Turbulence, Heat and Mass Transfer 8
 2015 Begell House, Inc.

Heat Transfer Characteristics of Viscoelastic Fluid in Transitional Flow through a
Serpentine Channel

K. Tatsumi, R. Kimura, N. Shinotsuka and K. Nakabe
1

Departiment of Mechanical Engineering and Science, Kyoto University,
Kyotodaigakukatsura, 615-8540 Kyoto, Japan, tatsumi@me.kyoto-u.ac.jp
Abstract – The local heat transfer, pressure loss and flow characteristics of the viscoelastic fluid in the transitionand developed flows through a serpentine channel are described in this study. The flows became unsteady andlongitudinal vortices-like secondary flows were generated even under low Reynolds number condition of Re~1
due to the normal stress differences produced by the viscoelasticity of the fluid. This enhanced the heat transfer
performance markedly. The vortex structures changed depending on the streamwise position and Weissenberg
number and showed three transition stages: a pair of moderate vortices, a single vortex with a drift of main flow
toward the wall, and a pair of strong vortices. These vortices affected the local heat transfer characteristics at
the top-bottom walls and sidewalls, their streamwise distributions and their unsteady behavior.

1. Introduction
Viscoelastic fluid produces interesting and effective flow structures and features from physicaland industrial point of view in various channels and condition. The viscoelasticity of the fluid
can provide an increase of the flow instability and generate unsteady flows under low Reynolds
number conditions. It can also generate secondary flows due to the appearance of the normal
stress differences which accompanies important transport phenomena as enhancement of fluid
mixing and heat transfer at the channel walls.
The influences of the rheological properties of the viscoelastic fluid on laminar heat transfer
have been keenly studied in the past several decades for various channel flows. Chunbo &Hartnett (1992) reported that the heat transfer coefficient in the case of viscoelastic fluid flowin straight channels was higher than the Newtonian fluid case. The main cause was attributed
to the secondary flow which was generated and enhanced by the normal stress difference.
Recently, several studies have shown that unsteady flow is observed in viscoelastic fluid offlows through a serpentine channel and good mixing can be achieved even under low Reynolds
number conditions of Re<10 [3-6].
The authors have carried out measurements of average heat transfer coefficients, pressure
losses and flow velocities of viscoelastic fluid in low Reynolds number (Re~1) flows through aserpentine channel [7, 8]. The influence of the fluid properties on these characteristics wasevaluated to understand the correlations of dimensionless fluid parameters. Effective secondary
flows were generated accompanying remarkable enhancement in the heat transfer with areasonable pressure loss increase. However, a full understanding of the relationship between
the vortices and heat transfer characteristics remains as a problem to be solved.
In this study, flow visualization and measurement of local heat transfer coefficient are
carried out for flow in a channel expanded in the streamwise direction. The influences of thelocal positions, flow conditions including the developing and developed regions, and the fluid
viscoelastic properties on the relationships between the flow structure and heat transfer
characteristics are discussed to understand the mechanism of heat transfer enhancement.

Turbulence, Heat and Mass Transfer 8

Figure 1: Experimental apparatus of the heat transfer and pressure loss measurements of flows in a
serpentine channel.

