The document describes a study that measured heat transfer during pasteurization of orange juice using a plate heat exchanger. The study measured the density and viscosity of orange juice at different temperatures. It found that the heat transfer coefficient of orange juice varied from 983 to 6500 W/m2°C, while water's coefficient varied higher from 8387 to 24245 W/m2°C. The study developed a correlation to predict the orange juice heat transfer coefficient as a function of its viscosity and channel velocity, independent of plate geometry.

1. Heat transfer in a plate exchanger during pasteurization of orange
juice 1
Han B. Kim a
, Carmen C. Tadini a
, Rakesh K. Singh b,*
a
Department of Chemical Engineering, Escola Politecnica, Sao Paulo University, Brazil
b
Department of Food Science, Purdue University, 1160 Food Sciences Building, West Lafayette, IN 47907-1160, USA
Received 5 May 1998; received in revised form 9 February 1999; accepted 24 May 1999
Abstract
The heat transfer ®lm coecient of orange juice (OJ) during pasteurization using a plate heat exchanger with intermating 316 SS
plates was studied. Mathematical models to predict OJ heat transfer ®lm coecient are presented. The OJ density was measured
using an in-line density sensor at pasteurization temperature and also measured o€-line by hygrometer at di€erent temperatures. The
OJ viscosity was measured by an o€-line instrument, in the temperature range from 5±90°C. The mean values of OJ density and OJ
viscosity at 20°C were 1046.0 ‹ 3.6 kg/m3
and 14.17 ‹ 4.75 mPa s, respectively. The values of heat transfer ®lm coecient for OJ
varied from 983 to 6500 W/m2
°C, whereas the water heat transfer ®lm coecient varied from 8387 to 24245 W/m2
°C. This study
has provided a suitable heat transfer correlation to predict the OJ heat transfer ®lm coecient as a function of its viscosity and the
channel velocity, that is, this correlation is independent of the plate geometry, for varied conditions of OJ pasteurization
process. Ó 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Heat transfer; Orange juice; Heat exchanger; Modeling
1. Introduction
Plate heat exchangers are used extensively in the food
and dairies industries, but very little basic information
has been published on their ¯ow and heat transfer
characteristics. The principal advantages of such units
are ¯exibility of ¯ow arrangements, extremely high heat
transfer rates, and ease of opening for cleaning and
sterilization to meet healthy and sanitary requirements.
They are used as conventional process heaters and
coolers, as well as condensers. The basic elements of a
plate heat exchanger are closely spaced plates with
Journal of Food Engineering 42 (1999) 79±84
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Nomenclature
AT total e€ective plate heat transfer area, m2
b mean channel spacing, m
Cp speci®c heat at constant pressure, at average of inlet
and outlet stream temperatures, J/kg °C
De equivalent diameter, m
F correction factor for DTm
G channel mass velocity, kg/m2
s
h heat transfer ®lm coecient, W/m2
°C
kw thermal conductivity of plate material, W/m °C
•m ¯uid mass ¯ow rate, kg/s
n number of channels per pass
nP number of passes
nT total number of plates
NTU number of transfer units, dimensionless
Nu Nusselt number, dimensionless
Pr Prandt number, dimensionless
Q heat transfer rate, W
Re Reynolds number, dimensionless
t plate thickness, m
Tc cold ¯uid temperature, °C
Th hot ¯uid temperature, °C
Uc clean overall heat transfer coecient, W/m2
°C
v channel velocity, m/s
w plate width inside gasket, m
Greek symbols
DTm mean temperature di€erence, °C
q density, kg/m3
l dynamic viscosity at average of inlet and outlet
stream temperatures, N s/m2
or Pa s
Subscripts
c cold ¯uid
h hot ¯uid
1 inlet
2 outlet
*
Corresponding author. Tel.: +1-765-494-8262; fax: +1-765-494-
7953; e-mail: singhr@foodsci.purdue.edu
1
Approved as Journal paper number 15728 of Purdue University
Agricultural Research Programs.
0260-8774/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 1 1 0 - 7

2. surfaces altered to create turbulence at Reynolds num-
bers as low as 200. Typical applications are mainly liq-
uid-to-liquid turbulent ¯ow situations.
