Turbulence, Heat and Mass Transfer 7
 2012 Begell House, Inc.

Flow Observation and Heat Transfer Performance of
Viscoelastic Fluid Flow in a Serpentine Channel
K. Tatsumi1,2, O. Nakajima1, W. Nagasaka1 and K. Nakabe1,2
1

Department of Mechanical Engineering and Science, Kyoto University,
Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan, tatsumi@me.kyoto-u.ac.jp
2
Advanced Research Institute of Fluid Science and Engineering, Kyoto University,
Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Abstract –This paper describes the results of heat transfer, flow visualization and PIV measurements conducted
for the viscoelastic fluid flow in a serpentine channel with square cross-section under low Reynolds number
conditions. Polyacrylamide water solution was used as viscoelastic fluid, and was compared with the results of
Newtonian fluid．In the visualization, flow fluctuations and secondary flows did not appear in the Newtonian
fluid case. On the other hand, unsteady flow and longitudinal vortices were observed in the viscoelastic fluidcase. The velocity fields showed that large flow fluctuations were generated in the downstream area of theinflection point of the serpentine channel. Single or a pair of longitudinal vortices was generated in this area.
The generation of these vortices can be attributed to the normal stress produced by the viscoelasticity of thefluid and the curvature of the channel. Considerable enhancement of heat transfer performance was obtained by
the flow fluctuation and longitudinal vortices.

1. Introduction
Applying the viscoelastic fluid as a working fluid in the channel flow is considered to be analternative solution to the geometrical and mechanical modification of the channel for heattransfer enhancement [1,2]. The high shear stress generated in the channel will cause thepolymers solved in the fluid to contract and expand leading to an appearance of the elasticity
and additional normal stresses in the flow. In combination with a certain flow pattern, thiselasticity of the fluid increases the flow instability resulting in generation of an unsteady flow
(viscoelastic turbulence) even in low Reynolds number regime [3,4].
Recently, several studies on the mixing characteristics of viscoelastic fluid in a
serpentine-curved channel under low Reynolds number condition have been published in theliteratures. Groisman & Steinberg (2001) carried out flow visualization and point
measurement of the flow velocities using laser Doppler anemometer. Flow fluctuation wasobserved even in the order of Re ~ 10, accompanying the enhancement of the fluid mixing.
Teodor et al. (2004) conducted a visualization experiment in serpentine microchannels using
fluorescent dye. Even in this scale, production of the unsteady flow and enhancement in thefluid mixing was observed. Tamano et al. (2009) made PIV measurements in curved channels
with circular cross-section and found a pair of vortices similar to the Taylor vortices in thetime-mean velocity fields. These results show that considerable fluctuations can be obtainedin such flows suggesting the possibility of enhancing the mixing performance or, moreover,mass and heat transfer at the channel wall effectively. To the knowledge of the authors,
however, there are no experiments conducted to link the viscoelastic turbulence with heattransfer performance in serpentine channels. It is essential to understand the turbulence andheat transfer characteristic of such flows in order to provide insights for evaluating theTurbulence, Heat and Mass Transfer 7(a) Heat transfer measurement(b) Flow visualization and PIV measurements
Figure 1: Experimental apparatus used for the heat transfer measurement, flow visualization and
PIV measurement.

feasibility and designing of effective channel shape for practical use in thermal engineering.
From this background, measurement of the heat transfer coefficient under isothermal wallcondition was carried out in the serpentine channel, the schematic of which is shown in Fig. 1.
Flow visualization and velocity measurement were carried out by supplying dye to the flow
and using the particle image velocimetry (PIV) in order to understand the flow behavior. Twotypes of working fluids were investigated. One was a viscoelastic fluid of 64wt% sucrose
water solution to which polyacrylamide of 500ppm was added, and the other was a
Newtonian fluid of a sucrose water solution.

2. Experimental Procedures
Figure 1 shows the schematic diagram of the experimental apparatus applied to themeasurements. The channel consisted of three parts: the inlet and outlet channel parts, and thetest section, the channel shape of which is a serpentine one with semicircle curves. In the heattransfer measurement, the walls of the test section were 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 of the fluid flowing out from the outlet of thechannel using an electronic balance, the accuracy of which was 0.01g. The mass of the fluidchanged linearly during the measurement, and the time average value was used to obtain the2

