Measurement on Flow and Heat Transfer Characteristics of
Viscoelastic Fluid Flow in a Serpentine Channel
Osamu Nakajima1, Kazuya Tatsumi1,2, Chee Leong Heong1 & Kazuyoshi Nakabe1,2
1

2

Department of Mechanical Engineering and Science, Kyoto University, Japan
Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Japan

Keywords: Heat transfer enhancement, PIV measurement, Viscoelastic fluid, Laminar flow
Abstract: Flow and heat transfer characteristics of diluted viscoelastic fluid flow in a serpentine-curved channel are described in this study. Measurement of two dimensional velocity field using the particle image velocimetry (PIV) and flow visualization was conducted in order to understand unsteady flow characteristics a
nd the vortex structure. In addition to this measurement, average heat transfer coefficient was measured und
er isothermal heated wall condition. The viscoelastic fluid was 64wt% sucrose water solution to which polyacrylamide of 500ppm was mixed. The results showed that in the viscoelastic fluid case, large fluctuations
were produced in the flow and their intensities increased markedly against the Reynolds number in the streamwise and spanwise directions even at Re =1.0~3.0. Larger fluctuation intensities were observed particularl
y at the inflection point of the channel curvature. These fluctuations were produced mainly due to the generation of the longitudinal vortices which was not observed in the Newtonian fluid case. By these flow fluctuations and secondary flows, the heat transfer coefficient increased dramatically.

1. Introduction
The influences of the rheological properties of theviscoelastic fluid on laminar heat transfer, particularlyin the case of straight channel, have been keenly
studied in the past several decades. Hartnett et al.
(1985) and Chunbo & Hartnet (1992) have reported
from their experiment that the heat transfer coefficientin the case of viscoelastic fluid flow increases markedly
compared with the Newtonian fluid flow case. The
main cause was believed to be attributed to thesecondary flow which was generated and enhanced by
the normal force difference. Flow instability ofviscoelastic fluid flow has also been studied with great
deal of interest. Larson et al. (1990) studied the flow
instability of Taylor-Cuette flows in rotating coaxial
cylinders. Joo & Shaqfeh (1994) investigated themechanism of the increase in the flow instability of
Taylor-Dean flows in coaxial cylinder. It is known
from these studies that the flow instability is enhanced
due to the fluid elasticity, and that Taylor vortices canbe generated even under very low Dean number flows.
Recently, several studies on the mixing
characteristics of viscoelastic fluid in a serpentinecurved channel under low Reynolds number condition
have been published in the literatures. Groisman &Steinberg (2001) showed in their measurement thatflow fluctuation can be observed even in the order ofRe ~ 10. Tamano et al. (2009) reported that a pair ofvortices was generated in the time-mean velocity fields
at the outlet of the serpentine channel with circularcross-section. All these results indicate the possibilityof effectively enhancing the mixing performance ormoreover mass and heat transfer at the channel wall. To

the knowledge of the authors, however, there are no
experiments conducted to link such unsteady flow andthe fluid mixing with the heat/mass transfer
performance. Moreover, the characteristics of the flow
fluctuation and vortices have not been understood yet.
It is essential to study these characteristics ofviscoelastic fluid flows in serpentine channels in orderto provide an insight for the feasibility of using theviscoelastic fluids as working fluids, and to aid thedesigning of an effective channel shape and conditions
in order to apply this technique to the fields of thermal
engineering, chemical engineering and medicine. In
this study, measurements of the heat transfer coefficientand velocity field of the viscoelastic fluid flow in a
serpentine channel with a square cross-section are
described.

2. Experimental method
2.1. Experimental apparatus
Figure 1 shows the schematic diagram of theexperimental apparatus applied to the present
measurements. The channel consists of three parts: theinlet and outlet straight channels, and the serpentine
channel. The serpentine channel used for the heattransfer measurement was made of copper in order toapply an isothermal condition to the wall. Constanttemperature water was supplied from the thermostat
bath to the circular cross-channels installed in the wall.
On the other hand, PIV measurements were carried out
using transparent acrylic channels. The channel had asquare cross-section of 5mm in width and height. The
serpentine channel had a periodical shape, which
consisted of 10 repeating units of circular curved parts.

