# Data center energy efficiency enhancement using a two-phase heat sink with
ultra-high heat transfer coefficient

Suhas Rao Tamvada  Saeed Moghaddam<EMAIL_ADDRESS>Mechanical and Aerospace
Engineering, University of Florida, Gainesville, FL 32611, United States

###### Abstract

This paper presents the latest progress on characterization of our membrane
assisted phase-change heat sink (MHS) at conditions suitable for
implementation in data centers (DCs). Experiments are conducted using water as
the working fluid at a vapor space pressure ($P_{vapor}$) of 16 kPa,
corresponding to a saturation temperature of $\sim$ 55∘C. This temperature is
sufficiently lower than the silicon junction temperature of 80∘C. As
anticipated, the overall performance of MHS at sub-atmospheric pressure is
lower compared to analogous tests at atmospheric pressure. In agreement with
previous studies on MHS, the critical heat flux limit (CHF) increases with
enhancement of the heat transfer area ratio ($A_{r}$) and liquid space
pressure ($P_{pool}$). We report a maximum CHF of 670 W/cm2 on a surface with
an enhanced area ratio of 3.45, multiple times greater than the CHF reported
hitherto by a comparable two-phase heat sink in literature. Heat transfer
coefficients (HTC) as high as $\sim$ 1 MW/m2-K are obtained. These record
performance data along with unique characteristics of the MHS promise to
greatly benefit next generation highly energy efficient DCs.

###### keywords:

data center cooling , heat transfer , phase change , boiling , two-phase flow

##  1 Introduction

Proliferation of high-power density electronics has engendered the development
of high-performance computing (HPC) to supplement the growing needs of
artificial intelligence, big data, and cloud computing [1]. The energy demands
of data centers (DCs) which house the IT hardware needed for these computing
resources have been on the rise in the past decade and are projected to
increase rapidly [2, 3]. A myriad of factors influences DCs energy efficiency,
including the DC size, compute density, ambient conditions, etc. [1]. While
hyperscale DCs promise increased efficiency, a demand for low latency is
promoting less efficient edge DCs (relatively smaller high-density facilities
located close to the end-user). Energy use for thermal management of servers
is a major component of the overall energy demand in a DC. A widely used
metric for characterization of DCs energy efficiency is the power usage
effectiveness (PUE) [4]. PUE is the ratio of the total power used in the DC to
the power used by the IT equipment, given in eq. 1

$PUE=\dfrac{P_{tot}}{P_{IT}}$ (1)

where $P_{tot}=P_{IT}+P_{T}+P_{e}$ is the total power supply to the DC, and
$P_{IT},P_{T},$ and $P_{e}$ denote power consumption by the IT equipment,
thermal management systems, and the electrical power distribution system,
respectively. Currently, the average PUE of a DC is about 1.7 [3] meaning that
70% of the power flowing into DCs is utilized for auxiliary purposes, most
important of which is the cooling system energy use [5].

The current technology involves cooling the server racks using raised floors
and computer room air conditioning (CRAC) and air handling (CRAH) units [6].
In a traditional air-cooled data center, thermal resistances ($\Omega$) from
multiple components including the thermal interface materials (TIM), cooler,
etc., between the junction and ambient (cf. fig. 1) make the heat flow path
complex and require the use of chillers (7-15 ∘C) to maintain an acceptable
junction temperature. Alternatively, systems involving a high-performance heat
sink at the chip level offers significantly lower thermal resistance and
enable rejection of heat to the ambient at a higher temperature [7, 8]. In
specific cases, this waste heat could be utilized in buildings and industrial
units.

Figure 1: Thermal resistances encountered in a typical heat flow path in
traditional data center (DC) cooling and a proposed heat flow path utilizing a
high-performance heat sink at the chip level. The resistances between the
thermal interface material, cooler, and fluids require the use of a chiller
below ambient temperatures. Conversely, a high-performance heat sink mounted
on the chip will eliminate multiple thermal resistances and need for power-
hungry chillers.

