## Abstract

High-performance computing (HPC) data centers demand cutting edge cooling techniques like direct contact liquid cooling (DCLC) for safe and secure operation of their high-power density servers. The two-phase flow boiling heat transfer technique is widely believed to address the heating problem posed by HPC racks. In this study, a novel liquid-cooled cold plate containing microchannel and jet impingement arrangement was characterized for its two-phase flow and thermal behavior. A sophisticated bench top setup involving a mock package was developed to carry out the experiments in a controlled fashion using a dielectric fluid Novec/HFE-7000. Two-phase flow boiling in cold plates which has a strong dependency on surface phenomena were carefully studied at various levels of inlet pressure, subcooling, flow rates, and heat flux levels to the mock package. A resistance network was invoked to determine the average heat transfer coefficient at various exit qualities estimated by the energy balance equation. While the results make it evident that, the high heat generating components can be kept at operable conditions using the two-phase cooling; a deeper insight at the outcomes could pave way for more energy efficient cold plate designs. The experiment was carried out with a large heated surface of 6.45 cm2 and maximum dissipated heat flux was around 63.6 W/cm2 corresponding to chip power of 410 W. Base temperature was kept below 75 °C and pressure drop did not exceed 21 kPa.

## 1 Introduction

Data centers (DC) in recent times are seeing an unprecedented rise in computing capability, especially with the advent of artificial intelligence (AI), deep learning, and machine learning platforms. Apart from the communication, social media, video-streaming services, and travel, the list of beneficiaries from AI and machine learning include the medical industry (DNA sequencing, genome mapping), autonomous vehicles, cryptocurrencies, and advanced scientific computing. High-performance computing (HPC) is made possible with the arrival of advanced hardware like graphical processing units, field programmable gate arrays (FPGAs), and application specific integrated circuits (ASICs) working sometimes in tandem with CPUs. For example, NVIDIA's V100 graphical processing unit and Intel Xeon's scalable processor (skylake) [1] are currently operating at wattage of 300 W and 205 W, respectively. These high chip wattages and the requirement to keep the minimum interconnect distance between the processors; translate to higher wattage densities at the rack level in a DC operation. Thus, the rack densities can go up to 25–35 kW.

Servers which are the major producers of heat in a datacenter operation are customarily stacked in a rack level arrangement facilitating serviceability, scalability, and more importantly cooling. Traditional air-cooled data center nowadays operate at a rack density of 7 kW. Air cooling using computer room air handlers (CRAHs), raised floors, hot/cold aisle containment systems, chillers and evaporative coolers are still the traditional method of cooling majority of current DCs. With the miniaturization of micro-electronic components and with the tendency toward growing component density, air cooling becomes inefficient and demand bigger heat sinks with bigger fans at the chassis level thus hindering a rise in the rack density. Though the bigger heat sink problem can be mitigated using an efficient heat pipe combined with high performing thermal interface material (TIM), air cooling could still be ineffective due to its low heat carrying capacity compared to liquids. As a result, majority of the current and older (legacy) DCs are facing the real high heat-generating issues and are looking for simple, cost-effective, energy-efficient, smaller, and smarter cooling solutions in order to accommodate this rise in computing capability.

Liquid cooling on the other hand can offer smaller size cooling options while also enriching the energy efficiency. It is because the heat carrying capacity of liquids like water, mineral oils, or dielectric fluids is generally greater than that of air. For example, Water's specific heat capacity is 4180 Jkg−1K−1 and air's specific heat capacity is 993 Jkg−1K−1 therefore water has 4.2 times more specific heat capacity. By using liquid cooling, the size of the heat sinks can be reduced drastically, thus promoting a natural rise in server component density. Comparing with air cooling, the reliability of the components is greatly improved in liquid cooling, by bringing the liquid closer to the component using cold plates with TIM thereby reducing the overall thermal resistance from the device's junction to ambience. Although liquid cooling is not a new solution to electronics thermal management, it is seeing its resurgence among the data center industries. One of the global frontrunners of AI industry and one of the pioneers of data center thermal management, Google [2] are looking at liquid cooling as a great option to cut down chilling expenditures, while also maximizing their cooling system efficiency. The tech giant also indicated that their latest high-performance racks equipped with tensor processing units (TPUs) are being liquid cooled.

The cooling system characterized in the current study is intended for a rack-level deployment. A typical rack-level direct contact liquid cooling (DCLC) system which is available in a data center of Binghamton University is as shown in Fig. 1. coolant distribution unit (CDU) which is the brain of a rack-level system usually sits on the top or bottom of a rack and could take sizes from 4 U to 6 U usually dictated by the cooling capability. The heat exchanger in the CDU contain two flow loops (1) a primary loop carrying the facility water and (2) a secondary loop carrying the coolant through individual servers as shown in the figure. The cold plates which are TIM attached to the processing chips exchange heat with the secondary side coolant as it runs through individual servers. Multiple pumps are positioned for redundancy. Various sensors are lined up in the fluid lines to identify the various states of the system. The number of cold plates hinge on the number of heat generating devices intended to be cooled by DCLC.

