ASCHT 2017
6th Asian Symposium on Computational Heat Transfer and Fluid Flow
10-13 December, 2017
Indian Institute of Technology Madras, Chennai, India

Paper No.265

CHANGE OF FLOW STRUCTURE AND HEAT TRANSFER PERFORMANCE
OF PHOTOSENSITIVE MICELLAR SOLUTIONS WITH LIGHT IRRADIATION

Shogo TSUCHIKAWA
Ikuya SAKANAKA
Dept. Mech. Eng. and Sci.
Dept. Mech. Eng. and Sci.
Kyoto University
Kyoto University
tsuchikawa.shogo.62n@st.kyoto-u.ac.jp sakanaka.ikuya.28r@st.kyoto-u.ac.jp
Takeshi ENYA
Dept. Mech. Eng. and Sci.
Kyoto University
enya.takeshi.68r@st.kyoto-u.ac.jp

Reiko KURIYAMA
Dept. Mech. Eng. and Sci.
Kyoto University
kuriyama@me.kyoto-u.ac.jp

Kazuya TATSUMI
Dept. Mech. Eng. and Sci.
Kyoto University
tatsumi@me.kyoto-u.ac.jp

Kazuyoshi NAKABE
Dept. Mech. Eng. and Sci.
Kyoto University
nakabe@me.kyoto-u.ac.jp

ABSTRACTThis study investigates how the change in flow structure of photosensitive micellar solutions with light irradiation is related to heat transfer performance. Flowvisualization and heat transfer measurement were conductedusing an aqueous solution of surfactant and counterions(CTAB/NaSal/OMCA) in serpentine channels under Re∗ ∼O(1). The results showed that the decrease in heat transfer
rate and pressure drop with the irradiation time are triggered by the decrease of the viscoelasticity of the solution.
Flow visualization revealed that the frequency of transitionof vortex structure between a single large-scaled vortex
and a pair of counter-rotating vortices decreases with theirradiation time, and hence fluid mixture deteriorates. In
addition, a pair of vortices are expected to be weakened bydecrease of circumferential normal stress, which inhibits theconvection of low temperature core to the near-wall area.
These two changes in flow structure lead to the deteriorationof heat transfer.
Keywords: viscoelastic fluid flow, heat transfer
enhancement, photo-rheological fluid, wormlike micelle

NOMENCLATUREAs Heat transfer area
cp Specific heat capacity
De Dean number
Dh Hydraulic diameterfFanning friction coefficient
G0 Plateau modulus
hm Mean heat transfer coefficient
1

k
K
L
ṁ
n
Num
∆P
Pr
Re∗
T
Um
Wi
γ̇
µ
λ
ρ
τ

Thermal conductivity
Power-law coefficient
Length of channel
Mass flow rate
Power-law exponent
Mean Nusselt number
Pressure drop
Prandtl number
Modified Reynolds number
Temperature
Cross-sectional mean velocity
Weissenberg number
Shear rate
Steady shear viscosity
Relaxation time
Density
Shear stressstructure which is closely linked with the micelle structures,
but the flow structure has not been clearly investigated yet.
The purpose of the present study is to investigate how
the change of the flow structure of CNO solution by UV
irradiation is related to the change in heat transfer performance. The authors conducted heat transfer and pressure
drop measurement using a heated copper serpentine channel
and flow visualization using a transparent channel of thesame shape and size. We referred to the previous numerical
study for steady flow of polymeric fluids [3, 4] to comparethem with both results and discuss closely.

