The Eleventh Seo.ul National- Kyoto- Tsinghua UnlveBity Thermal Engineering Conlerence

FLOW AND HEAT TRANSFER CHARACTERISTiCS OF
ViSCOELASTiC FLUID FLOW iN SERPENTINE CHANNELS

Kazuya Tatsumi, Chee Leong Heong, Yusuke Takeda and Kazuyoshi Nakabe
Department of Mechanical Engineering and Science, Kyoto University

ABSTRACTThis paper describes the results of heat transfer, pressure
loss, and flow visualization measurements of viscoelastic
fluid flow in a serpentine channel. The Reynolds number
was varied in the noge of 0.1< Re < 5 that was found in
this study to cover the regime from steady laminar flow
to unstsady elastic turbulent flow. Two types of fluids
were used as working fluids: one was 64.4Molo sucrose
solution that was a Newtonian fluid, and the other was a
64.4wtolo sucrose solution with which 500ppm
polyacrylamide was mixed that was a viscoelastic fluid.

In the visualization measurement, shong flow

fluctuations were observed in the serpentine channel as
Re increased in the case ofthe viscoelastic fluid. Thus, aneffective heat transfer enhancement in the polyacrylamide
solution case compared with the sucrose solution case
was observed. An increase of the pressure loss was
accompanied, too. However, a reasonable enhancement
was obtained considering the total performances.
(This paper has been submitted to the ISTP-22.)

l.INTROBUCTION
The chapter number may be introduced if the authors
prefer it. Enhancemelt technologies for convection heattransfer of laminar flows in channels have been keenly
studied in the past half century. Various techniques havebeen developed in result, as typified by those such as
using fins and cor.ugated channels to increase the heattransfer area and generating secondary flows, or applying
jet flows, heat pipes, porous media and microchannels.
An altemative solution to the above geometrical andmechanical improvements of the channel is changing lhe
properties of the operating fluid. The so-called"Nano-fluids" is a fluid in which nano-meter size

panicles are mixed in water or other solvents (Das el al.,2007). Although the physical reason is not fully
understood, it is known that the heat transfer co€fficignt
in channels can be increased compared with water in thiscase. Another working fluid that is of significant interestis viscoelastic fluids, for example polyacrylamide water

solutions. Such fluid possesses not only yiscous property
but also elastic property. Providing high shear stress tothe fluid by the shear flow will cause the polymers solvedin the fluid to contract, expand and rotate leading to an
appearance of the elasticity that produces additional
noImal stresses in the flow. Further, ir| combination witha certaia flow skucture, the elastjcity of the fluid and theaccompanied normal stress will increase the flow
instability. The increase of the flow instability evokes
unsteady flow with large fluctuation in the channel svenin very low Reynolds number regime. Such unsteadyflow is believed to possess a high potential to enhance thefluid mixing and wall heat transfer.
The influences of the rheological properties of thevisco€lastic fluid on laminar heat transfer have been
keenly studied in the past several decades, particularly inthe case of straight channel. Hartnctt et al. (1985) andChunbo & Hannet (1992) have reported from theirexperimeot that the heat transfer coefficient in the case ofviscoelastic fluid flow was higher than tho Newtonian
fluid flow case. The main cause was believed to be
attributed to the secondary flow which was generated andcnhanced by the normal force difference. Naccache et al.

(1996) conducted a numerical simulation otl the
non-Newtonian laminar heat transfer in a rectangular duct
and reporled that the heat kansfer was strongly enhanced
due to the secondary flow. Norouzi et al. (2009) havenumerically investigated the heat transfer characteristics
of viscoelastic flow in a curved duct. The resuhs showedthat the first normal stress dillerences encourage thesecondary flow generation and enhance the heat transfer
while the second normal stress differences suppress heattransfer efficiency.
Flow instability of viscoelastic fluid flow has also
been studied with slrong interest. Larson et al. (1990)
studied the now instability of Taylor-Cuette flows inrotating coaxial cylinders. Joo & Shaqfeh (1994)
investigated the mechanism of the increase in the flow
instability ofTaylor-Dean flows in coaxial cylinder.

