Thermal conductivity of tomato paste

Journal of Food Engineering 4 (1985) 157-I 68

Thermal Conductivity of Tomato Paste* A.E. Drusas and G.D. Saravacosf Chemical Engineering Department, National Technical University, GR-106 82 Athens, Greece

ABSTRACT Experimental measurements of the thermal conductivity and thermal diffusivity of tomato paste at concentrations of 27-44’ Brix are reported. The thermal conductivity was measured in a guarded hot-plate apparatus while the diffusivity was estimated by a simplified transient method. The thermal conductivity (X) values fell in the region of 0.460-0.660 W m-l K-l, decreasing with increasing solids concentration and increasing as the temperature was raised from 30 to 5O’C. The temperature effect was less pronounced at higher solids concentration. The thermal diffusivity of tomato paste at 35’ Brix and 20°C was estimated as 1.42 x 10e7 mz s-l, which is in good agreement with data from the steady-state method.

INTRODUCTION

Thermal conductivity is an important thermophysical property of foods which is useful in the design and operation of food processing equipment and in the processing and storage of food products. Tomato paste is produced in large quantities by vacuum concentration of tomato juice and is heat-sterilized in cans. It is markedly non-Newtonian and of high apparent viscosity, and heat is transmitted mainly by conduction. Slow heat penetration during heating or cooling may cause undesirable changes in quality, particularly if the product is heated or cooled in *Presented at the 44th Annual Meeting of the Institute of Food Technologists, Anaheim, California, lo-13th June, 1984. t Present address: Department of Food Science, Rutgers University, New Brunswick, New Jersey 08903, USA. 157 Journal of Food Engineering 0260-8774/85/$03,30 - 0 Publishers Ltd, England, 1985. Printed in Great Britain.

Elsevier Applied Science

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large containers. It is therefore important that the thermal conductivity or the thermal diffusivity of this product is known with reasonable accuracy, if more accurate calculations of the heating and cooling processes are to be made. The literature contains insufficient data on the thermal conductivity and diffusivity of tomato paste. The only two citations of Kolarov (1969) and of Maslikov and Medwedew (1969) (K.ostaropoulos, 197 1) give incomplete data which are not in agreement with each other. The experimental data of the co-operative project COST 90, reported by Kent et al. (1984), include materials similar to tomato paste, with which a comparison can be made. The models for predicting thermal conductivity of liquid foods were reviewed by Cuevas and Cheryan (1978).

METHODS

OF MEASUREMENT

Experimental methods for measurement of thermal properties of foods have been reviewed by Nesvadba (1982). The transient methods were in general favoured in the COST 90 project, because they are simpler and quicker than the steady-state methods, although they involve more complicated calculations. The steady-state methods have the advantage of greater accuracy and simpler calculations, but they require equipment with small dimensional tolerances and rigorous experimental procedure. For the purpose of comparison, two experimental methods were selected: (1) a steady-state method using a guarded hot-plate apparatus: and (2) a transient method involving measuring the temperature of the centre of a cylindrical sample as a function of time, while the external temperature is kept constant (Dickerson, 1965 ; Porsdal-Poulsen, 1982). The thermal conductivity (X) of a sample of thickness A.x is given by the equation

where 4 is the heat flux and AT is the temperature difference. In SI units, X is expressed in W m-l K-l. The transient heating of a product is represented by the Fourier eauation

Thermal

conductivity

dT -_=(x-

at

of tomato

paste

a2T

159

(2)

a.2

where (Y= X/PC,, the thermal diffusivity (usually in m2 s-l), which is assumed to remain constant. The transient heating time (t) of a product in a cylindrical container is given by the empirical equation (Ball and Olson, 1957) (3) where f = reciprocal of the slope of the heating line, j = the lag factor, T, = external temperature and T = T, = initial centre temperature, centre temperature after time t. For a long cylindrical container, with high surface heat transfer coefficient, eqn (3) is written as: r2

t = 0.398 ;log

1.6

Te- To T, - T >

(4)

where r = internal radius of the cylinder. For a given time-temperature plot, the inverse slope (f) can be determined and the thermal diffusivity is obtained from the relationship 01= 0.398 r’lf

