Heat transfer in a plate exchanger during pasteurization of orangejuice 1

Han B. Kim a, Carmen C. Tadini a, Rakesh K. Singh b,*

a Department of Chemical Engineering, Escola Politecnica, Sao Paulo University, Brazilb 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 foodand dairies industries, but very little basic informationhas been published on their ¯ow and heat transfercharacteristics. The principal advantages of such unitsare ¯exibility of ¯ow arrangements, extremely high heattransfer rates, and ease of opening for cleaning andsterilization to meet healthy and sanitary requirements.They are used as conventional process heaters andcoolers, as well as condensers. The basic elements of aplate heat exchanger are closely spaced plates with

Journal of Food Engineering 42 (1999) 79±84

www.elsevier.com/locate/jfoodeng

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.edu1 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

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 McKillopand Dunkley (1960), Buonopane, Trupe and Morgen(1963), Jackson and Troube, (1964), Usher (1970),Marriot (1971), Schl�undler (1983), Bassiouny andMartin (1985) and Kakacß and Liu (1997). McKillop andDunkley (1960), Buonopane et al. (1963) and Bassiounyand Martin (1985) presented excellent works about heattransfer correlation in a plate heat exchanger usingwater. The use of water as the only test ¯uid reduces theapplicability of the results. Most food products are non-Newtonian ¯uids and little is known about their ¯owand heat transfer behavior. Even so, much of theproducts have physical properties similar to those ofwater, as milk, fresh orange juice (OJ) and wine.

The main objective of this study was to determineheat transfer coe�cients for OJ during the pasteuriza-tion process using a plate heat exchanger. The aim ofthis study was also to achieve suitable heat transfercorrelation model with which to predict the OJ heattransfer coe�cient for varied operating conditions. Theexperimental data have provided the appropriate con-ditions necessary for this study. These data were the

inlet and outlet temperature in each section of theexchanger and OJ ¯ow rate.

2. Material and methods

2.1. Juice thermal processing

A DeLaval, model P5-VRB, plate heat exchangerwith 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 ina counter ¯ow pattern. The main characteristic dimen-sions for the plates and ¯ow arrangements are presentedin Table 1 and the ¯ow arrangement of the plate heateris shown in Fig. 2.

Inlet and outlet temperatures were recorded contin-uously by a data logger attached to an IBM compatiblepersonal computer using RTDs. A ¯owmeter (Taylor,model 1101L) was used to measure the OJ ¯ow rate. Aproduct backpressure gauge (Anderson Instrument,model SP-110-1025) was used to measure the OJ back-pressure. To eliminate the presence of fouling, the plateswere cleaned by a CIP system after each run and duringthe 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

fouling. The hot and cold water ¯ow rates were heldconstant. The temperatures of each inlet and outletstream 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 obtainedfrom 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 andin 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®eldviscometer, model DV-II, in a range from the heatingsection inlet temperature to the heating section outlettemperature.

· Thermal conductivity and speci®c heat were obtainedfrom the literature (Okos, 1986).

2.4. Thermal design

The following equations have been described in theliterature (Buonopane et al. (1963); Usher (1970);Schl�under (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 correctedlog mean temperature equation was used:

Q � Uc � AT � F � DTm: �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

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, thefollowing 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 conceptof a heat exchanger e�ectiveness, by the followingequation:

NTU � Uc � AT

_mCp

� Th1 ÿ Th2

DTm

or NTU � Uc � AT

_mCp

� Tc2 ÿ Tc1

DTm

:

�2�

Therefore, when all temperatures in a section of plateheat exchanger are known, we can determine the NTUfrom Eq. (2). After that, the actual overall heat transfercoe�cient can be determined.

Any attempt for the estimation of ®lm coe�cient ofheat transfer in a gasketed-plate heat exchanger involvesextension of correlation that are available for heattransfer between ¯at ¯ow passages. The conventionalapproach for each passage employs correlation appli-cable for tubes by de®ning an equivalent diameter fornoncircular passage, which is substituted for diameterDe, in the following correlation for turbulent ¯ow:

Nu � �const:� � �Re�m � �Pr�n � llwall

� �x

: �3�

The equivalent diameter of the channel, De, is de®nedas

De � 4 � channel flow area

wetted surface

or De � 4 � b � w2 � �b� w�

�4�

as b� w; De � 2 � b: �4a�The Reynolds number, Re, based on channel mass

velocity and the equivalent diameter, De, of the channelis de®ned as

Re � G � De

l: �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

The channel mass velocity is given by

G � _mn � b � w

; where n � nT ÿ 1

2 � nP

: �6�

The overall heat transfer coe�cient for a clean sur-face is

1

Uc

� 1

hh

� 1

hc

� tkm: �7�

From the actual overall heat transfer coe�cient de-termined by Eq. (2), and from water heat transfer ®lmcoe�cient calculated by Eq. (3), using constant val-ue� 0.28, m� 0.65, n� 0.4 and assuming l/lwall @ 1, wecan obtain the actual OJ heat transfer ®lm coe�cient.The values of coe�cients used in Eq. (3) to get the waterheat transfer ®lm coe�cient were obtained from pre-liminary runs with water in both sides and by the use ofan iterative calculation. These values were compared tothose reported by other authors, for water in turbulent¯ow, using plates with intermating corrugation (Jackson& Troube, 1964; Schl�under, 1983; Rahman, 1995).

