8th World Conference on Experimental Heat
Transfer, Fluid Mechanics, and Thermodynamics
June 16-20, 2013, Lisbon, Portugal

INFLUENCES OF FLUID PROPERTIES ON
HEAT TRANSFER AND PRESSURE LOSS CHARACTERISTICS OF
VISCOELASTIC FLUID FLOW IN SERPENTINE CHANNEL
Kazuya Tatsumi *,**, Wataru Nagasaka*, Katsuki Kanaiwa and Kazuyoshi Nakabe *,*** Kyoto University, Kyoto 615-8530, Japan** Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto 615-8530, Japan
E-mail : tatsumi@me.kyoto-u.ac.jp

ABSTRACTHeat transfer coefficient and pressure loss measurements and flow visualization were carried out for viscoelastic
fluid flow in a serpentine channel. Water solutions of polyacrylamide (PAAm) and surfactant (CTAC) were used as
viscoelastic fluids, and were compared with the Newtonian fluid case which was a sucrose solution. The visualized
flow patterns showed that in the viscoelastic fluid case, unsteady flows with longitudinal vortices were generated in
the serpentine channel even at Re < 2.0. A marked enhancement of heat transfer compared to the Newtonian fluid was
obtained in this case. Further, the influences of the sucrose concentration of the viscoelastic fluids on the heat transfer
and pressure loss characteristics were discussed. The results showed that a good correlation can be observed between
the mean Nusselt number with the Weissenberg number than the Reynolds number in the case of PAAm solution.
However, this correlation was not observed in the case of CTAC solution, the sucrose concentration of which waschanged as the PAAm solution.
Keywords : Viscoelastic fluids, Heat transfer enhancement, Laminar flow, Serpentine channel
1. INTRODUCTION
It is known that viscoelastic fluids such as polymer solutions
provide remarkable flow characteristics compared to Newtonian
fluids. For example, application of shear stress to the viscoelastic
fluid produces normal stresses which enhance the flow
instability and generation of secondary flows. These flows canenhance fluid mixing and heat transfer compared with
Newtonian fluids. Hartnett et al.[1] investigated laminar heattransfer characteristics of the viscoelastic fluid in a straightchannel at Re~1000 and showed that larger heat transfer
coefficient can be observed in the viscoelastic fluid case which isbelieved to be attributed to the generation of secondary flows
due to the normal stress differences. Groisman et al. [2] andTamano et al. [3] have shown that strong unsteady and secondary
flows are generated even under low Reynolds number conditions
for viscoelastic fluid flows in serpentine channels. Recently, Zilz
et al. [4] have carried out numerical and experimental
investigation of the purely elastic flow instability in theserpentine channel. They have shown that the instability ismainly attributed to the curvature of the streamlines.
Higher heat transfer coefficient may be obtained in this casecompared with the case of straight channel. However, heattransfer characteristics of such flows have not been studied yet.
Therefore, in this study, heat transfer coefficient and pressure
loss measurements were carried out for viscoelastic fluid flows
in the serpentine channel under low Reynolds number condition(Re ~1). In addition to this, influences of the sucrose
concentration of the viscoelastic fluid on the flow and heattransfercharacteristics
weremeasured.
Furthermore,measurement was be made for the heat transfer characterisitcs
using surfactant solution (cetyltrimethylammonium chloride,
CTAC) to see if the correlations using the present

Fig.1 Apparatus and channel dimension used for heat transfer
experiment.
non-dimensional values can be applied to different viscoelastic
fluids.
2. EXPERIMENT
Two channels of different shapes are used in the experiment.
One is a serpentine channel and the other is a straight channel.
Figure 1 shows the schematic diagram and dimensions of theserpentine channel. The channel has a square cross section of
55 mm, and consists of semi-circular parts connectedperiodically in the streamwise direction. The inner and outerradii of the semi-circular part are Ri=5mm and Ro=10mm,
respectively. The length along the serpentine channel, L, is
470mm. The straight channel was designed to have the samechannel length of 470mm. Water of constant temperature was
supplied to the copper block of the test section to heat thechannel wall isothermally. Working fluid was supplied from thepressurized tank to the channel, and the mass of the fluid flowing
from the outlet was measured by an electric weighting machineSucrose
PAAm(64)
PAAm(60)
PAAm(57)

Properties of the solutions (20oC, 𝛾̇ =50s-1).
PAAm Sucrose


Pr
[wt%]
[wt%]
[Pa・s] [s]
64.4
0.15
1030
500
64.4
0.37
4.0
2340
500
60.0
0.16
3.5
1030
500
57.0
0.09
2.5
650

Table. 2

Properties of the solutions (20oC, 𝛾̇ =50s-1).

