C.
, and
Hsieh
,
C.
,
2001
, “
MEMS-Enabled Thermal Management of High-Heat-Flux Devices EDIFICE: Embedded Droplet Impingement for Integrated Cooling of Electronics
,”
Exp. Therm. Fluid Sci.,
25
(
5
), pp.
231
242
.10.1016/S0894-1777(01)00071-1
4.
Robinson
,
A. J.
,
2009
, “
A Thermal—Hydraulic Comparison of Liquid Microchannel and Impinging Liquid Jet Array Heat Sinks for High-Power Electronics Cooling
,”
IEEE Transactions on Components and Packaging Technologies,
32
(
2
), pp.
347
357
.10.1109/T CAP T.2008.2010408
5.
Fabis
,
P. M.
,
Shum
,
D.
, and
Windischmann
,
H.
,
1999
, “
Thermal Modeling of Diamond-Based Power Electronics Packaging
,”
Fifteenth IEEE Semi-Therm Symposium,
San Diego, CA, Mar. 9–11, pp.
98
104
.10.1109/ST HERM.1999.762434
6.
Skidmore
,
J. A.
,
Freitas
,
B. L.
,
Crawford
,
J.
,
Satariano
,
J.
,
Utterback
,
E.
,
DiMercurio
,
L.
,
Cutter
,
K.
, and
Sutton
,
S.
,
2000
, “
Silicon Monolithic Microchannel-Cooled Laser Diode Array
,”
Appl. Phys. Lett.
,
77
(
1
), pp.
10
12
.10.1063/1.126860
7.
Burk
,
B. E.
,
2018
,
A Computational Examination of Conjugate Heat Transfer During Microchannel Flow Boiling Using Finite Element Analysis
,
, Fort Collins, CO.
8.
Bevis
,
T.
,
2016
,
High Heat Flux Phase Change Thermal Management of Laser Diode Arrays
,
, Fort Collins, CO.
9.
Kim
,
S.
, and
Mudawar
,
I.
,
2013
, “
Universal Approach to Predicting Saturated Flow Boiling Heat Transfer in Mini/Micro-Channels—Part I. Dryout Incipience Quality
,”
Int. J. Heat Mass Transfer
,
64
, pp.
1226
1238
.10.1016/j.ijheatmasstransfer.2013.04.016
10.
Agostini
,
B.
, and
Bontemps
,
A.
,
2005
, “
Vertical Flow Boiling of Refrigerant R134a in Small Channels
,”
Int. J. Heat Mass Transfer
,
26
(
2
), pp.
296
306
.10.1016/j.ijheatfluidflow.2004.08.003
11.
Bertsch
,
S. S.
,
Groll
,
E. A.
, and
Garimella
,
S. V.
,
2009
, “
A Composite Heat Transfer Correlation for Saturated Flow Boiling in Small Channels
,”
Int. J. Heat Mass Transfer
,
52
(
7–8
), pp.
2110
2118
.10.1016/j.ijheatmasstransfer.2008.10.022
12.
Basu
,
S.
,
Ndao
,
S.
,
Michna
,
G. J.
,
Peles
,
Y.
, and
Jensen
,
M. K.
,
2011
, “
Flow Boiling of R134a in Circular Microtubes—Part I: Study of Heat Transfer Characteristics
,”
ASME J. Heat Transfer-Trans. ASME
,
133
(
5
), p.
051502
.10.1115/1.4003159
13.
Nascimento
,
F. J. D.
,
Leao
,
H. L. S. L.
, and
Ribatski
,
G.
,
2012
, “
Flow Boiling Heat Transfer of R134a in a Microchannel Heat Sink
,”
ASME
Paper No. ICNMM2012-73026.ICNMM2012-73026
14.
Kuo
,
C.
, and
Peles
,
Y.
,
2008
, “
Critical Heat Flux of Water at Subatmospheric Pressures in Microchannels
,”
ASME J. Heat Transfer-Trans. ASME
,
130
(
7
), p. 072403.10.1115/1.2909077
15.
