THERMOPHYSICAL PROPERTIES OF TROPICAL FRUIT JUICESl

Sílvia Cristina Sobottka Rolim de MOURA2, Silvia Pimentel Marconi GERMER3, Denise Calil PereiraJARDIM4, Mitie Sônia SADAHlRAs

SUMMARY

Precise knowledge of the thermal and rheological properties of foods is of fundamental importance to establish thedesign of process equipment. However, for tropical fruit products such as juices, there is a complete lack of this informa­tion in the literature, seriously hindering processing procedures. Thermophysical properties of tropical fruit juices:thermal diffusivity, specific heat and density, were experimentally determined, and the values obtained compared withthose predicted by mathematical models already existent in the literature, based on the chemical composition. The juicesstudied were prepared from pulps of cupuaçu (Theobroma grandiflorum), açai (Euterpe oleracea, Mart.) and graviola (Annonamuricata), and the determinations were made in the temperature range from 10 to BO°e. The thermal conductivity wasdeduced from the knowledge of the other properties. The viscosity of the filtered juices was also determined using acapillary viscometer.

KEY WüRDS: Thermal properties; Tropical fruit juices; Viscosity; Thermal diffusivity; Specific heat.

RESUMO

PROPRIEDADES TERMOFÍSICAS DE SUCOS DE FRUTASTROPICAIS

o conhecimento preciso das propriedades térmicas e reológicas dos alimentos é de fundamental importância no dimensi­onamento de equipamentos. Porém, para produtos de frutas tropicais, como sucos, não existe na literatura referências destaspropriedades, o que dificulta seriamente o processamento dos mesmos. Propriedades termofísicas: difusividade térmica,calor específico e densidade, de sucos de frutas tropicais, foram determinadas experimentalmente e comparadas a valorespreditos por modelos matemáticos, já existentes na literatura, em função da sua composição química. Os sucos estudadosforam preparados com polpas de cupuaçu (Theobroma grandiflorum), açaí (Euterpe oleracea, Mart.) e graviola (Annona muricata)e as determinações foram realizadas na faixa de temperatura de 10 a BO°e. A condutividade térmica foi obtida através doconhecimento das demais propriedades. Determinou-se, também, a viscosidade dos sucos filtrados em um viscosímetrocapilar.

PALAVRAS-CHAVE: Propriedades térmicas; Sucos de frutas tropicais; Viscosidade; Difusividade térmica; Calor específico.

1 Recebido para publicação em 21/09/1998. Aprovado para publicação em 30/12/1998.2.3.4.sPesquisadores do Instituto de Tecnologia de Alimentos - FRUTHOTEC/ITAL. Av. Brasil, 2880 - Campinas/SP - CEP 13073-001emails:smoura@ital.org.brsgermer@ital.org.brdjardim@ital.org.brmitie@ital.org.br

70 Braz. J. Food Technol., Campinas, 1(1,2): 70-76, janldez.1998_______~-----_...I

2. METHODOLOGY

Viscosity (/l)

Determined at three temperatures using a capilla­ry glass viscometer, after filtering through cotton wool(VAN WAZER et aI., 1972).

2.2 Methods

Juices prepared from commercial pulps of cupuaçu(Theobroma grandiflorum), açaí (Euterpe oleracea, Mart.)and graviola (Annona muricata), chemically analysingusing official methods (WILLIAMS, 1990).

2.1 MateriaIs

Density (p)

Determined at three temperatures by fluid displa­cement using a pycnometer, according to AOAC me­thod n°. 985.19 (WILLIANS, 1990).

models to predict rise in boiling point, density, en­thalpy, specific heat, sucrose solubility, surface tensi­on, thermal conductivity and viscosity. The studyshows that good correlation exists between the ther­mophysical properties and the concentration andtemperature of fluid products.