Table 1 Flow conditions in the experiment.
Fluid
Re
De
Wi
Sucrose 1.01 − 4.29
0.59 − 2.48−
PAAm
0.33 − 1.92
0.19 − 1.11
7.0 − 50

Fig. 1 Experimental apparatus and channel shape.
The inner and outer radii were 5 and 10mm,
respectively.
The working fluid was supplied to the channel by apump driven by pressurized air. The mass flow rate wasmeasured by measuring the mass of the fluid flowing
out from the outlet of the channel using an electronic
weighing machine and data logger.

2.2. Heat transfer measurement
In order to measure the fluid temperature for bulkmeantemperature
calculations,temperature
measurement units were placed at the inlet and outlet ofthe copper test section. The fluid temperature at the
inlet was measured by a sheath K-type thermocouple of
0.5mm in diameter having its end point positioned at
the center of the channel cross section. Temperature ata single point only was measured since a uniform
temperature distribution was expected for the inlet flow.
The fluid temperature at the outlet was measured by 7
K-type thermocouples located evenly in the height
direction in the middle of the channel width. Since theavailable temperature distributions obtained from thismeasurement were only in one-dimensional form,
expansion of the temperature distribution from one- to
two-dimension was necessary. Thus, in this study, thefluid temperature was assumed to have a similar
distribution to the measured one at r = Rin in the r and z
directions. The temperature of the heated cupper partwas also measured by K-type thermocouples, thevariation of which was 0.5 °C. Streamwise velocity
distributions of laminar flow in a square duct (Shah,1978) were used in the sucrose solution case. We haveassumed that the velocity distribution in the PAAm
solution case is similar to the laminar flow of
Newtonian fluid case based on the discussion on thefriction factor. The temperatures and velocities
obtained from these processes were employed to
calculate the bulk mean temperatures, and the averageheat transfer coefficient of the serpentine channel..

2.3. PIV measurement
The PIV system was composed of a double pulse
Nd:YAG laser (New Wave Solo3: wave length 532nm)
and high resolution CCD camera (TSI, Powerview Plus
4MP: 12-bit monochrome, 4-Mpixels). A laser sheet
was irradiated to the channel in the direction from the
sidewall to illuminate the particles in that plane. The

height position of the laser sheet was located at thecenter (z/H=0.5) of the channel. The spatial resolutionof the image obtained by the camera was 15μm/pixels,
and the frame rate was 5fps. The total number ofimages and the corresponding time period were 600
and 120s. This condition was sufficient to calculate thestatistics values of the flow fluctuation. PIV analysis
software (TSI, Insight 6.0) was used to obtain the flow
velocity from the recorded images. Glass beads(LaVision,
glass
hollow
sphere:nominaldiameter=10μm, relative density=1.1) were mixed in
the fluid as tracer particles.

2.4. Experimental conditions
Two kinds of working fluids were prepared for theexperiment. One was a sucrose water solution (sucrose
64.4wt%), which was a Newtonian fluid. The other waspolyacrylamide (PAAm) water solution (sucrose
64,4wt%, NaCl 1wt%, PAAm 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 andfluid properties stable.
The fluid viscosity μ, density ρ and relaxation time γ
of PAAm solution were measured prior to theexperiment. μ measured by the rheometer (Anton paar,
MCR-301) were 123mPa·s and 359mPa·s for the
sucrose and PAAm solutions, respectively. The
relaxation time was 2~3s which was calculated byappying the Powell-Eyring (Hartnetl et al., 1985)
model to the measured results using the rheometer. The
heat capacity Cp and thermal conductivity λ, were
derived from the empirical equation shown in thereferences of Gucker and Ayers (1937) and Werner etal. (2007) for the fluid temperature of 25°C.
The flow conditions considered in this study aresummarized in Table 1. Re is the Reynolds number
defined as Re =ρUmDh/μ, where Um and Dh are theaverage velocity and hydraulic diameter, respectively.
De is the Dean number, which is defined as De=Re(2W/(Ri+Ro))0.5. W is the channel width, and Ri andRo are the inner and outer radii of the curved channel.
Wi is the Weissenberg number and is defined as Wi=γ
(Um/Dh). γ is the relaxation time of the solution.