Plate heat exchangers are fully described in McKillop
and Dunkley (1960), Buonopane, Trupe and Morgen
(1963), Jackson and Troube, (1964), Usher (1970),
Marriot (1971), Schlundler (1983), Bassiouny and
Martin (1985) and Kakacß and Liu (1997). McKillop and
Dunkley (1960), Buonopane et al. (1963) and Bassiouny
and Martin (1985) presented excellent works about heat
transfer correlation in a plate heat exchanger using
water. The use of water as the only test ¯uid reduces the
applicability of the results. Most food products are non-
Newtonian ¯uids and little is known about their ¯ow
and heat transfer behavior. Even so, much of the
products have physical properties similar to those of
water, as milk, fresh orange juice (OJ) and wine.
The main objective of this study was to determine
heat transfer coecients for OJ during the pasteuriza-
tion process using a plate heat exchanger. The aim of
this study was also to achieve suitable heat transfer
correlation model with which to predict the OJ heat
transfer coecient for varied operating conditions. The
experimental data have provided the appropriate con-
ditions necessary for this study. These data were the
inlet and outlet temperature in each section of the
exchanger and OJ ¯ow rate.
2. Material and methods
2.1. Juice thermal processing
A DeLaval, model P5-VRB, plate heat exchanger
with intermating 316 SS plates was used as OJ pas-
teurization unit, as shown in Fig. 1. The ¯ow con®gu-
ration used in both heating and cooling sections were in
a counter ¯ow pattern. The main characteristic dimen-
sions for the plates and ¯ow arrangements are presented
in Table 1 and the ¯ow arrangement of the plate heater
is shown in Fig. 2.
Inlet and outlet temperatures were recorded contin-
uously by a data logger attached to an IBM compatible
personal computer using RTDs. A ¯owmeter (Taylor,
model 1101L) was used to measure the OJ ¯ow rate. A
product backpressure gauge (Anderson Instrument,
model SP-110-1025) was used to measure the OJ back-
pressure. To eliminate the presence of fouling, the plates
were cleaned by a CIP system after each run and during
the process the OJ measured backpressure indicated no
Fig. 1. Flow diagram of orange juice pasteurization system.
80 H.B. Kim et al. / Journal of Food Engineering 42 (1999) 79±84

3. fouling. The hot and cold water ¯ow rates were held
constant. The temperatures of each inlet and outlet
stream were recorded once every 10 s. The mean tem-
perature di€erence values produced errors of less than
‹5% for all the runs.
2.2. Physical properties of water
The physical properties of water (density, viscosity,
thermal conductivity and speci®c heat) were obtained
from the literature (Incropera & DeWitt, 1996 ).
2.3. Physical properties of orange juice
The physical properties of OJ were obtained as fol-
lows:
· Density was measured o€-line using a hydrometer in
raw OJ at the heating section inlet temperature and
in pasteurized OJ at the cooling section outlet temper-
ature. Density was also measured in-line by a Micro-
motion (Fischer±Rosemound, model DL20032263U)
instrument installed at outlet of heating section.
· Viscosity was measured o€-line using a Brook®eld
viscometer, model DV-II, in a range from the heating
section inlet temperature to the heating section outlet
temperature.
· Thermal conductivity and speci®c heat were obtained
from the literature (Okos, 1986).
2.4. Thermal design
The following equations have been described in the
literature (Buonopane et al. (1963); Usher (1970);
Schlunder (1983); Bassiouny & Martin (1985); Kakacß &
Liu (1997)) and were programmed on a personal com-
puter for use in this study.
For conventional heat exchanger design a corrected
log mean temperature equation was used:
 ˆ …c à eT à p à D„mX …1†
Table 1
Main characteristic dimensions for the plates and ¯ow arrangement of the plate heat exchanger used in orange juice pasteurization
Characteristic P5-VRB plate
Plate length (port-to-port), m 0.5740
Plate width (available to ¯ow), m 0.1970
Plate thickness, m 0.0010
Mean channel spacing, m 0.0025
Mean hydraulic diameter, m 0.0050
Port diameter, m 0.0351
Heat transfer area, m2
0.1394
Total number of plates, nT Heating section Cooling section
17 13
Orange juice Hot water Orange juice Cold water
Number of passes, nP 8 1 6 1
Number of channels per pass, n 1 8 1 6
Fig. 2. Flow arrangement of the plate heat exchanger used in orange juice pasteurization.
H.B. Kim et al. / Journal of Food Engineering 42 (1999) 79±84 81

4. To apply Eq. (1) to the plate heat exchanger, empir-
ical correlation of the ®lm heat coecients are needed.
