Heat transfer engineering an international journal, tập 31, số 4, 2010

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Heat Transfer Engineering, 31(4):255–256, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903311652

editorial

Recent Developments in Flow Boiling
and Two-Phase Flow in Small
Channels and Microchannels
JOHN R. THOME and ANDREA CIONCOLINI
´
Heat and Mass Transfer Laboratory, Ecole
Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland

Microscale two-phase flow is at present one of the hottest topics of heat transfer research, both in academia and in
the industry. The miniaturization of two-phase flow systems, which has led to numerous experimental and theoretical
challenges not yet completely resolved, is primarily related to the dissipation of high heat duties typical of compact
systems such as CPU (central processing unit) chips, electronic devices, micro chemical reactors, and micro fuel cell
combustors.

Among the areas concerned with CPU (central processing
units) chips cooling [1], in particular, data centers have become
common and are found in nearly every sector of the economy,
such as manufacturing, universities, financial services, government institutions, etc. The increasing demand during the past 10
years for computer resources has led to a considerable increase
in the number of data centers and their corresponding energy
consumption. Energy considerations are becoming essential, as
the International Panel on Climate Change (IPPC) and the Kyoto treaty show that drastic reductions of CO2 emissions are
urgently needed. In this context, information technology has a

key role to play as the energy consumed in data centers represents almost 2% of the world electricity consumption and is
growing by 15% annually, while the current efficiency of such
systems is usually less than 20%. In addition to environmental
considerations, the rise in energy costs is a key motivator of
technological change, as the cooling process becomes the major
part of the data center operating costs.

Address correspondence to Professor John R. Thome, Heat and Mass Trans´
fer Laboratory, Ecole
Polytechnique F´ed´erale de Lausanne, EPFL-STI-IGMLTCM, Station 9, 1015 Lausanne, Switzerland. E-mail:

The market for cooling of personal computers (PCs), data
centers, and telecom equipment is at a crossroads between old
air-cooling technology and more effective solutions, mainly liquid and two-phase cooling. It appears that liquid cooling is the
preferred near-term solution because of its higher ease of implementation, but two-phase microscale cooling is of particular
interest due to evident performance advantages. For instance, the
latent heat allows operation at a lower mass flow rate than singlephase cooling, and thus can reduce pumping power requirements, resulting in a more energy-efficient system. The boiling
process takes place at an almost constant temperature, leading
to a small temperature gradient along the chip surface, which is
advantageous for thermal interface durability. Finally, primary
trends in boiling in multi-microchannels [2–4] show that the
boiling heat transfer coefficient increases with heat flux and
decreases slightly with increasing vapor quality. Consequently,
two-phase cooling is intrinsically well adapted to hot-spot management, which is a critical point for the electronics industry and
for obtaining a uniform operating temperature along the chip.
This issue collects seven papers originally presented at the
5th International Conference on Transport Phenomena in Multiphase Systems, HEAT 2008, June 30–July 3, 2008, Bialystok,
Poland. These studies address several aspects of flow boiling

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J. R. THOME AND A. CIONCOLINI

and two-phase flow in small channels and microchannels, both
experimentally and theoretically.

REFERENCES
[1] Thome, J. R., and Bruch, A., Refrigerated Cooling of Microprocessors With Micro-Evaporation Heat Sinks: New Developments
and Energy Conservation Prospects for Green Datacenters, Proc.
Institute of Refrigeration 2008–2009, 2–1.
[2] Agostini, B., Thome, J. R., Fabbri, M., Michel, B., Calmi, D.,
and Kloter, U., High Heat Flux Flow Boiling in Silicon MultiMicrochannels—Part I: Heat Transfer Characteristics of Refrigerant R236fa, International Journal of Heat and Mass Transfer, vol.
51, pp. 5400–5414, 2008.
[3] Agostini, B., Thome, J. R., Fabbri, M., Michel, B., Calmi, D.,
and Kloter, U., High Heat Flux Flow Boiling in Silicon MultiMicrochannels—Part II: Heat Transfer Characteristics of Refrigerant R245fa, International Journal of Heat and Mass Transfer, vol.
51, pp. 5415–5425, 2008.
[4] Agostini, B., Revellin, R., Thome, J. R., Fabbri, M., Michel, B.,
Calmi, D., and Kloter, U., High Heat Flux Flow Boiling in Silicon Multi-Microchannels—Part III: Saturated Critical Heat Flux
of R236fa and Two-Phase Pressure Drops, International Journal
of Heat and Mass Transfer, vol. 51, pp. 5426–5442, 2008.

heat transfer engineering

John R. Thome is a professor of heat and mass transfer at the Swiss Federal Institute of Technology in
Lausanne (EPFL), Switzerland, since 1998, where he
is director of the Laboratory of Heat and Mass Transfer (LTCM) in the Faculty of Engineering Science
and Technology (STI). His primary interests of research are two-phase flow and heat transfer, covering

boiling and condensation of internal flows, external
flows, enhanced surfaces, and microchannels. He received his Ph.D. at Oxford University, England, in
1978 and was formerly a professor at Michigan State University. He is the
author of several books: Enhanced Boiling Heat Transfer (1990), Convective
Boiling and Condensation (1994), and Wolverine Engineering Databook III
(2004). He received the ASME Heat Transfer Division’s Best Paper Award in
1998 for a three-part paper on flow boiling heat transfer published in the Journal
of Heat Transfer.

Andrea Cioncolini is a postdoctoral researcher in the
Laboratory of Heat and Mass Transfer (LTCM) at the
Swiss Federal Institute of Technology in Lausanne,
Switzerland (EPFL). He received his Laurea degree
and Ph.D. in nuclear engineering at the Polytechnic
University of Milan, Italy. He joined LTCM after 2
years as a senior engineer at Westinghouse Electric
Company, Science and Technology Department, in
Pittsburgh, Pennsylvania.

vol. 31 no. 4 2010

Heat Transfer Engineering, 31(4):257–275, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903311678

Flow Patterns and Heat Transfer for
Flow Boiling in Small to Micro
Diameter Tubes

TASSOS G. KARAYIANNIS1 , DEREJE SHIFERAW1 , DAVID B. R. KENNING1 ,
and VISHWAS V. WADEKAR2
1
2

School of Engineering and Design, Brunel University, West London, United Kingdom
HTFS, Aspen Technology Ltd., Reading, United Kingdom

An overview of the recent developments in the study of ﬂow patterns and boiling heat transfer in small to micro diameter
tubes is presented. The latest results of a long-term study of ﬂow boiling of R134a in ﬁve vertical stainless-steel tubes of
internal diameter 4.26, 2.88, 2.01, 1.1, and 0.52 mm are then discussed. During these experiments, the mass ﬂux was varied
from 100 to 700 kg/m2 s and the heat ﬂux from as low as 1.6 to 135 kW/m2 . Five different pressures were studied, namely,
6, 8, 10, 12, and 14 bar. The ﬂow regimes were observed at a glass section located directly at the exit of the heated test
section. The range of diameters was chosen to investigate thresholds for macro, small, or micro tube characteristics. The
heat transfer coefﬁcients in tubes ranging from 4.26 mm down to 1.1 mm increased with heat ﬂux and system pressure,
but did not change with vapor quality for low quality values. At higher quality, the heat transfer coefﬁcients decreased
with increasing quality, indicating local transient dry-out, instead of increasing as expected in macro tubes. There was
no signiﬁcant difference between the characteristics and magnitude of the heat transfer coefﬁcients in the 4.26 mm and
2.88 mm tubes but the coefﬁcients in the 2.01 and 1.1 mm tubes were higher. Conﬁned bubble ﬂow was ﬁrst observed in the
2.01 mm tube, which suggests that this size might be considered as a critical diameter to distinguish small from macro tubes.
Further differences have now been observed in the 0.52 mm tube: A transitional wavy ﬂow appeared over a signiﬁcant range
of quality/heat ﬂux and dispersed ﬂow was not observed. The heat transfer characteristics were also different from those in
the larger tubes. The data fell into two groups that exhibited different inﬂuences of heat ﬂux below and above a heat ﬂux
threshold. These differences, in both ﬂow patterns and heat transfer, indicate a possible second change from small to micro
behavior at diameters less than 1 mm for R134a.

INTRODUCTION

required to understand the mechanisms of ﬂow boiling in smallto micro-diameter passages.

Modeling and design of micro devices of high thermal performance, including electronic chips and other systems containing
compact and ultra-compact heat exchangers, require a fundamental understanding of thermal transport phenomena for the
ultra-compact systems. In this emerging area of great practical
interest, systematically measured boiling heat transfer data are

The authors thank Professor Andrea Luke of Hannover University and her
team, who carried out the surface roughness measurements for the 0.52 mm
tube, and acknowledge the contributions of Drs. Y. S. Tian, L. Chen, and X.
Huo to the earlier part of this long-term study.
Address correspondence to Prof. Tassos G. Karayiannis, Brunel University,
School of Engineering and Design, West London, Uxbridge, Middlesex, UB8
3PH, United Kingdom. E-mail:

Channel Size Classiﬁcation
Identifying the channel diameter threshold below which the
macro-scale heat transfer phenomena do not fully apply is important in validating and developing predictive criteria for the
thermal-hydraulic performance of small- to micro-scale channels. However, there is no clear and common agreement on
the deﬁnition and classiﬁcation criteria for the size ranges in
small/mini/microchannel two-phase ﬂow studies. One reason
could be the lack of comprehensive heat transfer data covering a wide range of channel diameters. Mehandale et al. [1]
deﬁned channel size ranges as follows: microchannel (1–100

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T. G. KARAYIANNIS ET AL.

µm), mesochannel (100 µm–1 mm), macrochannel (1–6 mm),

and conventional (dh > 6 mm). Kandlikar and Grande [2] suggested the classiﬁcation of microscale by hydraulic diameter,
given as conventional channels (dh ≥ 3 mm), minichannels
(200 µm ≤ dh < 3 mm), and microchannels (10 µm ≤ dh <
200 µm). These methods based only on size do not consider the
physical mechanisms and the variation of ﬂuid properties with
pressure. The absence of stratiﬁed ﬂow in horizontal microchannels, and hence the fact that the orientation of the channel has
virtually no effect on two phase ﬂow patterns, indicates the predominance of surface tension force over gravity. Consequently,
a number of attempts to deﬁne macro–micro transition have used
surface tension force as a base to formulate a nondimensional
criterion. These include E¨otv¨os number (E¨o > 1) recommended
by Brauner and Moalem-Maron [3] and conﬁnement number
(Co = 0.5) by Cornwell and Kew [4]. Thome [5] in his review
of boiling in microchannels indicated the importance of considering the effect of channel size on the physical mechanisms and
discussed the use of bubble departure diameter as a preliminary
criterion. He also mentioned the effects of shear on bubble departure diameter and the effect of reduced pressure on bubble
size that should be considered in addition to surface tension
forces. A comprehensive deﬁnition for normal and small size
tubes is required that considers all the fundamental phenomena,
based on experimental data for a wide range of conditions. The
research presented here addressed this requirement by systematic measurements of ﬂow boiling of R134a over wide ranges of
pressures, ﬂow rates, and heat ﬂuxes in ﬁve tubes with diameters
ranging from 4.26 to 0.52 mm. This choice of size range was
based on an initial assessment using the conﬁnement number
proposed by Cornwell and Kew [4].

ﬂow, and annular-slug ﬂow. Identiﬁcation of ﬂow patterns is
subject to uncertainty, which is not straightforward to quantify
and can also be signiﬁcantly inﬂuenced by the experimental
technique used. Besides, the transition from one ﬂow pattern
to another may be a gradual rather an abrupt transition, as is

often reported. Hence, ﬂow patterns may possess characteristics of more than one ﬂow pattern during transition. Chen et
al. [9] reported the results of a detailed study of ﬂow visualization experiments with R134a for a pressure range of 6–14
bar and tube diameter from 1.1, 2.01, 2.88, and 4.26 mm with
the same test rig as the present one. The typical ﬂow patterns
observed in the four tubes are presented in Figure 1. They included dispersed ﬂow, bubbly ﬂow, conﬁned ﬂow, slug ﬂow,
churn ﬂow, annular ﬂow, and mist ﬂow. The ﬂow patterns in
the 2.88 and 4.26 mm tubes exhibit characteristics found in
large tubes. The ﬂow patterns in the 2.01 mm tube demonstrate
some “small tube characteristics,” e.g., the appearance of conﬁned bubble ﬂow at the lowest pressure of 6 bar, and slimmer
vapor slug, thinner liquid ﬁlm, and a less chaotic vapor–liquid
interface in churn ﬂow. Conﬁned ﬂow was observed at all pressures when the diameter was reduced to 1.1 mm, indicating

Flow Patterns
Flow pattern studies in small/micro tubes have clearly shown
that there is a considerable difference in the ﬂow pattern characteristics compared with conventional size channels. These
include the predominance of surface tension force over gravity,
the absence of stratiﬁed ﬂow pattern in horizontal channels, and
the appearance of additional ﬂow patterns that are not common
in normal-diameter tubes. In the past some researchers have
proposed several ﬂow pattern classes, probably more than is
necessary for modeling. Although there are arguments on the
classiﬁcation of ﬂow patterns, the most commonly identiﬁed
ﬂow patterns so far are bubbly ﬂow, slug ﬂow, churn ﬂow, and
annular ﬂow. Barnea et al. [6] classiﬁed the ﬂow patterns as
dispersed bubble, elongated bubble, slug, churn, and annular.
Elongated bubble, slug, and churn were considered as intermittent ﬂow. Dispersed ﬂow and elongated bubble were replaced
by bubbly ﬂow in the Mishima and Hibiki [7] classiﬁcation.
Kew and Cornwell [8] experimentally observed ﬂow regimes
during their ﬂow boiling tests in small-diameter channels using
R141b, and proposed only three distinct ﬂow regimes. They deﬁned the ﬂow patterns as isolated bubble ﬂow, conﬁned bubble

heat transfer engineering

Figure 1 Flow patterns for R134a at 10 bar pressure: (a) d = 1.10 mm, (b)
d = 2.01 mm, (c) d = 2.88 mm, and (d) d = 4.26 mm (Chen et al. [9]).