Warrier
,
G. R.
,
Dhir
,
V. K.
, and
Momoda
,
L. A.
,
2002
, “
Heat Transfer and Pressure Drop in Narrow Rectangular Channels
,”
Exp. Therm. Fluid Sci.
,
26
(
1
), pp.
53
64
.10.1016/S0894-1777(02)00107-3
16.
Brutin
,
D.
,
2008
, “
Flow Boiling Instability
,” D. Li, ed.,
Encyclopedia of Microfluidics and Nanofluidics
, Springer, Boston, MA, pp.
687
695
.10.1007/978-0-387-48998-8_540
17.
Xu
,
J.
,
Zhou
,
J.
, and
Gan
,
Y.
,
2005
, “
Static and Dynamic Flow Instability of a Parallel Microchannel Heat Sink at High Heat Fluxes
,”
Energy Convers. Manage.
,
46
(
2
), pp.
313
334
.10.1016/j.enconman.2004.02.012
18.
Guodong
,
W.
,
Cheng
,
P.
, and
Wu
,
H.
,
2007
, “
Unstable and Stable Flow Boiling in Parallel Microchannels and in a Single Microchannel
,”
Int. J. Heat Mass Transfer
,
50
(
21–22
), pp.
4297
4310
.10.1016/j.ijheatmasstransfer.2007.01.033
19.
Koşar
,
A.
,
Kuo
,
C.-J.
, and
Peles
,
Y.
,
2006
, “
Suppression of Boiling Flow Oscillations in Parallel Microchannels by Inlet
,”
ASME J. Heat Transfer-Trans. ASME
,
128
(
3
), pp.
251
260
.10.1115/1.2150837
20.
Kuo
,
C.
, and
Peles
,
Y.
,
2008
, “
Flow Boiling Instabilities in Microchannels and Means for Mitigation by Reentrant Cavities
,”
ASME J. Heat Transfer-Trans. ASME
,
130
(
7
), p. 072402.10.1115/1.2908431
21.
Basu
,
S.
,
Werneke
,
B.
,
Peles
,
Y.
, and
Jensen
,
M. K.
,
2015
, “
Transient Microscale Flow Boiling Heat Transfer Characteristics of HFE-7000
,”
Int. J. Heat Mass Transfer
,
90
, pp.
396
405
.10.1016/j.ijheatmasstransfer.2015.06.038
22.
Chen
,
G.
, and
Cheng
,
P.
,
2009
, “
Nucleate and Film Boiling on a Microheater Under Pulse Heating in a Microchannel
,”
Int. Commun. Heat Mass Transfer
,
36
(
5
), pp.
391
396
.10.1016/j.icheatmasstransfer.2009.01.022
23.
Kingston
,
T. A.
,
Weibel
,
J. A.
, and
Garimella
,
S. V.
,
2020
, “
Time-Resolved Characterization of Microchannel Flow Boiling During Transient Heating: Part 1—Dynamic Response to a Single Heat Flux Pulse
,”
Int. J. Heat Mass Transfer
,
154
, p.
119643
.10.1016/j.ijheatmasstransfer.2020.119643
24.
Hodson
,
S.
,
McCarthy
,
K.
,
McCarthy
,
P.
, and
Issam
,
M.
,
2019
, “
A Dynamic Two-Phase Component Model Library for High Heat Flux Applications
,”
SAE
Technical Paper No. 2019-01-1386
.10.4271/2019-01-1386
25.
Huang
,
H.
,
Borhani
,
N.
, and
Thome
,
J. R.
,
2018
, “
Thermal Response of Multi- Microchannel Evaporators During Flow Boiling of Refrigerants Under Transient Heat Loads With Flow Visualization
,”
ASME J. Electron. Packag.,
138
(
3
), p. 031004.10.1115/1.4033487
26.
Zhang
,
T.
,
Tong
,
T.
,
Chang
,
J.
,
Peles
,
Y.
,
Prasher
,
R.
,
Jensen
,
M. K.
,
Wen
,
J. T.
, and
Phelan
,
P.
