Flow Regime Transition in Inner Grooved Minichannel Cold 

Plates for Cooling Hybrid Electric Power Electronics

by Darin J. Sharar, Nicholas R. Jankowski, and Avram Bar-Cohen

ARL-TR-6170 January 2013

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ARL-TR-6170 January 2013

Flow Regime Transition in Inner Grooved Minichannel Cold 

Plates for Cooling Hybrid Electric Power Electronics

Darin J. Sharar, Nicholas R. Jankowski, and Avram Bar-Cohen

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Flow Regime Transition in Inner Grooved Minichannel Cold Plates for Cooling 

Hybrid Electric Power Electronics

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14. ABSTRACT

Forced flow of fluids undergoing phase change in traditional single-phase cold plates is an effective way to manage waste heat 

removal of vehicle power electronics. Such cold plates come in a variety of standard styles, ranging from circular-tubed cold 

plates and flat-tube cold plates, to more exotic designs such as louvered and offset fin cold plates. The mechanisms of heat 

transfer in a two-phase system are different than single-phase, and as such, improvement can be made by custom designing 

cold plates for two-phase operation. Past research has focused on surface modifications that enhance nucleate boiling, 

convective vaporization, or both during two-phase operation. The method that has gained the most attention is the use of 

inner grooved tubes for performance improvement in refrigeration applications. Despite the popularity of inner grooved 

tubes, the flow mechanisms that deliver performance enhancement are not fully understood. The absence of 

phenomenological insights and physical models makes it difficult to transition inner grooved tube technology from 

conventional refrigeration equipment to cold plates. Therefore, understanding the physical mechanisms underpinning twophase performance enhancement in inner grooved tubes is at the heart of this report. 

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iii

Contents

List of Figures iv

List of Tables iv

1. Background 1

1.1 Power Requirements and Power Conversion Electronics...............................................1

1.2 Power Electronic Thermal Management.........................................................................3

2. Two-Phase Flow Boiling 5

2.1 Two-phase Flow Regimes...............................................................................................5

2.2 Flow Regime Maps .........................................................................................................7

2.3 Studies of Flow Regimes and Flow Regime Maps .........................................................8

3. Two-phase Surface Enhancements 9

3.1 Convective Vaporization...............................................................................................10

3.1.1 Inner Grooved Tube ..........................................................................................10

3.1.2 Heat Transfer Mechanisms in Inner Grooved Tubes ........................................11

3.1.3 Flow Regime Transition and Delayed Dryout in Inner Grooved Tubes...........12

4. Conclusion 18

Bibliography 19

Distribution List 24
iv

List of Figures

Figure 1. Midsize hybrid electric power requirements (3). ............................................................2

Figure 2. Dissipated heat vs flowrate for water using latent heat and sensible heat (8).................4

Figure 3. Hydroblok pressure-fit 6-pass serpentine cold plate (9)..................................................5

Figure 4. Two-phase flow regimes and associated heat transfer coefficients (10).........................6

Figure 5. Taitel-Dukler flow regime maps for R113 flowing in a horizontal channel of 

various diameters (a) 100 mm, (b) 10 mm, (c) 1 mm, and (d) 0.1 mm (28).............................9

Figure 6. (a) Schematic of inner grooved tube and (b) Photograph of inner grooved tube 

(courtesy Wieland)...................................................................................................................10

Figure 7. Experimental flow regime maps for (a) smooth tube with 10.7 mm ID, (b) inner 

grooved tube with 11.1 mm ID, and (c) average heat transfer coefficient for the smooth 

and inner grooved tube.............................................................................................................13

Figure 8. Film thickness profiles for smooth and 18 grooved tubes with mass fluxes of 

G=44 kg/m2s and qualities ranging from 0.6 to 0.76 (52). .....................................................15

Figure 9. Comparison between heat transfer coefficients of smooth and inner grooved tubes 

for two different mass fluxes and heat fluxes (53). ................................................................17

List of Tables

Table 1. Status and approximate technical targets for power electronics (3). ................................3

Table 2. Classification of flow boiling enhancement techniques. ................................................10

Table 3. Geometric parameters and fin efficiencies for three Wieland inner grooved tubes, ......11

Table 4. Comparison of leading refrigeration tube performance (42). .........................................11

Table 5. Specifications of smooth and inner grooved tubes tested, area enhancement ratios, 

and average heat transfer enhancement ratios for mass flow rates ranging from 205–215 

kg/m2s, heat flux of 11 kW/m2, and quality ranging from 0.2 to 0.85.....................................12

Table 6. Error analysis for various inner grooved tube heat transfer coefficient models (55). ....16
1

1. Background

The last several decades have witnessed a dramatic increase in the use of electronics on a vast 

variety of systems. This trend continues today in hybrid electric vehicle (HEV) and electric 

vehicle (EV) technologies for commercial and military applications. Military use can include 

both direct vehicle applications, such as propulsion, and indirect applications, such as electrically 

operated arms or interfacing with the vehicle electrical system to create a military base microgrid 

(1). 