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T. G. KARAYIANNIS ET AL.

a potential transition range for heat transfer between 2 and 1
mm.
Studies of even smaller diameter tubes are described next.
Serizawa et al. [10] studied two phase ﬂow in microchannels and
reported the visualization results for air–water and steam–water
ﬂows in circular tube of 20, 25, and 100 µm and 50 µm internal
diameter, respectively. They found several additional features
to those observed in small-diameter tubes. For air–water twophase ﬂow in a 25 µm silica tube the special ﬂow pattern features
found included liquid ring ﬂow and liquid lump ﬂow. The liquid ring ﬂow was described as the appearance of a symmetrical
liquid ring with long gas slugs passing in the middle. Serizawa
et al. hypothesized that the liquid ring ﬂow could develop from
slug ﬂow when the gas slug velocity is too high and the liquid
slug is too short to form a stable liquid bridge between consecutive gas slugs. At this condition, liquid lump ﬂow appeared with
further increases in the gas ﬂow rate. According to Serizawa
et al., “the high-speed core gas entrains the liquid phase and liquid lumps are sliding on the wall.” Experiments using the same
ﬂuid but in a 100 µm quartz tube gave similar results as for the
25 µm silicon tubes except that small liquid droplets in gas slug
ﬂow were sticking on the tube wall, indicating the absence of
a liquid ﬁlm at these locations between the slug and the wall.
Stable liquid ring ﬂow and liquid lump ﬂows were also reported

for the 100 µm tube. Flow patterns similar to those of air–water
ﬂow in the 25 µm silica tube were observed in the case of steam–
water ﬂow in a 50 µm silica tube, with the only difference being
the absence of liquid lump ﬂow, which, according to Serizawa et
al., was not a main ﬂow but transition type ﬂow. However, liquid
ring ﬂow was still found, which may indicate that the difference
in the method of forming the two-phase ﬂow, i.e., boiling or
adiabatic mixing of air–water, seems to have no considerable
effect, at least for these sizes.
Kawahara et al. [11] studied two-phase ﬂow characteristics
of nitrogen and deionized water in a 100 µm diameter tube
made of fused silica, and noted the absence of bubbly and churn
ﬂow as one of the differences between their results and results
for larger diameter tubes. They reported mainly intermittent and
semi-annular ﬂows. Recently, Xiong and Chung [12] studied experimentally adiabatic gas–liquid ﬂow patterns using nitrogen
and water in rectangular microchannels with hydraulic diameter of 0.209, 0.412, and 0.622 mm. They observed four different ﬂow patterns: bubbly-slug ﬂow, slug-ring ﬂow (liquid-ring
ﬂow), dispersed-churn ﬂow, and annular ﬂow in the 0.412 and
0.622 mm microchannels. The bubbly-slug ﬂow developed to
fully slug ﬂow. They reported that dispersed and churn ﬂows
were absent in the 0.209 mm channel.

259

that reducing the tube diameter shifted the transition boundaries
between intermittent-dispersed bubbly and intermittent-annular
ﬂow toward lower liquid velocity and higher gas velocity, respectively. Also, they did not observe stratiﬁed ﬂow regime
inside the 1 mm diameter tube. In the study of air–water ﬂow
patterns in tubes of 0.5 to 4.0 mm inside diameter, for vertical
ﬂow, Lin et al. [14] observed that decreasing the tube diameter
shifted the slug-churn and churn-annular transition boundaries

toward lower vapor velocity.
Recently, Chen et al. [9] noted that the diameter inﬂuences
the transition boundaries of dispersed bubble-bubbly, slug-churn
and churn-annular ﬂow. Also, the slug-churn and churn-annular
boundaries are weakly dependent on superﬁcial liquid velocity and strongly dependent on superﬁcial vapor velocity. There
seems to be no effect of diameter at the boundaries of dispersed
bubble-churn and bubbly-slug ﬂow. The ﬂow pattern transition
data of Chen et al. are plotted on a mass ﬂux versus quality
graph in Figure 2 for pressures of 6 and 8 bar. As shown in the
ﬁgure, when the diameter is reduced, the slug-churn and churnannular transition lines shift toward higher quality. The change
is more pronounced for moderate and low mass ﬂuxes. There
is no obvious effect on the bubbly/slug transition line. The ﬂow
regime boundaries are shifted to signiﬁcantly lower qualities as
the mass ﬂux increases. At higher quality, the transition lines
for different tubes merge into a single line. Chen et al. reported
that the Weber number may be the appropriate parameter to
deduce general correlations to predict the transition boundaries
that include the effect of diameter.
Recently, new correlations for transition of non-adiabatic
ﬂow patterns were introduced by Revellin and Thome [15].
They identiﬁed three main ﬂow patterns, named (a) the isolated
bubble regime, which includes bubbly ﬂow and short slugs—in
this regime coalescence is not signiﬁcant; (b) the coalescing
bubble regime, where slug ﬂow is the main ﬂow with some of
the bubbles coalescing to form a longer slug; and (c) the annular
regime. According to their observations, churn ﬂow is a transition from coalescing bubble to annular ﬂow, and it is considered
an indication of the end of coalescing bubble ﬂow. The ﬂow
pattern maps were plotted as mass ﬂux versus quality graphs.
Revellin and Thome proposed ﬂow pattern transition correlations, which give the quality at which the transition occurs. For
the transition from the isolated bubble to the coalescing bubble regime, their correlation contained the Reynolds, Boiling,

and Weber numbers, as in Eq. (1). A similar correlation for the
transition from the coalescing bubble to the annular regime contained only the Reynolds number and the Weber number, as in
Eq. (2).
x = 0.763 · Relo Bo Wego

Effect of Diameter on Transition Boundaries
The effect of tube diameter on ﬂow pattern transition boundaries was also studied by various researchers. Damianides and
Westwater [13] studied the ﬂow regimes in horizontal tubes
of 1 to 5 mm inside diameters using air–water. They reported
heat transfer engineering

0.41

x = 0.00014 · (Relo )1.47 · Welo −1.23

(1)
(2)

According to Eq. (1), the transition from isolated bubble to
slug is independent of tube diameter, which is conﬁrmed by the
present results of Figure 2 (bubbly to slug ﬂow). However, the
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260

T. G. KARAYIANNIS ET AL.

for large diameter tubes, e.g., the appearance of conﬁned ﬂow
at about 2 mm for R134a, which may indicate a threshold for

change from large to small diameter. For the same ﬂuid the
Cornwell and Kew [4] criterion gives a critical diameter of 1.7
mm for P = 6 bar pressure. Flow pattern studies for even smaller
tubes (near or less than 1 mm) revealed the existence of a number
of different ﬂow pattern types, e.g., ring ﬂow and lump liquid
ﬂow, which have not been found in larger diameter tubes. This
is indicative of a possible further change in ﬂow patterns and
hence in thermal characteristics at these even smaller diameters.
This is discussed later in the article in light of the recent results
from our own investigations.

Heat Transfer

Figure 2 Flow pattern transition boundary lines for the four tubes (Chen
et al. [9] data): (a) 6 bar and (b) 8 bar pressure.

transition from coalescing bubble to annular ﬂow regime, which
is equivalent to churn to annular transition, shifts to lower quality with decreasing diameter. This is contrary to the results of
Chen et al. [9] and could be due to the fact that the correlation
was developed using tests with a single tube diameter rather
than a range of tube diameters. For instance, at a mass ﬂux of
400 kg/m2 -s and pressure of 8 bar, the transition qualities for the
2.01 and 1.10 mm tubes are x = 0.38 and x = 0.32, respectively.
From the experimental results of Chen et al. [9], shown in Figure 2b, the corresponding values are 0.22 and 0.24, respectively.
From the preceding review, it appears that small-diameter
tubes exhibit ﬂow pattern characteristics different from those
heat transfer engineering

Nucleate boiling, forced convection, and a combination of
the two are the main mechanisms often reported in the literature for ﬂow boiling heat transfer in large-diameter tubes, e.g.,

Kenning and Cooper [16]. These have also been adopted in
identifying the heat transfer mechanism in small-diameter tubes
and microchannels, although different conclusions have been
drawn by researchers as to their prevalence. Some researchers
concluded that nucleate boiling is the dominant heat transfer
mechanism when it was observed that the heat transfer coefﬁcient is more or less independent of vapor quality and mass
ﬂux, while it is strongly dependent on heat ﬂux—e.g., Lazarek
and Black [17], Wambsganss et al. [18], Tran et al. [19], Bao
et al. [20], Yu et al. [21], and Fujita et al. [22]. On the other
hand, some experimental studies have also reported an effect
of the mass velocity and vapor quality but not of the heat ﬂux
on the heat transfer coefﬁcient. The interpretation given to this
is that forced convective boiling is the dominant heat transfer
mechanism—e.g., Carey et al. [23], Oh et al. [24], Lee and Lee
[25], and Qu and Mudawar [26]. Some researchers reported a
combined effect of both mechanisms, i.e., nucleate boiling at
low quality and forced convective boiling at high quality region,
in a way similar to that observed in large-diameter tubes—e.g.,
Kuznestov and Shamirzaev [27], Lin et al. [28], Sumith et al.
[29], and Saitoh et al. [30]. However, it is worth noting here that
macroscale boiling heat transfer correlations and models did not
predict well the heat transfer coefﬁcient in small-diameter tubes,
as noted by Qu and Mudawar [26], Owhaib and Palm [31], and
Huo et al. [32].
More complex behavior and differences dependent on the
ﬂuid tested were reported by other researchers. For example,
Dı’az and Schmidt [33] investigated transient boiling heat transfer in 0.3 × 12.7 mm microchannels using infrared thermography to measure the wall temperature. For water, the heat transfer
coefﬁcient decreased with quality near the zero quality region,
followed by a uniform heat transfer coefﬁcient. However, for
ethanol at high quality, an increase in heat transfer coefﬁcient

with quality was found to be independent of applied heat ﬂux.
A similar behavior, i.e., an increase in the heat transfer coefﬁcient with quality, was observed by Xu et al. [34] and Lie et al.
vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

[35]. Lie et al. [35] investigated experimentally evaporation heat
transfer of R134a and R407c ﬂow in horizontal small tubes of
0.83 and 2.0 mm internal diameter. The ﬂuid was preheated to
an inlet quality that varied from 0.2 to 0.8. The heat transfer coefﬁcient was observed to increase with quality almost linearly,
except at lower mass ﬂux and heat ﬂux. It also increased with
heat ﬂux, mass ﬂux, and saturation pressure. Saitoh et al. [30]
studied the effect of tube diameter on boiling heat transfer of
R134a in horizontal tubes with inner diameter of 0.51, 1.12,
and 3.1 mm. The heated lengths were 3.24, 0.935, and 0.550 m
respectively. The heat ﬂux ranged from 5 to 39 kW/m2 , mass
ﬂux from 150 to 450 kg/m2 s, saturation pressure from 3.5 to 4.7
bar, and inlet vapor quality from 0 to 0.2. For the 3.1 mm tube,
when the quality was less than 0.6, the heat transfer coefﬁcient
was strongly affected by heat ﬂux and was not a function of
mass ﬂux and quality. For quality greater than 0.5, heat transfer
coefﬁcient increased with mass ﬂux and quality, but was not
affected by heat ﬂux. This quality limit shifted to 0.4 for the
1.12 mm tube. The 0.51 mm results did not exhibit the same
heat transfer characteristic as the rest of the tubes. When the
quality was less than 0.5, the heat transfer coefﬁcient seemed to
increase with quality and heat ﬂux and slightly with mass ﬂux.
In this region, the heat transfer coefﬁcient was slightly higher
than the 1.12 and 3.1 mm tubes. There was also an early dry-out

compared with the other tubes, and the region of decreasing
heat transfer coefﬁcient with quality is not such a sharp drop
as the rest. They observed ﬂow instabilities in the two larger
tubes (3.1 and 1.12 mm), but not in the 0.51 mm tube. Agostini
and Thome [36] categorized the trends in the local heat transfer coefﬁcient versus vapor quality and its relation to heat and
mass ﬂux after reviewing 13 different studies. They noted that
in most of the cases reviewed that at low quality (<0.5) the heat
transfer coefﬁcient increases with heat ﬂux and decreases or is
relatively constant with vapor quality, and at high vapor quality
it decreases sharply with vapor quality and is independent of
heat ﬂux or mass ﬂux.
Initiation of Boiling
Flow boiling in very-small-diameter tubes is usually associated with high initial liquid superheat required to initiate boiling.
Yen et al. [37] conducted ﬂow boiling experiments in 0.19, 0.3,
and 0.51 mm inside diameter tubes using R123 and FC-72. They
observed a high liquid superheat that reached up to 70 K in their
experiments. In the low quality region, the heat transfer coefﬁcient was observed to decrease with quality up to approximately
x = 0.25 and then became almost constant with further increase
in quality. Hapke et al. [38] investigated boiling in a 1.5 mm
internal diameter tube and reported that the onset of boiling occurred at higher liquid superheat than required for conventional
tubes. Peng and Wang [39] and Peng et al. [40], based on their
observations of boiling in microchannels of hydraulic diameter
200–600 µm, argued that nucleation can hardly be seen in microchannels. They proposed a hypothesis of “evaporating space”
to explain the phenomenon. They also suggested a theoretical
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261

model to predict the superheat temperature. The unusually high
superheat in micro tubes was also reported to be related to the

reduction of active nucleation sites and vapor nucleation inside
very small channels, by Zhang et al. [41] and Brereton et al.
[42].