2. Experimental Methods
Fig. 1 shows the experimental apparatus and the serpentine channel of the present study. The
serpentine channel had a square cross section 5 mm on a side, and consists of semicircle partsconnected periodically in the streamwise direction. The inner and outer radii of the semicircle
part were Ri = 5mm and Ro = 10mm, respectively. To evaluate the heat transfer characteristics
in the transitional flow and developed flow regions, the number of the curve units, N, were set
as 30.
Constant heat flux conditions were applied to the channel walls in the heat transfer
measurements. Stainless steel films with thickness of 0.5mm were attached to the walls to which
direct current was supplied. The wall temperatures were measured by attaching thermocouples
to the stainless steel from the backside taking account of the heat and electric insulations. Twotest sections, one with the top and bottom walls heated, and the other with sidewalls heated
were employed in this study. The unheated walls were designed to be transparent in order toperform the flow visualization through these walls simultaneously with the heat transfer
measurement.
The bulk mean temperatures of the fluid at the inlet and outlet of the test section wereobtained using the fluid temperatures measured at each location. At the inlet a sheath-type
thermocouple was inserted to measure the fluid temperature at the center of the cross-section.
At the outlet, 5 and 7 thermocouples were placed with equal space in the spanwise and height
directions, respectively. Fully developed velocity profile of a square channel was applied tothese temperature to calculate the bulk mean temperature.
The heat transfer coefficients were calculated by the local heat flux, wall temperature Tw andthe local bulk mean temperature Tm,x. Tm,x of each streamwise position and the wall heat flux
qw can be estimated from the voltage and current applied to the heating plate, and the inlet andoutlet bulk mean temperatures. However, due to considerable effects of the heat conduction in
the streamwise direction and heat loss to the surrounding walls appearing under the low
Reynolds number conditions, three-dimensional numerical simulation was performed using theauthors’ original code to calculate Tm,x and qw.
As mentioned previously, flow visualization using dye was carried out simultaneously withthe heat transfer measurement to understand the flow behavior in the channel. A syringe needle

K. Tatsumi et al.

with a pore located at the side of its end was inserted from the sidewalls of the channel of which
the top and bottom walls were heated. Working fluid to which blue ink was added by 2wt%,
was supplied to the channel through the needle by a syringe pump (Harvard Apparatus:
econoflo). The images of the streak lines were recorded using a digital video camera (Sony:
HDR-CX370V) measured from the side walls of the channel.
Pressure loss was measured by two pressure gauges installed to the inlet and outlet of thetest section as shown in Fig. 1.
The working fluid was supplied from a pressurized tank to the channel without using any
mechanical pump to avoid flow fluctuation. The mass of the fluid flowing from the outlet wasmeasured by an electronic balance to measure the mass flow rate.
An aqueous solution of 500ppm polyacrylamide (PAAm, MW: 1.8×107), 1wt% NaCl, and64.4wt% sucrose was used as viscoelastic fluids. Sucrose was mixed in the fluid to mainly
increase the viscosity of the solution. NaCl was added as a counter ion to prevent the shear
thinning effects and the aggregation of the polymers. An aqueous solution of 64.4wt% sucrose
only was used as Newtonian fluids to compare with the viscoelastic fluids. The fluid viscosity
and relaxation time were measured by a rheometer in advance of the experiment to define thefollowing dimensionless values.
The sucrose concentration in the PAAm solution is changed to evaluate the effects of thephysical properties particularly the viscoelasticity on the heat transfer characteristics. In thiscase, solutions of three concentration conditions, i.e. 64.4, 60.0 and 57.0wt%, were preparedand measured.
The range of the flow conditions are summarized in Table 1. The parenthetic values of the
PAAm presents the sucrose concentration. The definition of the values are Reynolds number
Re=UmDh/, Dean number, ND=Re √𝐷ℎ /2𝑟 and Weissenberg number, Wi=4Um/Dh,
respectively. Um and Dh are the cross-sectional average velocity and the hydraulic diameter. , and  are the density, viscosity and relaxation time of the solution. Pr is the Prandtl number.
Table 1: Experimental conditions and dimensionless values.

Fluid
PAAm(64)
SucroseUm [mm/s]
4.677.4
5.129.8

Re
0.11.8
0.62.1

Pr12802470
420650ND
0.11.1
0.31.2

Wi
8220


As previously mentioned, the rheological properties of the working fluid are measured using
a rheometer (Anton Paar: MCR-301). The effects of temperature and shear rate on the viscosity and relaxation time  were evaluated by applying the Kampmeyer-Girifalco equation(modified version of Andrade and Guzman equation) [9, 10] to the relationship between theviscosity and temperature, and the shear rate as shown in Equations (1) and (2).