K. Tatsumi et al.

average volume flow rate, the accuracy of which was 0.3ml/min.
For the heat transfer measurement, the inlet and outlet units were made of acrylic, towhich a straight channel was embedded. The test section was made of copper in order toproduce an isothermal condition to the wall. As shown in Fig. 1 (a), cylindrical channels weretransversely drilled to the wall to which constant temperature water was supplied from thethermostat bath to keep the wall temperature of the channel constant. The inlet and outlet
parts were attached to the test section and sealed with silicon sealant. For the flow
visualization and PIV measurement, the channel made of transparent acrylic was used. 5mm
holes were drilled through the walls located at the end of the channels. Tubes were connectedto these holes supplying fluids to the channel from the pump, and leading the outlet fluid to acontainer to measure the mass flow rate.
The schematic and dimensions of the serpentine channel are shown in the lower part of
Figures 1 (a) and (b). The channel had a square cross-section of 5mm in width and height.
The serpentine channel had a periodical shape, which consisted of 10 repeating units ofcircular curved parts. The inner and outer radii were 5 and 10mm, respectively.
2.1 Heat transfer measurements
In order to measure the fluid temperature for bulk mean temperature calculations, temperature
measurement units were placed at the inlet and outlet of the cupper test section. The fluid
temperature at the inlet, Tb,i, was measured by a sheath K-type thermocouple of 0.5mm indiameter having its end point positioned at the center of the channel cross section.
Temperature at a single point only was measured since a uniform temperature distribution
was expected for the inlet flow. The fluid temperature at the outlet Tb,o was measured by 7
K-type thermocouples located evenly in the height direction in the middle of the channel
width. Since the available temperature distributions obtained from this measurement were
only in one-dimensional form, expansion of the temperature distribution from one- to
two-dimensional directions was necessary. Thus, in this study, the fluid temperature wasassumed to have a similar distribution in the y and z directions to the one measured at z = 0.
The temperature of the heated cupper part was measured by K-type thermocouples, whichwere embedded in the cupper surface. The variation of the temperature was 0.5 °C affirmingthat a constant wall temperature condition was obtained at the channel.
In combination with the measured temperature mentioned in above, the streamwise
velocity distributions of a square cross-section in a laminar flow case (Shah, 1978) were usedin the sucrose solution case in order to obtain the bulk mean temperatures of fluids at the inlet
and outlet. In the PAAm solution case, the velocity distribution was calculated on the basis of
the following procedure. First, we will use the velocity distribution of the power law fluid forthe flow in a circular duct shown by Wiginton and Dalton (1970).
n 1


u
3n  1   r  n 1  
Umn 1   a  



(1)

In order to convert this equation to the velocity distribution of a flow in a square duct, thedifference between the velocity distributions of flows in circular and square ducts of
Newtonian fluid is calculated and, then, multiplied to the Eq. (1). The result is shown inEq.(2).
3

Turbulence, Heat and Mass Transfer 7

Fluid
Sucrose
PAAm

Table 1: Flow conditions of the heat transfer experiment.
Um [mm/s]
Re
Wi
ND
10  400.82  2.4
0.1  0.5
10  810.30  2.64 0.05 0.49
14.2140u 0.1438ra4  0.334ra3  0.2829ra2  0.0161ra  1.0577
Um



(2)

1.2 n 1
1.2 n 1
3n  1   y  n    y  n 

1 
1 


   2.5 n  1   2.5 where ra = y/25 = z/2.5. The velocities obtained from Eq. (2) and the temperature distribution
were employed to calculate the bulk mean temperatures in the viscoelasic fluid flow case.
The average heat transfer coefficient was then calculated on the basis of the logarithmic
temperature difference as shown by Eq. (3).
Tw  Tb,iAs
Tw  Tb,owhere m and As are the mass flow rate and the heat transfer area.
hm c p ln(3)

2.2 Pressure loss measurement
To measure the pressure loss in the test section, electronic pressure gauges (Keyence Co.,
AP-C30), the measurement resolution of which was 0.1kPa, were connected to the inlet andoutlet of the test section through a 1mm hole drilled at the top wall as shown in Fig. 1 (a). The
static pressure at each position was measured and used to calculate the fanning friction factor,
f , defined as Eq. (4) .
2P Dhf (4)
U m 2 4 L
Dh and L are the hydraulic diameter and channel length, respectively. Um is the mean velocity.
2.3 Flow visualization
Flow visualization using dye was carried out in this study to understand the flow behavior in
the channel. Syringe pump (Harvard apparatus., econoflo) was used to supply the ink though
a 4mm inner diameter tube to a syringe needle, which was inserted to the channel through the
top wall. The images of the visualization were recorded using two digital video cameras(Sony, HDR-CX370V) measured from above and side of the channel simultaneously.
2.4 PIV measurement
The PIV system was composed of a double pulse Nd:YAG laser (New Wave Solo3: wave
length 532nm), high resolution CCD camera (TSI, Powerview Plus 4MP: 12-bit monochrome,
4-Mpixels) and a synchronizer (TSI, 610034). The spatial resolution of the image obtained by
the camera in combination with the lens (Nikon Co., AF-Zoom-Nikkor 24-85mm) was
15m/pixels. The frame rate of the measurement was 5 frames/s. 50 pairs, which was 10s
converted in time, of the images were recorded 12 times during the measurement. Therefore,
4K. Tatsumi et al.