Temperature and Pressure Fluctuations
Microchannel ﬂow boiling studies have demonstrated a decrease in heat transfer coefﬁcient with increasing quality, often
accompanied by ﬂuctuating wall temperatures—e.g., Lin et al.
[28], Yan and Lin [43], Wen et al. [44], and Huo et al. [32].
These have been attributed to transient dry-out, particularly at
low mass ﬂux, and relatively high heat ﬂux. Kenning et al. [45]
suggested that there are two different mechanisms of dry-out
around individual bubbles in microchannels. These are dry-out
as a result of depletion of the ﬁlm thickness below a certain
minimum by complete evaporation of the liquid ﬁlm beneath
the conﬁned bubble and dry-out due to surface-tension-driven
“capillary roll-up” on partially wetted surfaces with ﬁnite contact angles. Experimental studies also indicated ﬂuctuations in
pressure and wall temperature. Yan and Kenning [46] investigated water boiling at atmospheric pressure in a 2 × 1 mm
channel. They showed that the pressure ﬂuctuations were caused
by the acceleration of liquid slugs by expanding conﬁned bubbles, conﬁrming a model of Kew and Cornwell [47], and that
the corresponding ﬂuctuations in saturation temperature were of
magnitude similar to the mean superheat causing evaporation,
so they could not be neglected.

Effect of Decreasing Diameter
There are a limited number of experiments that have tested a
wide range of tube diameter to investigate the heat transfer trend
with channel size. Studies that have considered the effect of diameter are reviewed brieﬂy here. Yan and Lin [43] conducted
experiments with R134a using a single tube of internal diameter 2.0 mm and heated length 100 mm. They claimed that the
evaporation heat transfer coefﬁcient increased by 30% to 80%
compared with conventional diameter tubes. Oh et al. [24] experimentally investigated the evaporation heat transfer for three

different copper tubes of diameter 0.75, 1.0, and 2.0 mm using
R134a. For vapor quality less than 0.6, they found the heat transfer coefﬁcient for the 1.0 mm tube to be higher than that of the
2.0 mm tube by approximately 45%. However, decreasing the
tube diameter shifted to a lower quality the point at which the
heat transfer coefﬁcient started to decrease axially, presumably
due to dry-out. Owhaib et al. [48] studied experimentally evaporative heat transfer using R134a in vertical circular tubes of
internal diameter 1.7, 1.22, and 0.83 mm, and a uniform heated
length of 220 mm. Other parameter ranges are: mass ﬂux 50–
400 kg/m2 -s, heat ﬂux 3–34 kW/m2 , and pressure 6.5–8.6 bar.
They concluded that the heat transfer coefﬁcient increased with
decreasing tube diameter.
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T. G. KARAYIANNIS ET AL.

In general, experimental results indicate an increase in the
heat transfer coefﬁcient as the diameter decreases. However,
some contradictory results are also available. For example,
Kuwahara et al. [49] experimentally studied the ﬂow boiling
heat transfer characteristic and ﬂow pattern inside 0.84 and 2.0mm diameter tubes using R134a and found no difference in the
heat transfer characteristics between the two tubes. Baird et al.
[50] conducted boiling experiments on tubes of 0.92 and 1.95
mm diameter and found no signiﬁcant effect of diameter on the
heat transfer coefﬁcient. Khodabandeh [51] studied boiling in
a two-phase thermosyphon loop with iso-butene as a working
ﬂuid with tubes ranging from 1.1 to 6 mm in diameter. He also
concluded that the effect of diameter was small and not clear.

In the work of Saitoh et al. described earlier, there was no obvious effect of diameter on heat transfer coefﬁcient or it was not
straightforward to deduce the inﬂuence.
A theoretical three-zone model for predicting the local dynamic and local time-averaged heat transfer coefﬁcient was presented by Thome et al. [52] and Dupont et al. [53]. The model is
based on convective heat transfer in the conﬁned bubble regime
without a contribution from nucleate boiling. The model predictions indicate that the heat transfer coefﬁcient increases with
diameter for quality greater than 0.18, while it decreases with
diameter for quality less than 0.04. Dupont and Thome [54]
compared the model results with the experiments of Owhaib
et al. [48]. The model did not predict the trend of increasing
heat transfer coefﬁcient with decreasing diameter. Instead an
opposite prediction was observed in the quality range covered.
Dupont and Thome [54] noted the lack of adequate experimental data covering a wide range of tube diameter for boiling heat
transfer. The model predictions were also compared with experimental data for R134a and tubes of 2.01 and 4.26 mm in
diameter by Shiferaw et al. [55]; they reported that the model
predicts that the diameter has an opposite effect on the heat
transfer coefﬁcient compared to the measured data.
The preceding brief overview indicates that a lot of work
is still necessary to elucidate the effect of diameter on the rate
and mechanism of heat transfer, including the possible diameter
thresholds for distinguishing macro, small and microscale characteristics. Although more than two tubes were used in some
of the past studies, it was not possible to identify the inﬂuence
of diameter because different conditions were used for different
diameter tubes. Therefore the experimental facility described in
the next section was used to determine the heat transfer coefﬁcients for R134a in ﬁve tubes of different diameter for similar
wide ranges of heat and mass ﬂuxes and pressure, combined
with ﬂow visualization at the exit from the test section.

EXPERIMENTAL FACILITY AND PROCEDURE
The experimental facility consists of three main systems,
which are the R134a main circuit, data acquisition and control,

and the R22 cooling system. The main facility, which is shown
in Figure 3, was designed to allow testing of different ﬂuids and
heat transfer engineering

Figure 3 Schematic diagram of the experimental system.

a wide range of ﬂow conditions. Details of the experimental system were given in Huo et al. [32]. The test sections were made
of stainless-steel cold-drawn tubes. The dimensions of the ﬁve
test tubes are given in Table 1. They were heated by the direct
passage of alternating electric current. The outer wall temperatures for the 4.26 mm to 1.1 mm tubes were measured using
15 K-type thermocouples that were spot-welded to the outside
of the tube at a uniform spacing. The ﬁrst and last thermocouple readings were not used in the analysis so as to avoid errors
due to thermal conduction to the electrodes. Ten thermocouples
were spot-welded on the 0.52 mm tube; the two at each end
were located sufﬁciently far from the electrodes to be used in
the data analysis. The pressures and temperatures at the inlet
and outlet were measured using pressure transducers and T-type
thermocouples. A differential pressure transducer was installed
across the test section to provide the pressure drop measurement. At the exit from the heating section, a borosilicate glass
tube for ﬂow pattern observation was located. A digital highspeed camera (Phantom V4 B/W, 512 × 512 pixels resolution,
1000 pictures/s with full resolution and maximum 32,000 pictures/s with reduced resolution, 10 ms exposure time) was used
to observe the ﬂow patterns.
A series of ﬂow boiling tests was then performed at different
mass ﬂux and heat ﬂux. During these tests, the inlet temperature
was controlled at a subcooling of 1–5 K by adjusting the capacity
of the chiller and heating power to the preheater. The ﬂow rate

Table 1 Range of experiment parameters
Parameters
Diameter

Wall thickness
Heated length
Roughness
Mass ﬂux
Heat ﬂux
Vapor quality
Pressure

vol. 31 no. 4 2010

Range
4.26, 2.88, 2.01, 1.10, and 0.52 mm
0.245, 0.15, 0.19, 0.247, and 0.15 mm
500, 300, 211, 150, and 100 mm
1.75, 1.54, 1.82, 1.28, and 1.15 µm
100–700 kg/m2 -s
1.6–150 kW/m2
0–0.9
6, 8, 10, 12, and 14 bar

T. G. KARAYIANNIS ET AL.

where, hl and hv are the speciﬁc enthalpy of saturated liquid
and vapor, respectively.

Table 2 Measurement uncertainty
Parameter

Uncertainty

Temperature
Pressure
Differential pressure drop
Mass ﬂux
Heat ﬂux
Heat transfer coefﬁcient

0.16 K
0.15–0.27%
0.27–0.30%
0.44%
0.5–1.5%
6–12.5%

263

SINGLE-PHASE RESULTS

was set to the required value and the heat ﬂux was increased in
small steps until the exit quality reached about 90%. The data
were recorded after the system was steady at each heat ﬂux,
which normally took about 15 min but sometimes longer. Each
recording was the average of 20 measurements. The next test
was then performed at a different ﬂow rate. All the instruments
used were carefully calibrated. Tables 1 and 2 summarize the
range and uncertainties of the important parameters.

Single-phase pressure drop and heat transfer tests were conducted for the largest diameter tube before commencing the
boiling experiments. These were performed to determine the

heat loss coefﬁcient and for the purpose of validating the experimental technique, i.e., data acquisition, calibration procedure,
and overall instrumentation, by comparing with the well-known
single-phase pressure drop and heat transfer correlations. The
results of one of the comparisons are presented in Figure 4. The
single-phase friction factor results in Figure 4a agree well with
the Blasius [56] correlation, i.e., within the uncertainty of the
experiment. Also, the single-phase Nusselt number Nu results
in Figure 4b agree very well with Dittus and Boelter [57] and

DATA REDUCTION
The local heat transfer coefﬁcient α(z) at each thermocouple
position was calculated using local values of the inside wall
temperature and the saturation temperature and is given by:
α(z) =

q
(Twi )z − (Ts )z

(3)

where q is the inner wall heat ﬂux to the ﬂuid determined from
the electric power supply to the test section and the heat loss.
Twi is the local inner wall temperature, which can be determined
using the internal heat generation and radial heat conduction
across the tube wall as given by:
Twi = Two −

q · di
4k

(di /do )2 − 2 ln(di /do ) − 1
1 − (di /do )2

(4)

Ts is the local saturation temperature, deduced from the local
ﬂuid pressure assuming a linear pressure drop across the test
section. The local speciﬁc enthalpy, hi , at each thermocouple
position was determined from the energy balance in each heated
section considering the losses:
hi = hi−1 +

Li
(Q −
˙
mL

Q)

(5)

where the heat transfer (Q) is the total electric heat input, which
is equal to the product of the voltage and the current applied directly to the test section. ( Q) is the heat loss determined using
the loss coefﬁcient obtained from single-phase test before each
series of boiling tests. Therefore, the local vapor quality can be
calculated from the local speciﬁc enthalpy at each thermocouple
position and is given as:
xi =

hi − hl

h v − hl

(6)
heat transfer engineering

Figure 4 Single-phase results for d = 4.26 mm at 7.5 bar: (a) friction factor
vs. Re, (b) Nusselt number vs. Re.

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264

T. G. KARAYIANNIS ET AL.

Petukhov [58] correlation—again, below the uncertainty limit.
The preceding results veriﬁed the overall accuracy of the experimental system. Experimental accuracy becomes an increasing
difﬁcult challenge as the size of the passages decreases and either laminar or turbulent ﬂow may exist, depending on the mass
ﬂow rate. Therefore, additional single-phase experiments were
performed with the 0.52 mm tube to assess the ability of the
test rig to produce accurate results at this small diameter. The
comparisons of the experimental results with past results and
known correlations were presented in Shiferaw et al. [59]. The
results agreed fairly well with the modiﬁed Gnielinski [60] and
Adams et al. [61] for the turbulent regime and Choi et al. [62]
in the laminar regime. The reproducibility of the boiling tests
was also veriﬁed. The test results (4.26–1.1 mm tubes) were
mostly within the range of uncertainty of the data; see Shiferaw
et al. [63] for the 1.1 mm tube. The reproducibility of the
0.52 mm tube tests was acceptable in the lower range of heat ﬂux,

had differences in the intermediate range, and was acceptable
again at high heat ﬂuxes [64]. This could be due to the sparse
and/or unstable nucleation sites at this small size and will be
examined further. The preceding set of experiments conﬁrmed
the adequate accuracy and validity of the present results.