Fig. 1
Fig. 1
Close modal

The data center facility at Binghamton University houses multiple racks divided among three cold aisles covering a total area of 215 m2. A commercially available two-phase cooling system [3] is installed on to one such rack for analyzing its flow and thermal performance at a variety of data center operating conditions. The rack cooled by the two-phase cooling system contains 14 Dell PowerEdge (2 U chassis) servers, with two processing chips per chassis. The rack-level two-phase system is equipped with temperature, flow, and pressure sensors at multiple locations in order to track the behavior of the system at different levels of operation. The results obtained from investigating the rack level two-phase system will be published in a separate article from the authors.

Although the ultimate aim is to achieve an energy-efficient rack-level system, this article focuses on the results obtained at a component or cold plate level. This is required because the two-phase operation of a cold plate is often influenced by various factors like inlet pressure, inlet coolant subcooling, input power to the dies. On top of the operational parameters, two-phase cooling also depends on the surface-fluid combination and the geometry of the cold plate. The following three paragraphs narrate the highlights/advantages and the challenges/complexity which comes with the two-phase cooling technique before explaining the results obtained from experimentally characterizing a two-phase cold plate using a dielectric fluid.

The complexities associated with the two-phase system are greater than the conventional air-cooled or single-phase liquid-cooled system owing to its nature of coexisting in two-phases within the system. But the different intricacies of two-phase cooling can be overcome considering the several benefits it can offer which include high heat transfer capability, reduced system size, weight, and pumping power, temperature uniformity (isothermality), and ease of scalability.

The heat transfer coefficient associated with two-phase cooling is several times greater than what single-phase cooling could achieve. Two-phase heat transfer, by its principle, involves growth and departure of vapor bubbles from the heated surface. This action not only creates local turbulence near the heated surface but also draws liquid toward the surface at a very high frequency. This very nature of two-phase cooling helps in addressing hotspots (from the processors cores) much effective than single-phase cooling. The several advantages associated with two-phase heat transfer in fact drive the cooling scheme for future generation electronics. Several pioneering works [413] dedicated toward high heat flux thermal management has reported the high heat transfer capability associated with two-phase cooling comparing to air cooling or single-phase cooling. Two-phase cooling for high heat flux management have been reported on applications ranging from cooling heavy electronics (insulated-gate bipolar transistor power modules) [14,15] to high-performance data center servers [16]. Two-phase cooling in a data center environment can be realized in several ways like total immersion cooling of server modules [17] or embedded two-phase liquid-cooled microprocessor [18] or two-phase evaporators [19,20] or microchannel flow boiling using heat sinks/cold plates.

Agostini et al. [21] performed the thermal resistance vs pumping power variation comparing different cooling techniques. The various technologies subjected for comparison include microchannel (single-phase and two-phase), porous media (single-phase and two-phase), and jet impingement. It was observed that the two-phase microchannel cold plates offer the least thermal resistance while also requiring minimum pumping power for high heat flux thermal management. Various researchers in the past have explored the benefits of two-phase cooling in microchannel heat sink applications, but without identifying the numerous challenges posed by the two-phase flow. The presence of two-phase in microchannels can cause hydrodynamic instabilities and pressure drop oscillation in the channels as reported in the Refs. [14,22,23]. These instabilities in pressure drop can be mitigated by (a) using throttling valves [24], (b) developing artificial nucleation sites [25,26], (c) using divergent channels [25], or (d) use of surface enhancement coatings [27]. Experimental works on microgaps [28] reported issues due to flow reversal or oscillations especially at high heat flux and recommendation of a pressure restrictor at the heat sink inlet was provided.

Pool boiling characteristics of several fluorinated coolants like Novec/HFE 649 [29], Novec/HFE 7000 [30,31], and FC-72 [13] have been observed and well documented in the past. Unlike pool boiling, the mechanisms of flow boiling are more complicated; therefore, the knowledge of pumped two-phase cooling in server electronics or data center is limited. As a result, applications of pumped two-phase cooling in server electronics are rare. In order to improve knowledge of pumped two-phase cooling, thermal engineers and scientists in data center need to pay attention to two-phase cooling is not only server electronics applications but also other electronics applications. Works like [32] have been dedicated toward analyzing the saturated two-phase flow boiling in microchannels where correlations based on the available experimental data were developed to predict and later model the boiling heat transfer coefficient in small channels. As rightly pointed out in Ref. [23], the goals of flow boiling heat transfer intended for high-density applications would be (a) to promote onset of boiling (ONB) at a lower heat flux, (b) to increase the slope of the boiling curve (increasing nucleate boiling heat transfer coefficient), and (c) to increase the critical heat flux (CHF) value. This work aims to study the effects of operating parameters on the performance of a two-phase multijet/microchannel cold plate with coolant Novec/HFE-7000 intended for applications in the data center.