  K n 1
log10  m , Tm    m  (1)Tm  273

Tm  2732(2)

Shear rate is calculated as  =4Um/Dh.  and  are constants which were obtained by themeasurement carried out under the condition of Tm=20C. These two values were not largely
influenced by the temperature, and was used as constants for other temperature conditions. As
for  which is dependent with the shear rate, the value was obtained using Eq. (3), in which theTurbulence, Heat and Mass Transfer 8

values of Tm=20C was also applied.
 T20  273 T20  273 
The coefficients are summarized in Table 2.

 m   log10 K m, 20mn 1   







(3)

2

Table 2: Coefficients used to define the viscosity and relaxation times.

Fluid
PAAm(64)
PAAm(60)
PAAm(57)
Sucrose

K
0.54
0.29
0.20
0.13

n
0.86
0.85
0.83
1





3.1×103
3.6×103
3.8×103
3.1×103

.0×105
.0×105
.0×105
.0×105

The relaxation time was measured by applying the general Maxwell model (Eq. (4)) to thetime distribution of the shear stress observed after loading a step pattern stress to the fluid.
X
 t 
(4)
   0i exp   i 1
 i 

In the measurement, 3rd order approximation (X=3) was employed.  was thus obtained, andthe effects of temperature on  was derived in the same manner applied to the viscosity as
shown in Eq. (2).

log10    







(5)

Tm  273 Tm  2732
From the measurements of , it was found that the values of coefficients  and  were very
close to those obtained by the viscosity measurements. Thus, the values shown in Table 2 wereapplied to Eq. (3). During the experiment,  at the temperature of Tm=20C of each working
fluid was measured in advance. of the experiment was then calculated on the basis of thecharacteristic temperature of the experiment, which was defined as the average value of theinlet and outlet bulk mean temperatures. Table 3 shows the example of of different
temperatures.
Table 3: Relaxation time of 64.4wt% PAAm solution at various temperatures.

Temperature Tm [C]
Relaxation time  [s]

15
6.81

20
5.32







The specific heat capacity at constant pressure cp, the thermal conductivity k, and the density  ofthe solutions were referred to the values measured by Gucker et al. [11] and Werner et al. [12].

3. Results and Discussion
Figure 2 shows the distributions of the spatially averaged and time mean Nusselt number, Num,
distributions in relation to Reynolds number Re and Weissenberg number Wi. The solid line
presents the numerical results of Newtonian fluid flow in a straight channel with square crosssection in laminar flow regime [7, 8]. The results of solutions with different viscoelastic
properties are compared in the figure. Namely, the descriptions (57)-(64) shown in the legends
present the sucrose concentration of each solution as described also in Table 2. Num averaged
in the area between the 21st and 30th curve units (N21-30) is plotted in the figure. As will

K. Tatsumi et al.

20

Average Nusselt number: Num

Average Nusselt number: Num

20
PAAm(64)_N21-30_tb
PAAm(60)_N21-30_tb
PAAm(57)_N21-30_tb
SucroseNewtonian fluid(numerical)

15

15

10

10

5

0

PAAm(64)_N21-30_tb
PAAm(60)_N21-30_tb
PAAm(57)_N21-30_tb
Newtonian fluid (numerical)

0.1

1

10

Reynolds number: Re(a) Re vs Num in top/bottom walls heated case

5

0

10

100

Weissenberg number :Wi(b) Wi vs Num in top/bottom walls heated case

Figure 2: Distributions of locally averaged Nusselt number Num in relation to (a) Reynolds numberand (b) Weissenberg number. Nu is averaged in the area between the 21st curve and 30th curve (N2130) in the case of the top-bottom walls heated. Descriptions (57)-(64) of PAAm cases show the sucrose
concentration of the solution.

