Latent Heat Cooling Pays Off Until Vapor Quality Nears 0.7

The part that sets the limit in a two phase cold plate is the heated wall inside a channel, where liquid has to arrive as fast as it turns to vapor. Accelsius tested that wall with R-1233zd(E) on a copper block with a 26 × 35 mm² heated area. Thermal resistance had already turned upward by the time vapor quality passed 0.7 at 1,500 W. Latent heat cooling moves more heat per kilogram than warming a liquid does, and each cost it carries is arranged around that quality number.

The same kilogram carries 8 to 54 times more heat as it boils than as it warms by 10 K

Sensible transport follows Q = ṁ × cp × ΔT, where ṁ is mass flow in kg/s, cp is liquid specific heat in kJ/(kg·K) and ΔT is the coolant temperature rise in K. Phase change cooling follows Q = ṁ × x × hfg, where x is the vapor quality at the outlet (the mass fraction leaving as vapor) and hfg is the latent heat of vaporization in kJ/kg. Dividing hfg by cp × 10 K counts how many 10 K temperature rises one kilogram of boiling is worth.

Table 1 sets three fluids side by side. Water comes out at 53.5, R-1233zd(E) at 15.6 and Novec 649 at 8.0. The inputs are manufacturer sheets and NIST saturation data, and the ratio is computed from them.

Table 1. Latent heat against a 10 K sensible rise, three fluids (kJ/kg unless noted)

* Liquid specific heat taken at 100 °C for water (4.2157 kJ/(kg·K)), at 86 °F for R-1233zd(E) (0.298 Btu/lb, converted to 1.248 kJ/(kg·K)), and with no temperature stated for Novec 649 (1,103 J/(kg·K)). Ratio computed here. R-1233zd(E) boiling point is listed as 65 °F.

Source: NIST Chemistry WebBook, saturation properties for water (SRD 69); Honeywell, “R-1233zd Refrigerant (Solstice zd)” product page (undated); 3M, “Novec 649 Engineered Fluid” product information (undated)

Source: Honeywell, “R-1233zd Refrigerant (Solstice zd)” product page; 3M, “Novec 649 Engineered Fluid” product information; NIST Chemistry WebBook saturation properties for water.

The 10 K basis is a choice, and a larger rise would shrink every ratio in proportion. What the table shows at any basis is that boiling replaces a temperature rise with an energy exchange between 8 and 54 times larger per kilogram. That is the whole transport advantage, and the rest of this piece is about what it requires.

Why does the fluid with 11.6 times less latent heat get the job?

Water holds the larger number. From the NIST saturated vapor and liquid enthalpies at 100 °C:

hfg = 2,675.6 − 419.17 = 2,256.4 kJ/kg

R-1233zd(E) absorbs 195 kJ/kg at its boiling point, so water is the better phase change fluid per kilogram by a factor of 11.6. The cold plate work described here still uses a refrigerant, and the vapor volume and pressure figures below show one reason.

NIST gives water at 60 °C a saturation pressure of 0.019946 MPa.

The vapor specific volume there is 7.6672 m³/kg and the liquid specific volume 0.0010171 m³/kg, so the vapor occupies 7,538 times the volume of the liquid it came from, at about one fifth of the pressure at 100 °C. For 1 kW of heat removed by evaporation, with hfg = 2,608.8 − 251.18 = 2,357.6 kJ/kg at 60 °C:

vapor flow = 1 kW ÷ 2,357.6 kJ/kg × 7.6672 m³/kg = 3.25 L/s

That vapor has to travel through sub-atmospheric piping. The 60 °C case is a round number chosen for the arithmetic, not a value taken from a source.

R-1233zd(E) boils at 65 °F (18.3 °C) at 1 atm, so any saturation temperature above that puts it above atmospheric pressure. Its liquid-to-vapor density ratio at the boiling point is:

1,279 kg/m³ ÷ 5.7 kg/m³ = 224

Water gives 1,602 at 100 °C and 7,538 at 60 °C.