To realize such systems, there is an urgent need for development of robust
high performance heat sinks. Thus far, single phase heat sinks have advanced
electronic cooling limits in comparison to air cooling; however, the rapid
increase in power density and miniaturization of electronics demand more
efficient cooling. Utilizing phase change heat sinks is suggested to decrease
DCs total cost of ownership (TCO) through reduction in operational expenditure
(OpEx) [9, 10]. Phase change heat sinks have demonstrated higher heat transfer
coefficients (HTC) as a result of the phase change process and remove higher
heat per working fluid mass flow rate relative to single phase cooling [11,
12, 13]. Furthermore, two-phase heat sinks can enhance temperature uniformity
across the chip [14, 15]. Nonetheless, most studies in literature on two phase
heat sinks use water as the working liquid at atmospheric conditions where the
saturation temperature of water is 100 ∘C. These operating conditions are not
representative of the conditions in a data center wherein the silicon junction
temperature must be kept below $\sim$80 ℃ [16]. Two phase heat sinks utilizing
water must operate at saturation temperatures below the junction temperature.
Operation at reduced saturation temperature results in decrease in vapor
density and a drastic reduction in boiling performance [Van1975, 17, 18],
negating advantages of conventional two-phase over single-phase heat sinks
[19]. To replace single phase heat sinks with better alternatives in
applications requiring removal of high heat fluxes, the key question to be
answered is – Can two phase heat sinks achieve better performance at lower
pressures compared to single phase heat sinks? A major limitation of phase
change cooling is the occurrence of the boiling crisis at high heat fluxes due
to surface dryout and inadequate rewetting. The maximum heat flux that can be
removed from a surface prior to dryout is known as the critical heat flux
(CHF). Following the seminal study by Nukiyama [20], on identifying CHF, many
efforts have been directed towards understanding the limiting factors of CHF
and increasing its value. Following an understanding that the CHF limit can be
increased through efficient liquid delivery to the heater surface [21, 22, 23,
24, 25, 26, 27, 28, 29], efforts have focused on improving surface wettability
[27, 30] and wickability (using micro/nanostructures) [29, 31, 32, 33].
Separation of liquid-vapor pathways through surface modifications have also
resulted in enhancement of the CHF limit [34].

In recent inventions [35, 36], we have demonstrated that liquid and vapor
pathways can be quite effectively separated through direct extraction of
bubbles from above the boiling surface through a selectively permeable
membrane. The membrane must be hydrophobic to hold liquid water adjacent to
the boiling surface. We have coined the term Membrane assisted phase-change
Heat Sinks (MHS) for this technology. Earlier demonstration of the device
performance has shown unprecedented heat flux dissipations of 1-2 kW/cm2,
depending on MHS design and operating conditions, with water at atmospheric
pressure [37, 38], offering a promising alternative to conventional heat sinks
at conditions relevant to DCs. In this study, we evaluate boiling performance
of MHS at a sub-ambient pressure of 16 kPa. In the following sections, first,
the operating principle of the MHS and the experimental setup are discussed.
Next, results pertaining to CHF, HTC, surface temperature stability, and
pressure drop are discussed and conclusions are drawn. Finally, the MHS
performance is compared with other technologies and its thermal, device, and
system level benefits are discussed.

##  2 MHS operating principle

The schematic in fig. 2 (a) shows a cross-sectional view of the membrane-
assisted heat sink discussed in this study. Unlike conventional heat sinks
which have a liquid inlet and a two-phase flow outlet, a MHS contains only a
single liquid inlet through which the working liquid is supplied to the heater
surface at a pressure $P_{pool}$. A hydrophobic vapor permeable membrane
placed $\sim$1 mm above the heater surface allows vapor exit from the liquid
pool. This unique design confines the boiling liquid to the heater surface and
induces an omnidirectional pressure on bubbles. With sufficient growth of a
bubble, a vapor bridge is established between the heater surface and the
membrane, leading to the liquid contact line on the membrane to recede (due to
the membrane hydrophobicity) pulling and expelling the bubble from the heater
surface.

Figure 2: (a) Schematic of cross-section of a membrane-assisted heat sink (not
to scale) shows the vapor expulsion mechanism through an omnidirectional
pressure potential and vapor permeable membrane. (b) Visualization of a vapor
bubble extraction process from a pool of water constrained by a hydrophobic
membrane in an adiabatic test.