discussed shortly, the flow and heat transfer characteristics varies depending on the streamwise
location and Wi. Among these results, Nu converged to a relatively constant value in the area
downstream of the 22nd curve unit (N22) which is considered to be the developed region ofeach Wi. The influences of the viscoelasticity of the fluid is, therefore, discussed in this region.
First, the results of the sucrose solution is constant independent to Re and Wi, and corresponds
well with the solid line. This shows the validity of the present measurements.
In the PAAm solution case, Nu corresponds to the sucrose solution case in the low Re regions.
In this region, the effect of the viscoelasticity of the fluid is small and the flow is steady and nonoticeable vortex structure appears showing a similar flow pattern with those of Newtonian
fluids. As Re increases, the flow becomes unsteady and secondary flows are generated which
increase the Num. It is clearly shown in Fig. 2 (a) that the Re at which the Num starts to increasediffers among the cases of PAAm(57)-(64).
On the other hand, the distributions of PAAm(57)-(64) correlate well with Wi. Wi represents
several viscoelastic features of the fluid and flow. One of them is the normal stress differences.
The authors has shown that the longitudinal vortices like secondary flows generated in theserpentine channel is mainly attributed to the normal stress differences produced in the areaadjacent to the top and bottom walls of the channel [7, 8]. In combination with the curvature of
the channel, a force is produced near the walls to drive the fluid toward the center of thecurvature. The good correlation between the Num and Wi implies that in the developed regionalso, the heat transfer enhancement is due to the generation of the secondary flows.
Figure 3 shows the Num distributions in relation to Re and Wi in the cases of PAAm(64). Nu
shown here are the averaged values of the three sections dividing the channel in the streamwise
as the 1-10th, 11-20th and 21-30th curve units. The legend of these areas are shown as N1-10,
N11-20 and N21-30 in the figure. Based on the heat transfer characteristics, these areas
represent the entrance, transition and developed regions, respectively. Figs. (a) and (b) show
the results in the case of the top and bottom walls heated, while (c) and (d) show the cases ofthe sidewalls heated.

Turbulence, Heat and Mass Transfer 8

25

Average Nusselt number: Num

Average Nusselt number: Num

25
PAAm(64)_N1-10_tb
PAAm(64)_N11-20_tb
PAAm(64)_N21-30_tb
Newtonian fluid20

20

PAAm(64)_N1-10_tb
PAAm(64)_N11-20_tb
PAAm(64)_N21-30_tb
Newtonian fluid

15

15

10

10
5
0
0.1

1

10

5
0

10

(a) Re vs Num in top/bottom walls heated case(b) Wi vs Num in top/bottom walls heated case25

25

Average Nusselt number: Num

Average Nusselt number: Num

100

Weissenberg number: Wi

Reynolds number: Re

PAAm(64)_N1-10_s
PAAm(64)_N11-20_s
PAAm(64)_N21-30_s
Newtonian fluid

20
15
10
5
0
0.1

1

10

20

PAAm(64)_N1-10_s
PAAm(64)_N11-20_s
PAAm(64)_N21-30_s
Newtonian fluid

15
10
5

(A)
0

10

(B)

(C)

(D)
100

Reynolds number: Re

Weissenberg number: Wi(c) Re vs Num in sidewall heated case(d) Wi vs Num in sidewall heated case

Figure 3: Distributions of locally averaged Nusselt number Num in relation to Reynolds number andWeissenberg number. Comparison is made for different streamwise regions of the channel. (a) and(b) are the results of top/bottom walls heated case, and (c) and (d) are the sidewall heated case.
Descriptions N1-10, N11-20, N21-30 present the serial numbers of the curve unites in the area of
which Nu is averaged to obtain each Num.