WORKING FLUIDS
Wormlike Micellar Solution

INTRODUCTION
Since electronic devices have been undergoing further
integration and minimization of their circuits recently, generation of Joule’s heat per unit time and area has been
dramatically increasing. In order to remove the heat fromthe devices, innovative small heat exchangers should be
developed. The flows of working fluid in narrow heattransfer channels, however, become laminar because of low
Reynolds number flow condition, and thus the mixing andheat transfer performances deteriorate, so far as we use
conventional Newtonian fluids like air or water. To tackle
such heat transfer problems, the authors’ research group hassuggested that a photo-rheological fluid (PRF), one of viscoelastic non-Newtonian fluids, should be used as a working
fluid to control heat transfer rate with light irradiation [1, 2].
The key concept of this heat transfer control is switching
between two states by light irradiation to the fluid according
to the demand for heat transfer enhancement; one is the state
where heat transfer rate and pressure drop are both high, andthe other is the opposite state.
Kawaharada et al. [1] conducted rheological measurement on an aqueous solution of CTAB (cetyl-trimethylammonium bromide), NaSal (sodium salicylate), andOMCA (ortho-methoxy cinnamic acid). The result showedthat the viscoelasticity of the solution (hereafter CNO solution) decreased with UV irradiation time, owing to themitigation of entanglement of wormlike micelles in thesolution by photo-isomerization of OMCA. They also madethe measurement of heat transfer and pressure drop using
the same CNO solution, and showed that both heat transfer
coefficient and pressure drop decreased with UV irradiation
time, triggered by the decrease of viscoelasticity. The
obtained heat transfer results must be attributed to flow

The micelle structure varies with surfactant concentration, ionic strength and temperature and becomes wormlike
in certain conditions [5]. Wormlike micelles form entangled
networks in high concentration, and consequently wormlike micellar solutions exhibit distinctive non-Newtonian
rheological behaviors. The viscosities of most of such
solutions decrease as shear rate γ̇ increases, which is known
as shear-thinning phenomenon, and they generally obey
the power law (µ (γ̇ ) = K γ̇ n−1 ) in a particular range ofγ̇ [6]. K and n are referred to as power-law coefficientand power-law exponent, respectively. Furthermore, mostwormlike micellar solutions have viscoelasticity because
entangled networks of micelles add elasticity to viscosity.
The elastic stress of the solutions decreases with time due
to reptation motion and break-up of micelles. The timescale of the decrease of the elastic stress is referred to as
relaxation time. Most wormlike micellar solutions obey
Maxwell model, where the viscoelastic characteristics of thesolutions are represented by only two properties; relaxation
time (λ ) and plateau modulus (G0 ) [5]. Wormlike micellar
solutions seem to flow differently from Newtonian fluids
and consequently enhance heat transfer because of these
non-Newtonian behaviors.
In this study an aqueous solution of CTAB/NaSal/
OMCA (CNO solution) was used as a kind of wormlike
micellar solutions. CTAB is a cationic surfactant molecule.
NaSal and OMCA are both counterions of CTAB. Counterions stabilize the micelle structure by weakening therepulsion of hydrophilic groups of surfactant molecules. The
concentrations of CATB, NaSal and OMCA were 1.0wt%,
0.20wt% and 0.20wt%, respectively. 20mM NaOH wasadded to the solution in order to increase the solubility ofOMCA.
2Mercury lamp

Cover (Aluminum)

75mm

Sample (300g)
Magnetic Stirrer

TABLE 1. RHEOLOGICAL PROPERTIES OF CNOSOLUTIONS AT 20 ◦ C.
Fluid Name

K

n

λ [s]

G0 [Pa]

CNO0h

4.38

0.004

24.2

3.42

CNO2h

3.62

0.033

9.04

2.95

CNO4h

2.61

0.033

4.90

2.47

f90mm

FIGURE 1. LIGHT IRRADIATION APPARATUS.