It is important to emphasize the increasing demandfor processed food in the country (Brazil), bringing,as a consequence, the demand for industrial moder­nization, technological adequation and improvedquality. These demands can only be met if more sci­entific information on food processing becomes avai­lable, requiring knowledge of the physical propertiesin order to calculate the processes. Currently, the coun­tless data available in the literature on similar pro­ducts are inadequate, in the majority of cases, for bra­zilian products. For the majority of brazilian pro­ducts, the thermophysical properties are not availa­ble in the literature.

The objective of this research was to experimen­tally determine the density, viscosity, specific heat and

- thermal diffusivity as well as calculate the thermalconductivity of cupuaçu, açaí and graviola juices in thetemperature range from 10 to 80°e. ln addition, thepaper presents a comparison between the experimen­tal data and values obtained from mathematical mo­deIs found in the literature.

1.INTRODUCTION

ln order to determine the dimensions of food pro­cessing equipment, especially heat exchangers andother equipment requiring pumping of the product, itis essential to know the precise values of the thermalproperties of the products (thermal conductivity, ther­mal diffusivity and specific heat) and how these pro­perties react during processing as a function of tem­perature.

The need for precise knowledge of the thermal pro­perties has led to studies on the influence of compo­sition and temperature on these properties.

POLLEY et aI. (1980), have published a collectionof tables of the thermal properties of various foods,including meats, fruits, vegetables, milk and cereaIs.Some, but not all, of the thermal properties of the fo­llowing fruit juices can be found in these tables: ap­pIe, cherry, grape, orange and pear.

CONSTENLA et aI. (1989) published more specificdata on the thermophysical properties of clarifiedapple juice at various temperatures and concentrati­ons. This paper presents the experimental results ofthe determinations of density, viscosity, specific heatand thermal conductivity. The results show the greatinfluence of concentration and temperature on thedetermination of these properties, and model the dataas a function of these variables. VIRENDRA et aI.(1989) studied the prediction of the thermal conduc­tivity of various juices (apple, cherry, grape, orangeand strawberry), using several mathematical models,and a comparison of the theoretical values with theexperimental values showed an error of less than 10%.

Experimental values for the thermal diffusivity ofapple, cherry, grape, orange and tomato juices can befound in GEORGE (1990). Once again, the majority ofthe data are for sub-tropical fruit juices.

A knowledge of the rheological properties of foodsbecomes necessary in a series of applications suchas: quality control, knowledge of the physical struc­ture and principally the control and sizing of indus­trial processes.

The effect of temperature and concentration on thedensity and viscosity of apple juice was studied byBAYINDIRLI (1992). Mathematical models were obtai­ned from the experimental data, showing excellent cor­relation (r>0.99). The influence of temperature and vis­cosity on filtered fruit juices and sugar cane juice can befound inALVARADO (1993). The results show that theviscosity of the fruit juices follows Arrhenius' law, sho­wing activation energies of the order of 20kJ/ g.mo!.

A more recent prediction of the thermophysicalproperties, applied to clarified fruit juices as a functi- Specific heat (Cp)on of concentration and temperature, can be found in Specific heat was determined using an adaptationPEACOCK (1995). The paper presents mathematical of the method of mixtures of HWANG, HAYAKAWA

Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998 71

(1979). The calorimeter used for the measurement ofthe specific heat consisted of a ane liter thermos flask.Before starting the tests, the thermal capacity of thecalorimeter was obtained, by calibrating it in the tem­perature range to be used (10 to 70°C). 100 to 150gsamples of juice, packaged in polyethylene bags, wereplaced in a cold chamber (S°C) for 24 hours to stabili­ze the temperature.

Approximately 500g distilled water at 90°C wereintroduced into the calorimeter, and after stabilizingthe temperature, a sample package was placed in thecalorimeter after initially determining its internal tem­perature.

Using a calibrated T-type needle thermocouple,passing through the lid of the thermos flask, the tem­perature inside the calorimeter was recorded every30 seconds. The equipment was shaken constantly ina shaker, as shown in Figure 1.