In order to validate the use of the design equation, the
following conditions are imposed:
· The temperature and ¯ow transients in the plate heat
exchanger are negligible.
· The heat losses to the surroundings are negligible.
· The ¯uids exist only in the liquid phase within the
exchanger.
· The overall heat transfer coecient is constant
throughout the exchanger.
We can also de®ne an important parameter
NTU (number of transfer units) based on the concept
of a heat exchanger e€ectiveness, by the following
equation:
NTU ˆ
…c à eT
•mgp
ˆ
„h1 À „h2
D„m
or NTU ˆ
…c à eT
•mgp
ˆ
„c2 À „c1
D„m
X
…2†
Therefore, when all temperatures in a section of plate
heat exchanger are known, we can determine the NTU
from Eq. (2). After that, the actual overall heat transfer
coecient can be determined.
Any attempt for the estimation of ®lm coecient of
heat transfer in a gasketed-plate heat exchanger involves
extension of correlation that are available for heat
transfer between ¯at ¯ow passages. The conventional
approach for each passage employs correlation appli-
cable for tubes by de®ning an equivalent diameter for
noncircular passage, which is substituted for diameter
De, in the following correlation for turbulent ¯ow:
xu ˆ …constX† Ã …‚e†m
à …€r†n
Ã
l
lwall
x
X …3†
The equivalent diameter of the channel, De, is de®ned
as
he ˆ
4 Ã channel flow area
wetted surface
or he ˆ
4 Ã ˜ Ã w
2 Ã …˜ ‡ w†
…4†
as ˜ ( wY he ˆ 2 Ã ˜X …4a†
The Reynolds number, Re, based on channel mass
velocity and the equivalent diameter, De, of the channel
is de®ned as
‚e ˆ
q à he
l
X …5†
Table 2
Thermal conditions obtained for heating section of a plate exchanger during orange juice pasteurizationa
Run Experimental Calculated
OJ Fr
(kg/s)
OJ v
(m/s)
Temperature (°C) DTm
(°C)
nT HW Fr
(kg/s)
HW h
(W/m2
°C)
U
(W/m2
°C)
HW OJ
In Out In Out
1 0.342 0.69 82.30 71.67 5.00 79.37 20.39 13 2.255 23 277 3211
2 0.220 0.44 80.51 73.99 5.39 80.04 13.63 13 2.377 23 657 3102
3 0.190 0.37 81.51 76.02 5.15 80.11 17.68 17 2.444 22 013 1524
4 0.329 0.69 88.11 76.86 5.82 84.85 21.97 13 2.176 23 463 3046
5 0.220 0.46 87.58 79.97 6.09 83.60 23.91 13 2.110 23 350 1839
6 0.175 0.34 85.20 80.28 8.55 84.36 15.88 17 2.546 22 596 1581
7 0.324 0.66 92.06 82.02 13.12 91.13 15.77 17 2.375 22 437 3037
8 0.230 0.47 91.33 84.35 13.08 90.18 16.98 17 2.400 22 566 1980
9 0.172 0.34 93.84 88.49 9.34 91.95 20.69 17 2.505 23 086 1299
10 0.350 0.69 79.37 69.36 6.20 78.69 13.76 17 2.490 20 571 3640
11 0.244 0.47 80.40 73.49 5.39 79.88 13.82 17 2.474 21 950 2481
12 0.165 0.33 81.36 77.10 11.52 80.64 14.34 17 2.522 22 301 1629
13 0.345 0.69 85.76 76.14 12.69 84.42 16.04 17 2.426 22 131 2923
14 0.231 0.45 86.82 80.69 14.21 85.89 15.30 17 2.546 22 671 2046
15 0.152 0.30 87.99 83.77 13.44 84.74 21.79 17 2.247 22 494 942
16 0.346 0.68 89.66 78.97 5.92 88.75 16.47 17 2.522 22 649 3286
17 0.246 0.48 91.40 83.58 6.26 89.72 19.74 17 2.471 22 738 1968
18 0.160 0.32 92.39 87.56 11.68 90.55 19.89 17 2.471 22 912 1204
19 0.178 0.35 80.35 75.30 8.61 78.31 18.52 17 2.318 11 909 2659
20 0.169 0.33 83.05 78.92 13.73 81.09 18.01 17 2.583 22 547 1192
Mean 22 756 2196
Pooled s 138 70
a
OJ: orange juice; HW: hot water; Fr: ¯ow rate; v: channel velocity; HW h: hot water heat transfer ®lm coecient; U: overall heat transfer coecient.