C N O 0 h
C N O 2 h
C N O 4 h

[s]

1 0



1

0 .1

0 .0 1
2 0

2 5

3 0

3 5

Mercury lamp (Olympus, U-LH100HFAPO) for 0, 2 or 4hours, which is referred to as CNO0h, CNO2h or CNO4h,
respectively. During light irradiation, the samples werestirred by a magnetic stirrer at 150rpm with a 14×ϕ 40mm
cross-head stir bar.
Measurements of steady shear viscosity and dynamic
viscoelasticity were conducted for the prepared samples
using a rheometer (Anton Paar, MCR301). The measured
rheological properties at 20◦ C are listed in Tab. 1. The
measured values of steady viscosity was fully fitted with thepower law within the range of 10s−1 ≤ γ̇ ≤100s−1 , as isreported in the previous work [1]. In Tab. 1 K, λ and G0 decreased with light irradiation time, which means viscoelastic
properties decreased [5]. As shown in Fig. 2, λ of each
CNO solution exponentially decreases with temperature andbecomes one tenth as the temperature rises by 10K, althougha different tendency was observed in CNO4h case at higher
than 30◦ C.

4 0

T [ °C ]FIGURE 2. TEMPERATURE DEPENDENCE OF
RELAXATION TIME.

Rheological Change by Light Irradiation
OMCA is a photo-sensitive molecule which has two geometrical isomers. Exposed to UV, trans-OMCA isomerizes
to cis-OMCA. Although this isomerization is reversible, it
is apparently irreversible from trans-OMCA to cis-OMCA
because trans-OMCA is more likely to be activated by UVthan cis-OMCA is. Since trans-OMCA develops wormlike
micelles better than cis-OMCA, the viscoelasticity of CNO
solution decreases with UV irradiation owing to the gradualisomerization of OMCA.
In the present study CNO solutions were prepared withtrans-OMCA (without cis-OMCA) initially and exposed
to UV using the apparatus shown in Fig. 1. Each 300g
CNO solution was exposed to UV emitted from a 100W

EXPERIMENTAL METHOD
Test Channel
The schematic of the serpentine channel used in thisstudy is shown in Fig. 3. The channel has the squarecross-section of 5mm, and hydraulic diameter Dh is 5mm.
The serpentine section consists of semicircles of inner radius
Ri =5mm and outer radius Ro =10mm alternating from side
to side and repeating ten times periodically. We call thesemicircle unit which is Nth from upstream simply Nth unit.
The flows of micellar solutions in this channel were
evaluated by modified Reynolds number Re∗ and Weissenberg number Wi, which are defined byRe∗ =ρ Um2−n Dnh
n−1
8 K (B + A/n)n

Wi = λ γ̇m =
3

4Um λ
,
Dh

(1)

(2)

r
a sheathedthermocouple
5

q
R10

z

5

5

y
x
10

10

z

2

3

4

5

6

7

8

Pressuregauge

Outlet

5

10

Inlet

9

Acrylic
outletchannelAcrylic
inletchannelCartesian coordinate
N=1

five thermocouples
5

R5

Cylindrical coordinate

ﬂow

Thermometer Module

10

Heated copper channel
Pump
Constant temperature bath

Hot water supply
300

FIGURE 3. DIAGRAM OF TEST CHANNEL(UNIT: MILLIMETER).

FIGURE 4. DIAGRAM OF HEAT TRANSFER AND
PRESSURE DROP MEASUREMENT APPARATUS.

respectively. ρ , Um , and γ̇m are density of fluid, crosssectional mean velocity, and representative shear rate, respectively. A and B are geometric parameters, whose values
are 0.2121 and 0.6766, respectively, in a square channel.
The density of pure water was used as ρ because the solutesof CNO solutions are sufficiently dilute. Re∗ was definedso as to satisfy the relation that Fanning friction coefficient
f is equal to 16/Re∗ in a laminar flow in an arbitrary
cross-sectional straight channel in isothermal condition [7].
Weissenberg number Wi was used to evaluate the effect ofelastic stress.
In addition, Dean number De is defined by

TABLE 2. CONDITIONS OF HEAT TRANSFER AND
PRESSURE DROP MEASUREMENT.