‑17‑

Recently, several studies on the mixing characteristics
of viscoelastic fluid in a serpentine-curved channel under
low Reynolds numbcr condition have been published in
the literatures. Groisman & Steinberg (2001) carried out
flow visualization and point measurement of the flow
velocities using laser Doppler anemometer. Flowfluctuation was observed even in the order qfRe - 10.
accomphnying the enhancement of the fluid mixing.
Teodor e( al (2004) and Feng er al. (2010) conducted avisualization experiment in serpentine microchannels
using fluorescent dye. Even in this scale, production ofthc unsteady flow and enhancement in the fluid mixing
was observed. Tamano et al. (2009) made PIV
measurements in curved channels with circularcross-section and found a pair of vortices similar to the
Taylor vortices in the time-mean velocity fields. All theseresults indicate the possibility of effectively enhancing
the mixing performance or moreover mass and heattransfer at the channel wall. To the knowledge of theauthors, however, there are no experiments conducted tolink such unsteady flow and the fluid mixing with theheal/mass transfer performance. lt is essential toち(a) Apparatus
30

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understand the heat transfer characteristic of viscoelastic

fluid flows in serpentine channels in order to provide an

300

insight for the feasibility of using the viscoelastic fluids
as working fluids, and to aid the designing ofan effective
channel shape and conditions in order to apply thistechnique to the fields of thermal engineering, chemical(b) Channel shape and dimensions

Fig. I Experimental apparatus used for the heattransfer measurement.

engineering and medicine.

From this background, measuremeot on heat transfer
coemcient ol viscoelastic fluid flow in a serpentine
channel with a square cross-section is carried out underisothermal wall condition ia this study. The pressure loss
in the channel is measured together in order to evaluate
the relationship b€tween the heat transfer eohancement

and pressure loss penalty. Further, visualization
experiments arc caried out to measure the flow behavior
and discuss the mixing characteristic in the channel.

2. EXPERIMENT
2.1 Experimental Apparatus
Figure I shows the schematic diagram of theexperimental apparatus applied to the heat tmnsfer
measurement. The channel consists ofthe thre€ pans: theinlet and outlet channel parts, and the test section, thechannel walls of which are heated under isothermal
condition. The working fluid was supplied to the channel
by a pump driven by pressurized air. The mass flow rate
was measured by measuring the mass ofthe fluid flowing
out from the outlet of the channel using aa electronic
weighing machine. The average values was used to
calculate the flow rate, lhe accuracy of which was
0.6mI/min.
For the channel. the inlet and outlet units were madeof acrylic, to which a straight channel was embedded.
The test section was made of copper in order to produce
an isothermal condition to the wall. As shown in Fig. I(a), cylindrical channels were transversely drilled to thewall to which constan( temperature water was supplied

from the thcrmostat bath to keep the wall temperature of
the channel constant.

Two ty,pes of channel, the schematic and dimensions

ofwhich are shown in Fig. I (b), were investigated in thisstudy. Both channels had a square cross-section of 5mm

in width and height. The serpentine channel had aperiodical shape, which consisted of l0 repeating units ofcircular curved parts. The inner and outer radii were 5
and l0mm, respectively The length of the straightchannel was L = 0.2m, while the longth of the serpentine
channel measured along the curvature was L = 0.4? lm.
The inlet and outlet pafis were attached to the test
section and sealed with silicon sealant. 5mm holes were
drilled through the top plate at the end of the channels.
Tubes were connected to these holes supplying fluids tolhe channel from the pump, and leading the outlet fluid toa container to measure lhe mass flow mle.

2.2 Heat Transfer Measurement

ln order to measure the fluid tenrpera{ure lbr bulk
mean temperature calculations, temperature rneasurcmenl
units were placed at the inlet and outlel of the cupper lestwassection. The fluid temperature al the inlet,
measured by a sheath K-type thermocouple of 0.5mm inf,,diameter having its end point positioned at the cenler ofthe channel cross section- Temperature at a single point

only was measured since a uniform temperature

distribution was expected for the inlet flow. The fluid
tempcrature at the outlet 7o was measured by 7 K-type
thermocouples located evenly in the height direction in‑18‑

th€ middle of the channel width. Since the available

Table I Flow conditions in the experimcnt.

tcmperaturc distributions obtained from this measurement

are only in one-dimensional form, expansion of the

Fluid

Shapc

Re

De

temperature distribution fronr onc- to two-dimensional
directions is necessary. ln this study, the fluid temperature
was assumed to have a similar distribution to the

SucroseSerp

l.01‑4.29
0.33‑1.92
0.28‑0.88

0.59‑2.48

measured one at z = 0 in theand z directions. The
temperature of the heated cupper pan was measured by

PAAm

Se.p.