3. Results and discussion
3.1. Heat transfer performance
Figure 5 shows the relationship between the average
Nusselt number, Num, and the Reynolds number, Re,
for the cases of sucrose and PAAm solutions. The
analytical results for the Nusselt number of laminarflow in a straight channel with square cross-section isdepicted in the figure for comparison. This analysis

20
PAAm case
Sucrose case[1]
Chandrupatla et al.

Num

15

10

(a) uθ / U m (sucrose)(b) uθ / U m (PAAm)(c) u r / U m (sucrose)(d) u 'θ 2 / U m (PAAm)(e) u ' r 2 / U m (sucrose)(f) u 'θ u ' r / U m2 (PAAm)

5

0.0

0.5

1.0

1.5

Re

2.0

2.5

Fig. 2 Relationship between average Nusselt num
ber and Reynolds number.
considers the entrance region effect, and is derived by
Chandrupatla & Sastri (1977).
The Nusselt number Num of the sucrose solution
case slightly increases with Re due to the developmentof the thermal boundary layer at the inlet. Further, theresult agrees well with the analytical one showing thevalidation of the measurement. Therefore, the flow inthe serpentine channel is flowing along the curved
channel without accompanying any secondary flows,which is consistent with the small De shown in Table 1.
In the PAAm solution case, Num increases markedly
as Re increases, and shows a considerable heat transfer
enhancement compared to the sucrose solution case.
Num appears to approach to the value of sucrose
solution case as Re decreases. Therefore, it is expectedthat the increase of Num is related more to the
production of secondary flow rather than the change inthe velocity distribution due to the non-Newtonian
behavior such as shear thinning.

3.2. PIV measurement
Figures 3 (a)−(c) show the velocity distributions of
the streamwise (circumferential) and spanwise (radial)
components of the flow velocity measured at the 2nd
curve of the serpentine channel. The results are for the
sucrose (Re=3.3) and PAAm solutions (Re=2.1).
Figures 3 (d)−(f) show the fluctuation intensities andReynolds stress in the case of PAAm (Re =2.1).
As shown in Fig. 3 (a), in the sucrose solution case,which is a Newtonian fluid, a symmetric velocity
profile is observed along the streamwise direction of
the curved channel. On the contrary, in the PAAm
solution case, spanwise flow is generated at the
inflection point of the serpentine channel (X/Dh≅±1.5),
and an outward deviation of the position where thestreamwise velocity becomes maximum can beobserved. These results indicate that the flow flows
from the outside of a curve to the outside of the next
curve. Although not shown here, this secondary flow
was also observed in the streamline structure visualized
by the dye. This flow is one of the reasons why the heattransfer enhancement is obtained.

Fig. 3 Time-mean velocities and fluctuation inte
nsities contours at the 2nd curve.
In Figs. 3 (d), u 'θ 2 / U m shows a large value along
the channel curve near the channel centerline. The
streamwise fluctuation, therefore, exists through thechannel streamwise direction. On the other hand,u ' r 2 / U m is nearly zero in the curve area, and increase in
the area located slightly downstream of each inflection
point of the serpentine channel. As shown in Fig. 3(f),the Reynolds stress u 'θ u ' r / U m2 also increases in thearea adjacent to the inflection point. The increase of
these values is believed to be attributed to threefold.
One is the fluctuation produced along the streamline as
observed in the curved area shown in Fig. 3(b). Since
the flow crosses the channel near the inflection point,
the fluctuation along the streamline will accompany anapparent spanwise fluctuation. The second one is thefluctuation due to the variation of the streamwise
position at which the spanwise flow is located. Namely,
the maximum peak of u r / U m changed its streamwise
position, and increased the apparent spanwise
fluctuation. The third one is the additional fluctuation
generated by the secondary flow and increase of theflow instability. This spanwise fluctuation enhances theheat transfer performance in addition to the secondary
flow (longitudinal vortex) generated in the channel.
In order to evaluate the influence of the fluctuation
mentioned above on the heat transfer performance, thefluctuation energy km (=( u ' x u ' x + u ' y u ' y )/2) iscalculated and depicted against the Reynolds number in
Fig. 4. Note that, km is the value of the fluctuationenergy spatially averaged in the half-curve area of N=2;

20

400

PAAm kmSucrose km
PAAm Num
Sucrose Num

200

15

10

Num

2

2

km [m /s ]