Hk

= thermal capacity of the calorimeter (cal;oC)C w =specific heat of distilled water (cal/g.°C)v( = mass of distilled water (g)T fw = temperature corresponding to the start ofthe straight part of the time' temperature curvefor distilled water (0C)T

ow= initial temperature of the distilled water (0C)

dT/ dt =slope of the time' temperature curve fordistilled water (OC/min)te = time corresponding to Tfw of the time' tempe­rature curve for distilled water (min)C s =specific heat of the polyethylene bag (cal!g.0C)Ws =mass of the polyethylene bag (g)Wc =sample mass (g)Toe =initial temperature of sample (0C)

Assay for Specific Heat

(c)

\.

(a) ~J \ I \. J

74§: 72GI

70...j-lO 68...GIQ. 66EGI 64~

62o 50 100

time (min) 1

_- CarrectedTemperature

(d)FIGURE 2. Example of a time' temperature curve ob­tained using the calorimeter, for the determination ofspecific heat in tropical fruit juices.

Where:

Cp =~•.w). la, - To) - IdTldtlt).±...C,.•.W.,U,. - Toe - IdTldtlt) (1)

W, «Toe -TIw) + (dT/dt)t.)

FIGURE 1. Design of the apparatus constructed tomeasure specific heat: (a) calorimeter (b) digital ther­mometer (c) thermocouple lead (d) shaker.

Readings were taken until thermal equilibrium wasreached, and the data used to construct a graph of thetemperatures (duly corrected using a calibration equa­tion) as a function of time (Figure 2). The linear re­gression was determined from the linear part of thecurve. The specific heat of the sample was calculatedusing equation (1), which was derived as a functionof the energy balance.

Thermal diffusivity (a)Thermal diffusivity was determined based on the

method of DICKERSON (1965) using the apparatusshown in Figure 3. The Scm (diameter) by 29.8cm (hei­ght) celI, constructed in stainless steel, was connec­ted to two calibrated thermocouples: one at the surfa­ce to measure the temperature of the medium, and theother in the central plane, to measure the temperatureof the product. To avoid the formation of convectioncurrents, which would hamper the analysis, the sam­pIes were partialIy solidified by adding 1% agar. Themeasuring system was placed in a thermal bath con­taining ethylene glycol at O°C and alIowed to reachthermal equilibrium. Heating was then started at arate of 0.7°C/min, and stopped when the temperaturereached approximately 8S°C. During the experiment,the temperatures were registered every minute using the

Cp = specific heat of the sample (cal/ g.0C) Dianachart (16 bits) data aquisition system.

72 Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998

The evolution of the internal and external tempe­rature profiles were drawn (see example in Figure 4)and the thermal diffusivity calculated for each valueregistered using equation (2):

Thermal conductivity (k)

This was determined using equation 3, after deter­mining the other properties.

(2) k=r.C .up

(3)

where:A = rate of temperature rise of the bath (OC/min)R = radius of the cell (m)(Text-Tint) = temperature difference between theinside and outside of the cell (0C)

The value for A is a constant, since it is the rate oftemperature rise of the bath. The value (Text-Tint) de­creases as the temperature of the bath increases. The­refore the diffusivity was calculated for each registe­red temperature and the average value obtained inthe range under study.

STIRRER

HEATERJ

IJ

2.3 Analysis of the results

The experimentally obtained values (assays carriedout in triplicate) were compared with those obtainedusing mathematical modeIs available in the literature.

For Specific heat

Model I: HWANG and HAYAKAWA (1979)Cp = 4.184. (Cpw·Ww+Cpc,Wc+CpfWr)I 100 aI g.0C) (4)

Where: C = C b h d t = 0.41 cal/gOCpc .....p car o y ra e

C = L = 1 cal/gOCpw p water

C r = C rat = 0.53 call gOCW = % water

w

Wc = % carbohydrateWr=%fat

Where: Xw= sample moisture (in decimal form)

~__-l~+=~ THERMOCOUPLES

Model II: SIEBEL (1982)C = 0.837 + 3.349 . X (J Ig.°C)p w

(5)

For Thermal Diffusivity

FIGURE 3. Design of the apparatus for measuringthermal diffusivity.