There are several motivations for replacing the traditional internal combustion (IC) motors and 

mechanical drives with HEV equivalents on military platforms. One of the most important 

reasons is the high cost of fuel. Transporting fuel to the theater through dangerous routes and 

over long distances to geographically dispersed troops leads to significant increases in the cost of 

fuel. The cost can rise from a regular price of several dollars per gallon for civilians to about 

$400 in the battlefield. If an airlift is needed, the cost can reach $1000 per gallon (2). As such, 

even a modest saving in fuel can lead to huge cost savings on the order of billions of dollars per 

year. 

An additional issue in military vehicle applications is acoustic and heat signature noise, which

can be detected by the enemy. A HEV platform can significantly reduce noise and, as a result,

improve stealth capabilities and personnel safety in dangerous environments. Furthermore, 

HEVs can be designed with one motor per axle or even hub motors in each of the wheels for 

propulsion. This provides the added benefit of system redundancy so that the vehicle can operate 

in a degraded mode to reach a safe location in case one of the motors fails. 

An indirect benefit of HEVs for military applications is the ability to connect multiple HEVs to 

provide utility-level voltages to bases and other infrastructures in combat zones. With 

appropriate control electronics, several HEVs can form a microgrid with a robust source of 

utility power (1). This use of HEVs can reduce the need for ancillary generators and power 

units, therefore leading to savings stemming from acquisition and transportation costs. 

1.1 Power Requirements and Power Conversion Electronics

Figure 1 illustrates the continuous power needs for current commercial HEVs, full EVs, and 

plug-in hybrid electric vehicles (PHEVs). As shown, continuous power demands increase 

through the transition from commercial HEVs to PHEVs and all-electric drive applications, such 

as fuel cells or electric vehicles. In the case of HEVs and PHEVs, electrical power requirements 

approach 30–60 kW, while the all-electric platforms top out around 100 kW for short durations. 
2

Figure 1. Midsize hybrid electric power requirements (3).

A key enabling technology for the transition from traditional gasoline IC engines to hybrid and 

full electric vehicles is power electronics. Because the disparate electrical systems common to 

these programs need to draw from a platform’s common electrical bus, they all require power 

conversion electronics to meet operational specifications. This mainly involves the use of power 

semiconductor switches such as power diodes, metal oxide field effect transistors (MOSFETs), 

and insulated gate bipolar transistors (IGBTs). Power converters are typically classified by their 

input and output and, since AC and DC power are possible, there are four types of power 

converters: DC-DC converter, DC-AC inverter, AC-DC rectifier, and AC-AC converter. 

Aligned efforts aimed towards increasing power while simultaneously decreasing power 

electronic unit size and weight have led to improvements in cost and power density. As shown 

in table 1, the Department of Energy (DOE) and commercial sectors are targeting a 60% cost 

reduction, 30% specific power improvement, and 50% power density improvement by 2020. 

This analysis, although done for a commercial vehicle, is equally applicable to military 

applications. 
3

Table 1. Status and approximate technical targets for power electronics (3).

1.2 Power Electronic Thermal Management

Even with power electronic conversion efficiencies of 96–98%, a vehicle system requiring 

100 kW of electrical power would have losses of 2–4 kW. If a system has multiple powertrain

motors, high-power bidirectional DC-DC converters, and appropriate power electronics, heat 

generated in the vehicle system could be significant (1). The major concern for thermal 

management of power electronics is the maximum operation temperature of 125 °C for IGBTs. 

In general, lower die temperature results in lower losses and better electrical performance. As 

such, the thermal performance of a power electronics module is determined by the die 

temperature rise at a given power dissipation. 

Traditionally, electronics have relied on air-cooled heat sinks or liquid-cooled cold plates to 

manage electronic waste heat. However, the new power dense electronic systems are further 

increasing waste heat and presenting great challenges to the capabilities of conventional cooling 

systems; fast, compact IGBT devices would have to dissipate heat fluxes in upwards of 

250 W/cm2 (1). Considering strictly air cooling, the effect of higher heat flux electronics is 

larger, heavier, costlier heat sinks and fans to compensate for insufficient convective 

performance. The effect is equally dramatic with single-phase liquid cooling, with higher heat 

fluxes requiring larger coolant flow rates to sufficiently cool the system devices (4). These large 

flowrates and subsequent pumping powers result in increasingly bulky, heavy systems that 

consume more fuel (5). Thus, there is a drive to develop improved cooling components that are 

smaller and lighter, and have increased performance relative to conventional liquid cold plates.