Title

CTAC
[wt%]

CTAC(64)
CTAC(60)
CTAC(57)

1000
500
200

Table. 1
Title

Table. 3
solution
SucrosePAAm(64)
PAAm(60)
PAAm(57)
Table. 4
solutionCTAC(63)
CTAC (60)
CTAC (57)

Sucros
e
[wt%]
64.4
60.0
57.0





[Pa・s]

[s]

Pr

0.37
0.16
0.09

4.0
3.5
2.5

2340
1030
650

Experimental condition (PAAm solution).
Re
Gz
Wi
ND
0.7-2.5
4-34
0.2-2.2
0.2-2.6
3-40
11-137
0.1-1.5
0.4-5.1
5-38
10-136
0.2-2.9
0.5-5.8
4-39
8-125
0.3-3.5
Experimental condition (CTAC solution).
Re
1.3-3.7
0.9-5.1
0.8-7.5

Gz
6-22
4-30
4-49

Wi
45-18035-19035-250ND
0.8-2.2
0.5-3.0
0.5-4.2

to measure the mass flow rate, 𝑚̇. The bulk mean temperaturesof the fluid at the inlet and outlet of the test section (Tb,i, Tb,o)were obtained from the fluid temperature measured at eachlocation and the fully developed velocity profile of a squarechannel. Single sheath thermocouple was used to measure theinlet fluid temperature while the outlet fluid temperature wasmeasured by seven thermocouples located evenly in the height
direction at the center of the channel width. The wall
temperature, Tw, was a value of averaging the temperatures
measured at seven locations of the copper block surface. Averageheat transfer coefficient, hm was thus calculated by applying thebulk mean temperature and mass flow rate to Eq. (1).

hm=m c pAs× ln

Tw-Tb,iTw-Tb,o(1)

As is heat transfer surface area, 𝑚̇ is mass flow rate, and cp
is the constant pressure specific heat capacity. The average
Nusselt number was defined as Num=hmDh/k where Dh is thehydraulic diameter of the channel, and k is the thermal
conductivity.
Pressure loss, P, was measured by two pressure gauges
attached to the inlet and outlet of the test section as shown in Fig.
1. Visualization experiment was carried out for a serpentine
channel made of transparent acrylic capturing the streakline

Fig.2 Flow visualized from side and top of the channel.
(PAAm solution case).
images of dye using two video cameras. To supply the dye to thechannel, a 1mm diameter tube with a pore pierced at the end wasinserted perpendicular to the cross-section at the upstream of thechannel. The dye was injected from the pore to the channel by asyringe pump at flow rate of 1mL/min.
An aqueous solution of 500ppm polyacrylamide (PAAm,
Mw=1.8×107), 1wt% NaCl, and sucrose was used as viscoelastic
fluid. Sucrose was mixed in the fluid to modify the relaxation
time of solution, while NaCl was added to prevent theaggregation of the polymers. Sucrose concentration was changed
for three conditions, which are 57.0, 60.0 and 64.4 wt%, in orderto evaluate the influence of the fluid property. In addition to this,surfactant (CTAC, cetyltrimethyl ammonium chloride: Mw=320)
solution was investigated in this study. NaSal (Mw=160) sucrose
were mixed as counter ion and to change the viscosity of thesolution. Measurement of an aqueous solution of 64.4wt%
sucrose was carried out as Newtonian fluid case to compare withthe viscoelastic fluids case.
The viscosity and relaxation time  are measured by arheometer (ANTON PAAR, MCR301). The apparent viscosity of
PAAm solutions is a function of shear rate and temperature. The
relation of logarithm law shown in Eq. (2) is employed in thisstudy.

log10  (Tm )=  (Tm  273)

(Tm  273) 2(2)

In this case, coefficients  and  did not vary much in relation to
the temperature and are kept constant as  = 3.1103 and  =8.0105. As for , the relationship with the shear rate isexpressed by using the power law, = K𝛾̇ n−1 . 𝛾̇ is the flow
shear rate, n is constant, and K is a coefficient related to thetemperature[5]. K and n are obtained for temperature of 20C
and shear rate 𝛾̇ = 1 ~ 100s-1 using the working fluid of eachexperiment.
can be calculated from Eq. (2). Then,  of the reference
temperature of the fluid of which the experiment was carried out
is obtained. One example of K and n obtained from the PAAm