Model I: RIEDEL (1982)a =0.088.10-6 + (a

w- 0.088 x 10-6). X

w(m 2/s) (6)

Assay for Thermal Diffusivity

Where: a w= diffusivity of water (m2I s)Xw= sample moisture (in decimal form)

Te 100

m 80pe 60ra 40t --T ex!. temp

u 20 --Tint.tempre O

ICI O 50 100

time (min)

Model II: MARTENS (1982)a = [0.057363. X

w+ 0.000288 (T + 273)].10-6 (m2/s) (7)

Where: Xw= sample moisture (in decimal form)T = sample temperature (0C)

For Thermal Conductivity

Model I: KOLAROV and GROMOV (1989)k = 0.140 + 0.42. Xw(forjuices) (W Im.°C) (8)

Where: w = water

Model II: SWEAT (1989)k = 0.58. Xw+ 0.25. Xc + 0.16. Xr (W Im.°C) (9)

FIGURE 4. Example of a time' temperature curve re­gistered in an experimental assay to determine ther­mal diffusivity in tropical fruit juices.

Where: w = water c = carbohydrate f = fat

Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998 73'----------------

3. RESULTS AND DISCUSSION

Table 1 shows the compositions of the pulps and Ta­ble 2 the formulations used in the study. Table 3 pre­sents the values obtained for the proximate compositi­on of the formulated juices. These values were used in

the mathematical models for the theoretical calculationof the properties.

Table 4 shows the data obtained in the experimentalassays for density, viscosity, specific heat, thermal di­ffusivity and the calculated values for thermal conduc­tivity.

TABLE 1. Physico-chemical characterization of the cupuaçu, açaí and graviola pulps.

TYPE Moisture Carbohydrate Fat Brix pH(%) (%) (%) (o) (21°C)

Cupuaçu 89.83 10.17 8.9 3.74Açaí 93.80 2.84 3.36 3.5 4.75

Graviola 88.96 11.04 8.0 3.50

TABLE 2. Formulation of the cupuaçu, açaí and graviola juices.

TYPECupuaçu

AçaíGraviola

Pulp (%)21.044.731.6

Water (%)69.044.763.6

Sugar (%)9.410.64.9

Milk (%)0.6

TABLE 3. Physico-chemical characterization of the formulated cupuaçu, açaí and graviola juices.

TYPE Moisture Carbohydrate Fat Protein Brix(%) (%) (%) (%) (0)

pH(21°C)

Cupuaçu

Açaí

Graviola

87.86 11.54 0.6 11.5

86.63 11.87 1.50 11.9

91.70 8.39 8.40

4.02

4.95

4.50

TABLE 4. Experimental results for the thermophysical properties of cupuaçu, açaí and graviola juices.

Properties

Density (g/cm 3)

5°C

25°C (average)

87°C

Viscosity (cP)

5°C

25°C87°e

Thermal diffusivity (m 2/s)

AverageT=55°e

Specific heat(cal/g .oe )/(J/g. oe)AverageT=40oe

T h erm a I C ond u ctivity*(w/m.oe)

Cupuaçu

1.049

1.047 (1.036)

1.012

12.71

4.00

1.141.46 x 10.7

0.91184/3.82

0.578

Juices

Açaí

1.047

1.042 (1.032)

1.008

2.14

1.20

0.351.51 x 10.7

0.88246/3.69

0.575

Graviola

1.034

1.030 (1.013)

0.974

2.48

1.145

0.34

1.50x10·7

0.94821 /3.97

0.603

*Result calculated from other experimental data.