Cooling schemes using liquid-vapor phase change (two-phase cooling) have been examined as a 

practical and cost-conscious next step beyond single-phase cooling. A two-phase cooling system 

has several potential benefits over a standard single-phase liquid cooling approach. First, the 

latent heat of vaporization for a particular fluid, reflecting the heat absorbed to evaporate a unit 

mass, can be two orders of magnitude larger than the specific (sensible) heat used in single-phase 

liquid cooling (6). Therefore, boiling provides the possibility of increased heat absorption per 
4

unit mass and volume of fluid and improved heat acquisition effectiveness. The single-phase 

heat dissipation relationship for water can be expressed as:

 (1)

where q is the heat dissipation, is the mass flowrate, is the specific heat of the fluid 

(4186 kJ/kgK for water), and is the temperature rise of the fluid. Equation 1 assumes an 

allowable fluid temperature rise of 20 °C, such that the heat dissipation can be expressed as the 

product of mass flowrate and a constant. Similarly, the two-phase heat dissipation relationship 

for water can be expressed as:

 , (2)

where q is the heat dissipation, x is the quality (fraction of the mass flow rate that has been 

vaporized), is the mass flowrate, and is the latent heat of vaporization of the fluid 

(2,257 kJ/kg for water). Assuming a moderate exit quality of 0.5, this heat dissipation can also 

be expressed as the product of the flowrate and a constant. A comparison between equations 1

and 2, with reasonable operating conditions, shows that two-phase has the potential to dissipate 

an order-of-magnitude more heat than the single-phase case for equivalent flowrates.

As shown symbolically in equations 1 and 2, and graphically in figure 2, the increased heat 

acquisition effectiveness of two-phase flow translates into lower flowrates compared to singlephase flow for comparable heat dissipation. The potential benefit of lower flowrates includes: 

smaller fluid reservoirs; smaller onboard fluid volume; reduction in pumping power; smaller 

pumps; and a reduction in system weight and volume. Additionally, two-phase cooling has the 

potential benefit of a relatively isothermal cold plate surface, due to the use of latent heat 

absorption, which occurs at nearly isothermal conditions (7, 8), and order-of-magnitude larger 

heat transfer coefficients than equivalent single-phase forced convection methods (6, 8). 

Figure 2. Dissipated heat vs flowrate for water using latent heat and sensible heat (8).

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Dissipated Heat (kW)

Flowrate (cm3/s)

Latent Heat 

(x=0.5)

Sensible Heat (75C 

delta)

Sensible Heat (20C 

delta)
5

2. Two-Phase Flow Boiling

As shown by Sharar et al. (8) and Saums (7), performance improvement can be accomplished by 

simply taking an existing single-phase system, an IGBT minichannel cold plate for cooling 

power electronics and operating it in two-phase. However, by understanding the mechanisms 

that make two-phase advantageous, surface enhancements can be developed that work 

particularly well for two-phase cooling applications. Essential to this understanding is the 

concept of two-phase flow regime. The remainder of this report will discuss flow regimes in 

minichannels and introduce passive two-phase surface enhancement techniques. The discussion 

focuses on single tubes and channels that represent a minichannel cold plate “unit cell.” The 

cold plates could take a variety of forms; the easiest transition, however, may be to integrate the 

enhanced tubes in a pressure-fit serpentine brazed cold plate. An example of this cold plate 

design is shown in figure 3. 

Figure 3. Hydroblok pressure-fit 6-pass serpentine cold plate (9).

2.1 Two-phase Flow Regimes

In two-phase flow, the vapor and liquid phases are in simultaneous motion inside the channel or 

pipe. The physics involved are typically more complicated than single-phase flow. In addition 

to the viscous, pressure, and inertial effects existing in single-phase flow, two-phase flows are 

also affected by wall wetting characteristics of the liquid on the channel wall, momentum 

exchange between the liquid and vapor phases, and interfacial tension forces. The particular 

flow regime resulting from these interactions plays a critical role in the local heat and mass 
6

transfer. As indicated in equation 3, the two-phase heat transfer coefficient in a closed channel is 

a summation of the nucleate boiling and convective vaporization terms:

 (3)

Understanding these effects in plain tubes is an essential foundation for understanding 

performance of enhanced channels. Figure 4 is a schematic representation of a typical flow 

boiling process in a horizontal round tube. The fluid enters as single-phase saturated fluid. As 

the process proceeds down the length of the tube, the percentage of the flow that has been 

vaporized increases. Conservation of mass dictates that as the mean density of the flow 

decreases, due to the formation of vapor, the mean flow velocity must increase. The 

accompanied acceleration of the flow results in varying liquid and vapor velocities, which causes 

a series of changes in the flow regime. In other words, the two-phase flow regime is strongly 

dependent on the relative velocities of the two phases. 

Figure 4. Two-phase flow regimes and associated heat transfer coefficients (10).

At low quality, bubbly flow is often observed, where bubbles tend to flow mainly in the top of 

the tube due to buoyancy forces. In this regime, nucleate boiling is the dominant vaporization 

mechanism. The added turbulence and mixing resulting from the bubble formation results in a 

local maximum in the heat transfer coefficient. As the quality downstream increases, bubbles 

begin to coalesce and larger plugs of vapor form. Like bubbly flow, plugs of vapor tend to flow 

in the top of the channel due to buoyancy. In this regime, the tube wall is intermittently cooled 

by liquid slugs and vapor plugs, resulting in a decrease in the heat transfer coefficient. At very 

low flow rates, stratified flow may occur where the upper portion of the tube is completely 

occupied by vapor and the bottom by liquid. Stratified flow is marked by drastically reduced 
7

heat transfer coefficients due to the dry upper surface. If the flow rate or quality is increased in 

stratified flow, Helmholtz instabilities lead to wavy flow and eventually slug flow. 