82 H.B. Kim et al. / Journal of Food Engineering 42 (1999) 79±84

5. The channel mass velocity is given by
q ˆ
•m
n à ˜ à w
Y where n ˆ
nT À 1
2 Ã nP
X …6†
The overall heat transfer coecient for a clean sur-
face is
1
…c
ˆ
1
hh
‡
1
hc
‡
t
km
X …7†
From the actual overall heat transfer coecient de-
termined by Eq. (2), and from water heat transfer ®lm
coecient calculated by Eq. (3), using constant val-
ue ˆ 0.28, m ˆ 0.65, n ˆ 0.4 and assuming l/lwall @ 1, we
can obtain the actual OJ heat transfer ®lm coecient.
The values of coecients used in Eq. (3) to get the water
heat transfer ®lm coecient were obtained from pre-
liminary runs with water in both sides and by the use of
an iterative calculation. These values were compared to
those reported by other authors, for water in turbulent
¯ow, using plates with intermating corrugation (Jackson
Troube, 1964; Schlunder, 1983; Rahman, 1995).
3. Results and discussion
Tables 2 and 3 present the thermal conditions
achieved during pasteurization of OJ for heating and
cooling sections, respectively. The overall heat transfer
coecient varied from 942 to 3640 W/m2
°C from 20
runs with a total of 465 observations.
The values of in-line OJ density were correlated
with o€-line for each run and the results showed a
good ®t between the two methods of measurement
(R2
P 0.8667). The OJ viscosity was correlated with
temperature and the results also presented a good ®t
(R2
P 0.9780). The mean values of OJ density and OJ
viscosity at 20°C were 1046.0 ‹ 3.6 kg/m3
and
14.17 ‹ 4.75 mPa s, respectively.
From the obtained experimental values of U and the
water heat transfer ®lm coecient calculated as ex-
plained in Section 2.4, the OJ heat transfer ®lm coe-
cient was calculated by Eq. (7). The values of heat
transfer coecient for OJ varied from 983 to 6500 W/
m2
°C whereas the water heat transfer ®lm coecient
varied from 8387 to 24245 W/m2
°C. The turbulent
stream resistance referred on the water side represents
about 14% of the total resistance. So, the maximum
possible error introduced for determined OJ heat
transfer ®lm coecient was about 5%. Table 4 presents
mean values of the OJ heat transfer ®lm coecient ac-
cording to the plate heater section, pasteurization tem-
perature and channel velocity, showing a good
agreement among results.
Table 3
Thermal conditions obtained for cooling section of a plate exchanger during orange juice pasteurizationa
RUN Experimental Calculated
OJ Fr
(kg/s)
OJ v
(m/s)
Temperature (°C) DTm
(°C)
nT CW Fr
(kg/s)
CW h
(W/m2
°C)
U
(W/m2
°C)
OJ CW
In Out In Out
3 0.189 0.37 80.42 12.20 9.18 20.05 19.14 13 1.122 10 534 1737
4 0.324 0.68 85.09 15.81 13.28 26.94 17.75 13 1.566 13 703 3265
5 0.217 0.46 84.17 13.74 13.21 22.36 12.86 13 1.583 13 421 3072
6 0.175 0.34 84.32 12.87 12.49 20.24 12.39 13 1.530 12 942 2609
7 0.323 0.66 91.32 15.65 15.29 27.83 12.23 13 1.847 15 117 5168
9 0.172 0.34 92.05 12.93 12.54 20.80 13.57 13 1.556 13 113 2583
10 0.335 0.65 79.27 14.04 9.09 25.05 21.00 13 1.291 11 909 2659
11 0.265 0.47 80.23 12.76 9.12 22.16 19.65 13 1.296 11 094 2157
12 0.163 0.33 80.71 12.21 5.65 19.04 24.60 13 0.776 7754 1171
13 0.345 0.69 84.50 14.94 5.55 26.90 26.59 13 1.063 10 439 2325
14 0.231 0.45 85.63 12.95 6.36 22.41 25.05 13 0.989 9636 1726
15 0.155 0.32 85.35 12.24 6.35 19.04 24.96 13 0.845 8268 1171
16 0.343 0.67 88.85 14.77 5.92 27.35 27.15 13 1.122 10 895 2418
17 0.243 0.48 90.24 12.89 5.93 23.40 26.48 13 1.018 9895 1834
18 0.160 0.32 90.60 12.18 5.61 19.93 26.98 13 0.829 8156 1199
19 0.175 0.34 79.04 12.93 12.52 19.56 11.80 13 1.506 12810 2530
20 0.162 0.32 81.87 12.26 6.42 18.95 24.00 13 0.851 8296 1210
Mean 11021 2255
Pooled s 102 52
a
OJ: orange juice; CW: cold water; Fr: ¯ow rate; v: channel velocity; CW h: cold water heat transfer ®lm coecient; U: overall heat transfer co-
ecient.