Source: Honeywell, “R-1233zd Refrigerant (Solstice zd)” product page, heat of vaporization, liquid density and vapor density, each stated at the boiling point; NIST Chemistry WebBook.

The Accelsius authors give a different reason. They describe a dielectric refrigerant as one that does not cause disastrous damage to IT equipment if it leaks, and their orientation paper notes that AI hardware keeps rising in cost, and with it the cost of a water leak.

A 2 kW chip needs 0.69 L/min of refrigerant where water needs 2.92 L/min

The processor in the Accelsius pressure-drop model draws 2,000 W, and the authors set its flow by prescribing a nominal exit vapor quality of 0.7.

For the comparison, R-1233zd(E) takes hfg = 195 kJ/kg and a liquid density of 1,279 kg/m³, both Honeywell boiling-point values. Water takes cp = 4.1851 kJ/(kg·K) and 983.16 kg/m³ at 60 °C from NIST, with a 10 K rise.

Refrigerant: ṁ = 2.000 kW ÷ (0.7 × 195 kJ/kg) = 0.01465 kg/s = 11.46 mL/s = 0.687 L/min

Water: ṁ = 2.000 kW ÷ (4.1851 kJ/(kg·K) × 10 K) = 0.04779 kg/s = 2.916 L/min

The mass flow ratio is 3.3 and the volume flow ratio is 4.2. This is a design-point estimate, and it moves with its inputs. Letting the water rise 20 K halves its flow to 1.46 L/min and brings the volume ratio down to 2.1.

The refrigerant side uses boiling-point properties, while the Accelsius model evaluates properties at a 45 °C outlet, so latent heat and densities there differ from the values used here. A claim that two phase heat transfer needs a tenth of the flow should state its water temperature rise and exit quality before it can be set beside these numbers.

The liquid side is the quiet side. At quality 0.7 the same chip sends out vapor at:

0.7 × 14.65 g/s = 10.26 g/s ÷ 5.7 kg/m³ = 1.80 L/s

That is 157 times the 11.46 mL/s of liquid that went in.

A rack of such chips totaling 100 kW produces about 90 L/s on the same basis. Vapor density rises with saturation pressure, so this is a ceiling for the volume, and no density at the 45 °C operating point came from a document opened for this piece. The vapor line and the condenser take that volume, not the cold plate. The Accelsius loop description includes a refrigerant reservoir for the same reason, to absorb volume changes when the heat load varies.

Pool boiling reaches its critical heat flux before a 220 W/cm² chip does

Flow rate is the lever in a pumped cold plate. In a pool nothing sweeps the vapor away, and the limit arrives earlier. For saturated pool boiling on a flat surface, the Kutateladze-Zuber relation gives the critical heat flux (CHF):

qCHF = K × ρv^0.5 × hfg × (σ × g × (ρl − ρv))^0.25, with K = 0.131

Liang and Mudawar, reviewing the model, report that its derivation gives a value between 0.119 and 0.157 and that Zuber recommended 0.131.

For water at 1 atm, with NIST values hfg = 2,256.4 kJ/kg, ρv = 0.59817 kg/m³, ρl = 958.35 kg/m³ and σ = 0.058912 N/m:

qCHF = 0.131 × 0.59817^0.5 × 2.2564 × 10⁶ J/kg × (0.058912 × 9.80665 × (958.35 − 0.59817))^0.25 = 1.11 MW/m² = 111 W/cm²

This is a prediction for an infinite flat surface. Liang and Mudawar assessed the model against a consolidated database of 800 data points and, for horizontal upward-facing surfaces at pressures below critical, found a mean absolute error of 22.8%.

Source: Liang and Mudawar, “Pool boiling critical heat flux (CHF) – Part 1” and “Part 2”, International Journal of Heat and Mass Transfer 117 (2018).