74 Braz. J. Food Technol., Campinas, 1(1,2): 70-76, janldez.1998------------_.....

ln order to compare the experimental data for spe­cific heat, thermal conductivity and thermal diffusi­vity with the calculated data, the mathematical mo­deIs, specific for each property, presented in equati-

ons 4 to 9, were used.The results can be seen in Table 5 (for specific heat),

Tables 6, 7 and 8 (for thermal diffusivity) and Table 9(for thermal conductivity).

TABLE 5. A comparison between the values calculated for specific heat (Cp) using modeIs I and II and theexperimental data for cupuaçu, açaí and graviola juices.

Juices Cpmodell Cpmodelll CpexperimentalCupuaçu 3.88 3.78 3.82

Açaí 3.86 3.74 3.69

Graviola 3.98 3.91 3.97

%errar = (thearetical vaiue-experimental value)/(experimental value) x 100.

(%)errarmodel I

1.55

4.61

0.25

(%)errarmodelll

1.05

1.35

1.51

TABLE 6. Comparison between the values calculated using models I and II and the experimental data, for thethermal diffusivity (a) of cupuaçu juice.

Temperature (0C) amodell amodelll Uexperimental

40 1.43 X 10-7 1.41 x 10'7 1.42 X 10'7

50 1.47 X 10-7 1.43 X 10'7 1.38 X 10'7

60 1.50 X 10-7 1.46 X 10'7 1.43 X 10'7

70 1.52 X 10'7 1.49 x 10'7 1.62 X 10-7

(%) (%)

errarmodel I errarmodel II

0.70 0.70

6.52 3.62

4.90 2.10

6.17 8.02

%errar = (thearetical value-experimental value)/(experimental value) x 100.

TABLE 7_ Comparison between the values calculated using modeIs I and II and the experimental data, for thethermal diffusivity (a) of açaí juice.

Temperature (oC) amodell amodelll aexperimental

40 1.43 X 10'7 1.40 X 10'7 1.38 X 10'7

50 1.46 X 10-7 1.43 X 10'7 1.43 X 10-7

60 1.49 X 10-7 1.46 X 10'7 1.53 x 10'7

70 1.51 X 10-7 1.48 X 10-7 1.69 X 10-7

(%) (%)

errarmodell errarmodel II

3.50 1.45

2.10

2.61 4.58

10.65 12.43

%error = (thearetical vaiue-experimental value)/(experimental vaiue) x 100

An analysis of Tables 5 to 9 shows that the greatesterror was obtained for the prediction of thermal con­ductivity (13% error). This is due to the fact that thisproperty is calculated from the values for the otherproperties, and so the individual error for each pro­perty contributes to that of thermal conductivity. Theerror in the prediction of the other properties waswithin the expected value and that obtained by otherauthors (approximately 10%). It can also be seen that

the error between the values for thermal diffusivityincreases with increase in temperature, which maybe due to the dissolution of the agar added to the jui­ce, consequently increasing the convection of the sys­tem. For each property, the values obtained for thethree juices were very similar, with the exception ofviscosity (Table 4) which showed very distinct valu­es. It was also shown that the variation in viscositywith temperature was considerable, within the range

Braz. J. Food Technol., Campinas, 1(1,2): 70-76, jan/dez.1998'-------------- 75

studied, especially for cupuaçu juice. On the otherhand, thermal diffusivity (Tables 6 to 8) showed littlevariation with temperature within the sarne range.

4. CONCLUSIONS

It was conduded that the experimental results werevery dose to the calculated ones, based on the com­position and temperature (error of approximately10%). Thus the methodologies used here can be safe­ly applied to determining the thermal properties ofthis type of product. It is important to emphasize thatif these properties were not adequately determined, .this could result in under-processing or an incorrectcalculation of equipment dimensions.

ACKNOWLEDGEMENTS

The authors would like to thank Cia. Ciali. Ama­zonense for their authorization to publish the resultsobtained in this joint projecto We would also like tothank the trainee Áurea Maria Castelo Branco Lealfor her collaboration in the assays and in the evalua­tion of the results.