EXPERIMENTAL RESULTS AND DISCUSSION
Flow Pattern Results
Figure 5a and b, presents the ﬂow patterns observed during
the boiling test at a mass ﬂux of 400 kg/m2 -s and pressure
8 bar for the 0.52 mm tube and should be compared with the
results of Chen et al. [9], obtained with the same test facility and
procedure depicted in Figure 1. These ﬂow patterns were taken
simultaneously with the heat transfer tests presented hereinafter

Figure 5 (a) Flow patterns in 0.52 mm tube at 400 kg/m2 s and 8 bar; (b)
sequence of ﬂow patterns showing coalescence.

heat transfer engineering

at each value of heat ﬂux. They represent the more frequently
observed ﬂow pattern for the particular heat ﬂux. However,
more than one type of ﬂow pattern occurred intermittently in
some cases. Image 1 shows bubbly ﬂow. Conﬁned bubble ﬂow
(images 2 and 3) was observed at low heat ﬂux or exit quality. As
the heat ﬂux increased, the bubbles grew in length and became
elongated. Further increase in heat ﬂux resulted in the liquid
slug between the bubbles being “pushed” onto the downstream
bubble, creating coalescence of the bubbles and a wavy ﬁlm.
A similar phenomenon was observed by Revellin et al. [65].

Figure 5b shows a sequence of how three relatively short bubbles
coalesce in the adiabatic viewing section to form an elongated
bubble, leaving the liquid ﬁlm interface wavy. Note that these
observations were carried out at the exit of the test section and
coalescence may be different in the heated section. As shown
again in Figure 5a, when increasing the heat ﬂux even further,
a type of wavy ﬁlm ﬂow, similar in appearance to what was
described earlier as liquid ring ﬂow (Serizawa et al. [10]), is
obtained for a relatively wide range of quality (images 4–6). In
this case, the ﬁlm interface is highly nonuniform and can lead
to a transition to annular ﬂow (image 7), since further increase
in heat ﬂux reduces the wave irregularity and distributes the
waves almost uniformly: annular ﬂow (images 8–10). At high
heat ﬂux, the annular ﬂow patterns have small-scale roughness
of very short amplitude and wavelength.
Overall, the ﬂow patterns observed in the smaller tube of
internal diameter 0.52 mm were different from those observed
in the larger tubes by Chen et al. [9]. As mentioned earlier,
these differences include the absence of dispersed ﬂow and the
appearance of a transitional wavy ﬁlm ﬂow. In this tube, liquid
lump ﬂow (see Serizawa et al. [10]) was not observed.

Heat Transfer Results
Typical experimental data for the ﬁve tubes are plotted as
graphs of heat transfer coefﬁcient vs. quality, the presentation
conventionally used for large tubes. This implies that heat transfer depends only on local ﬂow conditions and not on how the
ﬂow is developed, so that the convective component depends
on the local ﬂow pattern. The relationship between ﬂow pattern
observations in an adiabatic section at the exit from the tube and
the ﬂow pattern within the heated section at the same quality

may require examination for the particular conditions in small
tubes, in which the growth of an individual bubble may inﬂuence
a considerable length of the tube.
Data at a pressure of 8 bar and a mass ﬂux of 400 kg/m2 s
in the tubes with diameters 4.26–0.52 mm are plotted in Figure
6a–e. As seen in, for example, Figure 6a for the 4.26 mm tube,
at a quality x < 0.5 approximately and moderate heat ﬂux, the
heat transfer coefﬁcient is constant within ±10% at a value that
increases with heat ﬂux and pressure, but that is independent of
quality. Huo et al. [32] and Shiferaw et al. [55] reported similar
trends at 8 bar and a mass ﬂux of 300 kg/m2 -s in the 4.26 and
2.01 mm tubes. Within this range, the local variations appear to
vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

265

Figure 6 Local heat transfer coefﬁcient as a function of vapor quality at mass ﬂux 400 kg/m2 -s and pressure 8 bar: (a) 4.26 mm; (b) 2.88 mm; (c) 2.01 mm; (d)
1.10 mm; (e) 0.52 mm.

follow a pattern associated with the axial positions of the measuring stations. As the variations do not appear in single-phase
ﬂow experiments, they are not associated with individual thermocouples or wall roughness that would affect the liquid ﬂow.
heat transfer engineering

They may indicate variations in wall characteristics that affect
bubble nucleation or the stability of thin liquid ﬁlms round conﬁned bubbles. At higher quality and/or heat ﬂux, these patterns
change to a general tendency for the heat transfer coefﬁcient
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266

T. G. KARAYIANNIS ET AL.

to decrease with increasing quality and to converge on a single
line that is independent of heat ﬂux. This trend cannot be fully
conﬁrmed in these experiments with a ﬁxed heated length for a
given diameter of tube, since high quality cannot be achieved at
low heat ﬂux. However, one can also observe that the quality at
which the heat transfer coefﬁcient becomes independent of heat
ﬂux and decreases with quality moves to lower values of quality
as the diameter is reduced (e.g., at approximately x = 0.5 for
d = 4.26 mm and x = 0.3 for d = 2.01 mm).
At very high heat ﬂux, the heat transfer coefﬁcient may decrease with heat ﬂux. The effect is particularly marked in the
2.01 mm tube, Figure 6c for q = 95–134 kW/m2 . The heat ﬂux
and quality at which this occurs both decrease with decreasing
tube diameter. Shiferaw et al. [55] and Huo et al. [32] reported
that the tube wall temperature was highly unstable in this particular region, which could indicate the occurrence of partial
(intermittent) dry-out with a long time scale. Lin et al. [28] and
Sumith et al. [29] observed wall temperature ﬂuctuations that
increased as the heat ﬂux increased. This was assumed to be
related to time varying local heat transfer coefﬁcient and local
pressure; see Lin et al. [28] and Wen et al. [44].
The behavior in the 0.52 mm tube at the same pressure and
mass ﬂux is signiﬁcantly different, as in Figure 6e. For this
tube, the liquid-only Reynolds number is 1100, which should
correspond to laminar ﬂow at the inlet, unlike the liquid-only Re
numbers in the 4.26, 2.88, 2.01, and 1.1 mm tubes which were

9500, 6400, 4500, and 2500, respectively. There is a different
dependence of the heat transfer coefﬁcient on heat ﬂux and
vapor quality below and above a heat ﬂux of 17.9 kW/m2 . This
heat ﬂux threshold coincides with the appearance of the wavy
ﬁlm ﬂow—see image 4 in Figure 5a—and the disappearance
of the small superheat that is recorded by the thermocouple in
the exit ﬂow. At the low heat ﬂuxes, the heat transfer coefﬁcient
does not depend on heat ﬂux and decreases slightly with quality.
However, it must be noted that the data here are limited to x <
0.15. At these low heat ﬂux values a longer tube would be
required to reach high exit quality. There is an abrupt increase
in the heat transfer coefﬁcient and a change in its trend with
quality and heat ﬂux at heat ﬂuxes of 17.9 kW/m2 and above. At
these heat ﬂuxes, the heat transfer coefﬁcient initially increases
rapidly with quality, as in Figure 6e. The data points for all
heat ﬂuxes converge on approximately the same line as far as
the third thermocouple in zone I. The initial variations may be
inﬂuenced by the small differences in the low inlet subcooling.
In zone II, between the third and fourth thermocouples, the
heat transfer coefﬁcient levels off at a maximum value that
depends on the heat ﬂux. This is followed by a large reduction
in heat transfer coefﬁcient in zone III between the fourth and
ﬁfth thermocouples. After that, the data fall on another line
of increasing heat transfer coefﬁcient that, within experimental
error, is almost independent of heat ﬂux in zone IV. At the
highest heat ﬂux only, there is a large fall in the heat transfer
coefﬁcient at the last measuring point at a quality x = 0.71. This
is not reproduced in other runs at nearly the same conditions,
so it may indicate that the system is on the threshold of the
heat transfer engineering

Figure 7 Heat transfer coefﬁcient vs. axial distance at mass ﬂux 400 kg/m2 -s
and pressure 8 bar for 0.52 mm tube. Heat ﬂux values as in Figure 6e.

transient dry-out that is thought to cause the reduction in heat
transfer coefﬁcient with increasing quality in the larger tubes.
When plotted against z/L, Figure 7, the pattern of variation of
the heat transfer coefﬁcient appears to be related to the axial
positions of the measuring stations more strongly than for the
larger tubes.
Figure 8 is a plot similar to Figure 6e for the same 0.52
mm tube at a lower mass ﬂux of 300 kg/m2 -s (liquid-only Re
number 720) and a lower pressure of 6 bar, reported in Shiferaw
et al. [59]. It conﬁrms that the heat transfer characteristics of
this tube are indeed different from the larger tubes. There are
again two groups of data, this time separated by a threshold heat
ﬂux of 12.5–14.8 kW/m2 , which also appears to coincide with
the change of slug or conﬁned ﬂow to the wavy ﬁlm type ﬂow
mentioned earlier at the exit from the heated section. At the
low heat ﬂuxes, the heat transfer coefﬁcient is approximately
independent of heat ﬂux although, in contrast to Figure 6e,
it initially falls signiﬁcantly with quality and then exhibits a
weak increase. At values higher than 14.8 kW/m2 , the α versus
x plot follows the same general pattern of axial development
through zones I–IV seen in Figure 6e, except that the values of
axially increasing heat transfer coefﬁcient in zone I depend on

Figure 8 Heat transfer coefﬁcient vs. quality at mass ﬂux 300 kg/m2 -s, pressure 6 bar in the 0.52 mm tube.

vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

Figure 9 Heat transfer coefﬁcient vs. axial distance at mass ﬂux 300 kg/m2 -s,
pressure 6 bar in 0.52 mm tube. (The marker x = 0 indicates the position where
saturation is achieved for q = 1.6 kW/m2 . For the rest, this happens at/before
the ﬁrst thermocouple position.) The symbols and colors are the same as for
Figure 8.

heat ﬂux and the inﬂuence of heat ﬂux extends into zone IV,
where the heat transfer coefﬁcient again increases axially. The
test section is not long enough at low heat ﬂuxes to show for
certain whether the data converge on a line independent of heat
ﬂux at high quality. For heat ﬂuxes above the threshold value,
the pattern of variations in α again appears to depend on the
fraction of heated length z/L, as in Figure 9, but the pattern is
not exactly the same as in Figure 7. The maximum heat transfer
coefﬁcient now occurs at thermocouple 3 instead of 4. The
subsequent reduction in zone III is less abrupt, still continuing
to thermocouple 5. There are also differences in the detail of the
pattern in zone IV. If the pattern depends on the effect of local
roughness on local nucleation of bubbles, the effect appears to
be moderated by the changes in ﬂow conditions and system
pressure.
Yet another way of plotting the same data in Figures 8 and
9 is as boiling curves at measuring points 3–8, as in Figure 10;
see Shiferaw et al. [59]. The plots look like pool boiling curves
for increasing heat ﬂux in a system with nucleation hysteresis
at 12.5 kW/m2 . If the nucleation characteristics vary axially, it

Figure 10 Wall superheat vs. heat ﬂux at each measuring station, D = 0.52
mm, mass ﬂux 300 kg/m2 -s, pressure 6 bar.

heat transfer engineering

267

is unlikely that the same threshold would apply at all stations.
Alternatively, nucleation may occur at upstream sites, and downstream positions are inﬂuenced by the growth of individual conﬁned bubbles that may cover a long axial length. It is impossible
to observe local nucleation in a metal tube and the observations
of ﬂow patterns are restricted to the tube exit. Conﬁned bubble
ﬂow with smooth liquid ﬁlms round long bubbles, as assumed
in the Thome et al. [52] convective model, is observed with low
heat transfer coefﬁcients just below the threshold heat ﬂux, as
in Figure 5a, image 3, at 400 kg/m2 -s, and wavy ﬁlm ﬂow just
above the threshold. The large increase in heat transfer coefﬁcient above the threshold occurs throughout the length of the
tube and particularly near the inlet in zones I and II, so it cannot
be caused by a gradual progression from the exit toward the
inlet of a ﬂow regime transition at a particular quality. Further
investigation is required of whether nucleation is triggered at a
single site, which could exert downstream inﬂuence through the
bubble frequency that is an important parameter in the Thome
et al. model for convective evaporation, or at more widely distributed sites. The availability of sites may become subject to
large statistical variability as the surface area decreases with
decreasing tube diameter, as in Zhang et al. [41] and Brereton
et al. [42].
A further special feature of the 0.52 mm tube is the decrease
in the heat transfer coefﬁcient in zone III, commencing at a
quality that increases with increasing heat ﬂux, followed by

constant or increasing heat transfer coefﬁcient in zone IV, with
a fall very close to the tube exit in some runs. It is therefore likely
to have a different mechanism from the axial decrease in heat
transfer coefﬁcient observed in the larger tubes of this study,
which commences at a quality that decreases with increasing
heat ﬂux and is then maintained to the end of the tube. Because
of its association with a particular axial length of the tube,
the heat transfer in zone III of the 0.52 mm tube may depend
on interactions between nucleation sites and the changing ﬂow
regime. From the observations of the exit ﬂow, as in Figure
5a, the ﬂow in zone IV is annular, with intensive disturbances
to the liquid ﬁlm that decrease in scale with increasing heat
ﬂux and quality. It is not possible to determine directly whether
nucleation occurs in the ﬁlm.
Conventionally, the relative importance of nucleate boiling
and convective evaporation are deduced from the dependence of
the heat transfer coefﬁcient on heat ﬂux or mass ﬂux and quality.
Thome et al. [52] showed that this could be misleading in small
channels. Shiferaw et al. [55] found that the Thome convective
model, which includes cyclic dry-out of the thin ﬁlms round conﬁned bubbles, provided satisfactory estimates for heat transfer
in the 4.26 and 2.01 mm tubes of this study under conditions apparently dominated by nucleate boiling, possibly because both
mechanisms involve the cyclic creation and evaporation to dryness of thin liquid ﬁlms. It must be noted from the ﬂow visualization by Chen et al. [9], Figure 2, and for the 0.52 mm
tube in this article, that the regime for which the Thome model
is valid (thin, undisturbed ﬁlms around discrete conﬁned bubbles) is restricted to low qualities. Convective models for high
vol. 31 no. 4 2010

268

Figure 11

low x.