ρ Um Dh
De =
µ

√

Dh
,
Ro + Ri(3)

so as to evaluate the effect of centrifugal force in the curved
channel. The value of Dean number was less than 10 inthis study, as will be mentioned below. In such low De
conditions, Dean instability does not occur for the flowof Newtonian fluid. It was experimetally confirmed that
there was no Dean instability by running Newtonian fluid(an aqueous solution of 64.4wt% sucrose) through our test
channel in the same range of Dean number condition.
Method of Heat Transfer and Pressure Drop
Measurement
The schematic of the experimental apparatus used inthis measurement is shown in Fig. 4. The shape and sizeof the channel are same as those shown in Fig. 3. This
experiment was conducted under a constant wall temperature condition by circulating hot water, whose temperature
was kept at 40◦ C, through the copper wall. Pressure drop

Fluid

Re∗

De

Wi

Pr

CNO0h

1.8-11

0.7-5.4

45-170800-1900

CNO2h

2.2-101.2-5.5

31- 71600-1300

CNO4h

1.7-12

0.9-6.2

8.4- 52

650-1400in the test section ∆P was measured using two pressuregauges (Keyence; AP-C30) connected to the upstream anddownstream of the test channel, and evaluated by Fanning
friction coefficient f = Dh ∆P/(2ρ Um2 L), where the totalchannel length L was 471mm. Wall temperature Tw wasmeasured using four K-type thermocouples attached on theouter surface of the copper channel. Spatial average of Tw
varied within 0.5◦ C with time. The inlet bulk temperature
Tb,i and the outlet bulk temperature Tb,o were measured
using thermocouples inserted in the channel as shown in
Fig. 4. We calculated Tb,o by weighting the theoreticalvelocity profile on the measured outlet temperature profile.
The theoretical velocity profile was obtained as[( y )(1.2n+1)/n ]u(y, z) 2.1157 3n + 1
·
1−
=
Um
2
n+1
2.5
[
( z )(1.2n+1)/n ]
· 1−
,
2.5

(4)

with regard to the fully-developed flow of power-law fluidin square-cross-sectional channel [8, 9]. Considering theequation of energy on the heat transfer target wall where heat4

Syringe pumpComputer

TABLE 3. CONDITIONS OF FLOW VISUALIZATION.

Video camera 1

Dye
Storage tank

Valve

ChannelChannel(Test section)
Electric balance
Flow
Valve

Pressurized tank

Fluid

Re∗

De

Wi

Dye flow rate [µ L/min]

CNO0h

2.1

2.8

677

250

CNO2h

2.3

1.6

259

180

CNO4h

1.8

1.3

104

190

z

Video camera 2

y

x
3 0

C N O 0 h

FIGURE 5. DIAGRAM OF FLOW VISUALIZATIONAPPARATUS.

C N O 2 h

2 0transfer coefficient is constant at hm , mean Nusselt number
Num is obtained asṁcp Dh
Tw − Tb,i
hm Dh
=
× ln
,
k
kAs
Tw − Tb,o

1 0

(5)

where k, As , ṁ, and cp are thermal conductivity of fluid, heattransfer area, mass flow rate and specific heat capacity of
fluid, respectively.
Heat transfer and pressure drop measurements wereconducted under the conditions shown in Tab. 2, where
Pr is Prandtl number. A series of measurements wereconducted under room temperature (20◦ C), and logarithmic
mean temperature of fluid (Tm ) varied from 25◦ C to 35◦ C
depending on the conditions. We substituted the values of
cp and k by those of pure water and used the thermal andrheological properties at Tm in each measurement.
Method of Flow Visualization
The test channel of this experiment was made of polycarbonate and has the shape and size shown in Fig. 3. The
diagram of flow visualization apparatus is shown in Fig. 5. A
0.8mm-outer-diameter SUS tube was inserted horizontally
into the test channel between 7th unit and 8th unit so as
to supply dye for visualization. One end of the SUS tube
was capped and the other was connected to a syringe pumpby way of the polyethylene tube. The SUS tube has a tinylateral hole at the center of cross-section of the channel,
through which dye was ejected by the syringe pump. We
put two video cameras and recorded flow patterns at the 9thunit from two different directions; top view from positive
z-direction (video camera 1) and side view from negative
y-direction (video camera 2). A series of experiments wereconducted under Re∗ ∼ 2, and detailed conditions are shownin Tab. 3.