300

100
5

0
-100
0.0

0.5

1.0

1.5

2.0

2.5

3.0

0
3.5

Re

Fig. 4 Relationship between Re and average fluctu
ation energy, k, at the 2nd curve.
i.e. the area shown in Fig. 3. For comparison, therelationship between Num and Re shown in Fig. 2 issuperimposed on the figure. In this case, the verticalrange is adjusted in the following way. First, the scaleof Num and km are adjusted so that Num of the sucrose
solution case and km=0 are located at the same level.
Then, the levels of the maximum values of Num and km
are roughly matched.
In the figure, km in the sucrose solution case remains
constant showing that now fluctuation occurs. This isreasonable since the working fluid is Newtonian fluidand Re is completely in the range of steady laminarflow condition. In the PAAm solution case, km is also
zero at Re <0.5. However, km increases as Re increases
indicating the production of the flow fluctuation in thechannel. Furthermore, the increase rate of km agrees
fairly well with that of Num showing that a considerable
correlation exists between the two values.
We believe that the fluctuation flow observed in thisstudy is more likely to be an unsteady laminar flow
fluctuation rather than the “viscoelastic turbulence”
called in the studies of Groisman and Steinberg. The
heat transfer enhancement is, therefore, attributed to
not only the flow fluctuation mentioned above, but also
by the longitudinal vortex like secondary flow
generated at the inflection point and the channel curve.
From Fig. 4, a correlation should exist between themagnitude of the secondary flow and fluctuation
intensity, and thus the Reynolds number. Further
measurement and discussion on the three-dimensional
structure will be made in the future work.

4. Conclusion
Measurements on the heat transfer coefficient andflow velocity were carried out for the viscoelastic fluid
flow in the square serpentine channel. The conclusions
obtained from the measurements are summarized asfollows:
Enhancement of heat transfer performance wasobserved in the PAAm solution (viscoelastic fluid) casecompared with the sucrose solution (Newtonian fluid)case. The average Nusselt number Num in the PAAM
case increased markedly as the Reynolds number Re
increased.

Streamwise fluctuation was observed along theserpentine channel in the PAAm solution case.
Spanwise fluctuation, and also spanwise flows was,however, only observed in the area located downstreamof the inflection point of the channel curvature. In
addition to these, a secondary flow flowing from theoutside of one curve to the outside of the next curve. A
reasonable correlation between the increase of Num andthe fluctuation energy against Re was observed.
Therefore, the increase of Num is mainly attributed
to the flow fluctuation and secondary flow generated in
the channel which is obtained only by the combinationof viscoelastic fluid and the serpentine channel.

Acknowledgement
This study was supported by the ministry ofeducation, culture, sports, science and technology ofJapan, and the authors acknowledge their financial
support.

References
Chandrupatla, A. R., and Sastri, V. M. K. 1977
Laminar Forced Convection Heat Transfer of a
Non-Newtonian Fluid in a Square Duct. Int. J.
Heat Mass Transfer, Vol. 20, pp. 1315-1324.
Chunbo, X., and Hartnett, J. P. 1992, Influence of
Rheology on Laminar Heat Transfer to
Viscoelastic Fluids in a Rectangular Channel, Ind.
Eng. Chem. Res., Vol. 31, pp.727-732.
Groisman, A., and Steinberg, V. 2001 Efficient Mixing
at Low Reynolds Numbers using Polymer
Additives, Nature, Vol. 410, pp. 905-908.
Gucker, F. T., and Ayers, F. D. 1937 The Specific Heatof Aqueous Sucrose Solutions at 20ºC and 25ºC
and the Apparent Molal Heat Capacity of Nonelectrolytes, J. American Chem. Society, Vol. 59
No. 3, pp. 447-452.
Hartnett, J. P., and Kostic, M. 1985 Heat Transfer to a
Viscoelastic Fluid in Laminar Flow Through a
Rectangular Channel, Int. J. Heat Mass Transfer,Vol. 28 No. 6, pp. 1147-1155.
Joo, Y. L., and Shaqfeh, E. S. G., 1994 Observation of
Purely Elastic Instabilities in the Taylor-Dean
Flow of a Boger Fluid, J. Fluid Mech., Vol. 262,
pp. 27-73.
Larson, R. G., Shaqfeh, E. S. G., and Muller, S. J. 1990
A Purely Elastic Instability in Taylor-Couette flow,
J. Fluid Mech., Vol. 218, pp. 573-800.
Shah, R. K., and London, A. L. 1978 Laminar Flow
Forced Convection in Ducts, Advances in Heat
Transfer, Supplement, Academic Press.
Tamano, S., Itoh, M, Sasakawa, A., and Yokota, K.
2009 PIV Measurement of Secondary Flow inCurvilinear Pipe Flow of Polymer Solution, Trans.
of JSME part B, Vol. 75 No. 9, pp. 2115-2121．
Werner, M., Baars, A., Werner, F., Eder, C., andDelgado, A. 2007 Thermal Conductivity of
Aqueous Sugar Solutions under High Pressure, Int.
J. Thermophys., Vol. 28, pp. 1161-1180.