At high vapor velocities, annular flow is observed where a thin liquid film is distributed along 

the perimeter of the tube and a high-velocity vapor core travels through the center. In the 

annular flow regime, evaporation from the liquid-vapor interface is the dominant heat transfer 

mechanism, and the second local maximum in figure 4 is observed. Buoyancy effects may thin 

the liquid film on the top of the tube and thicken it at the bottom; however, at acceptably high 

vapor velocities, strong shear stresses serve to redistribute the fluid more evenly around the 

perimeter of the tube. The strong shear may also lead to entrainment of liquid droplets in the 

vapor core. Entrained droplets along with continual vaporization tend to thin the liquid film and 

increase the heat transfer coefficient. Eventually, however, the film may completely disappear 

from portions of the tube wall. This is known as dryout or critical heat flux (CHF) and causes a 

decrease in the heat transfer coefficient. As shown in figure 4, gravity tends to cause the film on 

the top surface to dryout first. 

2.2 Flow Regime Maps

The dependence of heat transfer performance on flow regime led researchers to analytically 

describe and map the dominant flow regimes in channels. Baker (11) provided the earliest 

empirical flow regime map, and other generalized flow regime maps followed—Mandhane et al.

(12), Taitel and Dukler (13), and Weisman et al. (14). Most notable among these was the 

phenomenological maps by Taitel and Dukler, which defined and mapped four adiabatic flow 

regimes, stratified, intermittent, bubbly, and annular, with superficial liquid and gas coordinates. 

In 1990, the Unified Model was developed to predict the adiabatic flow regime in a variety of 

channel sizes and orientations based on two-phase non-dimensional groupings (15). These 

physics-based models contain little empirical fitting and should theoretically apply to most fluids 

and channel sizes. 

Adiabatic models do not account for thermal interactions inside the channel. This is important to 

consider in diabatic electronic cooling applications where heat is typically added to the twophase mixture. Specifically, diabatic conditions could be expected to shift transition boundaries 

between bubbly/intermittent and stratified/intermittent regimes (16). As a result, diabatic flow 

regime maps have been developed to account for the thermal interactions inside of the channel. 

Beginning in 1998, Kattan, Thome, and Favrat (17) empirically modified the Steiner map, which 

is a modification of the Taitel-Dukler map, and introduced a method for determining the onset of 

dryout during annular flow in a diabatic system. Since then, other empirically modified diabatic 

flow regime maps have followed—Zurcher, Thome, and Favrat (18), Zurcher, Favrat, and 

Thome (19), Thome and El Hajal (20), and Wojtan, Ursenbacher, and Thome (21). These 

modifications provide a more-accurate prediction of the flow regimes and dryout in real-world 

diabatic systems. 
8

2.3 Studies of Flow Regimes and Flow Regime Maps

The aforementioned models are well established for predicting flow regimes in macroscale 

channels (D>0.5”). Cheng et al. (10) gives a comprehensive review of studies in macroscale 

smooth channels and provides a summary of results for 24 papers. However, two-phase flow in 

small diameter channels has become important for compact cold plate applications because of 

their increased effectiveness, volume reduction, and overall performance improvement when 

compared to conventional channels. Therefore, it is equally important to discuss flow regime 

maps in context of mini- and microscale channels. 

In general, the empirically modified diabatic flow regime maps discussed previously do not 

suitably predict flow regimes in micro- and minichannels. As such, new diabatic flow regime 

maps for flow boiling in micro- and minichannels have been developed (22–27). However, the 

mechanistic model of Taitel-Dukler is in good agreement with a variety of microchannel results 

from Bar-Cohen and Rahim (28), Rahim et al. (29), and Triplett et al. (30). In addition to 

demonstrating first-order accuracy in numerous studies, the Taitel-Dukler model has also proven 

useful for diabatic conditions (31, 32). As a consequence, the physics-based model proposed in 

the Taitel-Dukler flow regime map appears to be appropriate for determining the flow regime 

during evaporation in various tube diameters. 

Recently, Ullmann and Brauner (33) studied the effect of tube diameter on the prevailing 

adiabatic flow regimes in 1.097 mm Pyrex tubes using the experimental data from Triplett et al. 

(30). Ullmann and Brauner indicated the importance of the non-dimensional Eotvos number on 

the flow regime transition in small tubes. They suggested that by reducing the tube diameter, the 

stratified region shrinks significantly, and slug, bubbly, and annular flow are the dominant 

regimes observed. This description of flow regime in mm-sized channels is supported by the 

aforementioned flow boiling studies in micro- and minichannels, particularly the study by Rahim 

et al. (29), and also consistent with trends predicted by the Taitel-Dukler flow regime maps. 