10
PAAm(64) & Serpentine
PAAm(64) & StraightSucrose & Serpentine
Sucrose & Straight
Modified value of 16 /Re*

0.5

3.2 Heat transfer enhancement of the PAAm solution
Figure 3 shows the relationship between the Fanning’s
friction factor, f =DhP/2Um2L, and modified Reynolds number,
Re*. Re* is defined by Eq. (2).
(2)

A and B are the geometrical constants. Figure 3 shows thefriction factors of the PAAm(64) and the sucrose solutions inboth case of the serpentine and straight channels. The theoreticalvalues depicted in Figure 3 are the friction factors of steady flow
in a square duct for Newtonian fluid [8] and non-Newtonian
power-low fluid [9]. The influences of the temperature
distribution appearing in the channel cross-section, and thedependency of the apparent fluid viscosity on the shear rate aretaken into consideration for the theoretical values.
In both cases of the straight and the serpentine channels, f of5

Fig.3 Relation between friction factor f and modified
Reynolds number Re* : comparison of serpentine andstraight channels.

16

Num

3.1 Visualization experiment
Figure 2 shows the result of the visualization for the flow of
PAAm solution in the serpentine channel at Re = 2.0 (Wi = 160
and ND = 1.2). The result shows that the spanwise and height
positions of the streaklines change as the fluid flows along the
curve of the serpentine channel and that secondary flows are
generated in the channel. Further, although not shown here,
fluctuations of the streaklines were observed indicating theexistence of unsteady flows. Particularly, in the area adjacent to
the inflection points of the curved channel, the generation of
longitudinal vortices was observed which accompanied a strong
fluctuation of the streaklines. On the other hand, no fluctuations
and secondary flows were observed in the sucrose solution caseunder all Re conditions tested in this study. Thus, the flow
characteristics observed in the PAAm solution are attributed to
the fluid viscoelasticity.

1

Re*

12

3. RESULTS AND DISCUSSION

ρU m2n Dhn
Re* = n 1
8 K ( B  A / n) n

100fsolution of the experiment are K = 0.55 and n = 0.88.
Since the PAAm concentration of the solution used in thisstudy is small, a reliable measurement of the the relaxation timeusing the rheometer directly was difficult. Therefore, theMaxwell law of the stress relaxation is applied to the stress
distribution after a constant strain is applied to the fluid.
Measurement is carried out for the fluid temperature of 15, 20,
30 and 40 C in order to obtain the relation based on Eq. (2).
Tables 1 and 2 summarize the values of  , and Prandtl
number, Pr = cp/k of the PAAm and CTAC solutions,
respectively. These values are the results of the measurement at
20˚C and 𝛾̇ =50s-1. cp, k, and the density  of the solutions arereferred to the values measured by Frank, T. [6] and Werner, M.
[7]. Logarithmic mean temperature of Tb,i and Tb,o is used as
reference temperature of the fluid in heat transfer measurement.
Tables 3 and 4 show the non-dimensional values of the eachsolution. The Reynolds number, Re = UmDh/ was varied from
0.2 to 7.5. The Graetz number, Gz = RePrDh/L , and Weissenberg
number, Wi = 4Um/Dh, and Dean number, ND =Re√𝐷h /(𝑅𝑖 + 𝑅𝑜 ), corresponding to the Re condition.

Numerical (Chandrupatla et al.)
PAAm(64) :serpentine
PAAm(64) :straightSucrose :serpentine
Sucrose :straight

8

4

0
1

2

3

Re
Fig.4 Relation between average Nusselt number Num andReynolds number Re : comparison of serpentine andstraight.
the sucrose solution agrees well with the theoretical one. This
result shows that the flow in sucrose solution case is steady anddoes not accompany any strong secondary flows even in theserpentine channel case. This is due to the small Dean number(ND ~ 1) condition under which a Taylor-Dean flow was not
generated. In the case of PAAm solution, the values of f of theexperiment agree well with the theoretical ones for Re*<0.4.
However, as Re* increases, the experimental values are larger
than the theoretical one. Therefore, a factor in addition to theshear thinning effect exists in the serpentine channel case, which
is believed to be the transition of the flow from steady tounsteady state and the generation of secondary flows. Comparing
the measurement results of the straight and serpentine channels,
the value of the straight channel is smaller than that of theserpentine channel. The value is, however, larger than thetheoretical one. Therefore, even in the straight channel case,secondary flows are generated which increases the pressure loss.
In Figure 3, an uncertainty of f is large for both cases of
PAAm and sucrose solutions. This main reason is expected to beeffects of temperature dependences of apparent viscosity. Whenthe apparent viscosity of a working fluid largely changes
depended on temperature, friction factor is different from a caseof a constant temperature fluid. Therefore, the f values change