In this paper, a bench top experimental setup was developed to characterize thermal and hydraulic performance of an impingement multijet/microchannel cold plate with dielectric coolant Novec/HFE-7000. Flow boiling performance of a commercially available cold plate was characterized in detail. The influence of coolant inlet subcooling, coolant flow rate, and input power to the performance of cold plate were analyzed. The thermal resistance and average heat transfer coefficient of the cold plate were obtained following a thermal resistance network and the approximate vapor quality was estimated by invoking the energy balance equation. The variation of pressure drop through the cold plate with heat flux and flow rate was presented. The experimental data were compared with prediction from an existing correlation for two-phase boiling. The scope this article is to elucidate the benefits of liquid cooling especially the two-phase cooling technique when deployed in a high-density data center environment using a novel cold plate design.

## 2 Experimental Setup and Data Reduction

This section discusses the choice of dielectric coolant, cold plate design, and the mock package used. The details of the coolant test loop which houses various instruments and their associated uncertainties would follow next. The final segment of this section details about the data collection and data reduction procedure.

### 2.1 Dielectric Coolant.

The choice of dielectric coolant depends on several factors like operating pressure, target junction temperature, working cost, safety, and compatibility of the elements in the processing loop. Even in the worst-case failure scenario in terms of leakage, unlike water or other single-phase coolants, dielectric fluids tend not to damage the electronics as they are electrically nonconductive. Hydrofluorocarbons (HFCs) and hydrofluoroethers (HFEs) are some of the most common dielectric coolants which are used in the electronics industry. A low global warming potential dielectric coolant from 3 M, Novec/HFE 7000 [33] which has a boiling point of 34 °C at atmospheric pressure is used in the current study. The coolant Novec/HFE 7000 developed by 3M company (St. Paul, MN) was chosen for this study based on the desired operating temperature dictated by its low boiling point. Its low boiling point would also allow operating at low pressures which is desirable when it comes to tubing/hoses. Also, Novec/HFE 7000 has better thermal properties (specific heat, latent heat of vaporization, thermal conductivity) compared to other fluids listed in Table 1. At the same time, the dielectric strength of Novec 7000 is much higher than its contemporaries making it a favorable choice for this study.

Table 1

Properties of dielectric coolant Novec 7000 at 1 atm

PropertiesFC 72 [34]FC 3284 [35]HFE 649 [36]FC 77 [37]HFE 7100 [38]HFE 7000 [33]
Saturation temp (°C)565049976134
Latent heat of vaporization ($kJ/kg$)881058889111.6142
Thermal conductivity ($W/mK$)0.0570.0620.0590.0630.06980.075
Specific heat ($J/kgK$)110011001103110011731300
Surface tension (mN/m)101310.81313.612.4
Dielectric constant (at 1 kHz)1.751.861.81.97.47.4
Global warming potentialHighHigh1320530
PropertiesFC 72 [34]FC 3284 [35]HFE 649 [36]FC 77 [37]HFE 7100 [38]HFE 7000 [33]
Saturation temp (°C)565049976134
Latent heat of vaporization ($kJ/kg$)881058889111.6142
Thermal conductivity ($W/mK$)0.0570.0620.0590.0630.06980.075
Specific heat ($J/kgK$)110011001103110011731300
Surface tension (mN/m)101310.81313.612.4
Dielectric constant (at 1 kHz)1.751.861.81.97.47.4
Global warming potentialHighHigh1320530

### 2.2 Cold Plate.

The Cold Plate module characterized in the article as shown in Fig. 2 is developed to have two-phase flow boiling inside them. The novelty of this cold plate lies in the arrangement of plastic cap containing the jets and the base part containing the microchannels. The plastic cap contains the inlet and outlet manifold. The plastic cap is 3D printed with the jets of required size which dictates the two-phase flow. The plastic cap is 360 deg rotatable which makes it easier for the cold plates to be installed in any orientation within the server chassis and thus facilitating easy fluid path. The orientation of the jets and the tilted top surface of the cap help the vapor to exit the evaporator easier and decrease the risk of flow reversal. The microchannels are manufactured using the skiving process. The base copper part of the cold plate was grooved to install two small T-type thermocouples for measuring the average base temperature $Tb$ (sometimes referred to as wall temperature, $Tw$ in two-phase terminology). The T-type thermocouples which are calibrated using a precision oven were thermally bonded to the grooves using a high conducting adhesive (Omegabond).

Fig. 2
Fig. 2
Close modal

The schematic of the cold plate containing the microchannel and jet impingement arrangement is shown in Fig. 3. The usage of jets eliminates channel-channel oscillations or the manifolds crosstalk issue in the microchannels as reported in the literature. The plastic top part contains the inlet and outlet section. The inlet section extends to a jet impinging arrangement as shown in Fig. 3. The two-phase mixture resulting from vaporization of the coolant exits through the outlet.

Fig. 3
Fig. 3
Close modal

Microchannels in the cold plate have a fin height of 3000 μm with fin thickness and channel width being 120 μm and 120 μm, respectively. The fin height does not entirely contribute like in conventional single-phase convective heat transfer but rather act as nucleation sites and helps in the growth and departure of vapor bubbles from the heater surface. Thus, the bubble departure size and nucleation site density are dictated by the microchannel size and the number of channels, respectively. Figure 4 schematically shows the bubble formation, growth, and departure from the cold plate surface.