T. G. KARAYIANNIS ET AL.

Effect of diameter on heat transfer coefﬁcient at 400 kg/m2 , 8 bar,

quality will have to account for the disturbances to the liquid
ﬁlm.
The experimental heat transfer coefﬁcients in the 4.26–1.10
mm tubes all exhibit at low quality “apparently nucleate boiling” characteristics, being nearly independent of quality and
mass ﬂux, if the region of heat transfer coefﬁcient decreasing
with quality, indicative of transient dry-out, is excluded. For the
0.52 mm tube, the heat transfer coefﬁcient is nearly independent
of quality and mass ﬂux in zone II. All these data are shown
in Figure 11 on a plot of heat transfer coefﬁcient vs. heat ﬂux
for a mass ﬂux of 400 kg/m2 s at 8 bar pressure. The data were
ﬁtted by a power-law equation of the form α = Cqn , as is conventional for nucleate boiling. As mentioned earlier, this could
be due to the fact that both mechanisms (pool and transient
ﬁlm evaporation) involve the cyclic creation and evaporation of
thin liquid ﬁlms. The exponent n is kept constant at 0.62 and
the values of the constant C for the 4.26, 2.88, 2.01, 1.10, and
0.52 mm diameter tubes are 14.3, 14.5, 16.6, 19.5, and 33.7,
respectively. The heat transfer coefﬁcients for the 4.26 and
2.88 mm diameter tubes are almost the same; the increases for
the 2.01, 1.10, and 0.52 mm tubes are 15, 35, and 134%, respectively. This last ﬁgure exaggerates the beneﬁt from decreasing
diameter, because it is based on the peak values in zone I and
the improvement averaged over zones I plus II is about 90%.
This approach may be useful for the design of cooling systems
for minimum temperature difference, achieved by operating at
low exit quality to avoid dry-out.

The dependence of the heat transfer coefﬁcient on mass
ﬂux and local quality is shown in Figure 12 for a heat
ﬂux of 54 (4.26 to 1.1 mm tubes) and 58 kW/m2 (0.52mm tube) and 8 bar pressure. At low qualities, the approximately constant values of the heat transfer coefﬁcient
are almost independent of mass ﬂux within the experimental uncertainty for the four larger diameter tubes. For the
4.26 mm tube, after x = 0.15, the heat transfer coefﬁcient decreases slightly with mass ﬂux, which could be related to an
inﬂuence on ﬁlm thickness. However, this is not repeated in the
2.88 to 1.1 mm tubes. As also noted earlier, further experiments
heat transfer engineering

are required to resolve the issue, using longer heated lengths to
achieve larger exit qualities, subject to any limitations imposed
by pressure drop. The results for the smallest diameter tube in
Figure 12e are clearly different. There is a signiﬁcant effect of
mass ﬂux in zone IV (increasing trend of heat transfer coefﬁcient with quality). In this region, the heat transfer coefﬁcient
increases with increasing mass ﬂux and, as seen in Figure 6e,
there is no obvious effect of heat ﬂux especially at high quality.
This, with the observations at the visualization section, apparently supports the previous speculation that convective evaporation of the annular ﬂow dominates the heat transfer mechanism
at high quality (Lin et al. [28], Sumith et al. [29], and Saitoh et
al. [30]). However, when plotted against axial distance z/L in
Figure 13, the data for the 0.52 mm tube collapse onto a single line independent of mass ﬂux but with large axial variations,
suggesting that time-averaged quality is not the controlling variable. By contrast, the data for the 1.1 mm tube follow a line of
nearly constant α at high mass ﬂux, with lines of decreasing α
branching off at points that move toward the tube inlet as the
mass ﬂux is reduced. It appears that quality is the relevant variable for the assumed process of transient dry-out in the larger
tubes of this study.
The inﬂuence of system pressure is illustrated in Figure 14
by plots of heat transfer coefﬁcient vs. quality for all the tubes
at the same mass ﬂux of 400 kg/m2 -s and heat ﬂux of 54 kW/m2
(4.26, 2.88, 2.01, and 1.10 mm tubes) and 58 kW/m2 (0.52
mm tube). (These are almost the same as plots of α vs. z/L.)

For quality x < 0.3, the heat transfer coefﬁcient increases with
system pressure for the 4.26 to 1.10 mm tubes. The effects of
pressure at higher qualities at various values of heat ﬂux and
mass ﬂux were reported in Shiferaw et al. [55]. For the 4.26
mm diameter tube, the effect of pressure was less signiﬁcant
at higher qualities (x > 0.5), while for the 2.01 mm diameter
tube there was a rather uniform increase in the coefﬁcient with
pressure throughout the experimental range of quality (x < 0.7).
Again, the 0.52 mm tube behaves differently, as in Figure
14e. Increasing pressure causes a much larger increase in the
heat transfer coefﬁcient at small x in zones I and II, compared to
zone IV at higher x, and the decrease in heat transfer coefﬁcient
in zone III becomes sharper. There is a drop in heat transfer
coefﬁcient at the last measuring point for 8 and 10 bar pressure,
which might indicate the onset of thin ﬁlm dry-out.

DISCUSSION
This article is based on ﬂow visualization studies and heat
transfer measurements obtained over a period of 6 years for ﬁve
tubes of different diameters. Some of the data are new and some
have been published previously. When some data sets were extended in range, the heat transfer coefﬁcients were found to be
reproducible within ±5%, even after intervals of 3 years. The
data for the 4.26 to 1.1 mm tubes have some features that are
conventionally and appropriately presented as functions of local
quality, combined with a weak dependence on the axial position
vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

269

Figure 12 Effect of mass ﬂux on heat transfer coefﬁcient versus quality at heat ﬂux (q = 54 and 58 kW/m2 ) and pressure (P = 8 bar): (a) 4.26 mm; (b) 2.88
mm; (c) 2.01 mm; (d) 1.1 mm; (e) 0.52 mm.

within a particular test section. This axial dependence was much
stronger in the data for the 0.52 mm tube. These axial patterns
are not present in single-phase tests, so they are consequences
of boiling. Very recent tests on this tube have shown that the
patterns tend to be stable during a series of tests on a particular
day but there may be a different pattern on other days. In the
parametric studies of heat ﬂux, mass ﬂux, and pressure reported
in this article, examples have been chosen from tests performed
at similar times. Similar variability on different days was observed in the “apparently nucleate” regime during ﬂow boiling
heat transfer engineering

of water in a large (9.6 mm) tube but not in the “apparently
convective” regime of Kenning and Cooper [16]. In that study,
polishing the tube surface also modiﬁed the nucleate but not the
convective boiling regime. Surface roughness has a large inﬂuence on bubble nucleation in pool boiling, so axial variations in
surface roughness may inﬂuence local nucleation. The inﬂuence
of surface conditions on boiling in small metal tubes has as yet
received little attention. Surface roughness may also affect a
parameter in the convective boiling model of Thome et al. [52]
for microchannels, namely, the minimum stable thickness of the
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270

T. G. KARAYIANNIS ET AL.

Figure 13 Effect of mass ﬂux on the heat transfer coefﬁcient versus axial
distance at 8 bar: (a) 0.52 mm tube at 58 kW/m2 and (b) 1.1 mm tube at 54
kW/m2 .

evaporating liquid ﬁlm round conﬁned bubbles. Shiferaw et al.
[55] showed that the predictions of the Thome et al. model were
improved if the experimental measurements of roughness were
used instead of the recommended ﬁlm thickness. The surface
roughness of samples from the four larger tubes used in this
study was measured after sectioning by scanning in an axial
direction with a conventional contact stylus; values are given in
Table 1. The surface roughness of the 0.52 mm tube was obtained from a three-dimensional (3-D) sample, captured using a
high-resolution non-contact probe.
In the experiments described here, and in those performed
earlier by Chen et al. [9], ﬂow patterns were observed at the
exit of the test section. Observations within a tube are possible
for transparent tubes with transparent thin-ﬁlm heaters, as in the
experiments of Owhaib et al. [48], but the nucleation characteristics are different and it is difﬁcult to obtain simultaneous
accurate measurements of the wall temperature. The ﬂow patterns observed at the exit from the 0.52 mm tube were certainly
different from those observed earlier in the relatively larger diameter tubes (4.26–1.1 mm) by Chen et al. [9]. These differences
include the absence of dispersed bubble ﬂow and the appearance of a transitional wavy ﬁlm ﬂow. Thus, there were further
heat transfer engineering

differences between the ﬂow patterns leaving the 2.88 and
4.26 mm diameter tubes and those from the 2.01 and 1.1 mm
tubes, which exhibited conﬁned ﬂow, slimmer vapor slugs, thinner liquid ﬁlms, and smoother vapor–liquid interfaces. These
differences coincided with the progressive transition to higher
heat transfer coefﬁcients in the 2.01 and 1.10 mm tubes. Using

the conﬁnement number (Cornwell and Kew [4]), the deviation
from large-tube characteristics should be observed at diameters of 1.4 to 1.7 mm at 6–14 bar pressure for R134a, which is
roughly in agreement with the present heat transfer results and
ﬂow visualization observations. “Small-tube characteristics” in
1.1 mm tubes were reported in the previous studies of Damianides and Westwater [13] and Mishima and Hibiki [7].
Flow maps such as Figure 2, based on observations at the
exit from the 4.26 to 1.10 mm tubes, show that, at the low
mass ﬂuxes covered in the present heat transfer tests, the transition to annular ﬂow shifts to higher qualities approaching
x ≈ 0.5. While the information on ﬂow regimes cannot be
transferred with certainty to upstream locations, it is likely
that slug/churn ﬂow is the typical ﬂow pattern in the region
of near-uniform high heat transfer coefﬁcient dependent primarily on heat ﬂux. This could be at least one of the reasons for the increase in the heat transfer coefﬁcient with a
reduction in the channel size. The relative importance of nucleate and convective boiling in this region is still unclear.
However, there are claims that suggest that, for small passages, the same behavior, i.e., uniform heat transfer coefﬁcient dependent on heat ﬂux and independent of quality, can
be explained if transient evaporation of the thin liquid ﬁlm
surrounding elongated bubbles, without nucleate boiling contribution, is the dominant heat transfer mechanism (Thome et
al. [52]). One may argue that the variations in heat transfer
coefﬁcient with axial position, evident in Figure 6, especially
for the larger tubes, may indicate some dependence on nucleate boiling. Kenning and Yan [66] observed cyclic triggering
of nucleate boiling in smooth ﬁlms around conﬁned bubbles in
water associated with pressure ﬂuctuations. This needs further
investigation.
The heat transfer results of the smallest diameter tube (0.52
mm) demonstrated different characteristics than the rest of the
tubes, particularly at the high quality region. It is the only tube
for which the incoming liquid ﬂow is laminar, and this may
inﬂuence the initiation of conﬁned bubble (slug) ﬂow. Unlike
the larger tubes that were examined in this study, which exhibit
dry-out phenomena at high quality as the heat ﬂux increases
with a drop of the heat transfer coefﬁcient with quality, a monotonic increase in heat transfer coefﬁcient was observed near the

exit for the smallest diameter tube. This could be related to
laminar ﬂow and domination of surface tension force over momentum, providing more uniform liquid ﬁlm thickness along
the circumference, with less interfacial waves and disturbances,
which improves wetting of the wall (Shiferaw et al. [59]). In
addition, the dependence of the heat transfer coefﬁcient on axial
position is much stronger in the 0.52 mm tube, as in Figure
13, extending to high quality in the annular ﬂow regime. The
vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