PAAm (64)
PAAm (60)
PAAm (57)
Modified value of 16 /Re*

12

f

Num

50

PAAm(64)
PAAm(60)
PAAm(57)

16

8

4

10

0

1

20

5

Re*
Fig.5 Relation between friction factor f and modified
Reynolds number Re* : comparison of PAAm(57)-(64).

Num

12

60

80

100

120

140

Wi
Fig.7 Relation between average Nusselt number Num andWeissenberg number Wi in the serpentine channel:
comparison of PAAm(57)-(64).
60

Numerical (Chandrupatla et al.)SucrosePAAm(64)
PAAm(60)
PAAm(57)

PAAm(64)
PAAm(60)
PAAm(57)

40

N1 [Pa]

16

40

8

20

4

0
1

2

3

4

5

6

Re
Fig.6 Relation between average Nusselt number Num andReynolds number Re in the serpentine channel:
comparison of PAAm(57)-(64).
depended on the inlet temperature which decided by room
temperature because a magnitude of the effects depends on
differences between the wall temperature and the bulk
temperature. Since experiments were carried out under various
inlet temperatures of the range from 18°C to 23°C, theuncertainty of f in the Figure 2 is large.
Figure 4 shows the relationship between the average Nusselt
number and Reynolds number. Both values of the serpentine andstraight channels are shown in the figure. The numerical values
shown in Figure 3 are the Nusselt number of steady Newtonian
fluid flow in a square duct of which the developing region of thethermal boundary layer is considered [10]. The effects of thetemperature dependence of the fluid viscosity are considered.
As Re increases, Num of the sucrose solution slightly
increases due to the influence of the entrance region of thethermal boundary layer. The result agrees excellently well with
the numerical values showing the validity of the present
measurement. In the case of sucrose solution, Num of theserpentine channel shows a same value with the straight channel.
This is because the present flow is in steady state, and moreover,the Dean number of the flow is small and no marked secondary
flow is generated. The values of PAAm solution in the serpentine
channel agree with the numerical one of the Newtonian fluid at
Re<0.4. However, as Re increases, Num of PAAm solution

0
0

20

40

60

80

100

120

140

Wi
Fig.8 Relation between normal stress difference N1 andWeissenberg number Wi : comparison of PAAm(57)-(64).

increases markedly and shows higher value compared with thecase of Newtonian fluid. This result shows that heat transfer canbe enhanced markedly by using the viscoelastic fluid andserpentine channel.
In the case of straight channel, Num of PAAm solution
increases as Re increases, and takes a greater value than the
numerical results indicating heat transfer enhancement comparedwith Newtonian fluid. However, the values are smaller than thecase of serpentine channel. Secondary flow is generated in thestraight channel due to the square cross-section and theviscoelasticity of the fluid as mentioned in Section 1, and theheat transfer in the channel is enhanced. The flow in the straightand serpentine channels, however are believed to be different
structure. The curve parts and inflection points in the serpentine
channel influence the flow. These results show that theserpentine channel is needed to generate high heat transfer
enhancement of viscoelastic fluid flow.

3.3 Influence of sucrose concentration of the PAAm solution
Figures 5 and 6 show the influences of the sucrose
concentration of the PAAm solution on the relationship between
f and Re*, and between Num and Re in the case of serpentine
channel. As Re* increases, the values of f increase in all cases

3.4 Heat transfer performance of the CTAC solution
Figure 9 shows the relationship between Num and Re in thecase of CTAC solutions. Num shows a greater value comparedwith sucrose solution case over the range of Re considered here.
Heat transfer enhancement is, therefore, achieved in the CTAC
solution. Comparing Num of PAAm and CTAC solutions, one
can see that the influence of Re on Num is relatively small andremains nearly constant in the CTAC solution case. Therefore,
larger Num is obtained in the CTAC case for smaller Re
conditions, and as Re increases, Num of PAAm solution case20
Numerical (Chandrupatla et al.)SucrosePAAm(57)
CTAC(57)
CTAC(60)
CTAC(63)