1

1 0

R e *

FIGURE 6. RELATION BETWEEN MODIFIEDREYNOLDS NUMBER AND MEAN NUSSELTNUMBER WITH CNO SOLUTIONS.

C N O 0 h
C N O 2 h
C N O 4 h

1 0

f

Num =

N u

m

C N O 4 h

1

1

R e *

1 0

FIGURE 7. RELATION BETWEEN MODIFIEDREYNOLDS NUMBER AND FANNING FRICTION
COEFFICIENT WITH CNO SOLUTIONS.

5

3 0

C N O 0 h
C N O 2 h
C N O 4 h

Top View

Flow

N u

m

2 0

1 0

Flow
Side View(a) CNO0h, Re∗ = 2.1, Wi = 677
1 0

W i

1 0 0
Top View

FIGURE 8. RELATION BETWEEN WEISSENBERG
NUMBER AND MEAN NUSSELT NUMBER WITH
CNO SOLUTIONS.
RESULTS AND DISCUSSTIONSResults of Heat Transfer and Pressure Drop
Measurement
Mean Nusselt number Num and Fanning friction coefficient f of CNO solutions are plotted in terms of modified
Reynolds number Re∗ in Figs. 6 and 7, respectively. The
symbol of each solution in these figures corresponds to thatin Fig. 2. In Fig. 6 Num decreases with light irradiation over
the whole range of Re∗ . In CNO4h case Num is smaller thanhalf the value of CNO0h case at each Re∗ . As shown in
Fig. 7, f gradually decreases with light irradiation, showing
a certain dispersion of the obtained data due to technicallimitation in the pressure measurement. The increase in
Num and f in a serpentine channel with the rise in K and
λ is consistent with previous study dealing with polymeric
solutions [3].
The results shown in Fig. 6 are also plotted in terms of
Weissenberg number Wi in Fig. 8, where Re∗ is not fixed
at a constant value. The figure shows that Num increases
with Wi. Further, the plots of every light irradiation timecase exist almost on a single curve. Tatsumi et al. [3]reported that a good agreement was observed in the relation
between Wi and Num among three polymeric fluids withdifferent concentration, and Num started to increase at Wi ∼30. These aspects are consistent with the present results.
These two studies suggest that Num has stronger dependence
on Wi than on Re∗ . In other words, the change of heattransfer characteristics by light irradiation time relies moreon viscoelastic behavior than on viscous behavior. The flow
structures which lead to heat transfer characteristics will be
discussed in the following subsections.

Flow

Flow
Side View(b) CNO2h, Re∗ = 2.3, Wi = 259

Top View

Flow

Flow
Side View(c) CNO4h, Re∗ = 1.8, Wi = 104

FIGURE 9. FLOW PATTERNS VISUALIZED IN A
SERPENTINE CHANNEL.

Results of Flow Visualization
Flows of CNO solutions in a serpentine channel werevisualized by dye streakline under the conditions listed in
Tab. 3. The rough flow pattern in the movies was unsteadyin both CNO0h and CNO2h cases, and it was more perturbed
in CNO0h case. In contrast, the flow pattern in CNO4h
case was almost steady although slight fluctuation of thestreakline was observed. Further, the fast flow near the sidewall was more frequently observed in CNO0h case than in
CNO2h and CNO4h cases.
Typical flow patterns visualized in the movies areshown by instantaneous snapshots of movies in Fig. 9. The
6