Under the low Re conditions, Num of PAAm cases matches with the solid line showing thatthe flow structure is similar to that of the Newtonian fluid flow across the whole channel. As
Re increases Num starts to increase as was observed in Fig. 2. However, in this case, the Re in
which Num starts to increase are of a same value in the three regions. This shows that the flow
becomes unsteady and vortex generation occurs nearly simultaneously in the streamwise
direction. Comparing the distributions in relation to Re and Wi in both wall heated case, theplots are correlated better with Wi in which the variation is relatively small. The distribution,
however, does not increase monotonically, but shows a characteristic pattern in relation to thestreamwise position and Wi particularly in the Num distribution of the sidewall heated case.
Considering the visualization results also, the heat transfer characteristics can be roughly
divided into several regions which are shown in Fig. 2 (d) as (A), (B), (C) and (D).
In region (A), as mention in above, the flow structure is nearly the same with the NewtonianK. Tatsumi et al.

Local Nusselt number: Nux

Local Nusselt number: Nux

fluid flow.
In region (B), secondary flow is observed30 and the flow become unsteady in the30
Top wallBottom wall
Newtonian fluid

25

20

20

15

15

10

10
5
0

Outer wall
Inner wall
Newtonian fluid

25

0

5
10
15
20
25
Streamwise position: x /L

5
0

30

0

(a) Wi=7-30 (top-bottom walls)
30

Local Nusselt number: Nux

Local Nusselt number: Nux

Top wallBottom wall
Newtonian fluid

25

Outer wall
Inner wall
Newtonian fluid

25
20

20

15

15

10

10
5
0

5
10
15
20
25
Streamwise position: x /L

5
0

30

0

(c) Wi=30-45 (top-bottom walls)
Local Nusselt number: Nux

Local Nusselt number: Nux

Outer wall
Inner wall
Newtonian fluid

25
20

20

15

15

10

10
5
0

5
10
15
20
25
Streamwise position: x /L

5
0

30

0

(e) Wi=50-85 (top-bottom walls)
30

30

Top wallBottom wall
Newtonian fluid

25

5
10
15
20
25
Streamwise position: x /L30(f) Wi=50-85 (sidewalls)
Local Nusselt number: Nux

Local Nusselt number: Nux

30

30
Top wallBottom wall
Newtonian fluid

25

Outer wall
Inner wall
Newtonian fluid

25
20

20

15

15

10

10
5
0

5
10
15
20
25
Streamwise position: x /L(d) Wi=30-45 (sidewalls)

30

0

30

(b) Wi=7-30 (sidewalls)

30

0

5
10
15
20
25
Streamwise position: x /L

0

5
10
15
20
25
Streamwise position: x /L30(g) Wi=100-150 (top-bottom walls)

5
0

0

5
10
15
20
25
Streamwise position: x /L30(h) Wi=100-150 (sidewalls)

Figure 4: Local Nusselt number Nux distributions along the streamwise direction. x is thestreamwise location along the curved channel and L is the length of one periodical unit. Left sidecolumn shows the results of the top-bottom walls heated case, and the filled and outlined symbols
show the Nux measured at the top and bottom walls, respectively. The right side column are of the
sidewall heated case with the filled and outlined symbols presenting the Nux measured at the outerand inner side of the curves.