Figure 5 shows flow regime maps for R113 flowing in channels with diameters ranging from 

100 mm to 0.1 mm, along with mass fluxes from 50 to 400 kg/m2s and qualities from 0.01 to 0.9. 

As shown, the result of smaller diameter tubes is a gradual expansion of the annular flow regime 

to lower superficial liquid and vapor velocities, and transition of the bubbly and intermittent flow 

regimes to lower superficial liquid velocities. Although the primary two-phase flow regimes 

observed in macroscale channels are also encountered in mini- and microscale channels, annular 

flow becomes the dominant flow regime as diameter decreases. In the context of inner grooved 

tubes, it is likely that similar trends exist when transitioning from large diameter macroscale

tubes to smaller tubes for compact cold plates of interest in this study. 
9

Figure 5. Taitel-Dukler flow regime maps for R113 flowing in a horizontal channel of various diameters 

(a) 100 mm, (b) 10 mm, (c) 1 mm, and (d) 0.1 mm (28).

3. Two-phase Surface Enhancements

Based on an understanding of the flow progression in tubes and the dominant factors affecting 

the two-phase heat transfer coefficients discussed in chapter 2, researchers have developed 

surface enhancements to improve thermal performance. Extensive surveys on this topic are 

reported by Bergles (34, 35), Thome (36), Webb (37), and Kandlikar (38). Specific to flow 

boiling heat transfer, these techniques can be classified into two distinct categories, (1) nucleate 

boiling techniques, which provide improvement in the first term of equation 3 and an increase in 

the first local maxima in figure 4 at low vapor qualities; and (2) convective vaporization 

techniques, which provide improvement in the second term of equation 3 and an increase in the 

second local maxima in figure 4 at high vapor qualities. A summary of these techniques can be 

found in table 2 and are discussed extensively in the previous surveys. Furthermore, a closer 

look at specific topics, including microporous coatings (39), reentrant cavities (40), nanoparticle 

fluid additives (41), twisted tape inserts (42, 43), corrugated tubes (42, 44), and inner grooved 

tubes, can be found in a presentation by Sharar et al. (45).
10

Table 2. Classification of flow boiling enhancement techniques.

Nucleate Boiling Convective Vaporization

Acoustic pulsation Fins

Mechanical and ultrasonic vibration Twisted tape inserts

Porous surfaces Helical wire inserts

Structured surfaces (reentrant cavities) Corrugated or fluted tubes

Screens Inner grooved tubes (microfin tubes)

Fins

Electrohydrodynamic field effect

3.1 Convective Vaporization

In order to take full advantage of a two-phase cooling scheme and the flowrate/pumping power 

benefits of latent heat transfer, a large percentage of fluid should be vaporized. As such, 

operation beyond the first maximum, where nucleate boiling is likely suppressed and convective 

vaporization dominates, is of particular interest. Not surprisingly, there are a variety of 

convective vaporization enhancements that have been explored deeply in academic settings and 

others that have been adopted commercially in refrigeration applications. The three main 

convective vaporization enhancement techniques that have been commercially adopted to 

improved tube-side performance of refrigeration tubes are twisted tape inserts, corrugated tubes, 

and inner grooved tubes. 

3.1.1 Inner Grooved Tube

Twisted tape inserts and corrugated tubes have been commercially available for many years;

both, however, have been largely displaced by inner grooved tubes. Inner grooved tubes were 

originally developed in Japan and gained widespread adoption in the 1980s (42). Seamless inner 

grooved tubes are typically manufactured by running a mandrel through a smooth bore copper 

tube but can also be made by embossing fin geometries on a metal strip, rolling, and seam 

welding. The latter manufacturing method provides a wider range of microfin geometries, 

including 3-D geometries, but most commercial vendors continue to manufacture seamless tubes

(46). Figure 6a shows the characteristic inner grooved tube geometry, which is defined by the 

internal diameter, number of fins, helix angle β (or axial pitch), fin height, fin angle γ, and the 

internal area ratio. Figure 6b shows a photograph of a commercial Wieland Cuprofin inner 

grooved tube along with appropriate geometric parameters. 

(a) (b)

Figure 6. (a) Schematic of inner grooved tube and (b) Photograph of inner grooved tube (courtesy Wieland).
11

Depending on the process, tube size, and manufacturer, the enhancement typically consists of 

40–80 small ~0.1 to 0.4 mm tall fins with helix angles from 7° to 23°. The majority of inner 

grooved tubes have fins with approximately trapezoidal cross-sectional shapes, but triangular and 

rectangular fins are also possible. Table 3 lists geometric parameters for three commercially 

available inner grooved tubes from Wieland. 