upper part of each figure shows the top view recorded byvideo camera 1 and the bottom part shows the side view byvideo camera 2. The solid arrows in Fig. 9 represent the flow
directions which are obvious from the streaklines, and thedotted arrows represent the expected flow directions. In the
top view movie of each condition, the flows orientated fromouter wall to outer wall (Fig. 9 (a)) and those orientated frominner wall to inner wall (Fig. 9 (b)(c)) were observed near
the inflection points of the channel, or connecting parts ofneighboring semi-circles. Note that the flow orientations in
CNO0h and CNO2h cases alternated intensively with timein contrast to CNO4h case, where it was steady from innerwall to inner wall.
Moreover, two types of vortices were observed in theside view movies; one is a single large-scaled vortex and theother is a pair of counter-rotating vortices, as shown in theside view of Fig. 9. A single vortex rotates in a large circle
over the whole cross-section. A pair of vortices rotate fromthe center of cross-section to the top/bottom walls. As will
be detailed in the next subsection, the previous numerical
work for steady flow of viscoelastic fluid showed that a pairof vortices are generated in cross-sections of a serpentine
channel [3]. Although a pair of vortices were not always
observed clearly, when either vortex was observed, we
expected that the other vortex rotating in a counter direction
existed considering the result of the previous computation.
Such expected vortices are drawn with the dotted arrows
in Fig. 9 (a)(b). In Fig. 9 a single vortex was observed in
the left-hand inflection point of (a), and pairs of vortices
were observed in the right-hand of (a) and in the both-handof (b).Both two types of vortices were observed alternately
in CNO0h and CNO2h cases. In contrast, secondary flows
were not distinct in CNO4h case. Emergence of a single
vortex was more frequent in CNO0h case than in CNO2h
case.
Relation between Flow Structure and Heat Transfer
Characteristics
The present experimental results shown in the former
subsections are summarized as follows. As the viscoelasticity of CNO solutions decreases with light irradiation time,flow unsteadiness and longitudinal type of a single vortex
gradually decreases, and the heat transfer performance deteriorates. In this case, the location of the area where the flow
velocity shows the maximum value in the cross-section is
not near the channel wall but near the center of the channel
and the pressure drop decreases. To further discuss therelationship between the flow structure and heat transfer
characteristics, we will compare our experimental resultswith those of numerical computation reported by Tatsumi
et al. [3].

: Driving force by t q q: Centrifugal force: Movement of low temperature core
: Low temperature core in cross-section: Developing Vortex: Developed Vortex

oute

Developing regionof reversed vortices

r
(B)

inne

r

Decaying regionof vortices

(C)

(A)

Velocity and dimensionless temperature
distribution by Tatsumi et al. [3]

FIGURE 10. SCHEMATIC OF THE FLOW PATTERNSWITH A PAIR OF VORTICES OBTAINED IN
PREVIOUS COMPUTATION.

Their computation was made for flow in a serpentine
channel of same geometry as the present study under thecondition of Re = 0.63, Wi = 205 and De = 0.13. Fromtheir results, we have drawn the schematic of the vortices
structure generated in the channel as shown in Fig.10. This
figure shows secondary flow structure, driving forces ofsecondary flow, and location of the low temperature region
on cross-sections which are located at the inflection points(A, C) and at the midpoint of the curve (B). In addition, thefigure involves the result of their computation corresponding
to the cross-section(C), which shows the distribution ofvelocity vectors and dimensionless temperature Tθ = (T −Tw )/(Tb,o − Tw ) in the cross-section. Tθ becomes large
when fluid temperature is low and becomes 0 when it issame as Tw . A pair of counter-rotating vortices is generated
in the cross-section (B) by radial forces produced in thenear wall region of top and bottom walls owing to thenormal stress differences and circumferential stress τθ θ . The
vortices develop by these forces along the curvature andshow maximum strength at the inflection point. Downstreamof the inflection point, the vortices decay and their rotating
7