Fig. 4
Fig. 4
Close modal

### 2.3 Mock Package.

A detailed two-dimensional representation of the mock package is as shown in Fig. 5. Copper blocks with a cross-sectional area of 1-in. × 1-in. (6.45 cm2) and with a total height of 4.25 in. was built to mimic a typical processor die. Four cartridge heaters (Omega: CIR 3020/120 V) were installed in its bottom and were powered using a DC power supply (Sorenson: DCS 100E). Three resistance temperature detectors (RTDs) (Minco Part no: S13282PD3T36) were installed along the length of the copper block to represent the temperature gradient. The heat flux at the top of the copper block was estimated using Fourier's law of heat conduction,
$Q¨in= −kA(ΔT/Δx)$
(1)

where k is the thermal conductivity of copper, A is the cross-sectional area of the block and ΔT is the measured temperature gradient along the copper block. The copper block heater arrangement is kept in place using high conducting Ultem material. The setup including the mock package was thoroughly insulated on all sides leaving out the top surface such that all the heat from the heater reaches the cold plate. Proper care was taken while manufacturing and assembling the different parts to put together the mock package. The fit and the flatness of the heater surface were ensured at all stages of manufacturing using a height gage and a flatness indicator.

Fig. 5
Fig. 5
Close modal

The advantages of building mock packages over thermal test vehicle or thermal load board are (a) it is relatively inexpensive and easy to build, (b) it can reach higher power levels than conventional thermal test vehicle/thermal load board, and (c) uniform heat flux can be achieved at the top surface. The cold plate subjected for characterization was installed on top of the copper blocks with a layer of thermal interface material. Graphite sheet (TIM HT C3200) [39] having a thermal conductivity of 7 W/mK was used as the thermal interface material reported in this study because of its ease of application and removal.

### 2.4 Bench Top Setup.

A sophisticated bench top setup as shown in Fig. 6 was carefully assembled to conduct experiments in a controlled fashion. The setup contains two reservoirs arranged in series. Pump 1 and pump 2 (Koolance, part no. PMP-500 pump, G 1/4 BSP) branches out of the common reservoir 2. While pump 2 pushes the dielectric fluid through the primary coolant loop containing the cold plate, pump 1 thrust the fluid through the heat exchanger loop containing a radiator. The reservoirs were setup this way such that the two-phase fluid coming out of cold plate enters into reservoir 1 and condenses upon mixing with the colder liquid. The uncondensed vapor in reservoir 1 rises to the top and the liquid coolant from reservoir 1 flows to reservoir 2 so that both pumps 1 and 2 do not undergo cavitation. Pump 1 and 2 were operated using an external power supply (Agilent, Part no. DCS- 100E), and the fan speed in the radiator was controlled using an external power supply. The inlet subcooling of the coolant entering the cold plate was maintained using a laboratory made liquid-liquid heat exchanger. An external chiller unit (Julabo, Part no. LH40) with an operating range of −40 to 250 °C was used to control the inlet subcooling at the heat exchanger.

Fig. 6
Fig. 6
Close modal

For the set of results discussed in this article, the temperature at the inlet of the cold plate was intentionally maintained at a temperature much lower than its corresponding saturation temperature. A flowmeter (Omega, Part no. FTB 313D) with an operating range of 0.2–2 lpm was used to measure the flow rate of the liquid coolant entering the cold plate. T type thermocouples and pressure gages were installed to represent system states at the cold plate inlet and exit. The pressure and temperature sensors were connected to a data acquisition system (DAQ) and a sophisticated LabVIEW program was developed to read/write the measurement data. The details of the different data sensing, their associated uncertainties and the corresponding DAQ device are listed in Table 2. The overall measurement uncertainty in sensible heat was estimated to be less than ±10%. The error analysis using root sum square method [40,41] was carried out for the experimental uncertainty in the heat transfer coefficient for various heat fluxes. The uncertainties of the heat transfer coefficient generally decrease with heat flux and drop from 13% at heat flux 8 W/cm2 to the minimum 2.7% at heat flux 46.5 W/cm2. The details of uncertainty analysis can be found in the Appendix. The fluid level in the reservoir was monitored at regular intervals for any fluid loss. It was observed that the fluid fill ratio in the reservoir can influence the system pressure and hence the boiling characteristics inside the cold plate. This is because; change in system pressure can alter the dielectric coolant's boiling point or saturation temperature. For the set of results discussed in this article, the fluid level in the reservoir was maintained at a constant level during all the test runs.