Table 3. Geometric parameters and fin efficiencies for three Wieland inner grooved tubes,

Name Diameter

(mm)

Wall

thickness

(mm)

# 

fins

Fin

Height

(mm)

Approximate

Fin base

(mm)

ηf (%)

h=1000

W/m2

ηf (%)

h=20,000

W/m2

Surface

enhancement

(A/Ap)

S2AD-5 5 0.23 40 0.15 0.20 99 98 1.52

S2AD-952 9.52 0.34 60 0.2 0.25 99 97.5 1.52

S2AD-15 15 0.4 75 0.3 0.31 99 96.7 1.53

As tabulated in table 3, the resulting fin efficiencies are greater than 95% for all three tubes, with 

heat transfer coefficients ranging from 1,000–20,000 W/m2K. Furthermore, the curves for 

triangular, rectangular, and parabolic fins converge at 

 

3/ 2 1/ 2

/

c p L h kA

values less than 0.3, which 

suggests that fin profile does not significantly affect fin efficiency in standard inner grooved 

tubes (47).

In horizontal orientations, inner grooved tubes typically show heat transfer enhancement ratios as 

high as three to four times at low mass velocities and improvement equal to or greater than the 

internal area ratio at high mass velocities (42). For vertical applications, heat transfer 

enhancement less than or equal to horizontal applications can be expected. Pressure drop 

increase compared to a smooth tube is typically small, ranging from 1.0 at low mass velocities to 

1.5 at high mass velocities. From a heat transfer versus pressure drop perspective, inner grooved 

tubes outperform twisted tape inserts and corrugated tubes. Heat transfer improvement and 

pressure drop increase for each of the three enhancement technologies are compiled in table 4.

Table 4. Comparison of leading refrigeration tube performance (42).

Metric Microfin Tube Twisted Tape Insert Corrugated Tube

Heat Transfer 

Augmentation @ low 

mass flux

3 to 4x that of a plain 

tube

1.2 to 1.5x that of a 

plain tube

1.2 to 1.8x that of a 

plain tube

Heat Transfer 

Augmentation @ high 

mass flux

> internal area ratio 1.2 to 1.5x that of a 

plain tube

Close to microfin tube 

performance

Pressure Drop Penalty 1 to 1.5x that of a plain 

tube 2x that of a plain tube 2x that of a plain tube

3.1.2 Heat Transfer Mechanisms in Inner Grooved Tubes

Despite widespread use and demonstrated performance improvement, the mechanisms leading to 

enhanced performance in inner grooved tubes are not well understood. Subsequently, there is a 

lack of physical models to predict performance in inner grooved tubes, which makes 
12

transitioning from conventional refrigeration equipment to cold plates difficult. Therefore, 

understanding the physical mechanisms underpinning two-phase performance enhancement in 

inner grooved tubes is a critical bottleneck.

Since the 1980s, a variety of studies have been performed to demonstrate and determine the 

enhancement mechanisms. In one example, Kim and Shin (48) performed an extensive 

experimental flow boiling study with R22 and R410A in one 9.52 mm OD (8.70 mm ID) smooth 

tube, five 9.52 mm OD (8.46–8.68 mm ID) inner grooved tubes, and two 9.52 mm OD (8.14–

8.51 mm ID) cross grooved tubes. The geometric parameters of interest and results summary are 

shown in table 5. As shown in the second-to-last column, the area enhancement (A/Ap) for each 

of the five inner grooved tubes varied from 1.28 to 1.85. The last column shows the average heat 

transfer coefficient for each fluid tested, with a mass flow rate of 205–215 kg/m2s, heat flux of 

11 kW/m2, and quality ranging from 0.2 to 0.85. Similar to other studies (49–51), a comparison 

of the area enhancement ratio to the heat transfer enhancement shows that inner grooved tubes 

provide enhancement greater than the area enhancement alone at moderate to low mass flux. 

These results are consistent with the trends discussed in table 4.

Table 5. Specifications of smooth and inner grooved tubes tested, area enhancement ratios, and average heat 

transfer enhancement ratios for mass flow rates ranging from 205–215 kg/m2s, heat flux of 11 kW/m2, and 

quality ranging from 0.2 to 0.85.

Researchers have speculated that the improvement beyond area enhancement is a result of 

several factors: thinning of liquid film in annular flow due to the larger surface area (48), 

redistribution of liquid in annular flow due to the helical grooves (52), and increased turbulence. 

However, generalized models that attempt to capture these effects have proven unreliable. Other 

research has suggested that flow regime transition (50, 51) and delay of dryout at high vapor 

qualities due to groove-induced fluid redistribution (53) appear to be two leading enhancement 

mechanisms (and benefits) of inner grooved tubes. To one degree or another, all of these 

mechanisms likely play a role in the enhanced performance in inner grooved tubes; however, the 

focus of the following sections is flow regime transition and delay of dryout.

3.1.3 Flow Regime Transition and Delayed Dryout in Inner Grooved Tubes

As previously discussed, the particular flow regime in a channel is intrinsically tied to the heat 

transfer performance. Therefore, transition from an undesirable flow regime, such as stratified 

flow (where only the bottom portion of the tube is wetted), to a desirable flow regime, such as 

annular flow (where thin film evaporation around the periphery leads to high heat transfer 
13

coefficients), could result in significant improvement. In this context, understanding flow 

regimes typical in inner grooved tubes relative to smooth tubes, and the effect of tube diameter 

on performance, is a key component to the successful transition to cold plate form factors. 