(a) Measured from above (x-y plane)(b) Measured from side (r-z plane)
Figure 2: The planes of the velocity fields measured by the PIV (laser sheet positions).

the total time was 120s, a period of which was sufficiently long to calculate the time averagevalues of the velocity and fluctuation quantities. PIV analysis software (TSI, Insight 6.0) wasused to calculate and analyze the velocity distribution from the recorded images. For the PIV
measurement, glass beads (La Vision, glass hollow sphere) with nominal diameter of 10mwere mixed in the fluids as tracer particles. The concentration of the particles was 0.016wt%.
The velocity fields were measured from two directions as depicted by the schematic
diagram shown in Fig. 2. One was from the top of the channel and the other was from the sideof the channel. For the xy plane, measurement was made at the middle of the channel height(z = 0.5H). For the xz plane, measurement was carried out so that the plane crossed theinflection point of the curved channel. Therefore, as shown in the Fig. 2(b), velocity fields at
two cross-sections, which were the upstream and downstream sides of the semi-circle, wereobtained. The thickness of the laser sheet was approximately 0.5mm.
2.5 Working fluid preparation
Two kinds of working fluids were prepared for the measurement. One was a sucrose water
solution (sucrose 64.4wt%), which was a Newtonian fluid. The other was the polyacrylamide(PAAm) water solution (sucrose 64,4wt%, NaCl 1wt%, PAAm 500ppm), which was aviscoelastic fluid. NaCl was mixed in the fluid to keep the polymer structure and fluid
properties stable. The fluids were prepared mixing the solute to water using a pot rotating mill.
Measurement was carried out within three days the working fluid was prepared confirmingthat degradation of the fluid was not observed within this period.
The fluid density , viscosity andrelaxation time  were measured prior to theexperiment.  and  were measured by the rheometer. In this case,  was calculated byapplying the logarithmic fitting against the fluid temperature on the basis of the equation
proposed by Kampmeyer and Girifalco. Curve fitting was also made against the shear rate
based on the power law approximation. The properties were calculated in each experimental
case applying the reference temperature and shear rate of the flow. The logarithm temperatureof the channel was used as the reference temperature in the heat transfer measurement.
4Um/Dh was applied as the reference shear rate. For reference,  of the sucrose and PAAm
solutions at the temperature of 20C and shear rate of 10s-1 were andPas,
respectively. The relaxation time was measured by adjusting the general Maxwell model tothe time history of the shear stress after a constant shear rate was suddenly applied to the fluid.
In this case, the influence of the fluid temperature was taken into account. For reference,was in the range of 3.1~3.6s in the case of fluid temperature equal to 20C.
The heat capacity Cp and thermal conductivity k used to obtain the heat transfer
coefficient were derived from the empirical equation shown in the references of Gucker et al.
(1937) and Werner et al. (2007) for the fluid temperature of 25°C.

5Turbulence, Heat and Mass Transfer 7

100

Present (sucrose)
14.227/Re
Modified friction factor fN '

50

f

f

Fitting line of f N'
10

10

5

Present (PAAm)*
16/Re
Modified friction factor fp 'Fitting line of fp '

1

2

3

0.5

1

Re*

Re

(a) Friction factor in sucrose case(b) Friction factor in PAAm case
Figure 3: Relationship between (a) friction factor and Reynolds number in the case of sucrose
solution, (b) friction factor and modified Reynolds number in the case of PAAm solution.
16
14

PAAm case
Sucrose case
Sucrose case (simulation)

12

PAAm case
Sucrose case (simulation)

10

10

Num

Num

12

14

8

8
6

6

4

4

0.5

1

Re

10

5

100

1000

PUm

(a) Influence of Reynolds number(b) Influence of pumping power
Figure 4: Relationship between (a) average Nusselt number Num and Reynolds number, (b) average
Nusselt number Num and the pumping power PUm.