(5)

EXPERIMENTAL Steady-state

measurements

Since there is no commercially available guarded hot-plate instrument for measuring the thermal conductivity of liquids and pastes, it was necessary to construct a laboratory apparatus according to specifications published in the literature. The basic design used was the ASTM (1968) apparatus, as modified for liquids by Fritz and Poltz (1962) and Poltz (1965). The apparatus is shown schematically in Fig. 1. The main unit was machined from brass slabs to the dimensions specified below. The homogeneity of the metal was checked by gamma radiography. The upper (hot) plate (P,) was of 98 mm diameter and 10 mm thick. An

A. E. Drusas, G. D. Saravacos

160

r

I

1

Water

Water

Fig. 1. Diagram of guarded hot-plate apparatus: P,, PJ, hot and cold plates; Pz, Pq, guard rings; R, electrical resistance; 1,2, thermostats; 3, power supply and measurement; 4, data logger.

electrical resistance (R), made of manganin wire of O-376 mm diameter and specific resistance 3.88 R m-l, was embedded in the plate. The upper guard ring (I’*) of 149 mm diameter and 23 mm thickness surrounded the hot plate, and a gap was formed between them by Teflon spacers, 2 mm at the top of the plate and 1 mm at the sides. The lower (cold) plate (P3) had a diameter of 108 mm and a thickness of 23 mm. It was surrounded by guard ring P4 of 181 mm diameter and 23 mm thickness, from which it was separated by two l-mm thick Teflon rings. The surfaces of the plates which contact the sample were machined to ensure a uniform sample thickness. Electrical input to the upper plate was controlled by a power stabilizer (4) and measured with an indicating digital ammeter and

Thermal conductivity

of tomato paste

161

voltmeter. Three copper-constantan thermocouples, insulated with magnesia, were used in the upper plate, and two in the lower, to measure the temperature of the plates during the experiments. The thermocouples were connected to a data logger, which recorded the temperature with a precision of +O.Ol”C. The plate assembly was supported in a horizontal position on three arms with levelling screws. Two thermostatically controlled water baths of 12 litres volumetric and 2 kW electrical capacity were used to maintain the desired temperature constant to within +O.l”C. Commercial canned tomato paste from Southern Greece was used in all experiments. The tomato paste was manufactured by the cold-break method and was stored for between 6 and 12 months before the measurements. The concentration of this paste varied from 32 to 36” Brix, as measured with a laboratory refractometer. More dilute samples were prepared by adding distilled water to the tomato paste and mixing thoroughly, and more concentrated samples were prepared by vacuum concentration at 10 torr and 5O’C. Most of the measurements were made using a thickness of tomato paste of 2 mm between the hot and the cold plates. The two plates were kept the desired distance apart by Teflon spacers of the appropriate thickness (e.g. 2 mm). Four hard Teflon cubes were placed symmetrically on the lower guard ring and one in the centre of the cold plate. The gap thickness was confirmed by micrometer measurement. Some measurements were made on 1 mm thickness of tomato paste and some on aqueous solutions. The tomato paste was spread on the lower plate in excess, and the upper plate was placed and moved on top of it, forcing to the sides the excess paste and any trapped air. The two water baths were then set and maintained at the selected temperature until the two plates and the sample all attained the same temperature. Then, the upper plate was heated by the electrical resistance to establish the desired temperature difference (2-5°C) between the two plates. The upper guard ring was maintained at the same temperature as the hot plate by using thermostat 1 (Fig. 1). After a steady state was established, the temperature difference (A7’) and the heat flux (4) were recorded. Duplicate measurements were normally made and the average values are reported. For a statistical validation of the results, five replicate sampies from the same can of the 36’ Brix tomato paste were measured at three different temperatures (30, 40 and 50’0.