PAAnr

Strai

I

K-type thermocouples, which were embedded in thecupper surface. The variation of the tsmperature was
0.5 'C affirming that a constant wall temperature
condition was obtained al the channel

Streamwise velocity distributions of a squarecross-section in a laminar flow case (Shah, 1978) wereused in the sucrose solution case. ln the PAAm solurioncase also, we have assumed that the velocity distribution

is similar to the laminar flow of Newtonian fluid case
based on the discussion on the friction factor, which will
be shown in the next section. The temperatures andvelocities obtaincd from these processes were employed
to calculate thc bulk mean temperatures.

2.3 Pressuro Loss Measuroment
To measure the pressure loss in the test section,
electronic pressure gauges (Keyence Co., AP-C30), themeasurement resolution of which was 0.lkPa, wereconnected to the inlet and outlet of the test section
through a lmm hole drilled at the top wall. The staticpressure at gach position was measured and used to
calculate the fanning friction factor,f

2.4 Flow Visualization
Flow visualization using dye is carried out in thisstudy to understand the flow behavior in the channel.
Syringe pump (Nihon Konden Co., CFV-3200) was used
to supply the ink though a 4mm inner diameter tube to asyringe needle, which was inserted to the channel throughthe top wall. The images of the visualization wasrecorded using a

digital video camera (Sony,

HDR-CX37OV) measured from above the channel. The
configurations of the test section are nearly the same as
those of the heat transfer experiment, except that the top
wall was replaced by transparent acrylic plate. Therefore,
the sidewalls and bottom walls only were heated in thevisualization measuremerlt.

2.5 Preparing the Working Fluid
Two kinds ol wo*ing fluids were prepared for aheexperiment. One was a sucrose water solution (sucrose
64.4wtYo\, which was a Newtonian fluid. The other was
the polyacrylamide (PAAm) water solution (sucrose
64,4wt%, NaCl lwt%, PAAn 500ppm), which was aviscoelastic fluid. The fluids were prepared mixing thesolute to water using a pot rotating mill. NaCl was mixed

in the fluid to keep the polymer structure and fluid
prope(ies stable.
The fluid viscosity p, density p and relaxation time 1
were measured prior to the experiment. p measured by
the rh€ometer were p =1.0 x lot and t.0 x loi for the-t9

0.19‑1.11,vi

7.0‑508.0‑24

sucrose and PAAm solutions, respectively. The relaxation

time was 2-3s which was calculated by appying the
Powell-Eyring (Hartnetl et al., 1985) model to rhemeasured results using the rheometsr The heat capacity

Co and thermal conductivity 1,, were derived from theempirical equation shown in the references ofCucker and

Ayen (1937) and Wemer et al. (200'7) for the fluid
temperature of25oC.

2.6 Exporimental Conditions. Thc flow rate waschange in the experiments, in order to examine th€
influence of the Reynolds number. Re, on lhe heattransfer coefficient, pressure loss and flow behavior in thechannel. The conditions are summarized in Table I. De
shown in the table is the Dean number, which is definedas Eq. (2).

o"=Pu-D,(r=2*= r\p[(R, +R,,)/(r)l/ is the channel width, and R; and R" are the inner andouter radii of the curved channel. Dean number can beused to assess the magnitude of the curvature effect on
the flow structure, for example the generation of the
Taylor-Dean vortices. ,/i is the Weissenberg number andis defined as follows.

L)″・ 空
4,==γ f̀∠

(D″ ノ

(2)

3. RESULTS AND DISCUSSION
Figure I shows the relationship between the average
Nusselt number, Na., and the Reynolds number, Re, forthe sucrose and PAAm solutions. The analytical results
for the Nusselt number of laminar flow in a sraightchannel with square cross-section is depicted in the figure
for comparison. This analysis also considering theentrance region effect, and is derived by Chandrupatla &Sastri (1977).
The Nusselt number Na. of the sucrose solution caseslightly increases with Re due to the development of thethermal boundary layer at the inlet. Further, the resull
agrees well with the analytical one showing the validationof the measurement. Therefore, the flow in the serpentine
channel is flowing along the curved chann€l withoulaccompanying any secondary flows, which is consistent
with the small Dean number shown in Table l.
ln the PAAm solution case, Nr. increases markedly
as Re increases, and shows a considerablc heat transfer
enhancement compared to the sucrose solution case. Nir.
appears to approach to the value of sucrosc solution casc
as Re decreases. Therefore, it is expected that the increaseof Nn. is related more to the production of secondary

︐
一

r

.i.