3. Results and discussion

Tables 2 and 3 present the thermal conditionsachieved during pasteurization of OJ for heating and

cooling sections, respectively. The overall heat transfercoe�cient varied from 942 to 3640 W/m2 °C from 20runs with a total of 465 observations.

The values of in-line OJ density were correlatedwith o�-line for each run and the results showed agood ®t between the two methods of measurement(R2 P 0.8667). The OJ viscosity was correlated withtemperature and the results also presented a good ®t(R2 P 0.9780). The mean values of OJ density and OJviscosity at 20°C were 1046.0 � 3.6 kg/m3 and14.17 � 4.75 mPa s, respectively.

From the obtained experimental values of U and thewater 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 heattransfer coe�cient for OJ varied from 983 to 6500 W/m2 °C whereas the water heat transfer ®lm coe�cientvaried from 8387 to 24245 W/m2 °C. The turbulentstream resistance referred on the water side representsabout 14% of the total resistance. So, the maximumpossible error introduced for determined OJ heattransfer ®lm coe�cient was about 5%. Table 4 presentsmean values of the OJ heat transfer ®lm coe�cient ac-cording to the plate heater section, pasteurization tem-perature and channel velocity, showing a goodagreement 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

Nusselt numbers were correlated as a function ofReynolds and Prandt numbers in the form of Eq. (3),assuming l @ lw for turbulent ¯ow, using a statisticalprogram (SAS (1995) for Windows, v. 6.12).

For the P5-VRB DeLaval plate, the following corre-lation (R2� 0.93) from the experimental data of OJpasteurization was achieved:

Nu � 1:12 � 10ÿ5 Re1:39 Pr1:63;

156 < Re < 567; 41 < Pr < 98:�8�

Fig. 1 presents the Nusselt number correlation amongthe experimental and predicted values, showing appro-priate correlation (Fig. 3).

The OJ heat transfer ®lm coe�cient was correlated asa linear function of channel velocity and its viscosity,obtaining an R2� 0.96:

h � ÿ1309:08� 58358:5l� 7810:06v;

0:0062 < l < 0:0148 Pa s; 0:32 < v < 0:69 m=s:�9�

The channel velocity was calculated from

v � Gq: �10�

Marriot (1971) states that the nominal velocities for``water-like'' liquids in turbulent ¯ow are usually in therange of 0.3±1.0 m/s. The value of v in this study was inthe 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 asa function of its viscosity and the channel velocity, thatis, this correlation is independent of the plate geometry,for varied conditions of pasteurization process. In thiscase, if the e�ective heat transfer area is designed basedon 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 CarmenC. Tadini to work for a period of ®ve months atDepartment of Food Science, Purdue University.

References

Bassiouny, M. K., & Martin, H. (1985). Temperature distribution in a

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,

59(7), 57±61.

Incropera, F. P., & DeWitt, P. de. (1996). Fundamentals of heat and

mass transfer (4th ed.). NY, USA: Wiley.

Jackson, B., & Troube, R. (1964). Laminar ¯ow in plate heat

exchanger. Chemical Engineering Progress, 60(7), 62±65.

Kakacß, S., & Liu, H. (1997). Heat exchangers. Selection, rating and

thermal design. Boca Raton, Florida, USA: CRC Press.

Marriot, J. (1971). Where and how to use plate heat exchangers.

Chemical Engineering, April 5, 127±134.

Mckillop, A. A., & Dunkley, W. L. (1960). Plate heat exchangers ±

Heat transfer. Industrial and Engineering Chemistry, 52(9), 740±744.

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.

SAS. (1995). SAS/ Insight UserÕs Guide, v. 6, 3rd ed., SAS Institute,

Cary, NC.

Schl�under, E. U. (1983). HEDH ± Heat exchanger design handbook

(Vols. 1±3). Washington, USA: International Center for Heat and

Mass Transfer.

Usher, J. (1970). Evaluating plate heat exchangers. Chemical Engi-

neering, February 23, 90±94.

Fig. 3. Nusselt number experimental values as a function of Nusselt

number predicted values by equation: Nu� 1.121*10ÿ5 Re1:3919 Pr1:6271.

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