The suggested link between flow regime and thermal performance is not a broadly accepted 

approach, but there is empirical and analytical evidence suggesting that this approach to 

explaining enhancement in inner grooved tubes is appropriate. In one example, Yu, Lin, and 

Tseng (50) performed a flow visualization and heat transfer study with R134a in a 10.7 mm ID 

smooth and an 11.1 mm ID inner grooved tube. Mass fluxes in the range of 163 to 408 kg/m2s, 

heat flux between 2,200 and 56,000 W/m2, and a fixed heated length of 1.5 m were tested. 

Figure 7 shows the results of the flow visualization, plotted in the coordinates of G (mass flow 

rate) and x (quality); figure 7a is the smooth tube experimental results and figure 7b is the inner 

grooved tube results. The transitions of flow pattern observed were wavy, intermittent, semiannular, and annular in the direction of increasing G and x. It was reported in the study, and also 

apparent from figure 7, that the transitions in the inner grooved tube occurred at lower G and x 

compared with the smooth tube. Under the same flow conditions, the flow pattern in the inner 

grooved tube transitioned to annular flow, while the smooth tube was still operating in the wavy 

flow regime. One clear example is at a mass flowrate of G=163 kg/m2s and a quality of x>0.3. 

Figure 7. Experimental flow regime maps for (a) smooth tube with 10.7 mm ID, (b) inner grooved 

tube with 11.1 mm ID, and (c) average heat transfer coefficient for the smooth and inner 

grooved tube.

(a) (b)

(c)
14

The earlier transitions in the inner grooved tube are a result of the helical grooves on the tube 

surface, which allow liquid to more easily reach the top portion of the tube. In the smooth tube, 

however, the liquid and vapor velocities have to become sufficiently high before transitions can 

“naturally” occur. As a result of flow regime transition, the heat transfer is enhanced in the inner 

grooved tube. Figure 7c shows the average heat transfer coefficient versus vapor quality for the 

smooth tube and inner grooved tube. It can be seen that the heat transfer coefficient increases 

with both G and x for the smooth tube and inner grooved tubes. The increase in the heat transfer 

coefficient is relatively smooth for conditions when the flow regime does not change. One 

example is the case of G=163 kg/m2s in the smooth tube, where wavy flow dominates; compare 

figures7a and c. However, the rise can be dramatic where flow pattern transitions occur; from

figure 7b, the flow regime transitions from intermittent to annular at a quality of 0.3 and a 

flowrate of G= 163 kg/m2s. This same condition on figure 7c marks a sharp increase in heat 

transfer coefficient from approximately 4,000 to 5,500 W/m2K (40% improvement). 

Consequently, the maximum heat transfer enhancement of 2 occurred at a flowrate of 163 kg/m2s 

and qualities 0.3<x<0.7, where wavy flow dominated in the smooth tube and flow transition 

from intermittent to annular in the inner grooved tube was achieved. This enhancement 

exceeded the reported area enhancement of 1.6. Similar performance improvements were 

demonstrated by Hatamipour and Akhavan-Behabadi (51) during flow boiling of R134a in 

8.92 mm ID smooth and inner grooved tubes. 

In yet another example, Shedd and Newell (52) used a non-intrusive optical film thickness 

measurement method to observe the liquid distribution in horizontal adiabatic water-air flow 

through 15.1 mm ID smooth and inner grooved tubes. Liquid film thickness profiles for 

stratified/annular flow through smooth and 18° helix tubes are shown in figure 8. The smooth 

tube films are represented by dotted lines, and the grooved tube film thicknesses are shown with 

solid lines. At low mass flux, 44 kg/m2s, the smooth tube profiles are basically symmetric from 

left to right, with thicker liquid films on the bottom and dry surfaces at the top surface due to 

gravity effects; this can be interpreted as stratified flow. The grooved tube profiles appear to be 

rotated counterclockwise (the same direction as the groove) and the periphery is almost entirely 

wetted; this can be interpreted as annular flow. Under these flow conditions, 62% of the smooth 

tube is wetted versus 94% of the 18° inner grooved tubes. The observed transition from 

stratified to annular flow, leading to a larger wetter perimeter, would almost certainly cause 

higher heat transfer coefficients and may explain the enhancement in inner grooved tubes. 

Shedd and Newell (52) also reported that the liquid film profiles for the smooth and inner 

grooved tubes tend to converge at higher mass flux, which provides an explanation for the 

decrease in enhancement at higher mass flux as seen in the literature and outlined in table 4.
15

Figure 8. Film thickness profiles for smooth and 18 grooved 

tubes with mass fluxes of G=44 kg/m2s and qualities 

ranging from 0.6 to 0.76 (52).