Figure 2(b) illustrates this phenomenon using an adiabatic test which
consisted of injecting air into a pressurized pool of liquid at a constant
flow rate of 100 ml/hr to replicate bubble growth. As the bubble departs, the
surrounding liquid is delivered to the dry patch on the heater surface. This
two-phase flow arrangement overcomes a key shortcoming of the pool boiling
process – the evaporation/recoil pressure at the heater surface pushing the
liquid away from the bubble nucleation site. This method of manipulating vapor
discharge is shown to enhance multiple performance characteristics during
boiling. For example, in addition to dissipating heat fluxes greater than one
order of magnitude [37, 38] above the Kutateladze [39] and Zuber [25] limit
(119 W/cm2 for a copper surface), rapid expulsion of vapor from the liquid
pool greatly lowers two-phase pressure drop relative to conventional heat
sinks [40].

##  3 Experimental studies

###  3.1 Heat sink test apparatus

The heat sink device consists of a 7$\times$7 mm2 heater area with a liquid
inlet channel of 1$\times$1 mm2 cross sectional area, fabricated from
superconductive copper 101 alloy (see fig. 3).

Figure 3: (a) Cross sectional view of the test device consisting of a furnace,
bridge section insulated by PEEK, and a membrane-assisted heat sink (MHS). (b)
cross sectional view of the MHS showing copper surface with micropillars,
silicone spacer, hydrophobic membrane, and perforated metal support sheet. (c)
surface micropillars machined with width w, spacing s, and height h (out of
plane, extruding out of paper).

To ensure that boiling occurs only on the test surface, the side walls of the
liquid delivery channel were covered with a 200-$\mu$m-thick layer of non-
conductive epoxy by first machining a trench of area 1.2$\times$1.2 mm2,
filling the trench with non-conductive epoxy and re-machining the channel to a
cross sectional area of 1$\times$1 mm2 (see fig. 3(b)). The surface of the
heater comprises of an array of micropillars machined on a micro-CNC as shown
in fig. 3(c). Micropillars increase the total heater area in contact with the
liquid, and the enhanced area ratio ($A_{r}$) is given by
$A_{r}=1+4wh\/(s+w)^{2}$ where w is the width of the pillars, h is the height
of the pillars, and s is the spacing between the pillars. By altering the
width, height, and spacing between the pillars, the total heat transfer area
and wickability of the surface can be enhanced by various degrees. Surface
wickability, the ability of a structured surface to transport liquid through
capillarity is known to enhance CHF [31]. Fazeli & Moghaddam [37] compared
different methods of calculating surface wickability and found that in most
cases, ad hoc parameters are required to determine wickability. To avoid
empirical assumptions, they defined wickability as the product of surface
permeability ($\kappa_{wick}$) and capillarity ($P_{c}$) which we utilize in
the current study. Micropillar dimensions, surface wickability, and
corresponding area ratios are provided in table 1.

Table 1: Geometry, wickability, and enhanced area ratio $A_{r}$ of micropillars  Device | s | w | h | $\kappa_{wick}P_{c}\times 10^{6}$ | $A_{r}$
---|---|---|---|---|---
| ($\mu$m) | ($\mu$m) | ($\mu$m) | (Pa/m2) |
1 | N/A | N/A | N/A | N/A | 1
2 | 200 | 100 | 150 | 0.478 | 1.67
3 | 300 | 350 | 350 | 0.754 | 2.16
4 | 200 | 150 | 500 | 0.757 | 3.45

An 800 nm-thick oxide layer was thermally grown on the heater surface using a
process used by Zhou and Yang [41] to ensure a consistent contact angle of
$\sim 5^{\circ}$ in all experiments. The copper heat sink was brazed to a
copper bridge section welded to a heating block using a high-temperature SnPb
solder with a thermal conductivity of 57 W/m-K (see fig. 3(a)). The bridge
section was insulated with Polyether Ether Ketone (PEEK) to minimize thermal
losses. A 500-$\mu$m-thick rubber gasket was placed between the membrane and
heat sink and fastened with the support of a perforated metal sheet. Three
T-type thermocouples were installed equidistantly at 4 mm spacing within the
copper bridge to determine the heat flux using a three-point backward
difference Taylor’s approximation as given in eq. 2.

$q^{\prime\prime}=k\times\dfrac{3T_{3}-4T_{2}+T_{1}}{2\Delta x}$ (2)

A fourth thermocouple was placed below the surface to record the surface
temperature.