Turbulence, Heat and Mass Transfer 8channel. Comparing Fig. 3 (b) and (c), Num increases in the sidewall heated case while Numslightly decreases in the top-bottom walls heated case. Further, a noticeable peak appears in theN21-30 region of the sidewall heated case.
In this Wi region, a pair of longitudinal vortices like secondary flows are generated in thechannel. This secondary flow generation is attributed to the normal stress difference of theviscoelastic fluid. Due to the shear stress of the main flow generated near the walls and thecurvature of the channel, the streamwise (circumferential) component of the stress, , produce
a driving force to the fluid to flow toward the center of the curvature[6, 7]. In the curved partof channel, the secondary flows convects the fluid located at the channel center toward the outerwall. On the other hand, the fluid located adjacent to the outer wall is driven toward the topbottom walls. Therefore, the heat transfer at the sidewalls is enhanced while the Num at the topbottom walls decrease. These secondary flow is fully developed at the downstream side of thechannel, and, thus, a marked increase of Num is observed in Fig. 3 (d).
In region (C), the pair of vortices mentioned in the previous paragraph develops to a single
vortex. The vortices in this region becomes unstable, and one of the two vortices increases its
size and occupy a large portion of the cross section. Further, the main flow, the region of which
the streamwise velocity becomes maximum in the cross section, located near the center of thislarger secondary flow. Therefore the main flow drifts toward one side of the top-bottom walls,
and enhances the heat transfer there.
In region (D), a pair of vortices appears again from the downstream of the channel. As Wi
increases, the normal stress described in the discussion of region (B) increases. This makes thepair of vortices become more stable, and thus the single vortex like secondary flow and the driftof the main flow decays. Therefore, the sidewall heat transfer enhances markedly and shows amuch greater value compared to the heat transfer at the top-bottom walls, particularly in theN21-30 region.
Figure 4 shows the local Nusselt number of each streamwise location Nux in the cases of
top-bottom walls and sidewalls heated, respectively. Nux of the top and bottom walls, and theouter and inner sidewalls of the curve are plotted, respectively. x is the streamwise location
measured along the serpentine channel and L is the length of one periodical unit. Distributionsof four Wi conditions are shown, which correspond to the (A)-(D) regions shown in Fig. 4.
In Figs. 4 (a) and (b), Nux is the same with the Newtonian fluid case. In this case, the flow
remains steady in all position of the channel. As Wi increases, Nux starts to increase from thedownstream of the channel. Particularly, Nux shows a considerable increase at the sidewalls asshown in Fig. (d). This is the reason why a peak was observed in Fig. 3. (d) in region (B). As
mentioned before, in this region, a pair of vortices like secondary flow is generated due to thenormal stress differences of the viscoelastic fluid. Further, as shown in the figure, the secondary
flow starts to develop from the downstream of the channel.
In Fig. 4 (e) and (f), Nux increases especially at the sidewalls and the range of the error bars
enlarges. It should be noted that the error bars does not mainly present the uncertainty of themeasurement method. It is more likely due to the drift of the flow toward one side of the topbottom walls or the sidewalls. The flow is strongly unsteady for a relatively large time period
which will be discusses shortly in the discussion of the visualization.
In Figs. (g) and (h), the error bars increases markedly in both walls. The error bars are large
especially in the middle of the streamwise direction in the top-bottom walls cases (Fig. (g)). In
this region, the generation of single vortex and the drift of the main flow are significant. Heattransfer coefficient of one side of the top and bottom walls increases while the heat transfer
deteriorate at the other side. Thus depending on the experiment, the heat transfer shows a large
variation.

K. Tatsumi et al.

Nux and the range of the error bars at the top-bottom walls decreases in the downstream ofLocal Nusselt number: Nux

30

N=15(Upper wall)
N=15(Lower wall)

25
20
15
10
5
0

(b)
0

(c) (d)
100

(e)
200

(f)

300

t [s]

(a) Time distribution of Nux at N=15(b) t=18s(c) t=95s(d) t=115s(e) t=271s(f) t=321s
Figure 5: (a) Time distributions of the local Nu of the top and bottom walls measured at the 15th
curve (N15). (b)-(f) the snapshots of the dye visualizing the streak lines of the flow in the area
between the 15th and 16th curves (N15-N16). (a) and (b)-(f) were measured simultaneously, and themoments the photos are taken corresponds to the vertical dash lines shown in (a). The flow conditions
are Re=0.82 and Wi=92.

