Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) Condutividade e difusividade térmica do mamão (Carica papaya L.) e do caju (Anacardium occidentale L.)

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Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) Condutividade e difusividade térmica do mamão (Carica papaya L.) e do caju (Anacardium occidentale L.) Autores | Authors Louise Emy KUROZAWA Universidade Estadual de Campinas (UNICAMP) Faculdade de Engenharia de Alimentos (FEA) Caixa Postal: 6121 CEP: 13083-970 Campinas/SP - Brasil e-mail: [email protected]

Kil Jin PARK Miriam Dupas HUBINGER Fernanda Elizabeth Xidieh MURR Universidade Estadual de Campinas (UNICAMP) e-mail: [email protected] [email protected] [email protected]

Patrícia Moreira AZOUBEL EMBRAPA Semi-Árido e-mail: [email protected] Autor Correspondente | Corresponding Author

Recebido | Received: 14/09/2007 Aprovado | Approved: 05/05/2008

Summary The objective of this work was to determine the thermal conductivity and the thermal diffusivity of papaya and cashew apple as a function of temperature. For the experimental determination, the heat source probe technique was used. Thermal properties were measured for the temperature range of 20-40 °C for papaya and 25-45 °C for cashew. Thermal conductivities ranged from 0.58 to 0.62 W/m °C and 0.57 to 0.61 W/m °C and thermal diffusivities varied from 1.03 × 10-7 to 1.18 ×10-7 m2/s and 0.98 × 10-7 to 1.16 × 10-7 m2/s for papaya and cashew, respectively. The empirical models for each property as a function of temperature were obtained. Key words: Thermal Properties; Heat Source Probe; Temperature.

Resumo O objetivo deste trabalho foi determinar a condutividade e a difusividade térmica do mamão e do caju em função da temperatura. Para determinação experimental, foi utilizado o método da sonda, em regime transiente. Propriedades térmicas foram medidas para uma faixa de temperatura de 20-40 °C para o mamão e 25-45 °C para o caju. A condutividade térmica variou de 0,58 to 0,62 W/m °C e 0,57 a 0,61 W/m °C e a difusividade térmica variou de 1,03 × 10-7 para 1,18 × 10-7 m2/s e 0,98 × 10-7 a 1,16 × 10-7 m2/s para o mamão e o caju, respectivamente. Modelos empíricos para cada propriedade em função da temperatura foram obtidos. Palavras-chave: Propriedades Térmicas; Método da Sonda; Temperatura.

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

1 Introduction Papaya (Carica papaya L.) is an important fruit crop grown widely in tropical and subtropical countries, and Brazil is one of the main producers, with a total of 1.3 million t/year (FAO, 2007). This fruit is nutritive, rich in minerals (calcium, iron, potassium and sodium), provitamin A and vitamin C (ascorbic acid), β-carotene and β-cryptoxanthin (WALL, 2006). Cashew apple (Anacardium occidentale L.) is the pseudofruit of the cashew tree, native to Brazil, and well established in many tropical regions. This fruit contains volatile compounds, carotenoids (α-carotene, β-carotene and β-cryptoxanthin), vitamin C, phenols and tannin (ASSUNÇÃO and MERCADANTE, 2003). In Brazil, cashew cultivation occupies an estimated area of 700,000  hectares and the cashew apple production reaches 2  million  t/year (FAO, 2007). Both fruits are commonly used to make juice, pulp, jam, fruit-candies in syrup, crystallized fruit, and other products. The knowledge of the thermal properties and how these properties change during processing as a function of temperature are of primary importance in heat transfer processes. This information is required to make proper design of food processing equipments, especially heat exchangers (DE MOURA et al., 1998). Several methods have been developed to estimate the thermal properties of foods by analyzing the heat conduction equation and they can be classified into two broad categories: steady and transient-state heat transfer methods. The tests using steady-state methods often require a long time to complete and moisture migration may introduce significant measurement errors (MOHSENIN, 1980). The line heat-source probe method is the most widely used transient-state method and can be employed for the determination of thermal conductivity and thermal diffusivity, simultaneously. It has been recommended for many food applications due to its short response time, simplicity, low cost and adequacy for small sample sizes (VOUDOURIS; HAYAKAWA, 1994). Over the years, both measured and calculated values of thermophysical properties of foodstuffs have been published (MARTÍNEZ-MONZÓ et al., 2000; ­TELIS-ROMERO et al., 1998; SHAMSUDIN et al., 2005). However, little information is available about the thermal properties of tropical fruits. Several models have been proposed to predict thermal properties of a material at desired conditions, but none of them can be used over a wide range of foods. The most promising approach is based on the chemical composition, temperature and physical characteristics. Besides, most structural models neglect interactions between components although these can be significant (HAMDAMI et al., 2004). The objective of this work was to determine the thermal conductivity and the thermal diffusivity of papaya