LITERATURE CITEO

ALVARADO, J.D. Nota. Viscosidad y energía deactivación de jugos filtrados, Revista Espano­la de Ciencia y Tecnología de Alimentos,33(1):87-93, 1993.

BAYINDIRLI, L. Mathematical Analysis of Varia­tion of Density and Viscosity of Apple Juicewith temperature and Concentration, Journalof Food Processing and Preservation, 16:23­28, 1992.

CONSTENLA, D.T., LOZANO, J.E., CRAPISTE,G.H. Thermophysical Properties of ClarifiedApple Juice as a Function of Concentration andTemperature, Journal of Food Science,54(3):663-668, 1989.

DICKERSON, RW. An apparatus for measure­ments of Thermal Diffusivity of Foods, FoodTechnology, 19(5):198-204, 1965.

GEORGE, RM. A Literature Survey of Thermal Di­ffusivity of Food Products, Campden Food &

Drink Research Association, Technical Bulle­tin, 73(2):1-23, 1990.

HWANG, M.P., HAYAKAWA, K. A specific heatcalorimeter for foods, Journal of Food Science,44(2):435-448, 1979.

KOLAROV, K.M., GROMOV, M.A. KhromitelnaPromishenost 2(10):32, ln: JOWITT, R, ES­CHER, F., HALLSTROM, H.F., MEFFERT, Th.,SPIESS, W.E.L., VOS, G. Physical Properties ofFoods. Applied Science Publisher, NY, 1973.Apud: VIRENDRA, K.B., SINGH, A.K., SIN­GHY. Prediction of Thermal Conductivity ofFruit Juices by Thermal Resistance Model, Jour­nal of Food Science, 54(4):1007-1012,1989.

MARTENS, T. Mathematical model of heat proces­sing in flat containers. Ph. D. thesis. Katholei­ke University, Leuven, Belgium, 1980. Apud:SINGH, RP. Thermal Diffusivity in food pro­cessing, Food Technology, 36(2):87-91, 1982.

PEACOCK, S. Predicting physical properties offactory juices and syrups, International SugarJournal, 97(1162):571-577,1995.

POLLEY, S.L., SNYDER, O.P., KOTNOUR, P. A com­pilation of Thermal Properties of Foods, FoodTechnology, 34(11):76-94, 1980.

RIEDEL, L. Measurements of thermal diffusivityof foodstuffs rich in water. Kaltetechnik-Klima­tisierung, v. 21, n. 11, p. 315, 1969. Apud: SIN­GH, RP. Thermal Diffusivity in food proces­sing, Food Technology, 36(2):87-91, 1982.

SIEBEL, J.E. Specific heat of various products. IceRefrig., 2:256-257, 1982.

SWEAT, Y.E. Thermal Properties of Foods. ln: RAO,M.A., RIZVI, S5.H. Engineering Properties ofFoods. Marcel Dekker Inc, NY, 1986. Apud:VIRENDRA, K.B., SINGH, A.K., SINGHY. Pre­diction of Thermal Conductivity of Fruit Juicesby Thermal Resistance Model, Journal of FoodScience, 54(4):1007-1012, 1989.

VAN WAZER, J.R, LYONS, J.w., KIM, K.Y., COLWE­LL, RE. Viscosity and Flow Measurement - ALaboratory Handbook of Rheology. New York:Intersience Publishers, 1972. p.215-230.

VIRENDRA, K.B., SINGH, A.K., SINGHY. Predictionof Thermal Conductivity of Fruit Juices by Ther­mal Resistance Model, Journal of Food Science,54(4):1007-1012, 1989.

WILLIAMS, S. (ed.) Official methods of analysis ofthe Association of Official Analytical Chernists.14'· ed., Arlington, AOAC Inc., 1990, 1141p.

76 Braz. J. Food Technol., Campinas, 1(1,2): 70-76, Jan eZ.1998-..:..;..~-~---------_-""'....:;.;.I