Figure 4: (a) Photograph of the experimental setup showing components of the
experimental setup including (i) pressure transducer, (ii) DC power supplies,
(iii) vacuum pump, (iv) chiller, (v) vacuum chamber, (vi) membrane assisted
heat sink (MHS), (vii) peltier cooler, and (viii) data acquisition system
(DAQ). (b) Schematic of the test loop.

###  3.2 Experimental setup and test section

A photograph and schematic of the experimental setup is illustrated in fig. 4.
The heat sink described in section 3.1 is installed in a chamber made from a
6$\times$6$\times$6 in3 (152.4$\times$152.4$\times$152.4 mm3) stainless steel
cube whose internal walls are coated with polytetrafluoroethylene (PTFE).
Glass viewports are installed on two opposite flanges to allow for
visualization of the apparatus while an electrical feedthrough on the top
flange enables power delivery and sensor measurements whilst maintaining
saturation conditions inside the chamber (16 kPa for the present experiments).
Deionized (DI) water is used as the working liquid and is delivered to the
heat sink by a piezoelectric micropump (Model MP6, manufactured by Bartels
Mikrotechnik GmbH). Two pressure transducers are utilized to monitor the test
chamber (Setra 730) and heat sink (Omega PX26) pressures. A thermoelectric
cooler (TEC) installed on the chamber sidewall is used to condense vapor
exiting the heat sink and a data acquisition system (DAQ) (Agilent
Technologies 34970A) is used to record temperature and pressure data. During
an experiment, the pressure inside the chamber ($P_{vapor}$) is reduced to 16
kPa using a vacuum pump. Next, heat is supplied to the test surface through
the cartridge heaters and the working liquid inside the MHS is maintained at a
constant absolute pressure $P_{pool}$. The induced device pressure in the MHS
relative to the chamber is thus $\Delta{P}=P_{pool}-P_{vapor}$. The applied
heat flux is increased incrementally in steps of 10 W/cm2 until a sudden jump
in the temperature is observed. The heat flux at this point is recorded to be
the CHF at the specific device pressure P.

###  3.3 Uncertainty analysis

To determine the uncertainty in heat flux and heat transfer coefficient, the
error and uncertainty associated with the thermocouples is considered. The
uncertainty in determining the heat flux is caused by uncertainty in
temperature readings, thermal conductivity of copper, and spacing between the
thermocouples. Equation 3 was used to calculate the uncertainty in heat flux

$\dfrac{\delta q^{\prime\prime}}{q^{\prime\prime}}=\sqrt{\left(\dfrac{\delta
k}{k}\right)^{2}+\left(\dfrac{\delta\Delta T}{\Delta
T}\right)^{2}+\left(\dfrac{\delta\Delta x}{\Delta x}\right)^{2}}$ (3)

where $\delta$k, $\delta\Delta$T, $\delta$x are the uncertainties in thermal
conductivity, temperature gradient, and distance between thermocouples,
respectively. Since $\Delta{T}=3T_{3}-4T_{2}+T_{1}$, $\delta\Delta$T can be
calculated using eq. 4

$\delta\Delta T=\sqrt{\left[(3\delta T)^{2}+(4\delta T)^{2}+(\delta
T)^{2}\right]}\sim 5.09\delta T$ (4)

The uncertainty associated with different experimental variables are tabulated
in table 2. The uncertainty in heat flux measurement is found to be $\pm$11.2%
at a lower value of 70 W/cm2 and $\pm$7.1% at the highest value of 700 W/cm2.
The uncertainty associated with calculating the heat transfer coefficient (HTC
= $q/(A\times{T}_{sup})$), where q, $T_{sup}$, and A are the heat rate,
surface superheat, and heater surface area, respectively, is estimated using
eq. 5

$\dfrac{\delta HTC}{HTC}=\sqrt{\left(\dfrac{\delta
q}{q}\right)^{2}+\left(\dfrac{\delta
T_{sup}}{T_{sup}}\right)^{2}+\left(\dfrac{\delta A}{A}\right)^{2}}$ (5)

where $\delta{q}$, $\delta{T}_{sup}$, and $\delta{A}$ are the errors in
measuring the heat rate, surface superheat, and heater area, respectively. The
uncertainty in HTC is determined to be $\pm$6.9% at the lowest value of 310
kW/m2K and $\pm$33.5% at the highest value of 890 kW/m2K.