271

Figure 14 Effect of pressure on heat transfer coefﬁcient vs. quality, G = 400 kg/m2 s, q = 54 and 58 kW/m2 : (a) 4.26 mm; (b) 2.88 mm; (c) 2.01 mm; (d) 1.1
mm; (e) 0.52 mm.

experiments in this tube are currently being repeated for the
complete range of variables and further conﬁrmation of these
characteristics.
These observations indicate additional changes as the size
diminishes further into microscales. In general, the complex dependence of the heat transfer rate on various parameters suggests
the difﬁculty of interpreting the heat transfer mechanisms using
heat transfer engineering

simple conventional terms and the challenge of heat transfer
modeling.
CONCLUSIONS
Flow boiling patterns and heat transfer results with R134a
and ﬁve tubes of diameter 4.26, 2.88, 2.01, 1.10, and 0.52 mm

vol. 31 no. 4 2010

272

T. G. KARAYIANNIS ET AL.

were presented in this article. It was anticipated that the wide
range of data at different diameters could be used to identify
the threshold(s) where the small or micro diameter effects become signiﬁcant. The major conclusions that can be drawn from
the current part of this long-term study are as follows:

1. In the 4.26 and 2.88 mm diameter tubes, the heat transfer
coefﬁcient increases with heat ﬂux and system pressure, but
does not change with vapor quality when the quality is less
than about 40% to 50%, for low heat ﬂux. The boundary
moves to 20–30% for the 2.01 and 1.10 mm diameter tubes.
The actual quality values depend also on the heat ﬂux. In this
region, there is no signiﬁcant difference in the magnitude of
the heat transfer coefﬁcient of the 4.26 and 2.88 mm tubes.
However, there is an increase of 15% and 35% when the tube
diameter is reduced to 2.01 and 1.10 mm, respectively.
2. The heat transfer coefﬁcient behavior of the tubes (4.26–
1.1 mm) at low quality could be interpreted as the evidence
that nucleate boiling is the dominant heat transfer mechanism. However, transient evaporation of the thin liquid ﬁlm
surrounding elongated bubbles, which is a dominant ﬂow
pattern in small passages, without a nucleate boiling contribution, may also result in similar heat transfer coefﬁcient
dependence and magnitude. For higher vapor qualities, the
heat transfer coefﬁcient becomes independent of heat ﬂux
and decreases with vapor quality. This could be caused by

partial (intermittent) dry-out in the convection-dominated
region. This leads to the design recommendation that exit
qualities be kept low (Zhang et al. [67, 68]).
3. Chen et al. [9] concluded that ﬂow patterns for the 4.26 and
2.88 mm diameter tubes exhibit ﬂow pattern characteristics
similar to those of “normal” diameter tubes, while “small
tube characteristics,” e.g., the appearance of conﬁned ﬂow,
were observed when the tube diameter was reduced to 2.01
mm and further to 1.10 mm. This is consistent with a criterion based on the ratio of surface tension and gravitational
forces. The change in behavior may be progressive, rather
than occurring at a sharp threshold.
4. The heat transfer data suggest that there is some deviation
from “normal” behavior even for the 4.26 mm tube, because
the expected increase in heat transfer coefﬁcient with increasing high quality was replaced by a decrease attributed
to intermittent dry-out. This may indicate that ﬁlm stability
in the heated zone depends on the ratio of surface tension to
other forces. This cannot be detected by ﬂow visualization at
the exit from the test section.
5. As the tube diameter decreased further down to 0.52 mm,
different ﬂow and heat transfer characteristics were observed, indicating a possible further change as the size diminished. These include: (a) The ﬂow patterns observed in the
0.52 mm tube are different, i.e., absence of dispersed bubble
ﬂow, and the appearance of a wavy ﬁlm type ﬂow that leads
into annular ﬂow. (b) The dependence of the heat transfer coefﬁcient on quality, heat ﬂux, and mass ﬂux changes sharply
heat transfer engineering

in character at a threshold value of heat ﬂux. In the low heat
ﬂux region, there is no signiﬁcant effect of heat ﬂux but the
heat transfer coefﬁcient decreases (at low mass ﬂux and pressure) or remains constant (at higher mass ﬂux and pressure),
then increases gradually with quality. At moderate and high
heat ﬂux, in the front part of the channel, the heat transfer

coefﬁcient increases with increasing heat ﬂux and also depends in a complex way on quality. It reaches a maximum at
an intermediate quality, which might be caused by transient
partial dry-out or dry patches in the conﬁned bubble regime.
At higher quality, toward the test section exit, the heat transfer
coefﬁcient gradually increases again with quality but there
is no clear effect of heat ﬂux. The heat transfer coefﬁcient
also increases with mass ﬂux in this region. According to the
conventional interpretation, this is evidence for a convective
boiling dominant heat transfer mechanism in annular ﬂow.
An alternative plotting of heat transfer coefﬁcient suggests
that it is more dependent on the surface conditions associated with particular axial positions than on quality. These
might inﬂuence bubble nucleation or the stability of thin liquid ﬁlms. The slender evidence as yet available may indicate
some variability in the activation of the small population of
nucleation sites available in a channel of small surface area.
The results of the 0.52 mm tube are currently being repeated.
The complexity of interpreting heat transfer characteristics and understanding the prevailing mechanisms and, consequently, the difﬁculty of developing generalized models are
veriﬁed by the work presented in this article. Phenomenological
models that are based on the local ﬂow structure may be developed for clearly speciﬁed ranges. Therefore, it is important
to identify the range of applicability of dominant ﬂow regimes.
Current results also indicate that much more research is needed
to understand the different characteristics associated with microtubes and channels.

NOMENCLATURE
Bo
E¨o
Co
d
G
g
h

k
L
m
Nu
P
Q
q
Re

Boiling number, q /G · hlv
E¨otv¨os number, g(ρl − ρg ) d 2 /σ
Conﬁnement number, [σ/g(ρl − ρv )]1/2 /d
diameter, m
mass ﬂux, kg/m2 s
gravitational acceleration, m/s2
enthalpy, J/kg
thermal conductivity (W/m-K)
length, m
mass ﬂow rate, kg/s
Nusselt number, α · d λ
pressure, Pa
heat, W
heat ﬂux, W/m2
Reynolds number, G · d/µ
vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

T

t
Ugs
Uls
We
x
z

temperature, K
time (s)
superﬁcial gas velocity, m/s
superﬁcila liquid velocity, m/s
Weber number, G2 · d ρl · σ
quality
axial distance, m

Greek Symbols
α
λ
µ
ρ
σ

heat transfer coefﬁcient, W/(m2 -K)
ﬁnite increment
thermal conductivity, W/m-K
dynamic viscosity kg/m s
density, kg/m3
surface tension, N/m

subscripts

h
i
l
lo
o
sp
tp
v
w
wi
wo
z
0

hydraulic
index, internal
liquid
liquid only
outer
single-phase
two-phase
vapor
wall
inner wall
outer wall
along tube axis
Initial

REFERENCES
[1] Mehendale, S. S., Jacobi, A. M., and Shah, R. K., Fluid Flow

and Heat Transfer at Micro- and Meso-Scales with Application to
Heat Exchanger Design, Applied Mechanics Reviews, vol. 53, no.
7, pp. 175–193, 2000.
[2] Kandlikar, S. G., and Grande, W. J., Evolution of Microchannel
Flow Passages—Thermohydraulic Performance and Fabrication
Technology, Heat Transfer Engineering, vol. 25, no. 1, pp. 3–17,
2003.
[3] Brauner, N., and Moalem-Maron, D., Identiﬁcation of the Range
of Small Diameter Conduits, Regarding Two-Phase Flow Pattern Transitions, International Communications in Heat and Mass
Transfer, vol. 19, pp. 29–39, 1992.
[4] Cornwell, P. A. K., and Kew, P. A., Boiling in Small Parallel
Channels, in Energy Efﬁciency in Process Technology, ed. P. A.
Pilavachi, Elsevier Applied Science, London, pp. 624–638, 1993.
[5] Thome, J. R., Boiling in Microchannels: A Review of Experiment
and Theory, International Journal of Heat and Fluid Flow, vol.
25, pp. 128–139, 2004.

heat transfer engineering

273

[6] Barnea, D., Luninski, Y., and Taitel, Y., Flow Pattern in Horizontal
and Vertical Two Phase Flow in Small Diameter Pipes, Canadian
Journal of Chemical Engineering, vol. 61, no. 5, pp. 617–620,
1983.
[7] Mishima, K., and Hibiki, T., Some Characteristics of Air-Water
Two-Phase Flow in Small Diameter Vertical Tubes, International Journal of Multiphase Flow, vol. 22, no. 4, pp. 703–712,
1996.
[8] Kew, P. A., and Cornwell, K., Correlations for the Prediction
of Boiling Heat Transfer in Small Diameter Channels, Applied Thermal Engineering, vol. 17, no. 8–10, pp. 705–715,

1997.
[9] Chen, L., Tian, Y. S., and Karayiannis, T. G., The Effect of Tube
Diameter on Vertical Two-Phase Flow Regimes in Small Tubes,
International Journal of Heat and Mass Transfer, vol. 49, pp.
4220–4230, 2006.
[10] Serizawa, A., Feng, Z., and Kawara, Z., Two Phase Flow in Microchannels, Experimental Thermal Fluid Sciences, vol. 26, pp.
703–714, 2002.
[11] Kawahara, A., Chung, P. M.-Y., and Kawaji, M., Investigation of
Two-Phase Flow Patterns, Void Fraction and Pressure Drop in a
Micro-Channel, International Journal of Multiphase Flow, vol.
28, pp. 1411–1435, 2002.
[12] Xiong, R., and Chung, J. N., An Experimental Study of the Size Effect on Adiabatic Gas-Liquid Two-Phase Flow Patterns and Void
Fraction in Microchannels, Physics of Fluids, vol. 19, 033301,
2007.
[13] Damianides, D. A., and Westwater, J. W., Two-Phase Flow Patterns in a Compact Heat Exchanger and in Small Tubes, Second
UK National Conference on Heat Transfer, vol. 11, Sessions 4A–
6C, pp. 1257–1268, 1988.
[14] Lin, S., Kew, P. A., and Cornwell, K., Two-Phase Flow Regimes
and Heat Transfer in Small Tubes and Channels, Heat Transfer
1998, Proceedings of 11th IHTC, vol. 2, August 23–28, Kyongju,
Korea, pp. 45–50, 1998.
[15] Revellin, R., and Thome, J. R., A New Type of Diabatic Flow
Pattern Map for Boiling Heat Transfer in Microchannels, Journal
of Micromechanics and Microengineering, vol. 17, pp. 788–796,
2007.
[16] Kenning, D. B. R., and Cooper, M. G., Saturated Flow Boiling of
Water in Vertical Tubes, International Journal of Heat and Mass
Transfer, vol. 32, pp. 445–458, 1989.
[17] Lazarek, G. M., and Black, S. H., Evaporative Heat Transfer,
Pressure Drop and Critical Heat Flux in a Small Vertical Tube

With R-113, International Journal of Heat and Mass Transfer,
vol. 25, no.7, pp. 945–960, 1982.
[18] Wambsganss, M. W., France, D. M., Jendraejczyk, J. A., and
Tran, T. N., Boiling Heat Transfer in a Horizontal SmallDiameter Tube, Journal of Heat Transfer, vol. 115, pp. 963–972,
1993.
[19] Tran, T. N., Wambsganss, M. W., and France, D. M., Small
Circular- and Rectangular-Channel Boiling With Two Refrigerants, International Journal of Multiphase Flow, vol. 22, no. 3, pp.
485–498, 1996.
[20] Bao, Z. Y., Fletcher, D. F., and Haynes, B. S., Flow Boiling Heat
Transfer of Freon R11 and HCFC123 in Narrow Passages, International Journal of Heat and Mass Transfer, vol. 43, pp. 3347–
3358, 2000.
[21] Yu, W., France, D. M., Wambsganss, M. W., and Hull, J. R., TwoPhase Pressure Drop, Boiling Heat Transfer, and Critical Heat

vol. 31 no. 4 2010

274

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

T. G. KARAYIANNIS ET AL.
Flux to Water in a Small Diameter Horizontal Tube, International
Journal of Multiphase Flow, vol. 28, pp. 927–941, 2002.
Fujita, Y., Yang, Y., and Nami, F., Flow Boiling Heat Transfer and
Pressure Drop in Uniformly Heated Small Tubes, in Proc. 12th
International Heat Transfer Conf., Grenoble, vol. 3, pp. 743–748,
2002.
Carey V. P., Tervo, P., and Shullenberger, K., Partial Dryout in
Enhanced Evaporator Tubes and Its Impact On Heat Transfer Performance, SAE Technical Paper 920551, 1992. Available online
at
Oh, H. K., Katsuta, M., and Shibata, K., Heat Transfer Characteristics of R134a in a Capillary Tube Heat Exchanger, in Proc. 11th
IHTC, vol. 6, pp. 131–136, 1998.