2.6 Experimental conditions
The flow rate was changed in the experiments in order to examine the influence of the
Reynolds number (Re = UmDh/) on the heat transfer coefficient, pressure loss and flow
behavior in the channel. The conditions are summarized in Table 1. ND shown in the table isthe Dean number, which is defined as Eq. (5).
0.5

 2D 
N D  Re h 
(5)
 R 
W is the channel width, and Ri and Ro are the inner and outer radii of the curved channel.
Dean number can be used to assess the magnitude of the curvature effect on the flow structure,for example the generation of the Taylor-Dean vortices. Wi is the Weissenberg number and isdefined as follows.
 4U 
Wi    m 
(6)
 Dh 

6

K. Tatsumi et al.

3. Results and Discussion
3.1 Heat transfer and pressure loss characteristics
Figure 3 shows the friction factor distributions in relation to the Reynolds number Re and themodified value Re* in the cases of sucrose and PAAm solutions. Re* is a value defined as Eq.
(7), which is used to rearrange the relationship with the friction factor in the case of powerlaw fluids.
U m2n Dhn
Re *  n1n(7)
8 K B  A / n Constants A and B appearing in Eq. (7) are respectively 0.2121 and 0.6766 in the case ofsquare duct [1].
The relationship between the friction factor and the Reynolds number can be described asfollows. For the case of sucrose, which is Newtonian fluid, the correlation of f =14.2/Re issatisfied for the flow through a square duct. For the power law fluid flow, the relationshipbetween f and Re* can be shown as f =16/Re* [1]. These correlations are shown by the dashlines in Figures 3 (a) and (b). Comparing these lines with the measurement results, one cansee that the theoretical value over predicts the f distributions particularly in the case of sucrose
solution. This is mainly attributed to the variation of the fluid property in the cross-sectional
plane of the channel owing to the temperature distribution generated during the heat transfer
measurement (the friction factor is measured simultaneously with the heat transfer
measurement). This leads to the change of the velocity distribution in the cross-section.
Although the temperature difference between the fluid and wall is not large, the hightemperature dependency of the fluid mainly due to the sucrose produces such effect. In orderto take this influence into account, f is modified using the following modification coefficient.


14.2   (Tw ) 
16   (m , Tw ) 
fN '
(8)


 , fp'
Re*   (m , Tm ) Re   (Tm ) 
The numerator and denominator are the fluid viscosities based on the wall and logarithm
temperature of the fluid, respectively.  is constant and is 0.58 [12]. The results are shown in
Figure 3 depicted by the solid line. In Fig. 3 (a), the measurement results and modified
friction factor agree very well showing the validity of the present measurement. In Fig. 3 (b),the measurement results agree well with fp’ in the low Re* area, the condition of which theflow is believed to be steady. As Re* increases, the measurement result increases and deviatesfrom fp’. As will be discussed by the visualization results, the flow becomes unsteady as Re
increases and large scale vortices are generated in the serpentine channel. The increase of fp’
is believed to be attributed to this change of the flow behavior.
The relationship between the average Nusselt number, Num, and Re is shown in Fig. 4 (a).
The solid line shown in the figure plots the numerical results of Chandrupatla et al. (1977),
which presents the average Nusselt number of laminar flow in a square duct considering theentrance region effect. In this case also, we will modify the value by taking the temperaturedependency of the fluid properties into account by applying the modification shown by
Eq.(9).

  (m , Tw ) 
Nu N '  Nu N   (m , Tm ) 
7



(9)

Turbulence, Heat and Mass Transfer 7(a) Re=0.1, Wi=21.2, ND=0.1(b) Re=1.3, Wi=184, ND=1.1 (period 1)(c) Re=1.3, Wi=184, ND=1.1 (period 2)(d) Re=1.3, Wi=184, ND=1.1 (period 3)
Figure 5: Visualization of the streak lines at the 2nd curve of the serpentine channel in the
PAAm solution case (measurement of the side and top views are synchronized).