,
2009
, “
Ledinegg Instability in Microchannels
,”
Int. J. Heat Mass Transfer
,
52
(
25–26
), pp.
5661
5674
.10.1016/j.ijheatmasstransfer.2009.09.008
27.
Boure
,
J. A.
,
Bergles
,
A. E.
, and
Tong
,
L. S.
,
1973
, “
Review of Two-Phase Flow Instability
,”
Nucl. Eng. Des.
,
25
(
2
), pp.
165
192
.10.1016/0029-5493(73)90043-5
28.
Bergles
,
A. E.
, and
Kandlikar
,
S.
,
2005
, “
On the Nature of Critical Heat Flux in Microchannels
,”
ASME J. Heat Transfer-Trans. ASME,
127
(
1
), pp.
101
107
.10.1115/1.1839587
29.
Wang
,
G.
,
Cheng
,
P.
, and
Bergles
,
A. E.
,
2008
, “
Effects of Inlet/Outlet Configurations on Flow Boiling Instability in Parallel Microchannels
,”
Int. J. Heat Mass Transfer
,
51
(
9–10
), pp.
2267
2281
.10.1016/j.ijheatmasstransfer.2007.08.027
30.
Bandhauer
,
T. M.
, and
Bevis
,
T. A.
,
2016
, “
High Heat Flux Boiling Heat Transfer for Laser Diode Arrays
,”
ASME
Paper No. ICNMM2016-7947.10.1115/ICNMM2016-7947
31.
Burk
,
B. E.
,
Grumstrup
,
T. P.
,
Bevis
,
T. A.
,
Kotovsky
,
J.
, and
Bandhauer
,
T. M.
,
2019
, “
Computational Examination of Two-Phase Microchannel Heat Transfer Correlations With Conjugate Heat Spreading
,”
Int. J. Heat Mass Transfer
,
132
, pp.
68
79
.10.1016/j.ijheatmasstransfer.2018.11.068
32.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
2009
,
Experimentation, Validation, and Uncertainty Analysis for Engineers
, pp.
33
50
.
33.
Bergles
,
A. E.
, and
Rohsenow
,
W. M.
,
1964
, “
The Determination of Forced-Convection Surface-Boiling Heat Transfer
,”
ASME J. Heat Transfer-Trans. ASME,
86
(
3
), pp.
365
372
.10.1115/1.3688697
34.
Sato
,
T.
, and
Matsumura
,
H.
,
1964
, “
On the Conditions of Incipient Subcooled-Boiling With Forced Convection
,”
Bulletin of JSME
,
7
(
26
), pp.
392
398
.10.1299/jsme1958.7.392
35.
Davis
,
E. J.
, and
Anderson
,
G. H.
,
1966
, “
The Incipience of Nucleate Boiling in Forced Convection Flow
,”
AIChE J.
,
12
(
4
), pp.
774
780
.10.1002/aic.690120426
36.
Hsu
,
Y. Y.
,
1962
, “
On the Size Range of Active Nucleation Cavities on a Heating Surface
,”
ASME J. Heat Transfer-Trans. ASME
,
84
(
3
), pp.
207
213
.10.1115/1.3684339
37.
Kandlikar
,
S. G.
,
2006
, “
Nucleation Characteristics and Stability Considerations During Flow Boiling in Microchannels
,”
Exp. Therm. Fluid Sci.,
30
(
5
), pp.
441
447
.10.1016/j.expthermflusci.2005.10.001
38.
Cooper
,
M. G.
,
1984
, “
Heat Flow Rates in Saturated Nucleate Pool Boiling-A Wide-Ranging Examination Using Reduced Properties
,”
,
16
, pp.
157
239
.10.1016/S0065-2717(08)70205-3
39.
Heas
,
S.
,
Robidou
,
H.
,
Raynaud
,
M.
, and
Lallemand
,
M.
,
2003
, “
Onset of Transient Nucleate Boiling From a Thick Flat Sample
,”
Int. J. Heat Mass Transfer
,
46
(
2
), pp.
355
365
.10.1016/S0017-9310(02)00267-3