Extended Abstracts of the Second Asian Conference on Thermal Sciences, 2nd ACTS
October 3-7, 2021, Online
ACTS- 1058

HEAT TRANSFER ENHANCEMENT EFFECTS OF SECONDARY FLOWS
OF VISCOELASTIC FLUIDS IN SERPENTINE CHANNEL
Kazuya Tatsumi*, Yousuke Tanaka, Reiko Kuriyama, Kazuyoshi Nakabe
Kyoto University, Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan

KEY WORDS: Viscoelastic fluid, Serpentine channel, Dean flow, Heat transfer enhancement, Computation
1. INTRODUCTION
Viscoelastic fluid is a non-Newtonian fluid that exhibits elastic properties in addition to viscosity. The
elasticity will produce normal stresses in the flow, when shear and stress are applied to the fluid. This forcechanges the main flow structure, generates secondary flows, and increases the flow instability, which
enhance the fluid mixing and heat transfer compared to Newtonian fluid. Especially in a channel withcurvature, longitudinal vortex-like secondary flow similar to Dean vortex is produced due to the normal
stress differences of the viscoelastic fluid. In the serpentine channel, the vortices are generated at thecurvature, and the strength of the radial flow and the flow instability are increased by the inflection point of
the curvatures [1-3]. The vortices enhance the heat transfer coefficient of the sidewalls, significantly [4,5].
The flow in these channels is a mixture of the viscoelastic fluid flow and the Dean vortices. However, thedifference between the contribution of the two flow on the heat transfer characteristics, and moreover, thecombined effects of these two flows are not investigated in detail. In this study, flow and heat transfer
characteristics of viscoelastic fluid in serpentine channel under low Reynolds number condition are mainly
investigated by numerical computation using Oldroyd-B model. Firstly, we introduce a dimensionlessnormal stress difference, and show that the average Nusselt number can be correlated well with this value forboth, the numerical and measurement results. The aspects of the flow structure of the viscoelastic flow and
Dean flow are compared and discussed in relation to the Weissenberg number and Dean number. Finally, thetemperature field and heat transfer enhancement effect of these flows are evaluated.

2. METHODS
Unsteady and three-dimensional form of the continuous equation, Navier-Stokes equation, and energy
conservation equation were solved in the present computation. The viscoelasticity of the fluid was applied to thecomputation by employing the Oldroyd-B model as the constitutive equation and adding the additional stressterm to the Navier-Stokes equation. Oldroyd-B model is a fundamental model derived by also considering thebehaviour of the viscoelasticity in molecular level. We used this model to simplify the problem for comparing
the stress and flow structure with the measurements. Non-slip and constant temperature conditions were applied
to the channel walls, and periodic boundary condition was applied to the streamwise boundaries.
Heat transfer measurement was conducted under isothermal wall condition for serpentine channel. The wall
temperature and the bulk mean temperatures of the inlet and outlet flow were measured to obtain the averageheat transfer coefficient. Velocity distribution of the cross-sectional planes were measured using the particle
image velocimetry (PIV) method.
The serpentine channel consists of two semi-circular parts with curvature of opposite direction (Fig. 1). The
channel has a square cross section of 5 mm (=H) on side, and the inner and outer radii of the semicircle part are20yHNumHxO zR o =2 H

Calculation
Measurement

161284

Ri=H00Fig. 1 Periodic region of serpentine channel.

100200N*1 300

Fig. 2 Num and dimensionless normal stress differences N1*.

*Corresponding Author: tatsumi@me.kyoto-u.ac.jp

ACTS-1058

Fig. 3 Mapping of flow structure in relationship to Weissenberg number and Reynolds number.
Ri/H = 1 and Ro/H = 2, respectively. The periodic region with two semicircle curves shown in the figure was set
as the domain to be solved in the computation. For the measurement, the number of the periodic region was 10.
The range of the Reynolds number Re, Dean number ND, Weissenberg number Wi were Re=0.5-2.8, ND=0.28-16,and Wi=0.5-6 for the computation, and Re=1.0-2.1, ND=0.57-1.2, and Wi=6.0 for the measurement, respectively.

3. RESULTS AND DISCUSSION
The average Nusselt number Num is compared with the measurements for validation. We will introduce adimensionless parameter related to the normal stress to compare these results. The term expressed as ( rr)/r, which appears in the equation of motion of the radial direction as the normal stress difference N1, plays
an important role in the generation of the secondary flow. We can derive the following dimensionlessparameter by normalizing the equation of motion applying H and the streamwise mean velocity Um as thecharacteristic length and velocity.
(1)

We rearranged the relationship of the Num with the Re and Wi to N1* and will show it in Fig. 2. The results
give a reasonable agreement, showing that N1* can be an index to represent the flow and heat transfer
characteristics, and the validity of the computation.
To roughly demonstrate the effects of the centrifugal force and viscoelasticity, the secondary flow andstreamwise velocity at the cross-section of =0 obtained by the computation are plotted against Re and Wi
which is shown in Fig. 3. Secondary flow increases as Re and Wi increases, and by these flows, the flow coreregion of low temperature is carried toward the outer sidewall and enhance the heat transfer of the outer andtop-bottom walls. The Dean vortex and the viscoelastic fluid show similar flow structure. However, the Dean
flow fully developed in the curved channel, while in the viscoelastic fluid case, flow structure changed as thenormal stress distribution changed depending of the position of the flow core region. The results showed that
this viscoelastic effect can increase the strength of the secondary flow, give larger movement of the flowcore region leading to the redevelopment of the thermal boundary layer, and further increase of the overall
heat transfer coefficient. These discussions will be extended more in the presentation.

REFERENCES
[1]
[2]
[3]
[4]
[5]

Burghelea, T., Segre, E., Bar-Joseph, I., Groisman, A., Steinberg, V., “Chaotic Flow and Efficient Mixing in a Microchannel
with Polymer Solutions”, Physical Review E, 69, p. 0066305 (2004).
Tatsumi, K., Takeda, Y., Suga, K., Nakabe, K., “Turbulence Characteristics and Mixing Performance of Viscoelastic Fluid
Flow in a Serpentine Microchannel”, J. Physics Conference Series, 318, p. 092020, (2011).
Zilz, J., Poole, R. J., Alves, M. A., Bartolo, D., Levaché, B., Lindner, A., “Geometric Scaling of a Purely Elastic Flow
Instability in Serpentine Channels”, J. Fluid Mech., 712, pp. 203-218, (2012).
Abed, W. M., Whalley, R. D., Dennis, D. J. C., Poole, R. J., “Experimental Investigation of the Impact of Elastic Turbulence
on Heat Transfer in a Serpentine Channel”, J. Non-Newtonian Fluid Mech., 231, pp. 68-78, (2016).
Tatsumi, K., Nagasaka, W., Kimura, R., Shinotsuka, N., Kuriyama, R., Nakabe, “Local Flow and Heat Transfer Characteristicsof Viscoelastic Fluid in a Serpentine Channel”, Int. J. Heat Mass Transfer, 138, pp. 432-442, (2019).