 is constant and is -0.14 [12]. In Fig. 4 (a), the measurement results of the sucrose case agree
well with the solid line confirming the validity of the measurement. On the other hand, Num inthe case of PAAm solution shows a similar value with the sucrose case in the region of Re<0.5. Then Num increases as Re increases. The starting point of the increase of Num matcheswith the one observed in the f distribution shown in Fig. 3 (b). Therefore, the increase of theheat transfer coefficient is believed to be attributed to the generation of the unsteady flow andvortices. At Re  2, Num in PAAm case takes 3 time greater value than the sucrose caseshowing an effective heat transfer enhancement.
As the f and Num both increase, the relationship between Num and the pumping powerPUm is discussed in Fig. 4 (b). As shown in the figure, larger Num is observed in the region
where the flow becomes unsteady and vortices are generated. Therefore, when an equivalentpumping power is applied to the channel, larger heat transfer rate is obtained showing a highoverall performance of the PAAm solution case.
3.2 Flow visualization
The streak lines visualized by the dye in the case of PAAm solution are shown in Fig. 5. Fig.
5 (a) shows the results of the flow under the lower Reynolds number condition (Re = 0.1), and(b) ~ (d) are the results of the same flow of Re = 1.3 each presenting the images at different
time period. Visualized images taken from the side and top of the channel, which wererecorded simultaneously, are both shown in each figure.
As shown in Fig. 5 (a), the streak lines flow along the channel and their relative positions
to the channel cross-section are kept constant. Therefore, the flow is in steady state, and nonoticeable secondary flows, such as Taylor-Dean vortices, are generated in the channel. As Re
increases, the flow starts to fluctuate, and a strong secondary flow similar to a longitudinalvortex is observed in the channel particularly in the downstream area of the inflection point of8

K. Tatsumi et al.

(b) u r / U m(a) u / U m(c)u'2 / U m(d)u r'2 / U m

Figure 6: Mean velocity and fluctuation intensity distributions at the N = 2 curve in the case of
PAAm solution (x-y plane at z = 0.5H, Re = 2.2, Wi = 120).

the serpentine channel. As Re increases Wi also increases. Since no such fluctuation or
vortices were observed in the sucrose solution case even under high Re conditions, these
phenomena are believed to be attributed to the increase of the normal stress owing to theviscoelasticity of the fluid as Wi increases. This will be discussed in the next section.
Comparing the patterns of the streak lines shown in Figures 5 (b) ~ (d), one can see thatthe vortices patterns differ with time. In Fig. 5 (b), downstream of the position  = 90, two
streak lines are observed. The one located at the upper side of the channel will move upwards
and also inwards toward the inner side of the channel curve. The other one located at thelower side of the channel will move downwards and outwards as the dye flows downstream of
the curved part. This streak pattern shows that a pair of longitudinal vortices is generated in
the channel. In Figures 5 (c) and (d), all the streak lines located at the outside of the channel
curve at  = 90 moves downwards in the downstream area. The streak lines located at theupper half of the channel move outwards of the curve while the streak lines located at thelower half of the channel flow inwards. Therefore, the results show that a single anticlockwise
vortex is generated in these cases. These pair and single vortices appear alternatively in thechannel, which produces the fluctuation of the streak lines mentioned above.

9

Turbulence, Heat and Mass Transfer 7(a)  = 90(b)  = 90(c)  = 78Figure 7: Mean velocity distributions on the xz plane measured at the N = 2 curve in the case of
PAAm solution ((a) and (b): Re = 2.0, Wi = 333, (c): Re = 2.2, Wi = 319. Conditions are different
due to the change in the fluid properties when the solution was prepared).

3.3 PIV measurement
Figures 6 (a) and (b) show the velocity distributions of the streamwise (circumferential) andspanwise (radial) components of the flow velocity measured on the xy plane of the channel
middle height at the 2nd curve of the serpentine channel. Figures 6 (c) and (d) show the
fluctuation intensities.
Although not shown here, the spanwise velocities and the fluctuation intensities were
nearly zero, and the streamwise velocity distributions showed a similar pattern with thesucrose solution case under the lower Re and Wi conditions. As shown in Figures 6 (c) and (d),as the flow rate increases the fluctuation intensities increase in the streamwise and spanwise
directions. These values increase greatly particularly in the area downstream of the inflection
point of the serpentine channel. This characteristic agrees well with the one observed in theflow visualization shown in Fig. 5.
Figures 6 (a) and (b) show that the main flow, the area of which the streamwise velocity
takes its maximum value, flow along the outside of the curved channel and crosses thechannel downstream of the infection point. The location of the area where the fluctuation
intensities take their maximum peaks matches with this position. On the other hand, thespanwise velocity and the fluctuation intensities show considerably small value at the curved
part (  0). Larson et al. (1990) have reported that in the rotating co-axial cylinder case,Taylor vortices are generated in the curved channel due to the increase of the instability of theviscoelastic fluid flow. However, in the present case, the magnitude of the spanwise flow andintensities observed in the curve part was small indicating that no such vortex is generated.
These might be attributed to twofold. The first one is the relatively small Wi number of thepresent study which is Wi  100. And the change of the curvature direction of the semi-circle
10