Table 2: Uncertainties in measured experimental parameters  Variable | Uncertainty
---|---
$\delta{T}/T$ |  $\pm$0.65 K
$\delta{k}/k$ |  $\pm$2%
$\delta\Delta{x}/\Delta{x}$ |  $\pm$0.3%
$\delta{A}/A$ |  $\pm$0.2%
$\delta\Delta{P}/\Delta{P}$ |  $\pm$0.25%

##  4 Results and Discussion

###  4.1 Critical heat flux in membrane based heat sinks

The MHS performance was analyzed through a set of boiling tests conducted on
all four surfaces listed in table 1, at device pressures
($\Delta{P}=P_{pool}-P_{vapor}$, see fig. 2) ranging from 2-10 kPa. To ensure
repeatability, each test was repeated 3 times and the CHF reported in fig. 5
is an average of the three tests. As described in section 2, an increase in
device pressure $\Delta{P}$ reduces bubble residence time and vapor contact
area on the heater surface, leading to enhanced liquid replenishment to the
surface. Hence, we expect to see an increase in CHF with an increase in
$\Delta{P}$. Further, an increase in $A_{r}$ is known to increase CHF [37,
38]. As evidenced in fig. 5, a marked increase in CHF is observed with an
increase in surface area as well as device pressure, consistent with our prior
studies [38]. The yellow band in fig. 5 denotes the maximum heat flux limit
for a given device pressure based on membrane permeability. Consistent with
results obtained at atmospheric pressure [37, 38, 40], above a certain
pressure ($\sim$2 kPa), CHF is not limited by the membrane permeability, but
by surface properties. It can also be inferred from fig. 5 that the rate of
CHF enhancement with increase in $\Delta{P}$ declines at higher pressures.

Figure 5: Critical heat flux (CHF) obtained on test surfaces with different
$A_{r}$ as a function of device pressure $\Delta{P}=P_{pool}-P_{vapor}$. The
dotted line represents the theoretical model described by Fazeli & Moghaddam
[37] and fits the experimental data well. The yellow band represents the
maximum heat flux based on the membrane permeability limit. The red and blue
bands represent the contribution of membrane ($P_{m}$) and two-phase pressure
drop ($P_{tp}$) to total device pressure drop ($\Delta{P}$), respectively.

The dashed lines in Fig. 5 represents a semi-empirical correlation developed
by Fazeli & Moghaddam [37]. The model accounts for effect of wickability
($\mathfrak{W}$), effective heat transfer area ($A_{r,\epsilon}$), and liquid
pressure on CHF. Test results at atmospheric pressure [37] and here suggest
that on structures with similar wickability, increasing surface area almost
linearly enhances the CHF limit; hence, it is expected that $q"_{CHF}\propto
A_{r}$. It has also been demonstrated that structures with higher wickability
can facilitate higher CHF values at low $\Delta{P}$, and that the impact of
wickability and $A_{r}$ is directly dependent on $\Delta{P}$. Accordingly, eq.
6 represents the additive and multiplicative effect of wickability and heat
transfer area, respectively, on CHF:

$q^{\prime\prime}_{CHF}(A_{r,\epsilon},\Delta{P},\mathfrak{W})=\left[q^{\prime\prime}_{nw}(A_{r,\epsilon}=1,\Delta{P}\sim
0,\mathfrak{W}\sim 0)\right.\\\
\left.+q^{\prime\prime}_{w}(A_{r,\epsilon}=1,\Delta{P},\mathfrak{W})\right]f\left(A_{r,\epsilon},\Delta{P}\right)$
(6)

where $A_{r,\epsilon}$ denotes effective heat transfer area which is
determined by considering the thermal effectiveness of surface structures
(viz., $A_{r}$, with its thermal efficiency accounted for), and $\mathfrak{W}$
denotes surface wickability. Here, $q"_{nw}$ represents CHF on a plain surface
(i.e. $A_{r,\epsilon}=1,\mathfrak{W}\sim 0$) at $\Delta{P}\sim 0$. Therefore,
its value is independent of the surface wickability and heat transfer area and
can only be changed by altering the liquid contact angle. $q"_{w}$, on the
other hand, represents heat flux associated with the wicking process and
changes with $\mathfrak{W}$ and $\Delta{P}$. Finally, f denotes the effect of
enhanced heat transfer area as well as liquid pressure on surface structure
effectiveness. Figure 5 shows a close agreement of the experimental data with
the model, suggesting that when CHF is not limited by membrane permeability,
effective heat transfer area and wickability contribute additively and
multiplicatively as described by Fazeli & Moghaddam [37] even at lower
pressures. It is important to note that since the model only factors in the
effect of surface structures and fluid properties, it is solely valid below
the membrane transport limit.