Turbulence, Heat and Mass Transfer 8

the channel compared with the middle region as shown in Fig. (g). On the other hand, Nux
increase at the sidewalls. As discussed in Fig. 3, the amplitude of the pair of vortices increases
due to the increase of the normal stress differences, and the vortices becomes symmetric. In thiscase, the heat transfer of the top-bottom walls decreases due to the decay of the drift of the main
flow. On the other hand, the sidewall heat transfer increases attributed to the flow convected
toward the outer walls. The flow is still unsteady and the flow fluctuate mainly owing to thevariation of the vortices size and its position. Since only one thermocouple is attached to eachwall, a slight change of the position at which the flow impinges accompanies different Nux.
Therefore, although the drift of the main flow is not as large as the one observed in the single
vortex-like secondary flow case, a certain variation of the average heat transfer coefficient
appears in the high Wi condition case, too.
Figure 5 shows the time distribution of Nux and the visualization results using the dye. The
two distributions in Fig. 5 (a) are the Nux measured at the top and bottom walls at the 15th
curve unit. The Re and Wi condition of the measurement are Re=0.82 and Wi=92 , respectively.
Figs. (b)-(f) are snapshots of the streak lines visualized by the dye and viewed from the sidewall.
The 15th and 16th curves are shown in the photographs. The dash lines with the labels (b)-(f)shown in Fig. (a) correspond to the period when the snapshots shown in Figs. (b)-(f) are taken.
As shown in Fig. 5 (a), Nux fluctuate with time having a relatively long cycle ofapproximately 200s. The Wi of this case is in region between (C) and (D) introduced in Fig. 3
and 4. And the N15 curve is located at x/L=15. Under this condition, a single vortex-likesecondary flow is generated and the main flow drifts toward the top or bottom wall. The
increase of Nux at the top or bottom wall and the decrease at the other wall shows the effects ofthe drift on the heat transfer. The change of the walls at which Nux increases indicates that themain flow changes its position to the area closer to the top and bottom walls by time.
To see the structure of the secondary flow and the position of the main flow in the crosssection, we now focus on the flow at the cross section near the inflection point which is shownin Figs. (b)-(f) the square drawn by the dashed lines. The streak lines clearly show the two
vortices generated and changing their size with time. The schematics of these vortices and theirdirection are illustrated in right hand side figures. The directions and side of the vortices were
estimated by observing the movement of the streak lines in the movie.
The main flow is expected to flow at the positon close to the center of the larger vortex. In
this case, the locations of the main flow drift are (b) bottom wall, (c)-(e) top wall, and (f) bottom
wall, respectively. This corresponds to which side Nux increases confirming the mechanism of
the heat transfer enhancement under this Wi condition. It is interesting that the direction of thevortices are the same in the two cases having the main flow located close to the top and bottom
walls. On the other hand, the vortices turns to the opposite direction when the main flow drifts
from one side to the opposite side. This is believed to be due to the fact that when the vortex
drifts from one side to the other side it interrupts the secondary flow flowing toward the sidewall.
In this case, the flow at the inflection point will flow from the outer sidewall of the upstream
curve to the outer sidewall of the downstream curve. This flow will produce an apparent vortices
with opposite direction. The detail of the transition of the main flow is, however, still not clear,and further measurement is planned as future work.

4. Conclusions
Heat transfer and flow characteristics of viscoelastic fluid in serpentine channel were measured.
In the measurement applying fluids with different properties, the Nusselt number averaged overeither the top or bottom walls showed a good correlation with the Weissenberg number Wi

K. Tatsumi et al.

while the distributions dispersed largely in relation to Reynolds number Re. This was due to thefact that the heat transfer enhancement was mainly attributed to the vortex generation, theamplitude of which can be evaluated by Wi.
The local heat transfer distribution and the flow visualization results showed that the flow
structure and related heat transfer characteristics in the transition and developed regions can bedivided into four regions in the case of the examined range of the present study. As Wi increaseda pair of longitudinal vortices is generated which enhance the heat transfer at the sidewalls.
When Wi further increased, the vortices develop to a single vortex and the main flow drifts
toward either top or bottom walls. The heat transfer at the top and bottom walls increases in thiscase. In the developed region, a pair of vortices is generated again from the downstream due tothe increase of the normal stress differences. Heat transfer enhanced markedly at the sidewallsin this case.

Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 24360080 and 25630066.

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