Lee, H. J., and Lee, S. Y., Heat Transfer Correlation for Boiling
Flows in Small Rectangular Horizontal Channels With Low Aspect Ratios, International Journal of Multiphase Flow, vol. 27,
pp. 2043–2062, 2001.
Qu, W., and Mudawar, I., Flow Boiling Heat Transfer in Two
Phase Microchannel Heat Sinks. I. Experimental Investigation
and Assessment of Correlation Methods, International Journal of
Heat and Mass Transfer, vol. 46, pp. 2755–2771, 2003.
Kuznetsov, V. V., and Shamirzaev, A. S., Two Phase Flow Pattern
and Flow Boiling Heat Transfer in Non-Circular Channel With
a Small Gap, Two-Phase Flow Modeling and Experimentation,
Pisa, Italy, vol. 1, pp. 249–253, 1999.
Lin, S., Kew, P. A., and Cornwell, K., Two-Phase Heat Transfer
to a Refrigerant in a 1 mm Diameter Tube, International Journal
of Refrigeration, vol. 24, pp. 51–56, 2001.
Sumith, B., Kaminaga, F., and Matsumura, K., Saturated Flow
Boiling of Water in a Vertical Small Diameter Tube, Experimental
Thermal Fluid Sciences, vol. 27, pp. 789–801, 2003.
Saitoh, S., Daiguji, H., and Hihara, E., Effect of Tube Diameter
on Boiling Heat Transfer of R134a in Horizontal Small Diameter
Tubes, International Journal of Heat and Mass Transfer, vol. 48,
pp. 4973–4984, 2005.
Owhaib, W., and Palm, B., Flow Boiling Heat Transfer in a Vertical Circular Microchannel Tube, Eurotherm Seminar, no. 72,
Valencia, Spain, 2003.
Huo, X., Tian, Y. S., and Karayiannis, T. G., R134a Flow Boiling Heat Transfer in Small Diameter Tubes, Advances in Compact Heat Exchangers, R. T. Edwards, Philadelphia, pp. 95–111,
2007.
D´ıaz, M. C., and Schmidt, J., Experimental investigation of transient boiling heat transfer in microchannels, Int. Journal of Heat
and Fluid Flow, vol. 28, pp. 95–102, 2007.
Xu, J., Shen, S., Gan, Y., Li, Y., Zhang, W., Su, Q., Transient
ﬂow pattern based microscale boiling heat transfer mechanisms,
Journal of Micromechanics and Microengineering, vol. 15, pp.

1344-1361, 2005.
Lie, Y. M., Su, F. Q., Lai, R.L., Lin, T. F., Experimental
Study of Evaporation Heat Transfer Characteristics of Refrigerants R-134a and R-407C in Horizontal Small Tubes, International Journal of Heat and Mass Transfer, vol. 49, pp. 207–218,
2006.
Agostini, B., and Thome, J. R., Comparison of an Extended
Database of Flow Boiling Heat Transfer Coefﬁcient in MultiMicrochannel Elements With the Three-Zone Model, in ECI International Conference on Heat Transfer and Fluid Flow in Microscale, Castelvecchio Pascoli, Italy, 2005.

heat transfer engineering

[37] Yen, T., Kasagi, N., and Suzuki, Y., Forced Convective Boiling
Heat Transfer in Microtubes at Low Mass and Heat Fluxes, International Journal of Multiphase Flow, vol. 29, pp. 1771–1792,
2003.
[38] Hapke, I., Boye, H., and Schmidt, J., Onset of Nucleate Boiling
in Minichannels, International Journal of Thermal Sciences, vol.
39, pp. 505–513, 2000.
[39] Peng, X. F., and Wang, B. X., Forced Convection and Flow Boiling Heat Transfer for Liquid Flowing Through Microchannels,
International Journal of Heat and Mass Transfer, vol. 26, pp.
3421–3427, 1993.
[40] Peng, X. F., Hu, H. Y., and Wang, B. X., Boiling Nucleation
During Liquid Flow in Microchannels, International Journal of
Heat and Mass Transfer, vol. 41, pp. 101–106, 1998.
[41] Zhang, L., Koo, J., Jiang, L., Goodson, K. E., Santiago, J. G.,
and Kenny, T. W., Study of Boiling Regimes and Transient Signal
Measurements in Microchannels, Proc. Transducers ’01, Munich,
Germany, pp. 1514–1517, 2001.
[42] Brereton, G. J., Crilly, R. J., and Spears, J. R., Nucleation in
Small Capillary Tubes, Chemical Physics, vol. 230, pp. 253–265,
1998.
[43] Yan, Y. Y., and Lin, T. F, Evaporation Heat Transfer and Pressure Drop of Refrigerant R-134a in a Small Pipe, International
Journal of Heat and Mass Transfer, vol. 41, pp. 4183–4194,

1998.
[44] Wen, D. S., Kenning, D. B. R., and Yan, Y., Flow Boiling of
Water in a Narrow Vertical Channel at Low Mass Flux: Observations of Local Phenomena, Proc. 12th International Heat Transfer
Conference, Grenoble, vol. 3, pp. 773–778, 2002.
[45] Kenning, D. B. R., Wen, D. S., Das, K. S., and Wilson, S. K.,
Conﬁned Growth of a Vapor Bubble in a Capillary Tube at Initially Uniform Superheat: Experiments and Modeling, International Journal of Heat and Mass Transfer, vol. 49, pp. 4653–4671,
2006.
[46] Yan, Y., and Kenning, D. B. R., Pressure and Temperature Fluctuations During Boiling in Narrow Channel, Eurotherm 62: Heat
Transfer in Condensation and Evaporation, Grenoble, pp. 107–
1223, 1998.
[47] Kew, P. A., and Cornwell, K., On Pressure Fluctuations During
Boiling in Narrow Channels, 2nd European Thermal-Science and
14th UIT National Heat Transfer Conference, Rome, pp. 1323–
1327, 1996.
[48] Owhaib, W., Martin-Callizo, C., and Palm, B., Evaporative Heat
Transfer in Vertical Circular Microchannels, Applied Thermal Engineering, vol. 24, pp. 1241–1253, 2004.
[49] Kuwahara, K., Koyama, S., and Hashimoto, Y., Characteristics of
Evaporation Heat Transfer and Flow Pattern of Pure Refrigerant
HFC134a in a Horizontal Capillary Tube, in Proc. 4th JSMEKSME Thermal Engineering Conference, pp. 385–390, 2000.
[50] Baird, J. R., Bao, Z. Y., Fletcher, D. F., and Haynes, B. S., Local
Flow Boiling Heat Transfer Coefﬁcients in Narrow Conduits, in
Boiling: Phenomena and Engineering Applications, Multiphase
Science and Technology, vol. 12, no. 3–4, pp. 129–144, 2000.
[51] Khodabandeh, R., Inﬂuence of Channel Diameter on Boiling Heat
Transfer in a Closed Advanced Two-Phase Thermosiphon Loop,
Proc. 5th International Boiling Conference, Montego Bay, Jamaica, 2003.
[52] Thome, J. R., Dupont, V., and Jacobi, A. M, Heat Transfer Model
for Evaporation in Microchannels, Part I: Presentation of the

vol. 31 no. 4 2010

T. G. KARAYIANNIS ET AL.

[53]

[54]

[55]

[56]

[57]

[58]

[59]

[60]
[61]

[62]

[63]

[64]
[65]

[66]

[67]

Model, International Journal of Heat and Mass Transfer, vol.
47, pp. 3375–3385, 2004.
Dupont, V., Thome, J. R., and Jacobi, A. M., Heat Transfer Model
for Evaporation in Microchannels, Part II: Comparison With the
Database, International Journal of Heat and Mass Transfer, vol.
47, pp. 3387–3401, 2004.
Dupont, D., and Thorne, J. R., Evaporation in Microchannels:
Inﬂuence of the Channel Diameter on Heat Transfer, Journal of
Microﬂuidics and Nanoﬂuidics, vol. 1, no. 2, pp. 119–125, 2005.
Shiferaw, D., Huo, X., Karayiannis, T. G., and Kenning, D. B.
R., Examination of Heat Transfer Correlations and a Model for
Flow Boiling of R134a in Small Diameter Tubes, International
Journal of Heat and Mass Transfer, vol. 50, pp. 5177–5193,
2007.
Blasius, H., Das Ahnlichkeitsgesetz bei Reibungsvorgangen in
Flussigkeiten, Forschungs-Arbeit des lgenieur-wesens, vol. 131,
no. 1, 1913.
Dittus, F. W., and Boelter L. M. K., Heat Transfer in Automobile
Radiators of Tubular Type, University California, Berkeley, Publ.
Eng. 2/13, pp. 443–461, 1930.
Petukhov, B. S., Heat Transfer and Friction in Turbulent Pipe Flow
With Variable Physical Properties, in Advances in Heat Transfer,
vol. 6, Academic Press, New York, pp. 503–564, 1970.
Shiferaw, D., Mahmoud, M. M., Karayiannis, T. G., and Kenning,
D. B. R., Experimental Flow Boiling Study in a 0.52 mm Diameter Vertical Tube Using R134a, 5th European Thermal-Sciences
Conference, Eindhoven, the Netherlands, 2008.
Gnielinski, V., VDI-W¨armeatlas, Springer-Verlag, Berlin, 1997.
Adams, T. M., Abdel-khalik S. I., Jeter S. M., and Qureshi Z. H.,

An Experimental Investigation of Single-Phase Forced Convection in Micro-Channels, International Journal of Heat and Mass
Transfer, vol. 41, no. 6–7, pp. 851–857, 1998.
Choi, S. B. Barron, R. F., and Warrington, R. O., Fluid Flow and
Heat Transfer in Microtubes, Micromechanical Sensors, Actuators and Systems, ASME DSC, vol. 32, pp. 123–128, 1991.
Shiferaw, D., Karayiannis, T. G., and Kenning, D. B. R., Flow
Boiling in a 1.1 mm Vertical Tube With R134a: Experimental
Results and Comparison With Model, International Journal of
Thermal Sciences, doi:10.1016/j.ijthermalsci.2008.02.009, 2008.
Shiferaw, D., Two-Phase Flow Boiling in Small- to MicroDiameter Tubes, Ph.D. Thesis, Brunel University, 2008.
Revellin, R., Dupont, V., Ursenbacher, T. Thome, J. R., and Zun,
I., Characterization of Diabatic Two-Phase Flows in Microchannels: Flow Parameter Results for R-134a in a 0.5 mm Channel,
International Journal of Multiphase Flow, vol. 32, pp. 755–774,
2006.
Kenning, D. B. R., and Yan, Y., Saturated Flow Boiling of Water
in a Narrow Channel: Experimental Investigation of Local Phenomena, IChemE Trans. A, Chemical Engineering Research and
Design, vol. 79, pp. 425–436, 2001.
Zhang, L., Goodson, K. E., and Kenny, T. W., Silicon Microchannel Heat Sinks, Theories and Phenomena, Springer, Berlin, chaps.
5–7, 2004.

heat transfer engineering

275

[68] Zhang, L., Wang, E. N., Goodson, K. E., and Kenny, T. W., Phase
Change Phenomena in Silicon Microchannels, International Journal of Heat and Mass Transfer, vol. 48, pp. 1572–1582, 2005.

Tassos G. Karayiannis is a professor of thermal engineering in the School of Engineering and Design of
Brunel University, UK, where he is co-director of the
Centre for Energy and Built Environment Research.
He obtained a B.Sc. in mechanical engineering from

City University (UK) in 1981 and a Ph.D. from the
University of Western Ontario (Canada) in 1986. He
has carried out research in single-phase heat transfer,
enhanced heat transfer, and thermal systems. He has
been involved with research in two-phase ﬂow and
heat transfer for about 20 years. He is a fellow of the Institution of Mechanical
Engineers and the Institute of Energy.

Dereje Shiferaw received his M.Sc. in sustainable
energy engineering in 2004 from the Royal Institute
of Technology (Sweden) and his Ph.D. from Brunel
University (UK) in 2008. He won an award for the
best master’s thesis from the Swedish Center for Nuclear Research. His research interests include singleand two-phase ﬂow heat transfer in microchannels,
nanoﬂuids, compact heat exchangers, cooling of electronics, and renewable energy systems.

David Kenning graduated in mechanical sciences
from Cambridge University in 1957 and worked for
the UK Atomic Energy Authority for 3 years before
returning to Cambridge to start his career of research
on multiphase ﬂows and boiling heat transfer. He
joined Oxford University in 1963 and was a university lecturer in engineering science and tutorial fellow
of Lincoln College from 1967 until his ofﬁcial retirement in 2003. He then joined the research group of
Professor Tassos Karayiannis as a visiting professor,
ﬁrst at London South Bank University and now at Brunel University.
Vishwas V. Wadekar is Technology Director, HTFS
Research, at AspenTech Ltd, UK. In addition to managing HTFS research, he chairs the HTFS Industrial
Review Panel on Compact Heat Exchangers. He has
authored or co-authored a number of technical and research papers in the area of compact heat exchangers,
multiphase ﬂow heat and mass transfer, and boiling.
He has held visiting faculty positions in a number of

universities United Kingdom and abroad. Currently
he serves as a visiting professor at the University of
Hamburg in Germany and the Lund Institute of Technology in Sweden. He
obtained his B.Chem.Eng. and Ph.D. degrees from UDCT, Bombay University.
He is a member of AIChE and is actively involved in organizing technical sessions at AIChE and ASME conferences. He is also a member of the Eurotherm
Committee and an associate editor of Heat Transfer Engineering.

vol. 31 no. 4 2010

Heat Transfer Engineering, 31(4):276–287, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903311694

A New Method for Determination
of Flow Boiling Heat Transfer
Coefficient in Conventional-Diameter
Channels and Minichannels
DARIUSZ MIKIELEWICZ
Faculty of Mechanical Engineering, Gdansk University of Technology, Gdansk, Poland

Presented in this article are considerations regarding modeling of flow boiling in conventional, small-diameter channels and
minichannels. A concise survey of available methods for prediction of heat transfer coefficient in saturated boiling regime is
given and in that light a modified author’s own model is presented. The presented model, contrary to other approaches, finds
application in the cases of both conventional and small-diameter channels. The results of calculations are compared with
some experimental data available from literature on conventional-size tubes and also minichannels. Obtained agreement is
satisfactory.