Num

16
12
8
4
0
1

2

3

4

5

6

7

8

Re

Fig.9 Relation between average Nusselt number Num andReynolds number Re in the CTAC solution case.
20
16
12

Num

and show a larger value than the theoretical ones. However,since the viscosity and the relaxation time differs among thesolutions with different sucrose concentrations, the Num
distributions shows a different tendency against Re. Namely,
Num of the three PAAm solutions increase markedly compared tonumerical values. However the Reynolds number at which Num
starts to increase changes depending on the sucrose
concentration. The distribution, therefore, cannot be correlatedby the Reynolds number only, which implies that the flow andheat transfer characteristics of the PAAm solution relies on otherphysical properties of the viscoelastic fluid.
Figure 7 shows the relation of Weissenberg number Wi andNum. One can see that a good agreement is observed among thethree cases. Weissenberg number is known to represent the
influence of the fluid viscoelasticity on the flow characteristics,
particularly the normal stress differences. In order to see theinfluence of the first normal stress differences N1=11-22 on theheat transfer characteristics, Figure 7 shows the relation between
Wi and N1, which is the value measured by the rheometer foreach PAAm solution. In Figure 8, N1 starts to increase at Wi ~20
which is a value close to the one at which Num starts to increase.
Further, N1 of the PAAm (64), (60) and (54) solutions agree wellwith each other particularly in the area of Wi <60. These results
show that Wi has a correlation with N1, and that the normal stresswhich increases as Wi increases is one of the main reasons forthe secondary flow generation and triggering the unsteady flow.
As Wi increases, a variation of Num is observed in Figure 7.
The reason for this is considered to be threefold. The first one isthe variation of N1 which becomes significant as Wi increases asshown in Figure 8. The second reason can be the influences of
the increase of the Reynolds number and Dean number. As Re
increases, the viscous dissipation decreases and the vortices
generated at the inflection point in the channel are convected
downstream. Under such situation, the dominant factor topresent the flow structure in the serpentine channel might not
only be the normal stress, i.e. Weissenberg number. The third
reason can be related to the fact that the flow of the present study
is in the region where the viscoelastic fluid flow transits fromsteady to unsteady flow. In such region, the flow can easilytransit by any small disturbance such as the difference of inlet
temperature. This region makes it difficult to carry out accurate
measurements. The condition for generation of vortices isdecided by Weissenberg number but the following flow iscomplicated and difficult to discuss heat transfer characteristics
only by dimensionless number.

PAAm(64)
PAAm(60)
PAAm(57)
CTAC(57)
CTAC(60)
CTAC(63)

8
4
0
50

100

150

200

250

300

Wi

Fig.10 Relation between average Nusselt number Num
and Weissenberg number Wi in the CTAC solution case.
becomes larger than that of the CTAC case.
Comparing the Num of the CTAC solutions with different
sucrose concentrations (57), (60) and (63), CTAC solution withhigher sucrose concentration shows larger Num. In any case, agood correlation cannot be found between the Re and Num.
Figure 10 shows the relationship between Wi and Num. As
was found in Fig. 7, Num increased with Wi in the case of PAAm
solution. However, in the case of CTAC solution, Num remains
constant. Furthermore, different distributions are observed for
different sucrose concentration in the case of CTAC solution
indicating that Wi may not be the effective to represent the flow
and heat transfer characteristics of the CTAC solution in theserpentine channel.
One reason may be the difference in the relaxation time.
Greater value is obtained in the CTAC solution compared with
the PAAm solution as shown in Tables 1 and 2. Considering theflow velocity and the periodical structure of the serpentine
channel, the influence presented by the Deborah number canbecome more conspicuous in the CTAC solution case. Anothercan be the influence of the entrance region effect. In the present
heat transfer measurement includes a long range of the entrance
region. If this region shows a dominant effect on the heat transfer
performance, and if the Wi characterizes more of the heattransfer performance in that area, then the CTAC solution, theflow of which could be fully developed in a shorter length, may
not be represented by Wi. Further discussion is needed as future

16
PAAm(64) :serpentine
PAAm(60) :serpentine
PAAm(57) :serpentine
PAAm(64) :straightSucrose (Numerical)

Num

12

8

correlation was obtained by using the Weissenberg number.
However, in the case of CTAC solution, Num could not becharacterized by Wi. The present experimental results showedthat as Weissenberg number increases, several fluid properties
would influence the flow field, thus, particularly Re, Pr and 
should be taken into consideration to describe the heat transfer
characteristics.