Table 2

Data sensing instruments used in the cold plate characterization

InstrumentMeasurandUncertaintyDAQ module
Pressure gages (2 numbers) Omega: PX309050A5VPressure at inlet, and outlet±0.8 kPaNI- USB-6009, National Instrument, Austin, TX
T-type thermocouples (2 numbers) (Omega: TTSS-14E-6)Coolant temperature at inlet, and outlet±0.3 °CNI 9219
T-type thermocouple (2 numbers) Laboratory MadeCold plate base metal temperature measurement±0.5 °CNI-9219
RTDs (3 numbers)Measuring temperature gradient across the mock package±0.3 °CNI-9219
InstrumentMeasurandUncertaintyDAQ module
Pressure gages (2 numbers) Omega: PX309050A5VPressure at inlet, and outlet±0.8 kPaNI- USB-6009, National Instrument, Austin, TX
T-type thermocouples (2 numbers) (Omega: TTSS-14E-6)Coolant temperature at inlet, and outlet±0.3 °CNI 9219
T-type thermocouple (2 numbers) Laboratory MadeCold plate base metal temperature measurement±0.5 °CNI-9219
RTDs (3 numbers)Measuring temperature gradient across the mock package±0.3 °CNI-9219
Figure 7 shows the variation of input power and output power for the tests conducted using a severely subcooled coolant. This was done such that heat captured at the cold plates is by purely single-phase heat transfer for major portion of the tests. Thus, any discrepancies which may occur from estimation of heat picked by the latent heat of vaporization are avoided. The input power $Qin$ to the mock package was estimated according to
$Qin= −kA(ΔTCu block/Δx)$
(2)
Fig. 7
Fig. 7
Close modal
And the output power $Qout$ (sensible heat) picked by the cold plates was estimated according to
$Qout= m˙NovecCp,Novec(T out−Tin)$
(3)

But after 200 W mark, $Twall$>$Tsat$ thus kick-starting latent heat removal process. Based on the knowledge gained from an earlier study (mock package and warm water cooling), the energy loss did not vary greatly going from 200 W to 300 W. The heat loss associated with the test setup was estimated to be about 10% at the maximum power level tested.

A tight experimental procedure was followed to conduct tests in an organized way. A typical test run takes about 4.5–5 h to complete. Before collecting any actual data by powering the dies, the dielectric coolant was allowed to run through the system loop at constant flow rate and at the desired set coolant temperature for about 30 min to degasify any previously formed/trapped vapor molecules. The heat flux to the dies was then varied in small increments by adjusting the power supply. The wall temperature was recorded after the system reaches a steady-state. Data were recorded during increasing and decreasing heat flux cycles in order to capture any hysteresis in two-phase heat transfer which typically occurs at the ONB. The majority of the data presented in this article belong to the increasing heat flux cycle of the test runs. Hence, it also should be noted that that the results carry with them any inconsistencies and unpredictability of the temperature overshoot phenomenon which accompanies the increasing heat flux portion of tests. A good repeatability with the tests was observed showing the efficacy of the test setup and the test procedure followed.

## 3 Results and Discussion

### 3.1 Effect of Subcooling.

The primary independent variables in the current study are coolant inlet subcooling, coolant flow rate, and input power to the dies. Tests were conducted at various levels of coolant temperatures ranging from 38 °C to 54 °C to study the effect of coolant subcooling on the boiling characteristics. The pressure at the inlet and outlet of the cold plate was recorded and the coolant's corresponding saturation temperature was matched by looking up the data sheet from the coolant manufacturer. Figure 8 shows the flow boiling curve showing the variation of wall super heat ($Tw−Tsat$) to the applied heat flux heat flux, ($q)˙$ in the coordinate axes. The following are the major inferences:

Fig. 8
Fig. 8
Close modal

When $Tw$ < $Tsat$, heat transfer would occur primarily by single-phase convection. This behavior is very much noticeable when the degree of subcooling is higher as indicated by the blue dotted lines in Fig. 8. Albeit when the wall temperature is higher than the saturation temperature, this excess temperature (or wall super heat) is insufficient to support bubble formation and growth. It is possible for the onset of nucleate boiling to be delayed until the mean coolant enthalpy is higher than that of the saturated liquid [42]. The value of ONB heat flux decreases slightly with rise in inlet coolant temperature. When the ONB value is reached, bubbles begin forming at nucleation sites on the cold plate microchannels. The nucleation sites are generally associated with crevices or pits on the surface in which the nondissolved gas or vapor accumulates and results in bubble formation. As the bubble grow and depart from the surface, they carry latent heat away from the surface producing turbulence and mixing that increases the heat transfer rate. Boiling under these conditions is referred to as nucleate boiling [42]. The heat transfer in this region is a complicated mixture of single-phase forced convection and nucleate boiling. This regime continues to rise with wall superheat until the bubble formation occupies the entire heat-generating surface.

In the partial subcooling regime, when the degree of subcooling is lower than the coolant's saturation temperature. Figure 9 shows the variation in coolant temperatures for three levels of inlet subcooling while dissipating a total power of 300 W at a flow rate of 1 lpm. This figure also indicates the transition from combined sensible + latent heat transfer process (partial subcooled nucleate boiling) to entirely two-phase process (fully developed nucleate boiling) as the inlet coolant temperature is increased toward its saturation temperature.

Fig. 9
Fig. 9
Close modal

Figure 10 shows the variation in cold plate wall temperature $(Twall$) and the junction temperature $(Tj$) at different heat input condition at a coolant flow rate of 1 lpm and at a coolant temperature of 38 °C. The junction temperature was extrapolated from the RTD measurements used in the mock package. Whereas the cold plate temperature was measured using thermocouples installed in the bottom of the cold plate. Resistances including the TIM, spreading, convection/caloric resistance, conduction in cold plate base account for the difference between the junction ($Tj$) and the cold plate base temperature ($Twall$).