direction becomes opposite due to change of the curvature
direction. By the pair of vortices, low temperature coreregion is convected from the inner wall area to the outer wallarea as it flows downstream through the semi-circle region.
Heat transfer is, therefore, enhanced at the inner sidewall
at upstream inflection point and at the outer sidewall at
downstream inflection point.
The present experimental results showed that heattransfer performance of CNO solutions decreases as theviscoelasticity decreases by light irradiation. The cause
is considered as follows referring to the numerical results
mentioned above. Decrease in viscoelasticity leads to decrease of the driving force generated by τθ θ . This decreases
the strength of the pair of vortices. Consequently, lowtemperature fluids region is located at the center of thecross-section, and thus, the heat transfer at the sidewalls
decreases.
Considering the present results of flow visualization,
further discussion can be given as follows. While apair of counter-rotating vortices were observed in both theflow visualization and the previous computation, a single
large-scaled vortex was observed only in the flow visualization. The reason seemed that the computation was
conducted for steady flow, and namely the term dependingon time was eliminated. Therefore, the term may enhance
the instability of flow and generate a single vortex. Suchflow instability may increase as Wi increases, considering
the results of the flow visualization. According to the present
results, heat transfer performance increases with increase in
the frequency of a single vortex. The transition from a pairof vortices to a single vortex can increase the mixture of
fluid and enhance heat transfer. Namely, the strength ofa pair of vortices and the mixture of fluid by transition ofvortex structure seem the cause of the change of heat transfer
performance by light irradiation to CNO solutions. Since thequantitative values for these aspects were not obtained in thisstudy, extra quantitative experiments like PIV measurement
should be conducted henceforth.

CONCLUSION
Heat transfer and pressure drop measurement and flow
visualization in serpentine channels were conducted usinga kind of photosensitive micellar solutions. The results
obtained in the present study are summarized as follows.
• As time of light irradiation to the solution increases,
the relaxation time, a representative of viscoelastic
properties, of the solution was decreased, and heattransfer rate and pressure drop were decreased in therange where Reynolds number is 1 to 20.
• Two types of vortical flow patterns were visualized; oneis a single large-scaled vortex and the other is a pair ofcounter-rotating vortices. As the viscoelasticity of thesolution decreased with light irradiation, emergence ofa single vortex became infrequent, and thus mixture of
fluid decreased. In addition, the strength of a pair ofvortices is expected to be weakened owing to decreaseof the circumferential normal stress. These changes inflow structure can be main causes of the decrease in heattransfer performance.

REFERENCES[1] Kawaharada, K., Fujii, T., Enya, T., Tatsumi, K., andNakabe, K., ”Light-turning of Heat Transfer Performance for Low Reynolds Number Flow of Micellar
Solution”, Proc 1st Int. Pac. Rim Thermal Eng. Conf.,
PRTEC-14717,(2016).
[2] Enya, T., Kuriyama, R., Tatsumi, K., and Nakabe, K.,
Heat Transfer Control by Light Irradiation to Low
Reynolds Number Flows Using Photosensitive Micellar Solution”, Proc 4th Int. Forum on Heat Transfer,
IFHT2016-1986,(2016).
[3] Tatsumi, K., Nagasaka, W., Matsuo, T., and Nakabe,K., A Numerical and Experimental Study on Flowand Heat Transfer Characteristics of Viscoelastic
Fluid Flow in a Serpentine Channel”, Proc 15th Int.
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Channels”, Proc 1st Int. Pac. Rim Thermal Eng. Conf.,
PRTEC-14859, (2016).
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[6] Miller, E., and Rothstein, J. P., Transient Evolution of
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[7] Kozicki, W., Chi. H., and Tiu, C., Non-Newtonian
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[8] Wiginton, C. L., and Dalton, C., Incompressible
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[9] Shah, R. K. and London, A. L., Laminar Flow Forced
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8