###  4.2 Heat transfer coefficient (HTC)

As discussed in section 1, cooling in DCs demand efficient heat transfer as it
is directly tied to their cost of operation. We thus evaluate the heat
transfer coefficient HTC = $q\/(A\times\Delta{T})$ of MHS, where q is the heat
rate, A is the heat transfer area, and $\Delta{T}$ (= $T_{sur}–T_{sat}$) is
the surface superheat. Figure 6 plots HTC as a function of $\Delta{T}$ for
tests conducted at $\Delta{P}$ = 8 kPa on surfaces with different $A_{r}$. For
a given surface, HTC is found to decrease with an increase in $\Delta{T}$,
eventually reaching a near-constant value beyond a superheat of 10∘C. This
suggests that an initial increase in heat flux occurs at the expense of heat
transfer efficiency; however, at later stages, no significant detriment in HTC
is observed. Furthermore, a trend of increase in HTC with increase in $A_{r}$
is observed for a given $\Delta{T}$, corroborating previous reports that
surface structures enable higher heat transfer coefficients through increased
heat transfer area [37].

Figure 6: Heat transfer coefficient (HTC) as a function of surface superheat
for surfaces with different enhanced area ratios ($A_{r}$ = 1, 2.16, 3.45)
operated at a pressure potential of 8 kPa.

Next, to investigate the effect of device pressure on HTC, we consider a
surface with $A_{r}$ = 3.45. HTC is plotted as a function of $\Delta{T}$ in
fig. 7 and it is observed that as $\Delta{P}$ increases, HTC increases for a
given $\Delta{T}$. This is consistent with the MHS operating principle, since
an increase in device pressure improves surface rewetting leading to maximal
heat transfer through phase change. Surface structures and induced pressure
thus increase HTC as envisaged, and a maximum heat transfer coefficient of 890
kW/m2K is obtained on a surface with $A_{r}$ = 3.45 at a $\Delta{P}$ of 8 kPa.

Figure 7: Heat transfer coefficient (HTC) as a function of surface superheat
for various device pressures $\Delta{P}=P_{pool}–P{vapor}$ on a surface with
$A_{r}$ = 3.45.

Although an increase in heat flux reduces HTC at higher superheats, an
efficient vapor generation and discharge process facilitated by the membrane
allows even high heat fluxes of 580.4 W/cm2 to be dissipated at an HTC of
502.6 kW/m2K.

The maximum HTC obtained using MHS is compared with existing two-phase cooling
technologies operated using water at comparable system pressures and plotted
in fig. 8 [42, 43, 44]. The pressure reported in fig. 8 is the liquid
saturation pressure where the HTC is reported while the size of the bubbles
represents the heat flux (W/cm2) at which the HTC is obtained. We find that
reports of phase-change heat sinks operated using water at sub-ambient
pressures is relatively sparse. Han et al. [43], who utilized pin-fin
structures and reported a maximum HTC of 85 kW/m2K at a liquid saturation
pressure of 28 kPa, while Diglio et al. [44] recently demonstrated that HTCs
of 131 kW/m2K can be dissipated through direct device impingement (DDI). Kosar
et al. [42] studied boiling in a microchannel with reentrant cavities and
reported a maximum HTC of 71 kW/m2K. In comparison, MHS achieves a maximum HTC
of 890 kW/m2K (at a heat flux of 324 W/cm2), roughly an order of magnitude
higher than other two-phase heat sinks studied at comparable pressures with
water as the working fluid. We also note that the performance of MHS
drastically decreases when operated at sub-ambient system pressures (cf. Refs.
[37, 38]).