Sucrose case..3

chandru patla et al.r1l

10

●

\10

I
●

ＤＤ

!'

o Sucrose case
1

0.5

1.0

1.5

2.0

2.5

'10

1

0.1

Ra

Re

(a) Re vs/(a) Sucrose vs PAAm solutionis
・●●. Se.peiline (PAAm)o Slraight (PAAm)

100● ａ︶ ３
︐

ミ≧

． ．ザ

IJ
'10

.i.; "
0

20

1

40

60

80

0.1

100
Re

10

1

Re*

(b) Re* vs/factordistributions: (a) relationship with
Fig. 3 Friction
Reynolds rumber, and (b) relationship with modifted
Reynolds number based on the power law.

(b) Serpentine vs Straight channels

Fig. 2 Average Nusselt number distributions: (a)comparison of the sucrose aod PAAm solutions inserpentine channel, and (b) comparison of thes€rpentioe and strai8ht channels in the PAAm solution

study.

Figure 3 shows the relationship between the fanningcase.

flow than thc change in the velocity distribution due tothe non-Newtonian behavior such as shear thinging.
ln order to see whether the heat transfer enhancement

is achieved by the viscoelasticity of the fluid only, or if it
is a combinational effect of the viscoelastic fluid and thecurvature of the serpeotine channel, heat transfer
measurement was carried out for a straight channel using
the same PAAm solution. The results are shown in Fig 2(b). Since the channel length is different between the two
cascs, Graetz number G;, defined by Eq. (4), is taken as
the abscissas axis in this case.

G, =

ヽ

10

..t

5

し

︒

14.2/Re

0.0

ヽ．

ヽ
ミ

ｂ ●´・ｂ
︲
． ｏ ヽ

15

100

Re4-PpL(l)

7'"

In the figure, we can see that the Nlr"' does not increass inthe straight channel case for the Re conditions
investigated in this study as it did in the serPentine

channcl casc. lt remains nearly cons(ant at a value close
to Nu,,, -- 3. which is the value of lully dcveloped flow
and thermal boundary layers in a square duct. This showsthat the increase of heat transfer coefficient can beobtained only by the combination of (he viscoelastic fluid
flow and the serpentine channel, a( least under theconditions of the Reynolds numbcr considered in thisfriction faclor, f and the rRe in both solution. The solidline in the figure presents the value of 14.2/Re, whichshows the friction factor of a Newtonian fluid flow in asquare duct. Although the results in the sucrose solution(hecase shows a relatively smaller value compared withareasonablc
plots
show
solid line, the scatteringagreement with the theoretical valuc. Since the Reynolds
number and Dean number are both very small, it isbelieved that no roticeablc secondary flow is generated in
the channel. Thereforc, samc as in the case of Nri,, shownin Fig. 2, the results indicate lhat the flow in thc

serpentine channel in the sucrose solution case can beconsidered to be a lanlinar flow in a straight duct withsquare cross-section.

, On the other hand,/in the PAAm solution case showsa different distribution comparcd with the sucrose
solution casc. . Particularly. a larger increase is observedin the region of larger Re. The reason for this increase canbe two-fold. One is the change in the velocity distribution
due to (hc viscoelaslic properties of the fluid ln this case,the velocity gradient increases in the area adjacent to thechannel wall, and a more flat distribution is obtained at
the channel center. This produces a larger friction at thechannel wall. The other reason is the generation of theflow lluctuation or secondary flow is the chann€1.