A. E. Drusas. G. D. Saravacos

162

Transient measurements A simple thermal diffusivity apparatus, like that originally used by Dickerson (1965) and modified by Porsdal-Poulsen (1982), was constructed and used in this work. The basic unit consists of a brass tube of 48 mm inside diameter, 1 mm wall thickness and 200 mm length, with Teflon caps at the ends (Fig. 2). The tube, filled with the sample, was placed in a water bath, maintained at a constant temperature (+O.l’C). The temperature of the centre of the sample was measured with a copper-constantan thermocouple, which was supported in an open glass tube of 1 mm inside diameter, and inserted along the axis of the cylinder. Another thermocouple was used to measure the bath temperature. The two temperatures were recorded at intervals of 2 min in a data logger.

EXPERIMENTAL

RESULTS

Table 1 and Fig. 3 show the measured thermal conductivity (h) of tomato paste at six concentrations and three temperatures, using the guarded hot-plate apparatus. The mean value of h (five replicates) of the 36” Brix paste increased from O-525 to 0.557 W m-l K-’ as the temperature was raised from 30 to 5O’C. The precision of the measurements was quite satisfactory, the relative standard deviation ranging from 1 .l to 2.9%.

Food Sample

1 Fig. 2.

Water

Bath

Diagram of thermal diffusivity

apparatus.

Thermal conductivity

of tomato paste

163

TABLE 1 Thermal Conductivity (X) of Tomato Paste A(Wm-‘K-‘) oBi-lk

JGV

27 30 32 36 39 44

0.708 0.678 0.657 0.618 0.588 0.538

30°c

40°C

50°C

0.595 0.560 0.550 0.525a 0.485 0.460

0.630 O-590 0.575 0.546’ 0.505 0.478

0.660 0.620 0.600 0.557a 0.512 0.490

a Standard deviations of(h) of the 36’ Brix samples: s = 0.0068 (30°C), s = 0.0158 (4O’C) and s = 0.0062 (5O’C).

I kO.70

-

OBrix o 27

0.65 ii%

0 0

. 0

0.55-

:

t

t xJ

0

0 39

.

l

0.50 -

t 0

0.45 -

Fig. 3.

.J)

0.60 -

Thermal conductivity

0 32

44

.

versus temperature

of tomato pastes (27-44’

Brix).

The data of Table 1 are plotted in Fig. 3 as h versus T and in Fig. 4 as X versus X,. The water fractions (X,) of the pastes were calculated from the “Brix values, using the conversion tables of “Brix to total solids for tomato paste (NCA, 1950). Diluted samples at concentrations below 27’ Brix presented problems of phase separation (serum/sus-

A. E. Drusas, G. D. Saravacos

164

0.70 k

+sooc

W0.6E

+

ix

040°C

+ o 0

0.60 0.5:

2

l

3ooc

.

’

I +

cl5c

0

2

l

0.4: I

I

050

(160

I

0.70

x,

Fig. 4.

Thermal conductivity versus concentration of tomato pastes (30-5O’C).

pended solids) during the experimental measurement. As a result, inconsistent values of thermal conductivity were obtained, particularly at higher temperatures. Linear regression analysis of the experimental data for the 36” Brix paste (Fig. 3) resulted in the following equation: X = 0.482 + 0.0015T

(6)

where X is in W m-l K-l and Tin ‘C. The correlation coefficient (Y = 0.786) was rather poor, suggesting that a non-linear model might be more appropriate. Figure 4 shows a sharp increase in X at any temperature with increasing water content (X,). The data appear to deviate from the linear relationship. More experitiental data are needed for estimating an appropriate non-linear model. Transient

method

Figure 5 shows the temperature of the tomato paste (35’ Brix) in the centre of the thermal conductivity apparatus. It rises exponentially with time and there appears to be a change in the slope of the heating line near 30°C. Similar results were obtained with tomato paste of 32’ Brix. Diluted samples at concentrations less than 30” Brix gave unsatis-