Figure 8: Comparison of heat transfer coefficient (HTC) obtained by MHS with
other heat sinks operated using water at lower pressures [42, 43, 44]. The
pressure indicated here is the liquid saturation pressure. The size of the
bubbles represents the heat flux at which the heat transfer coefficient is
obtained.

###  4.3 Surface temperature

Due to constantly varying heat loads in a DC, it is desirable for a heat sink
to dissipate a range of fluxes without significant temperature variations
i.e., maintaining stable surface temperatures below silicon junction
temperature is of paramount importance to ensure safe and reliable operation
of electronics. The experimental data points in fig. 9 correspond to the
distinct test cases presented in fig. 5 for all test surfaces and device
pressures. The saturation temperature of water for the corresponding
$P_{pool}$ is also plotted for comparison. In conventional heat sinks,
increasing the heat flux often results in a higher pressure drop and change in
the saturation temperature of the fluid, and consequently the heater surface
temperature. In contrast, membrane assisted vapor removal augmented by induced
liquid pressure transpires as a decrease in surface superheat with an increase
in device pressure.

Figure 9: Surface temperatures of test surfaces with different Ar as a
function of liquid pressure ($P_{pool}$), plotted alongside saturation
temperature of water (dashed line). Surface temperatures do not vary
appreciably with varying device pressure which results in reduced superheat at
higher pressures.

###  4.4 Analysis of pressure distribution within the heat sink

Pressure drop is an important performance characteristic of MHS that has not
been analyzed in our prior publications. To understand the underlying physics
of pressure drop, we have considered various factors contributing to the
pressure drop when CHF is not limited by the membrane permeability. Pressure
drop in MHS is caused by 3 factors - (i) liquid pressure drop at the inlet
channel and partly over the heater surface, (ii) pressure drop due to phase
change ($\Delta{P}_{tp}$), and (iii) vapor pressure drop through the membrane
($\Delta{P}_{m}$). Liquid enters the heat sink through a channel of cross
section 1$\times$1 mm2 and expands into an enclosure with lateral cross-
sectional area of 1$\times$7 mm2 (see fig. 3(b)). This pressure drop in the
channel, estimated using the Darcy-Weisbach equation, is negligible ($\sim$100
Pa) [45]. Therefore, the major contributors towards pressure drop are
$\Delta{P}_{tp}$ and $\Delta{P}_{m}$. The individual contribution of these
factors can be inferred from fig. 5. For example, considering the test on a
surface with $A_{r}$ = 2.16 at a $\Delta{P}$ of 10 kPa, $\Delta{P}_{m}$ is
represented by the red band while $\Delta{P}_{tp}$ is represented by the blue
band. We suppose that $\Delta{P}_{tp}$ is due to the effect of growing vapor
bubbles during boiling that is commonly known to push against the incoming
fluid to the heat sink [46]. Hence, an increase in two-phase pressure drop is
expected with increasing nucleation. This is evident when considering the
pressure drop on the plain surface ($A_{r}$ = 1) – the contribution of two-
phase pressure drop increases with an increase in heat flux. Evidently,
$\Delta{P}_{tp}$ is the highest on this surface even though its CHF is much
less than those of the structured surfaces. We believe that increase in
frequency and density of stable vapor columns on structured surfaces is
responsible for this unique pressure drop characteristic of the MHS. Surface
structures greatly enhance direct evaporation of liquid films, feeding into
vapor columns. In comparison with nucleation, the pressure drop across these
stable vapor columns is significantly lower since these columns do not rapidly
expand. However, an increase in heat flux through direct evaporation (i.e.,
thin film and contact line evaporation) leads to a higher vapor generation
rate resulting in a higher pressure drop through the membrane. These trends
are all evident in fig. 5; as the surface structures area is increased, the
contribution of two-phase pressure drop ($\Delta{P}_{tp}$) decreases while the
contribution of membrane pressure drop ($\Delta{P}_{m}$) increases.

##  5 Implications for future data centers

###  5.1 Replacing existing technologies

Figure 10 shows the state-of-the-art performance of various passive and active
technologies including thermosiphons, cold plates, jet impingement, etc. [47,
48, 49, 50, 51, 52, 53, 54] in comparison with MHS, in the form of the HTC
plotted against surface superheat, with the size of the bubbles representing
the heat flux at which the HTC is obtained.