Honda and Wang (54), and Mikishi, Honda, and Wang (55) recognized the dependence of heat 

transfer on the particular flow regime and, as such, developed stratified and annular flow models 

for evaporative heat transfer in inner grooved tubes. In doing so, they modified the flow regime 

transition from stratified-wavy to annular flow proposed by Kattan et al. (17) to predict the heat 

transfer coefficient in the intermediate region between the stratified and annular flow models. In 

both the stratified and annular models, nucleate boiling and forced convection were accounted 

for (55). The predictions of the new theoretical models and previously proposed empirical 

models by Koyama et al. (56), Murata (57), Thome et al. (58), Cavallini et al. (59), Yun et al.

(60), and Mori et al. (61) were compared to available experimental data for 10 inner grooved 

tubes and four refrigerants. As shown in table 6, the models developed to account for the 

dependence of flow regime (labeled Present 1 and Present 2) had smaller rms errors than the 

empirical models. The rms errors of the “present” models are still fairly high and improvements

could be made. However, the underlying conclusion remains: heat transfer in inner grooved 

tubes appears to be dependent on flow regime (and flow regime transition), and 

phenomenological models need to be developed that appropriately reflect this point. 
16

Table 6. Error analysis for various inner grooved tube heat transfer coefficient models (55).

The inner grooved tube studies discussed so far have had internal diameters in the range 7–

15 mm, and the empirical studies were developed based on tubes this size. Furthermore, no 

inner grooved tube flow visualization studies below 8.5 mm ID were reported, despite the known 

dependence of flow regime on tube diameter. In fact, only one study by Dang, Haraguchi, and 

Hihara (53) addressed flow boiling in small inner grooved tubes. In this study, flow boiling heat 

transfer of carbon dioxide inside a small-sized 2 mm ID inner grooved tube with heat fluxes 

ranging from 4.5–18 kW/m2 and mass fluxes from 360–720 kg/m2s was investigated. As shown 

in figure 9, the heat transfer coefficients in the inner grooved tubes were 1.88 to 2.2 times larger 

than the smooth tube values under the same experimental conditions; the area enhancement was 

close to 2.0 in this study. These trends are consistent with the trends discussed in table 4; heat 

transfer improvement in inner grooved tubes approaches the area enhancement at high mass 

fluxes. Despite the modest heat transfer improvement, the dryout quality for the inner grooved 

tubes was much higher than the smooth tubes, ranging from 0.9–0.95 versus 0.6–0.8, 

respectively. These experimental results indicate that using small 2 mm ID microfin tubes may 

considerably increase the overall heat transfer performance and delay dryout in annular flow at 

high qualities. In the future, an accompanying flow visualization study, lower flowrates to 

promote stratified flow and observe flow regime transition, and a detailed look at the delay of 

liquid film dryout in small inner grooved tubes could provide insight.
17

Figure 9. Comparison between heat transfer coefficients of smooth and inner grooved tubes for two 

different mass fluxes and heat fluxes (53).

It is likely that extrapolating empirical correlations to smaller tube diameters will provide 

inaccurate predictions because, as shown previously, flow regime and heat transfer coefficient 

changes with tube diameter. In addition, the “present” models (55, 54) rely on the modified 

Kattan et al. (17) stratified-wavy to annular flow regime transition, which, as discussed 

previously, does not suitably predict flow regimes in mini- and microchannels. Finally, Makishi 

et al. (55) combine nucleate boiling and convection in the model to reduce error. While this may 

be necessary for large tubes where the liquid film is thicker, nucleate boiling likely becomes 

progressively less important as the diameter shrinks, the quality grows, and thinner films are 

experienced. 
18

4. Conclusion

Two-phase cooling solutions are being explored to dissipate waste heat associated with nextgeneration power conversion electronics. Essential to two-phase heat transfer performance is the 

particular flow regime; annular flow is desirable because it provides high heat transfer 

coefficients. In standard channels, liquid and vapor velocities have to become sufficiently high 

before transition into annular flow can occur. Inner grooved tubes, on the other hand, have been 

shown to demonstrate earlier transition into annular flow and enhanced heat transfer as a result. 

By incorporating inner grooved tubes into power electronic cold plates, improvement may be 

obtained. 

Flow boiling in smooth tubes (channels) of various sizes has been explored, and adequate 

physical models predicting flow regime and heat transfer are available. Unfortunately, inner 

grooved tube flow visualization studies have been limited to tubes ranging in size from 8.62 to 

11.1 mm OD, fin angles from 15 to 18°, and fin heights from 0.25 to 0.3 mm with R-134a and 

CO2 as the working fluids. There is an apparent lack of inner grooved tube flow visualization 

data in the literature, and the few studies that have been conducted have not explored a variety of 

tube diameters and fluids. Therefore, motivation exists to study flow visualization in inner 

grooved tubes through a spectrum of tube diameters—particularly minichannels and 

microchannels for cold plate form factors. In addition to contributing valuable data to the 

scientific community, these studies would provide the data necessary to perform a more 

complete assessment of flow regime maps for application to inner grooved tubes and improve the 

communities understanding of the mechanisms leading to enhanced heat transfer in inner 

grooved tubes. Results obtained from such studies would aid in developing next-generation cold 

plates incorporating inner grooved tube technologies for enhanced performance.
19

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