Fig. 10
Fig. 10
Close modal

### 3.2 Cold Plate Thermal Resistance and Heat Transfer Coefficient.

The two-phase flow boiling which has a strong dependency on input power can be explained well with the help of a resistance network model. The cold plate thermal resistance $Rcp$ as shown in Eq. (4) is defined as the ratio of the difference between average wall temperature $(Twall,avg)$ and the coolant inlet temperature $(Tin$) to the input power supplied (Q)
$Rcp= Twall,avg−TinQ$
(4)

The cold plate thermal resistance was observed to be independent of inlet subcooling, at the same time appeared to have a strong dependency on input power levels as shown in Fig. 11. This behavior is very different compared to single-phase cooling where the input power level or inlet subcooling does not have an influence on the cold plate thermal resistance at a constant flow rate. It can be observed in Fig. 11 that there were two regimes when input power increases from 30 W to maximum power 300 W. From 30 W to 160 W, thermal resistance reduced with heat flux due to nucleate boiling. When input power exceeded 160 W, thermal resistance did not change much with input power due to convective boiling. In convective boiling regime, thermal resistance and heat transfer coefficient are more dependent on flow rate [43].

Fig. 11
Fig. 11
Close modal

At the lower heat flux level, the bubbles generated do not have enough superheat to detach from the surface thus hindering the new coolant reach the heated surface. This behavior at lower heat flux is pronounced when the inlet temperature is high where there's a natural tendency for bubbles to grow bigger and not condense with the colder bulk fluid. As the ONB is crossed, the cold plate thermal resistance drops with increasing input power showing the efficiency in latent heat removal process where the vapor bubbles grow and detach from the surface creating turbulence.

When the wall temperature exceeds the local saturation temperature, boiling occurs. Even though there is a significant level of vapor production from the heated surface, the amount of vapor produced may not be sufficient enough to alter the quality of the bulk coolant. The results reported in the current article belong entirely to the subcooled boiling regime where the inlet temperature of the bulk coolant at the cold plate was lower than saturation temperature.

An approximate estimation of vapor quality (vapor production) at various heat flux levels was carried out by calculating the heat picked by the coolant according to the latent heat of vaporization ($Qvapor$). First, the sensible heat ($Qsensible$) picked by the coolant was calculated according to
$Qsensible= mliquid˙Cp(Tout−Tin)$
(5)
Where the mass flow rate ($mliquid˙$) of the subcooled coolant was measured using a flowmeter, the coolant temperatures ($Tout, Tin$) were measured using the thermocouples stationed at the inlet and outlet of the cold plate and the specific heat of the coolant ($Cp$) was estimated based on average coolant temperatures. With the knowledge of heat losses from the setup and uncertainty associated with the measurements, the heat picked by vapor was approximately estimated according to
$Qvapor=(Qtotal−Qsens−Qloss)$
(6)
The mass flow rate of vapor ($m˙vapor$) produced was then estimated according to ($Qvapor/hfg)$, where $hfg$ is the “latent of heat of vaporization” obtained using the coolant property chart. Since the latent heat of vaporization is much larger than the coolant's sensible heat, the mass flow rate of vapor generated is much smaller compared to that of bulk liquid coolant's flow. The percentage quality was then calculated using the relation as shown in the following equation:
$x = mvapor˙mliquid + ˙mvapor˙*100%$
(7)
The plot in Fig. 12 shows the percentage vapor production on the primary y axis and the corresponding the heat transfer coefficient on secondary y axis with respect to heat flux supplied on x-axis. In order to plot the uncertainty of experimental data, the error bar was added to heat transfer coefficient in the case of coolant inlet temperature 38 °C. The error bar was added to only one case of inlet temperature in order to avoid the overlap in uncertainty in Fig. 12. The uncertainty of heat transfer coefficient for the other cases of inlet temperature is similar to the case of inlet temperature 38 °C. It can be noticed that the amount of vapor production increases with the increasing heat flux especially at lower heat flux levels indicating bubble formation and latent heat removal process. The approximate percentage of vapor produced reaches a plateau after a certain heat flux level indicating the absence of fresher nucleation sites to help sustain the nucleate boiling heat transfer. A heat average heat transfer coefficient, $h$ was estimated from the calculated cold plate thermal resistance while assuming negligible conduction and spreading resistance. The heat transfer coefficient was calculated by
$h=QA(Tb−Tin)$
(8)

where Q is the input power (W), A is the area covered by microchannel (m2), Tb is wall temperature (°C) and Tin is the inlet temperature (°C). Accordingly, the average heat transfer coefficient, $h$ increases with the input heat flux especially at lower input power levels and reaches a saturation point. A maximum average heat transfer coefficient of 12,500 $W/m2K$ was estimated while dissipating a total power of 300 W at a flow rate of 1 lpm.