K. Tatsumi et al.

part can be another reason. Namely, the curvature direction could have changed before thevortex was able to develop due to the normal stress produced by the viscoelastic fluid.
Figure 7 show the mean velocity vectors on the y z plane (cross-section) measured at
the streamwise positions of  = 90, 78 and 90. In all figures, one can clearly find thegeneration of the longitudinal vortices. Comparing (a) and (b), the direction of the vortices are
the same, and this trend was also observed in the instantaneous velocity distributions. This
indicates that the vortex observed at  =90 is not the one which was convected downstream
from the location of  =90. Further, the vortex generated at the infection point of thechannel decays as it flows downstream in the curved area, and the generation of the next
vortex starts when the flow reaches the next infection point.
Generation of a pair of vortices is observed in Fig. (c). As discussed in the previous
sections, the Dean number ND of the flow examined in this study is small, and indeed Dean
flow was not observed in the sucrose solution case. Therefore, the pair of vortices observed inFig. (c) can be attributed more to the normal stress difference of the viscoelastic fluid flow.
As is well known, the curvature of the channel will produce a stress with a direction pointing
toward the center of the curvature due to the normal stress difference, (τ11τ22)/r [14]. As thefluid flows through the curve part, a force generating a flow flowing toward the inner side of
the curve will work on the fluid in the area near the top and bottom walls due to the large
shear stress. On the contrary, this force will be relatively small in the middle of the channel.
Thus, the main flow located in the middle of the channel height will tend to flow through theouter sides of each curve as shown in Fig. 6 (a). This flow pattern will produce a flowcrossing the channel in the area near the inflection point. This is believed to be one of thereasons for the generation of a pair of vortices observed in Fig. 7 (c). This flow and vortex
structure change by time and leads to the fluctuation of the streak lines observed in Figures 5(b)(d). As described previously, the fluctuation of the spanwise component observed in Fig.
6 (d) is believed to be attributed mainly to this temporal behavior of the vortices.
From these measurements, the increase of the fluctuation intensities observed in Fig. 6
can be attributed to twofold. One is the fluctuation produced along the streamline as observedin the curved area shown in Fig. 6 (c). Since the flow crosses the channel near the inflection
point, the fluctuation along the streamline will accompany an apparent spanwise fluctuation.
The second one is the fluctuation due to the variation of the vortex pattern observed in Fig. 7.
As mentioned in Section 3.2 and in above, the vortex changes its pattern from a single vortex
to a pair of vortices with time. Even with the pair of vortices, the shape of the two vortices is
not always symmetric. Further, the streamwise position and the direction of the vortices
change. Such behavior of the vortices will consequently produce the flow fluctuation
observed in Fig. 6. The heat transfer enhancement is, therefore, attributed not only to theunsteady flow, but also by the longitudinal vortex like secondary flow generated at the
inflection point and the channel curve shown in Fig. 7.

4. Conclusions
Measurements of the heat transfer coefficient, flow visualization and flow velocity werecarried out for the viscoelastic fluid flow in the serpentine channel with square cross-section.
The conclusions obtained from the measurements are summarized as follows:
Enhancement of heat transfer performance was observed in the PAAm solution casecompared with the sucrose solution case. The average Nusselt number Num in the PAAm caseincreased markedly as the Reynolds number Re increased, and showed three times greater
value at Re  3. For the overall performance considering the pumping power, a larger Num
11Turbulence, Heat and Mass Transfer 7

was obtained with the same pumping power in the PAAm solution case compared with thesucrose solution case.
The streak lines visualized by the dye showed that steady flow was obtained when the Re(and Wi) was small in the PAAm solution case. As Re increases the flow starts to fluctuate
and a generation of secondary flow was observed.
Streamwise fluctuation was observed along the serpentine channel in the PAAm solution
case. Spanwise fluctuation, and also spanwise flows was, however, only observed in the area
located downstream of the inflection point of the serpentine channel. In the same area,
generation of longitudinal vortices was observed at the cross-sectional plane, which was
believed to be attributed to the normal stress produced by the viscoelastic fluid. The variationof the vortex size and position was one of the reasons for the flow fluctuation.

5. Acknowledgements
This study was supported by the ministry of education, culture, sports, science and technologyof Japan, and the authors acknowledge their financial support.

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