The Accelsius test chip dissipated up to 2,000 W through its heated area:

2,000 W ÷ (2.6 cm × 3.5 cm) = 2,000 W ÷ 9.1 cm² = 220 W/cm²

The paper itself gives heat fluxes above 200 W/cm². Water’s pool-boiling limit under the correlation is about half of that flux, and the one dielectric fluid with a measurement here sits lower.

MIT researchers measured an average CHF of 200 kW/m² for Novec 649 on a 0.01 in. nickel wire at its atmospheric saturation temperature of 49 °C, a little under their Zuber-based prediction for a small cylinder.

That is 20 W/cm², one eleventh of the chip’s flux. A wire is not a chip lid and neither number shares a geometry with a processor package, so the gap indicates an order of magnitude and does not set a design margin.

Source: Forrest, Hu, Buongiorno and McKrell, “Pool Boiling Performance of Novec 649 Engineered Fluid”, ECI International Conference on Boiling Heat Transfer (2009).

Tank-style designs sit on the pool side of this limit, and how single phase and two phase immersion differ in operation covers that arrangement. A bare, flat surface in a pool of dielectric fluid has far less heat-flux headroom than a flowing channel does.

The boundary is a vapor quality near 0.7, and pressure drop bills for approaching it

A pumped channel moves the CHF problem from the pool to the exit of the channel. In the Accelsius orientation test, about 500 mL/min of R-1233zd(E) entered a cold plate on the same heater while power was swept from 0 to 2,000 W. Thermal resistance first fell, then rose.

The minimum sat at vapor quality 0.2 to 0.6, where nucleate boiling is fully developed. By 1,500 W the quality exceeded 0.7, which the authors give as the cause of the rise: departure from nucleate boiling.

Raising the flow to about 750 mL/min kept resistance low up to 2,000 W, with quality held under 0.6.

Source: Wang and Bonner, “High-Performance Two-Phase Cooling under Different Cold Plate Orientations”, Accelsius.

The energy balance reproduces the pattern. At 500 mL/min and 1,279 kg/m³ the flow is 0.01066 kg/s, which absorbs 0.01066 × 195 = 2.08 kW if fully evaporated:

x = 1.5 kW ÷ 2.08 kW = 0.72 at 1,500 W

That matches the reported figure above 0.7.

At 750 mL/min and 2,000 W the same arithmetic gives 0.64 against the reported figure under 0.6. Inlet subcooling and denser cold liquid push the true quality down, and a lower latent heat at the operating temperature pushes it up, so the agreement is a consistency check and not a validation.

The companion Accelsius paper states that the designed vapor quality for a two phase cold plate is usually near 0.7, to avoid dry-out and flooding at once. A design value of 0.7 and a test that shows resistance rising above 0.7 leave almost no quality margin between the two. A plate sized for 2 kW at that quality has little room if the chip draws more or the pump delivers less. In a single phase loop the same shortfall raises the outlet temperature in proportion, while here it changes the heat transfer regime.

The second cost is pressure. The Accelsius model sets the inlet fluid subcooled at 35 °C and the outlet saturated at 45 °C.

Saturation temperature falls as pressure falls along the channel, so a pressure drop inside the plate means the fluid boils hotter at the heated wall than at the outlet. Taking a 3 °C penalty as significant, the authors find it corresponds to about 3 psi for R-1233zd(E) and about 9 psi for R515B, a medium-pressure refrigerant. For the low-pressure fluid, channel geometry and manifold design become thermal parameters.

Their model shows why this matters when comparing plates. Two geometries with the same flow, inlet and outlet conditions reached case temperatures of 84.1 and 82.4 °C, and the plate with the lower case-to-fluid resistance ran 1.7 K hotter. The authors propose a case-to-outlet resistance that includes the pressure-drop term. They state the model is not meant to predict performance accurately and leaves out flow instabilities and the outlet plenum, so the 1.7 K is better taken as a demonstration of a failure mode than as a size estimate. For the system-level comparison with a single phase loop, how single phase and two phase direct liquid cooling compare covers what latent heat buys.