4

0

400

800

1200

1600

PUm [N/(m・s)]

Fig.11 Relation between average Nusselt number Num andpumping power.
work for this problem.
3.5 Pumping power
Figure 11 shows the relation between Num and pumping
power PUm. The values of Num of PAAm solutions in the caseof serpentine channel is larger than those of the sucrose solution
particularly in the range of PUm >100. In the case of PAAm
solution in the straight channel, the values are almost the same as
the sucrose solution. Thus, even if the pressure loss increases dueto the fluctuations and secondary flows, PAAm solution in theserpentine channel under the conditions of high viscosity andlow Reynolds number shows the highest overall performance.
In Figure 8, comparing Num of the three PAAm solutions, thecase of PAAm (57) shows the largest value in the area of
PUm>300 indicating that the solution of smaller sucrose
concentration shows higher overall performance. The reason forthis is considered to be as follows. As shown in Figure 7, N1
takes larger value in the order of PAAm (57), (60), and (64) for
the same Wi. Thus, largest Num is observed in the case of PAAm
(57) in Figure 6. In addition to this, as shown in Table 1, thefluid viscosity decreases significantly as the sucrose
concentration decreases, while the difference of the relaxation
time  is relatively small. Therefore, when considering identical
Wi condition, a similar or larger Num can be obtained in the
PAAm (57) case for the same Um. Obviously, smaller pumping
poweris required for PAAm (57) case since  is considerably
small compared to other PAAm solutions.

4. CONCLUSIONSThe heat transfer and pressure loss characteristics ofviscoelastic fluid in the serpentine channel was experimentallyinvestigated. The average Nusselt number Num increased in thecase of viscoelastic fluid (PAAm solution) in the serpentine
channel compared with the cases of PAAm solution in thestraight channel and sucrose solution (Newtonian fluid). The
highest overall performance considering the pumping power wasobserved in the case of viscoelastic fluid flow in serpentine
channel. When the sucrose concentration of the PAAm solution
was changed, a poor correlation was observed between the
Reynolds number and Num. On the other hand, a good

ACKNOWLEDGEMENT
This work was supported by Japan Society for the Promotion of
Science (JSPS) KAKENHI Grant-in-Aid for Scientific
Research(B), grant Number 24360080.
REFERENCES
1. Hartnett, J. P. and Kostic, M., 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, 1985.
2. Groisman, A. and Steinberg, V., Efficient Mixing at Low
Reynolds Numbers Using Polymer Additives, Nature, vol.
410, pp. 905-908, 2001.
3. Tamano, S., Itoh, M., Sasakawa, A. and Yokota, K., PIV
Measurement of Secondary Flow in Curvilinear Pipe Flow ofPolymer Solution, Trans. JSME, Ser. B, vol. 75, no. 759, pp.
2115-2121, 2009.
4. Zilz, J., Poole, R.J., Alves, M.A., Bartolo, D., Levache, B.
and Lindner, A., Geometric Scaling of a Purely Elastic Flow
Instability in Serpentine Channels, J. Fluid Mech. vol. 712,
no. 712, pp. 203-218, 2012.
5. Mirsa, B. N. and Varshni, Y. P., Viscosity-Temperature
Relation for Solution, J. Chem. Eng. Data, vol. 6, no. 2, pp.
194-196, 1961.
6. Frank, T., Gucker, Jr. and Fred, D. A., The Specific Heat ofAqueous Sucrose Solutions at 20°C and 25°C and theApparent Molal Heat Capacity of Non-Electrolytes, J.
American Chem. Society, vol. 59, no. 3, pp. 447-452, 1937.
7. Werner, M., Baars, A., Werner, F., Eder, C. and Delgado, A.,
Thermal Conductivity of Aqueous Sugar Solutions UnderHigh Pressure, Int. J. Thermophysics, vol. 28, pp. 1161-1180,
2007.
8. Kays, W. N. and Crawford, M. E., Convective Heat andMass Transfer, Second Edition, McGraw-Hill, pp. 275-287,
1980.
9. Kozicki, W., Chou,C. H. and Tiu, C., Non-Newtonian Flowin Ducts of Arbitrary Cross-Sectional Shape, Chemical
Engineering Science, vol. 21, pp. 665-679, 1966.
10. Chandrupatla, A. R. and Sastri, V. M. K., Laminar Forced
Convection Heat Transfer of a Non-Newtonian Fluid in a
Square Duct, Int. J. Heat Mass Transfer, vol. 20, pp.
1315-1324, 1977.