Figure 10: Comparison of different cooling strategies for electronics. Cold
plates [50, 53], thermosiphons [48, 49, 52], jet impingement strategies [47,
51], and air cooled heat sinks with 2-phase heat spreaders (vapor chambers)
[54] are compared with membrane assisted heat sinks (MHS). The heat transfer
coefficient (HTC) is plotted as a function of the surface superheat
($\Delta$T) while the size of the bubbles represents the heat flux at which
the HTC is obtained. Membrane assisted heat sinks (MHS) exhibit an HTC at
least an order of magnitude higher than air cooled heat sinks [47, 48, 49, 50,
51, 52, 53, 54].

It is important to note that comparing these vastly different technologies
using a common benchmark is complex and does not convey a holistic picture
about the technologies since they are constructed for different application
needs. Some applications demand removal of high heat fluxes while others
necessitate low surface temperatures, and some others require a low operating
power. However, the HTC (accounting for $\Delta{T}$) is a crucial metric to DC
cooling due to its direct impact on DC operating expenditure (OpEx) and can be
evaluated to determine favorable technologies to be employed. We choose
technologies that are closest in their working conditions to DC environment
and exclude system level parameters such as pumping power, pressure drop, etc.
in our analysis. It is clear that MHS outperforms other technologies by
exhibiting a HTC of 500 kW/m2K at a heat flux of 580 W/cm2. Although current
power densities do not largely exceed this level [55], MHS promises a future-
readiness without the need for frequent capital expenditure (CapEx) in the
form of constant replacement of cooling systems at the rack level.

###  5.2 System level integration benefits

Figure 11: A schematic showing the benefits of system level integration of
MHS. (a) Any hotspots in the heat sinks will be quenched as an imposed
pressure promotes liquid supply to the hotspots. (b) Prospect of multiple heat
sinks at different heat loads being connected on a common liquid supply and
vapor exit line.

Further, from the analysis presented in section 4, the system level benefits
of incorporating MHS into a DC become apparent. Figure 11 shows a schematic
representation of the system level benefits associated with MHS. Due to the
architecture of MHS which imposes a positive omnidirectional pressure on the
liquid (see fig. 2(b)), any hotspots generated on the chip surface is quickly
mitigated through the rushing of the liquid to the hotspots (see fig. 11(a))
as opposed to the common problem of vapor backflow suffered by conventional
microchannel heat sinks [56]. Secondly, MHSs exhibit a self-regulating
pressure control due to the presence of the membrane, which can be leveraged
to connect multiple heat sinks through a common liquid and vapor loop (see
fig. 11(b)). Consider three heat sinks under different heat loads connected
through a common liquid and vapor line as shown in fig. 11(b).

Liquid will automatically be diverted to the heat sink with the most heat load
without the need for mass controllers whilst maintaining a 100% vapor quality.
Heat sinks at lower heat loads would also be maintained at 100% vapor quality
due to the constant liquid pressure in the liquid line and the membrane,
enabling a self-regulating mechanism. The vapor line can be used to collect
and condense vapor from all heat sinks to be directed back to the heat sinks.

##  6 Conclusions

This work provides a comprehensive analysis of the membrane assisted heat sink
performance characteristics at operating conditions pertinent to DCs. The
results show a substantial decline in CHF at low operating pressures relative
to operation at the atmospheric pressure. Our experiments reveal that CHF and
HTC increase with an increase in device pressure (Ppool) and enhanced area
ratio ($A_{r}$), and we report a maximum CHF and HTC of 670 W/cm2 and close to
$\sim$ 1 MW/m2K, respectively. We predicted CHF using the model proposed by
Fazeli and Moghaddam, considering the effect of wickability, effective heat
transfer area, and liquid pressure. MHS exhibits great surface temperature
controllability over a wide range of operating conditions and unique pressure
drop characteristics. Results presented here not only imply an exceptional
proposition for the use of MHS in high performance DCs, but also raise
performance benchmarks for phase change heat sinks. Lastly, we expound system
level benefits of integrating MHS in DCs such as hotspot mitigation and self-
regulating loop control.

##  7 Acknowledgements

This work was supported by the National Science Foundation grant number CBET -
1934354 with Dr. Ying Sun as program manager. The authors thank Dr. Morteza
Alipanah and Mr. Sourabh Kakade for assistance with experiments.

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