Fig. 12
Fig. 12
Close modal

### 3.3 Boiling Curve.

The mechanism of subcooled boiling has been an active field of interest/research in the past. Several researchers have devised many prediction methods based on the premise that both forced convection and nucleate boiling mechanisms exist and act independently in the subcooled flow boiling regime. Upon several investigations, it has been postulated that the total heat flux is often a sum of contribution due to single-phase liquid $qspl˙$ convection and nucleate boiling $qsnb˙$. Rohsenow's model [42] is widely used in predicting the partial subcooled boiling heat transfer. Rohsenow proposed to use conventional single-phase correlation according to Eq. (9) to predict the single-phase contribution to the total heat flux. Rohsenow further postulated that the nucleate boiling contribution to the total heat flux could be computed using the correlation developed for nucleate pool boiling according to Eq. (10). It can be seen in Eq. (10) that heat flux is a function of coolant properties such as liquid viscosity μL, liquid and vapor density ρL, ρv, latent heat hfg, surface tension σ, specific heat CpL and Prandtl number. In addition, heat flux varies with the third power of wall temperature and saturation temperature. The term Csf represents the interaction between copper surface and the coolant. Breaking down the flow boiling curve to know the characteristic behavior of different regimes is of extreme importance both in terms of a better understanding of results and for developing semi-empirical numerical models. The flow boiling curve as shown in Fig. 13 was plotted for the case when the coolant inlet temperature is 38 °C and inlet flow rate is 1 lpm. The applied heat flux was plotted on the y axis, while the measured wall temperature was plotted on the x axis.
$Q/A= hle[Tw−Tl(z)]$
(9)
$QA=μLhfg[g(ρL−ρv)σ]1/2[CpL(TW−Tsat)CsfhfgPrLn]3$
(10)
Fig. 13
Fig. 13
Close modal

The single-phase contribution when $Tw$< $Tsat$ was extrapolated linearly based on the experimental results. The nucleate boiling contribution was found out according to Eq. (7). The physical properties of the coolant were obtained from the coolant property sheet, while the constants $Csf$ was estimated at the maximum heat flux dissipated, r and s were found to be 0.33 and 1.7, respectively, from the literature. The surface correction factor $Csf$ which is based on surface-fluid combination was found to be a crucial factor in determining the nucleate boiling contribution. The nucleate boiling portion was added to the single-phase contribution to predict the partial subcooling regime as shown in Fig. 13.

In the low heat flux region, the experimental data outperformed Rohsenow's correlation. This is possibly due to the combined convection and nucleation behavior in this region. After the 200 W mark, single-phase convective heat transfer dominates the heat transfer process thus letting Rohensow's prediction to perform better. Considering the various complexities and uncertainties posed by the two-phase flow boiling, it was observed that the prediction using the Rohsenow method was within an acceptable range to the applied heat flux especially at the lower heat flux levels. The predicted results were also compared with that of a pool boiling scenario [29] and were found to be in reasonable agreement especially at the lower heat flux range before it transitions to single-phase.

### 3.4 Effects of Flow Rate.

The set of results discussed in Secs. 3.13.3 were obtained for different coolant inlet temperature conditions (inlet subcooling), at a constant flow rate of 1 lpm. However, in order to study the effect of coolant flow rate on flow boiling behavior, all the different tests conducted at a flow rate of 1 lpm were carefully repeated but this time at a flow rate of 0.7 lpm and 1.25 lpm. It was observed that the two-phase flow boiling has minimum dependency on flow rate in the range of heat flux tested. Cold plate thermal resistance was estimated at different input power levels and at different flow rates for a constant coolant inlet temperature of 38 °C using Eq. (2). It can be observed in Fig. 14 that the cold plate thermal resistance has minimum dependence on the flow rate especially while transitioning from single-phase to nucleate boiling mechanism. In the nucleate boiling region, thermal performance is weekly dependent on flow rate and highly dependent on fin configuration, surface roughness, and nucleate site density [41,42,44,45].

Fig. 14
Fig. 14
Close modal

While the thermal resistance has minimal dependence on coolant flow rate, the pressure drop across the cold plates varies significantly going from 0.7 lpm to 1.25 lpm. The following Fig. 15 shows the variation in pressure drop at different input power conditions at three different flow rates (0.7, 1, and 1.25 lpm) using a coolant temperature of 38 °C. The pressure drop increases with input power showing the addition of two-phase vapor bubbles to the stream. At the power level tested 300 W, the pumping power requirement decreases by about 60% going from 1 to 0.7 lpm which is significant in terms of savings.

Fig. 15
Fig. 15
Close modal

The results reported in this article correspond to the partial subcooled nucleate boiling regime. It also should be noted that the CHF was never reached in the set of results obtained at any given input condition. The scope of the current article is limited to subcooled boiling while it is well understood from the theory and literature that, flow boiling peaks with its performance only in the fully developed nucleate boiling regime exhibiting maximum heat transfer coefficient. Fully developed saturated flow boiling can be achieved by climbing to higher power levels using a subcooled coolant or operating at different inlet qualities using a saturated coolant. Several literatures reported great heat transfer capability while operating at an exit quality ranging from 0.3 to 0.5. The mock package and the system flow loop needed design tweaks to enable operating at higher power levels and at different inlet quality conditions without compromising the experimental quality.