Thermal conductivity

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165

factory plots, evidently due to the separation of the serum from the tomato paste. Considering the lower part of the heating line of Fig. 5, the slope was found to be f = 1612 s, and the thermal diffusivity of tomato paste of 35’ Brix at about 20°C was calculated from eqn (5) to be (11= 1.42 X lo-’ m2 Cl. In order to calculate the thermal conductivity h of a material from its known thermal diffusivity ar, the density p and the specific heat C, are needed. The density of the tomato paste at 35’ Brix was determined, by the standard gravimetric method, as p = 1163 kg rne3. The specific heat was estimated from its water content (X, = O-627) after Miles er al. (1983) to be C, = 3302 J kg-’ K-l. From these data, the thermal conductivity of the tomato paste at 35’ Brix was calculated to be h = 0.546 W m-l K-l. The extrapolated value of h for the tomato paste at 35’ Brix and 20°C, as determined by the hot-plate method (Fig. 3), is O-520 W m-l K-i. The values of X, determined by the two different methods, differ

t,

Fig. 5.

Centre temperature

min

of tomato paste (3.5’ Brix) in the thermal diffusivity apparatus versus time.

166

A. E. Drusas, G. D. Saravacos

by about S%, which can be considered engineering purposes.

DISCUSSION

as a satisfactory

agreement

for

AND CONCLUSIONS

The values determined for the thermal conductivity of tomato paste at concentrations 32-44’ Brix and 30-50°C (0.460-0.660 W m-l K-l) are similar to those for aqueous sucrose solutions of similar concentration (0.473-0.574 W m-l K-l) reported in the literature (Kostaropoulos, 1971). At lower concentrations, the values for tomato paste were in general higher than the sucrose solutions and they approached the thermal conductivity of water. The values of X for tomato concentrates reported by Kolarov and by Maslikov and Medwedew, as cited by Kostaropoulos (197 l), are smaller than the present results by nearly 20%. The correlation of thermal conductivity for fruits and vegetables proposed by Sweat (1974) gave significantly lower values than those determined experimentally for tomato paste. No satisfactory agreement could be found between the present data and the correlations of h with water content and temperature compiled by Miles et al. (1983). The thermal conductivity of tomato paste is similar to the values obtained for apple pulp, meat paste and fish paste (Kent et al., 1984). The X of these materials increased slightly with temperature, following a pattern similar to that for tomato paste at high concentrations (Fig. 3). The experimentally determined thermal diffusivity of tomato paste (CX= 1.42 X lo-’ m2 s-l at 35” Brix and 20°C) is similar to the values reported in the literature for water, _7% carrageenan gels and apple pulp (Kent et al., 1984), and some other fruits and vegetables (Kostaropoulos et al., 1975). The ‘break’ in the heating line of tomato paste (Fig. 5) is similar to those observed in other food materials (Ball and Olson, 1957). Tomato paste is markedly non-Newtonian (Saravacos et al., 1967; Fito et al., 1983), and temperature has a small effect on its thermal conductivity and apparent viscosity. Heat transfer in tomato paste can be improved by high shear rates (e.g. by agitation) which results in reduced apparent viscosities (Saravacos, 1970, 1974). In measurements on diluted tomato paste and aqueous solutions with convection may cause apparently the guarded hot-plate apparatus, greater thermal conductivities. This effect may also explain the high thermal conductivity of water observed in this apparatus.

Thermal conductivity of tomato paste

167

COMPUTER PREDICTION The experimental thermal conductivity data of tomato paste at 27, 30, 32, 39 and 44’ Brix were compared with the computer predictions of the COSTHERM program, developed in the COST 90 project (Miles et al., 1983). The tomato paste was assumed to consist of carbohydrates (% Brix) and water. A difference of 6% between the predicted and the experimental values was found for thermal conductivity, and the agreement can be considered as satisfactory. The values of thermal diffusivity differed by 16%, and this difference is attributed to the experimental method. The measurements in the cylindrical apparatus were influenced by the physical state of the semi-fluid sample (tomato paste), and a significant variation in the results was noticed.