The evidence has limits that reach every number above. Both Accelsius papers come from one company’s laboratory; the orientation test uses a copper heater block rather than a processor, and the pressure-drop paper is a simplified model by its authors’ own description. The Honeywell and 3M values are manufacturer figures at the boiling point on undated pages, and the 3M sheet states no temperature for its specific heat. The flow, vapor volume and quality estimates here use boiling-point properties because operating-point data were not in a document opened for this piece. The Zuber relation is a flat-plate correlation with the scatter noted above. None of this settles a cooling design, which needs qualified engineering review with the fluid supplier’s data at the actual operating pressure.

Before comparing a two phase cold plate claim with a single phase one, look for these in the test report:

• Exit vapor quality at the rated power, or the flow rate, fluid and latent heat needed to compute it
• Heated area, and whether the stated heat flux is per footprint or per wetted wall
• Saturation temperature at the heater, and the pressure drop between heater and outlet
• Vapor density at the operating pressure, which sets the size of the return line and condenser
• Cold plate orientation, since the Accelsius test ranked vertical and horizontal plates differently below about 800 W and above about 1,200 W

References

• R-1233zd Refrigerant (Solstice zd) / Honeywell / undated product page / https://www.solstice.com/us/en/products/air-conditioning-refrigeration-and-heating/solstice-hfos/solstice-zd-r-1233zd
• 3M Novec 649 Engineered Fluid, product information / 3M / undated / https://multimedia.3m.com/mws/media/569865O/3m-novec-engineered-fluid-649.pdf
• Saturation Properties for Water, NIST Chemistry WebBook, SRD 69 / National Institute of Standards and Technology / accessed 2026-10-09 / https://webbook.nist.gov/cgi/fluid.cgi?TLow=30&THigh=100&TInc=10&Digits=5&ID=C7732185&Action=Load&Type=SatP&TUnit=C&PUnit=MPa&DUnit=kg%2Fm3&HUnit=kJ%2Fkg&WUnit=m%2Fs&VisUnit=uPa%2As&STUnit=N%2Fm&RefState=DEF
• Pool Boiling Performance of Novec 649 Engineered Fluid / E. Forrest, L.-W. Hu, J. Buongiorno, T. McKrell, MIT / ECI International Conference on Boiling Heat Transfer, Florianopolis, 3-7 May 2009 / https://www.osti.gov/etdeweb/servlets/purl/21208451
• Pool boiling critical heat flux (CHF) – Part 1: Review of mechanisms, models, and correlations / G. Liang, I. Mudawar / International Journal of Heat and Mass Transfer 117 (2018) 1352-1367 / https://engineering.purdue.edu/mudawar/files/articles-all/2018/2018-01.pdf
• Pool boiling critical heat flux (CHF) – Part 2: Assessment of models and correlations / G. Liang, I. Mudawar / International Journal of Heat and Mass Transfer 117 (2018) 1368-1383 / https://engineering.purdue.edu/mudawar/files/articles-all/2018/2018-02.pdf
• High-Performance Two-Phase Cooling under Different Cold Plate Orientations / Q. Wang, R. Bonner, Accelsius, hosted by DatacenterDynamics / date not printed / https://media.datacenterdynamics.com/media/documents/High-Performance-Two-Phase-Cooling-under-Different-Cold-Plate-Orientations.pdf
• A Practical Metric for Cold Plate Thermal Performance in Two-Phase Direct-to-Chip Cooling / Q. Wang, S. Ozguc, R. Bonner, Accelsius / date not printed / https://accelsius.com/wp-content/uploads/A-Practical-Metric-for-Cold-Plate-Thermal-Performance-in-Two-Phase-Direct-to-Chip-Cooling.pdf