-20-

ln order to clarify each influence in the friction factor
shown in Fig.3 (a), thc relarionship between/and Re is
replotted by using the modified Reynolds number, Re*.
Re* is calculat€d by Eq. (4).
/v=8

r(e'=
: PU"-'D"t\u
B*t

K@;;rn'l'(4\This equation considers the influence of theviscoelasticity of the fluid on the velocity profile, andshows the relationship between the friction factor and themodified Reynolds number ln this case, the relationshipbetween jf and Re* can be shows as f = l6/Re* tor
viscoelastic fluid flows. The parameters a and happearing in Eq. (5) are used to describe the eflecr of thecross-sectional shape of the channel. As a squarecross-section, a = 0.21 and b = 0.68 are used in this study.
K urd n ue calculated from the logarithm law describedin the referencx of Hartnetl et al. (1985) and Kozicki etal. (1966). The resuls are shown in Fig. 3 @).
In Fig. 3 (b), the presenr results agree well with thesolid line (theoretical value) in the regions of small Re*.
Then, f deviates from the solid line as Re* increases.
Therefore, under the small f,e* conditions, the flow isbelieved to be steady, and the increase of the friction
factor is mainly attributed to the power law distributionof the velocity field. On the other hand, as Re* increases,
the flow is believed to become unsteady. And, thus,
additional increase ofthe friction factor is obtained due tothe generations of the flow fluctuation and secondary
flow. lt should be marked that the transition region inwhich the 1r'a. and./starts to incr€ase matches raasonably
showing a change in the flow structure is occurring.
Finally, the visualization results are shown in Fig.4.
The figures show the snapshots taken at several
streamwise positions in the cases of sucrose and PAAm
solutions. In the PAAm solution case, the results ofle =0.369 and 1.65, lower and higher Re conditions, areshown to discuss the influence of the Re on the flow
characteristics.
In Fig. 4 (a), the streamlines ofthe ink flows along thecurvature of the serpentine channel. This pattem
remained steady throughout the movie showing thai asteady flow without any no(iceable secondary flow isformed in ahe channel. ln Fig. 4 (b) showing ihe PAAm
solution case ofRe = 0.369, a similar pattem is observed.
Although some disturbance in the streamlines of the dye
was observed instantaneously in other periods of themovie, the flow could be considered to be in steady state.
On the other hand, in l'ig. 4 (c), one can see that rhe

ink panems are greatly dis(urbed in all streamwise
positions, showing that unsteady flow with flow
fluctuation is produced in thc channcl. ln the movie, thefluctuation of the flow shedding downstream of thechannel was clearly observed. It is clear now that thisflow fluctuation causes the heat transfer enhancement andincrease of the pressure loss in the serpentine channel
shown in the previous figures. lt is difficuk to estimate
the exact flow pattern from the visualization results since
the flow appeared to have a three-dimensional structure(a) Sucrose solution case (8e : 2.49, Oe : 1.44)

!=8

rY=9

(b)PAA,,solution case(Rピ =0.369.D̀=0̲213),rr'.9,v.10(c) PAAm solution case (Re = 1.64, De = 0.945)

Fig. 4 Friction factor distributions: (a) relationshipwith Reynolds number, and (b) modified Reynolds[umber based on the power law.
and the camera time resultion was not high cnough tofollow the unsteady flow behaviour in detail. We believe
that, however, in the early stages of the fluid
viscoelasticity influencing the flow, a deviation of the
spanwise velocity distribution is produced at the curved
part of the channel due to the radial flow heading
outwards. This generation of radial flow should be basedon a similar reason described in the instability studies of

Joo and Shaqfeh (1994). That is, the hoop-stressproduced by the polymer motion increases the flow
instability leading the generaie the Taylor-Dean voctices
or a similar secondary flow. Once such asymmetric flowor vortices are formed, then the flow fluctuation could beenhanced at inflection point of the serpentince channel
due to the change ofthe flow direcrions.

4. CONCLUSION
Heat transfer and pressure loss measurements, andflow visualization were carried oul for viscoelastic fluid
flow in serpentine channels. The conclusions obtained
from the exf,eriments are summarized as follows:
Enhancement of heat ransfer performance wasobserved in the PAAm solution (viscoelastic fluid) casecompared with the sucrose solution (Newtonian fluid)case. The average Nusselt number in the PAAM caseincreased markedly as the Re increased Further, average-21-

Nusselt number 1y'a. in the case of the pAAm solution
a straight channel did not show a large diflerenceinwith thesucrose casc indicating that the enhancemenl effect could

be obtained only by the combimtion of the channel
curvature and the fluid viscoelasticity.
Pressurc loss increased markedly as (he Re increased.