ACKNOWLEDGEMENT We acknowledge the help of Ir. G. van Beek of the Sprenger Institute, Wageningen, The Netherlands, who ran the COSTHERM computer calculation.

REFERENCES ASTM (1968). Standard method of test for thermal conductivity of materials by means of the guarded hot plate. American Society for Testing and Materials. ASTM Standard C 177-63. Ball, C. 0. and Olson, F. C. W. (1957). Sterilization in Food Technology, Academic Press. New York. Cuevas, R. and Cheryan, M. (1978). Thermal conductivity of liquid foods - A review. J. Food Process Engineering, 2, 283-306. Dickerson, R. W. (1965). An apparatus for the measurement of thermal properties of foods. Food Technology, 19, 198-204. Fito, P. J.. Clemente, G. and Sanz, F. J. (1983). Rheological behaviour of tomato concentrate (hot break and cold break). J. Food Engineering, 2, 51-62. Fritz, W. and Poltz, H. (1962). Absolutbestimmung der Warmeleitfahigkeit von Fliissigkeiten - I. Kritische Versuche in einer neuen Plattenapparatur. Znt. J. Heat Mass Transfer, 5, 307-16. Kent, M., Christiansen, K., van Haneghem, 1. A., Holtz, E., Morley, M. J., Nesvadba, P. and Poulsen, K. P. (1984). COST 90 collaborative measurements of thermal properties of foods. J. Food Engineering, 3. 117-50.

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Kolarov, K. (1969). Konserwnaja i. Owostsches Promischl., 24 (S), 34-6. Kostaropoulos, A. E. (197 1). Wtirmeleitzahlen von Lebensmitteln und Methoden zu deren Bestimmung. VDMA, No. 16, Maschinenbau Verlag, Frankfurt. Kostaropoulos, A. E., Spiess, W. E. L. and Wolf, W. (1975). Anhaltswerte fur die Temperaturleitfahigkeit von Lebensmitteln. Lebensm.-Wiss. u. Technol., 8, 108-10. Maslikov, W. A. and Medwedew, 0. K. (1969). Pistschewaja Technol., 64 (6), 69-70. Miles, C. A., van Beek, G. and Veerkamp, C. H. (1983). Calculation of Thermophysical Properties of Foods. In: Physical Properties of Foods, eds R. Jowitt et al., Elsevier Applied Science Publishers Ltd, London. NCA (1950). Tomato Products. National Canners Association, Research Bulletin No. 27-L, Washington, DC. Nesvadba, P. (1982). Methods for the measurement of thermal conductivity and diffusivity of foods. J. Food Engineering, 1,93- 113. Poltz, H. (1965). Die Warmeleitfahigkeit von Fliissigkeiten III. Abhangigkeit der Wlrmeleitfahigkeit von der Schichtdicke bei organ&hen Flussigkeiten. ht. J. Heat Mass Transfer, 8,609-20. Porsdal-Poulsen, K. (1982). Thermal diffusivity of foods measured by simple equipment. J. Food Engineering, 1, 115-22. Saravacos, G. D. (1970). Effect of temperature on viscosity of fruit juices and purees. J. Food Sci., 35, 122-5. Saravacos, G. D. (1974). Rheological Aspects of Fruit luice Evaporation. In: Advances in Preconcentration and Dehydration oj‘Foods. ed. A. Spicer, Elsevier Applied Science Publishers Ltd, London. Saravacos, G. D., Oda. Y., and Moyer, J. C. (1967). Tube viscometry of tomato juice and concentrates. Report. NY State Agric. Exp. Station. Geneva, New York, 11 pp. Sweat, V. E. (1974). Experimental values of thermal conductivity of selected fruits and vegetables. J. Food Sci.. 39, 1080-3.