INTRODUCTION

Boiling heat transfer, as one of the most efficient techniques
for removing high heat fluxes, has been studied and applied in
practice for a very long time. Nowadays, rapid development
of practical engineering applications for micro-devices, microsystems, advanced material designs, manufacturing of compact
heat exchangers, high-capacity micro heat pipes for spacecraft
thermal control, and electronic microchips increases the demand
for better understanding of small and micro-scale transport phenomena. The last decade of the 20th century witnessed rapid
progress in the research into micro- and nano-scale transport
phenomena, which bore important applications in modern technologies such as microelectronics.
Despite numerous applications, the theoretical approaches
to modeling of flow boiling still require substantial progress, as
determination of heat transfer and pressure losses is done mostly
by means of empirical correlations. Their drawback is that they
feature fluid-dependent coefficients and thus are not general.
Such correlations must be therefore used with special care and
precautions, only in the range of conditions that such correlations have been developed for. That fact also disables direct application of correlations developed for conventional channels to
Address correspondence to Professor Dariusz Mikielewicz, Faculty of Mechanical Engineering, Gdañsk University of Technology, ul. G. Narutowicza
11/12, 80-952 Gdañsk, Poland. E-mail:

small-diameter channels. Recently there has also been progress
attained using structure-dependent modeling using flow maps,
which is, however, tedious and not very convenient for engineering applications.
Following a brief presentation of available approaches to
modeling of flow boiling, a model is presented here that is developed on the basis of considerations of dissipation of energy
in the flow and is deemed to be applicable to both conventional and small-diameter channels, laminar and turbulent flow
regimes, and flow with bubble generation and without it.

REVIEW OF EXISTING FLOW BOILING
CORRELATIONS
The topic of flow boiling predictions has been scrutinized for

over half a century, as the interest in that kind of heat transfer
started in the early 1960s. In the present article it is not the
intention of the author to provide a survey of all available methods for that purpose, but only to indicate the major approaches
to modeling of flow boiling heat transfer in conventional and
small diameter channels. For an extensive literature survey of
flow boiling in conventional-size channels the reader is referred
to Thome [1] or for small-diameter channels to Bergles et al. [2],
Kandlikar [3], or Thome [4]. In general, all existing approaches
are either the empirical fits to the experimental data, or form

276

D. MIKIELEWICZ

an attempt to combine two major influences to heat transfer,
namely, the convective flow boiling without bubble generation
and nucleate boiling. Generally that is done in a linear or nonlinear manner. Alternatively, there is a group of modern approaches
based on models that start from modeling a specific flow structure and in such a way postulate more accurate flow boiling
models, usually pertinent to slug and annular flows.
The empirical correlations suggested to date are based on
reduction of a restricted number of authors’ own experimental
data or form a generalization of a greater number of experimental data from various authors. In the latter case correlations are
usually of less accuracy in predicting the heat transfer coefficient, or the pressure drop, due to the fact that each experiment
contributes with its own systematic measurement error; however, such correlations are of more general character. All such
empirical correlations, however, are the fits to experimental data,
which restricts their generality. In the case of a lack of generation
of bubbles the experimental data in conventional-size tubes, i.e.,
having diameters greater than 3 mm [3], are usually modeled as
a function of the Martinelli parameter Xtt in the form:

αTP
= a (Xtt )b
αL

(1)

Dengler and Addoms [5] suggested values of a and b to be a =
3.5 and b = –0.5, respectively, whereas Guerrieri and Talty [6]
determined as a = 3.4 and b = –0.45. In the case when bubble
generation in the flow is present, such an approach encounters
some limitations, and in order to alleviate that an approach
based on incorporation of the Bond number, Bo = qw /(Ghlg ),
into the correlation is often used. A general form of heat transfer
coefficient with account of bubble generation yields:
αTP
= a (Bo + mXtt )b
αL

(2)

Schrock and Grossman [7] recommended a correlation where
coefficients a , b , and m assume values of a = 7400, b = 0.66,
and m = 0.00015. Collier and Pulling [8] suggested another
set of coefficients in Eq. (2): a = 6700, b = 0.66, and m =
0.00035. On the basis of that approach several other correlations
for conventional channels have been developed, and here is just
a mention of those due to Shah [9], Kandlikar [10], and Gungor
and Winterton [11].
The most popular approach, however, to model flow boiling
is to present the resulting heat transfer coefficient in terms of

a combination of nucleate boiling heat transfer coefficient and
convective boiling heat transfer coefficient:
αTP = [(αcb F )n + (αPB S)n ]1/n

(3)

where αPB is the pool boiling heat transfer coefficient, and αcb
the liquid convective heat transfer coefficient, which can be
evaluated using, for example, the Dittus–Boelter type of correlation. Exponent n is an experimentally fitted coefficient without recourse to any theoretical foundations. Function S is the
so-called suppression factor, which accounts for the fact that together with increase of vapor flow rate the effect related to forced
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277

convection increases, which on the other hand impairs the contribution from nucleate boiling, as the thermal layer is reduced.
The parameter F accounts for the increase of convective heat
transfer with increase of vapor quality. That parameter always
assumes values greater than unity, as flow velocities in twophase flow are always greater than in the case of single-phase
flow. The approach represented by Eq. (3) is usually dedicated
to Rohsenow [12], who suggested a linear superposition with
n = 1, which has been later modified by Chen [13], who incorporated the suppression and enhancement functions, S and F ,
respectively. The correlation due to Chen is used up to date with
a significant appreciation in the case of flows in conventionalsize tubes. It was also Kutateladze [14] who recommended a
superposition approach, but combined in a geometrical rather
than linear manner with the value of exponent n = 2. A similar summative nonlinear approach was recommended later by
Steiner and Taborek [15] with n = 3. There is also an issue
of the choice of appropriate correlation selection for calculation of pool boiling heat transfer coefficient, as Chen [13] used
the model due to Forster and Zuber [16], whereas later studies
tend to use rather the more general correlation due to Cooper
[17], which enables calculations of pool boiling heat transfer

coefficient for different modern fluids.
Kattan et al. [18] concluded that only the models based on
distinguishing between flow regimes should be genuinely considered for a general use in prediction of heat transfer coefficient
in channels. A model for flow boiling in horizontal tubes has
been developed by him based on a flow map. It was assumed that
in the flow the upper part of the tube inside is usually contacting
vapor and the remaining part is flooded with liquid. The heat
transfer coefficient for such case was taking that fact into account and the heat transfer for these two regions was evaluated
in the following manner:
αTPB = [R · θdry αv + R(2π − θdry )αwet ]/2πR

(4)

The heat transfer coefficient for a wetted part of the tube, αwet ,
is to be obtained from the form of Eq. (3) with n = 3. The
nucleate boiling heat transfer coefficient αPB is calculated from
the Cooper’s [17] correlation, whereas αcb is from this author’s
own empirical correlation. Some refinement to that approach
was introduced by Wojtan et al. [19]. That kind of approach
to modeling seems to be promising and falls to the class of
the regime-dependent models. It requires prior knowledge of
the particular flow regime, as well as the proportion of liquid
and gaseous phase in the flow. For that reason such a model is
difficult to apply in engineering practice. Following that brief
survey of superposition models, the question arises of how to
select the appropriate value of exponent n, in Eq. (3). Should
there be a value of n = 1 or 2 or 3 assumed? Or maybe some
other value of that exponent ought to be looked for? Mikielewicz
[20] provided an answer to that question, showing on the basis of consideration of energy dissipation in the two-phase
flow that the exponent should be n = 2. A modified version

of that model will be examined in the course of the present
study.
vol. 31 no. 4 2010

278

D. MIKIELEWICZ

A completely different kind of approach to model flow boiling is presented in tackling the problem from the principles of
conservation of mass, momentum, and energy, and subsequently
through a numerical solution to such problem. An example of
such an approach is a four-field two-fluid model due to Lahey
and Drew [21]. In such an approach the two phases of fluid can
exist in continuous or dispersed form, leading to the occurrence
of four fields, namely, continuous liquid–dispersed gas and continuous gas–dispersed liquid. Some success has been obtained in
modeling of bubbly flows and annular flows; however, the major
challenge is to predict the flow development and transformation
through consecutively developing flow structures (Podowski
[22]). The closure models and jump conditions form a very
difficult task to be implemented into the calculation procedure,
similar to the transient conditions. Apparently the research is
still being exercised in that direction but there is still some time
to go before useful results are to be obtained of simulation of
the entire transformation from subcooled liquid to superheated
vapor.
For that reason most of the approaches to date use empirical correlations. Presented next in brief is a model due to
Mikielewicz [20], which, as mentioned earlier, has been developed on the basis of consideration of dissipation in the flow
and recently modified to its final form, in Mikielewicz et al.
[23]. In the present article its further extension to transitional

and laminar flows is presented. Such cases are often found in
minichannels, i.e., channels with diameters ranging from 600
µm to 3 mm [3]. Empirical correlations known to date cannot distinguish between the laminar and turbulent flow regimes.
They are specially tailored to either one of the flow regimes.

MODEL OF FLOW BOILING
The principal idea in the development of the model by
Mikielewicz [20] was a hypothesis that evaluation of energy
dissipation of major contributions in the flow boiling process
with bubble generation will lead to determination of heat transfer in such flow. Energy dissipation results from the friction in
the flow, which, on the basis of thermal hydraulic analogy, is
linked to heat transfer. The flow is considered as an equivalent
liquid flow with properties of a two-phase flow.
A fundamental hypothesis in the original model under
scrutiny [20] here is the fact that heat transfer in flow boiling with bubble generation, treated here as an equivalent flow
of liquid with properties of a two-phase flow, can be modeled as
a sum of two contributions leading to the total energy dissipation in the flow, namely, energy dissipation due to shearing flow
without the bubbles, ETP , and dissipation resulting from bubble
generation, EPB :
ET P B = ETP + EPB

laminar boundary layer, which dominates in heat and momentum transfer in the considered process. Expressed as a power
lost in a unit volume of a boundary layer of two-phase flow it
yields [20]:
ETP =

heat transfer engineering

(6)

Analogically the energy dissipation due to bubble generation
in the two-phase flow can be expressed with velocity wTP and
friction factor ξPB :
EPB =

4
ξ2PB ρ2L wTP
64µL

(7)

In the Russian literature there are a number of contributions
where investigations into flow resistance caused merely by the
generation of bubbles on the wall are reported [24], which confirm that the modeling approach presented in this article is possible.
The final term in Eq. (5), ETPB , is modeled as the total energy
dissipation in the equivalent two-phase flow with velocity wTP
and some friction factor ξTPB , which after Eq. (6) can be modeled
as:
ETPB =

4
ξ2TPB ρ2L wTP
64µL

(8)

Substituting Eqs. (6), (7), and (8) into (5) a geometrical relation
between respective friction factors is obtained:
ξ2TPB = ξ2TP + ξ2PB

(9)

Making use of the analogy between the momentum and heat
we can generalize the preceding result to extend it over to heat
transfer coefficients to yield heat transfer coefficient in flow
boiling with bubble generation in terms of simpler modes of heat
transfer, namely, heat transfer coefficient in flow without bubble
generation and heat transfer coefficient in nucleate boiling:
α2TPB = α2TP + α2PB

(10)

We can now see why the exponent n in relation (1) assumes a
value of n = 2, which is here confirmed on theoretical grounds.

Heat Transfer in Flow Boiling Without Nucleation
Let’s focus our attention first on the case without nucleation,
which will lead to determination of a problem where convective
boiling is dominant. From the definition of the two-phase flow
multiplier, the pressure drop in two-phase flow can be related to
the pressure drop of a flow where only liquid at a flow rate G is
present:
pTP = R

(5)

Energy dissipation under steady-state conditions in the twophase flow can be approximated as energy dissipation in the

2
τTP

ξ2 ρ2 w 4
= TP L TP
µL
64µL

pL

(11)

The pressure drop in the two-phase flow without bubble generation can also be considered as a pressure drop in the equivalent
vol. 31 no. 4 2010

Heat transfer engineering an international journal, tập 31, số 4, 2010

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