By discussing the relationship berween Re and thefriction factor f using rhe modified Re based on the

power law fluid, showed that the increase ofthe pressure
loss is mainly attributed to the flow fluctuation and not tothe power law velocity distributions.

The tendency of the flow behavior shown by thevisualization results con€sponded well with heat trarsfer
and pressure loss measurements mentioned above.

Ducts, lnt. J. Heat on(l-Fhtitl Ftol.,, yot. I 7, pp. 6l l:620.
t 996.
Nomuzi. M., Kayhani. M. H., Nobari. M. R. H.. and Demneh.
M. K-, Convectivc lleat Tmnsfer of Viscoclastic Flou. in a

Curved Duct. ltbt kl Atttdem. el S<.ictt(.(, l:nginccrin| .Ivl
Tec

hrclog . Yol. 5O, pp. J27 -33J - 2cf,g .

Shah, R. K., and London, A. L., Laminar Flow For<.ed
Convectioh irl Du..rr, Advances in Heal Transfer, Supplement,
Academic Press. | 978.

Tamano, S., Iloh, M, Sasakawa, A., and yokota. K., plv
Measurcrnent of Secondsry Flow in Cu.vilinear pipe Flow ofPolymcr Solution. Trans. of JSME part B, Vol. 75 No. 9, pp.
2ll5-2121, 2009 (in Jap6nese).
Teodor, 8., Enrico, S., Groisnlan, A., and Steinbcrg, V, Chaotic

flow and eflicienl mixing in a microchannel wilh a polymer

ACKNOWLEOGEMENTS
This study was suppo(ed by the ministry of education,
culture, spons, science and technology of Japan, and theauthors acknowledge their financial support.

solu.tion, Physical Review E 69,066305,2004.

Wemet M-, Baars, A.. Wemer, p., Eder. C., and Dclgado, A..
Thermal Conductivity of Aqueous Sugar Solutions under High
Pressure, /rr J. Theraophys. \,lol. 28. pp. I l6 t . t | 80, 2007.

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Ka2uya Tatsumi received M.E.
(1999) and PhD (2003) in Kyo.o
Univ Dept. Mech. Eng. He is now
an Associate Professor of Dept. of

V M. K.. Laminar Forced

Conveclion Heat TEnsfer of a Non-Newtonian Fluid in a&uare Ducl, /nr./. Heat Mass Transfer,Vol. 20, pp. l3l5-1324,
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Mech. Eng. and Science, Kyoto
Univ. His current interests include

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Groisman, A., and Steinberg, V, Efficient Mixing al Low
Reynolds Numbers using Polymer Additives, /Vorrrre, Vol. 410,

measurements and simulations of
micro and biological flows,

non-Newtonian flowsinmicrochannels, and compact heatexchangers.

Chee Leong Heong received M.E(201 l) in Kyoto Univ. Dept. Mech.

Eng. He is now working at the
Toshiba Co. Power Systern
Company. His subject of research

was heat transl'er ol viscoelastic
fluid flow in serpentine channels.

pp. 905-908, 2001.

Yusuke Takeda rcceived M.E.

Cucker, F. T., and Ayers, F. D., The Specific Heat of Aqueous(201l) in Kyoto Univ. Dept. Mech.
Eng. He is now working at the

Sucrose Solurions at 20PC and 25'C and the Apparcnt Molal
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Joo, Y. L., and Shaqfeh. E. S. c, Obsewation of Purely Elastic
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Kozicki, W, Chou, C. H., and Tiu, C., Non-Newtonian flow inducts of arbitrary crosssectional slape, Chemicol Engineering
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Naccache, M. F., and Mendes. P R. S., I.lert Tmnsfer to

Non-Newlonian Fluids in Laminar Plow Through Rectangular

-22-

」ヽ

Kazuyoshi Nakabe received M.E.
(1983) in Kyoto Univ. Dept. Mech.

Eng and PhD (1991) in Osaka
University. Hc is now Prof. of Dept.

of Mech. Engineering and Science,
Kyoto Univ. His current interests arc

in (he l'ields ol turbulent mixing.
thermal fluids in nricro devices. heattransfcr and combuslion.