While at this point, the discussions pertain to a single cold plate scenario, evaluating the performance of two-phase flow boiling by operating multiple devices in series and parallel mode will be covered in the subsequent article from the authors. While the future tests are not only restricted to changing inlet coolant conditions, efforts are made to characterize and evaluate the performance of different fluid-surface combinations as well in an attempt to reduce the ONB and increase the CHF. Although the overall aim is to boost up the energy efficiency in a rack-level operation, the two-phase boiling behavior at the component level has to be thoroughly understood before translating that to address a system-level problem.

## 4 Conclusion

A sophisticated test setup was built to observe the flow boiling performance of a novel cold plate using a dielectric fluid Novec/HFE 7000 under a variety of operating conditions like flow rate, coolant subcooling, and input power to the dies. The characterized cold plate was able to dissipate 410 W comfortably while operating well below the CHF. A maximum heat transfer coefficient of 12500 W/m2K was estimated using a resistance network at an inlet coolant temperature of 38 °C and at a flow rate of 1 lpm. Reduced flow rate tests reveal that significant savings with the pumping power could be achieved by two-phase cooling. The obtained results were identified to be in the partial subcooled nucleate boiling regime. A classic Rohsenow model was evoked in identifying the single-phase convection and nucleate boiling contribution in the partial subcooled boiling.

The real benefit of two-phase flow boiling could be reaped while operating multiple cold plates (devices) together in series. Two-phase cold plates when properly designed and put together for operation can mitigate modern compute or HPC rack-level cooling problem much better than existing air cooling and single-phase cooling options and will also be scalable for future generation computing. Future studies are planned to optimize the cold plate and to test a rack-level multiserver system for efficiency and stability under various power levels and different flow rates.

## Acknowledgment

This work is supported by NSF IUCRC Award No. IIP-1738793. The author would like to express gratitude toward Steven Schon (Quantacool), Mark Seymour (Futurefacilites) for their valuable inputs during the work. The author would like to thank Pat and Ron from Progressive Tool Co. at Endwell, NY for their help toward putting the mock package setup.

## Funding Data

• National Science Foundation (Grant No. IIP-1738793; Funder ID: 10.13039/100000001).

## Nomenclature

• $Cp$ =

specific heat of the coolant (kJ/kg·K)

•
• $Csf$ =

surface correction factor

•
• $hfg$ =

latent heat of vaporization (J/kg)

•
• lpm =

liters per minute

•
• $m˙liquid$ =

mass flow rate of the coolant (kg/s)

•
• $m˙vapor$ =

mass flow rate of the vapor (kg/s)

•
• Pr =

Prandtl number

•
• $Qw$ =

heat picked by the coolant

•
• $Tin$ =

inlet temperature (°C)

•
• $Tj$ =

junction temperature (°C)

•
• $Tout$ =

outlet temperature (°C)

•
• $Tsat$ =

saturation temperature (°C)

•
• $Twall$ =

wall temperature (°C)

•
• TIM =

thermal interface material

•
• $q″spl$ =

single-phase liquid heat flux (W/cm2)

•
• $q″snb$ =

subcooled nucleate boiling heat flux (W/cm2)

•
• $Qtotal$ =

total heat dissipated (W)

•
• $Qsens$ =

sensible heat picked by coolant (W)

•
• $Qvapor$ =

latent heat picked by vapor (W)

•
• $Qloss$ =

heat loss from the package (W)

•
• U =

rack unit (1 U =1.75 in.)

•
• $x$ =

vapor quality (%)

•
• ΔT =

temperature difference (°C)

•
• Δx =

distance between RTDs (m)

### Greek Symbols

Greek Symbols

• μ =

dynamic viscosity (kg/ms)

•
• ρ =

mass density (kg/m3)

Subscripts

• l =

liquid state

•
• v =

vapor state

### Appendix

The uncertainty of thermal resistance in this paper was calculated using the root sum square method [40,41]
$δR={∑i=1N(∂R∂Xi×ΔXi)2}1/2$
(A1)

Equation (A1) is the basic equation of uncertainty analysis. Each term represents the contribution made by the uncertainty in one variable, Xi, to the overall uncertainty in the result, δR. Each term has the same form: the partial derivative of R with respect to Xi multiplied by the uncertainty interval for that variable ΔXi.

Three RTDs mounted to copper block (Fig. 16) were used for measuring power dissipated to cold plate. Power Q is calculated using Fourier's law (Eq. (A2)). In which, Tbot and Ttop are the temperature readings using RTD 1 at the bottom and RTD 3 at the top as shown in Fig. 16, respectively, and Δx is the distance between these two RTDs. A stands for the top surface area of copper block where heat transfer goes through
$Q= KA(Tbot−Ttop)Δx$
(A2)
Fig. 16
Fig. 16
Close modal
Substituting Q from Eq. (A2) to Eq. (8), we obtain the equation for heat transfer coefficient
$h=K(Tbot−Ttop)Δx(Tb−Tin)$
(A3)

Uncertainty of heat transfer coefficient can be obtained by applying basic equation of uncertainty (A1) for the heat transfer coefficient Eq. (A3) with five variables (N = 5): Tb, Tin, Δx, Tbot, and Ttop.

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