H.B. Kim et al. / Journal of Food Engineering 42 (1999) 79±84 83

6. Nusselt numbers were correlated as a function of
Reynolds and Prandt numbers in the form of Eq. (3),
assuming l @ lw for turbulent ¯ow, using a statistical
program (SAS (1995) for Windows, v. 6.12).
For the P5-VRB DeLaval plate, the following corre-
lation (R2
ˆ 0.93) from the experimental data of OJ
pasteurization was achieved:
xu ˆ 1X12 Ã 10À5
‚e1X39
€r1X63
Y
156 ` ‚e ` 567Y 41 ` €r ` 98X
…8†
Fig. 1 presents the Nusselt number correlation among
the experimental and predicted values, showing appro-
priate correlation (Fig. 3).
The OJ heat transfer ®lm coecient was correlated as
a linear function of channel velocity and its viscosity,
obtaining an R2
ˆ 0.96:
h ˆ À1309X08 ‡ 58358X5l ‡ 7810X06vY
0X0062 ` l ` 0X0148 Pa sY 0X32 ` v ` 0X69 masX
…9†
The channel velocity was calculated from
v ˆ
q
q
X …10†
Marriot (1971) states that the nominal velocities for
``water-like'' liquids in turbulent ¯ow are usually in the
range of 0.3±1.0 m/s. The value of v in this study was in
the same range of values as mentioned by Marriot.
This study has provided a suitable heat transfer cor-
relation to predict the OJ heat transfer ®lm coecient as
a function of its viscosity and the channel velocity, that
is, this correlation is independent of the plate geometry,
for varied conditions of pasteurization process. In this
case, if the e€ective heat transfer area is designed based
on heat transfer models, considering OJ as a ``water-
like'' ¯uid, it will result a 25% less necessary area,
resulting in an inadequate process.
Acknowledgements
To FAPESP for research grant that enabled Carmen
C. Tadini to work for a period of ®ve months at
Department of Food Science, Purdue University.
References
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four channel plate heat exchanger. Heat Transfer Engineering, 6(2),
58±72.
Buonopane, R., Trupe, R., Morgan, J. (1963). Heat transfer design
method for plate heat exchangers. Chemical Engineering Progress,
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Incropera, F. P., DeWitt, P. de. (1996). Fundamentals of heat and
mass transfer (4th ed.). NY, USA: Wiley.
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exchanger. Chemical Engineering Progress, 60(7), 62±65.
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thermal design. Boca Raton, Florida, USA: CRC Press.
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Okos, M. R. (1986). Physical and chemical properties of food. MI,
USA: ASAE St. Joseph.
Rahman, S. (1995). Food properties handbook. Boca Raton, Florida,
USA: CRS Press.
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Cary, NC.
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Fig. 3. Nusselt number experimental values as a function of Nusselt
number predicted values by equation: Nu ˆ 1.121*10À5
Re1X3919
Pr1X6271
.
Table 4
Mean values of orange heat transfer ®lm coecient according the plate
heater section, pasteurization temperature and channel velocity
Level Observation Meana
Standard
Errora
Grand mean 465 3821.87
Section
Heating section 164 3100.46 202.91
Cooling section 301 4543.28 157.38
Temperature
80°C 106 3440.16 253.45
85°C 192 3281.11 191.82
90°C 167 4744.34 206.25
Channel velocity
0.69 m/s 137 6352.47 224.35
0.46 m/s 132 3105.11 230.54
0.33 m/s 196 2008.03 193.55
a
95% Con®dence intervals.
84 H.B. Kim et al. / Journal of Food Engineering 42 (1999) 79±84