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and cashew apple fruits using the heat source probe method and to obtain good empirical models as a function of temperature. 1.1 Theoretical basis The basic theory of the line heat-source probe has been discussed previously by several authors (­M OHSENIN, 1980; REIDY and RIPPEN, 1971). This method is based on the application of a constant heat flux to a semi-infinite solid, using an ideal line heat-source of infinitesimal diameter and infinite length. The temperature increases at a point close to the line heat-source, as function of time, thermal properties of the material and source power (INGERSOLL et al., 1954; DICKERSON, 1965; NIX et al., 1967; JASANSKY and BILANSKI, 1973; PARK et al., 1997; CHOI and OKOS, 1983; CHANG, 1986). Thermal conductivity can be obtained by the following Equation 1: k=

t −t  Q' ln 2 0 4.π . (T2 − T1 )  t1 − t0 



(1)

where Q’ is the power released by the heater wire (W/m), calculated according to equation 7; t1 and t2 are the initial and final times (s), and T1 and T2 are the temperatures (°C) at times t1 and t2, respectively. The slope of the linear section of the plot logarithm of time versus temperature is used to obtain k from Equation 1. In order to minimize the effect of finite heater diameter and any resistance to heat transfer between the heat-source and sample, Van der Held and Van Drunen (1949) introduced a time correction factor (t0). The determination of thermal diffusivity (α) by the line source technique is possible without any information of density and specific heat, by applying the following equation (NIX et al., 1967; CHOI and OKOS, 1983):

( )

2 Q ' α exp − β dβ 2.π .k ∫β β r β= 2 α.t

T =



(2) (3)

Nix et al. (1967) suggested the following series expression for evaluation of the above definite integral, in which Ce is the Euler constant (0.577): T =

Q' 2.π .k

 Ce  β2 β4 − ln β + − + ... − 2.1! 4.2!  2 



(4)

Equation 4 is used to determine the thermal diffusivity. Nix et al. (1967) found that the first 40 terms of the above equation need to be evaluated to ensure convergence for values of 0.16 < β < 3.1. However, for values of β < 0.16, the error is negligible if only the first two terms of the series are considered. This condition is easily attained, if the probe and the point where temperature is measured, are closely located and the time is in the order of minutes (URBICAIN and LOZANO, 1997). The error introduced by different values of β is presented on Table 1. 79

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

Table 1. Error as function of β. Error (%) β 0.02 0.006 0.04 0.027 0.06 0.071 0.08 0.143 0.10 0.247 0.12 0.390 0.13 0.478 0.14 0.578 0.15 0.691 0.16 0.817

β 0.17 0.18 0.19 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Error (%) 0.958 1.114 1.287 1.477 2.727 4.587 7.241 10.916 15.892 22.523

Fonte: Murakami et al. (1996-a).

The sample and probe dimensions must obey the following considerations (SWEAT, 1974b; RAHMAN et al., 1997): The sample diameter (Dsam) must satisfy:

Dsam ≥ 5.2 α t

(5)

The probe (length, Lprob, and diameter, Dprob) must satisfy: Lprob

Dprob

≥ 25



(6)

ate de Figuras - BJFT 2 Material ITC Eras BT (Medium), tamanho 8.and

methods

o" - linhas com 0.5 de Stroke.

hypodermic needles (length of 5 cm and diameter of 0.2 cm, for the thermal conductivity probe; length of 5 cm and diameter of 0.1 cm, for the thermal diffusivity probe). The probe dimension satisfies the condition of Equation 6. A constant electrical current of 3.6 A was applied to the heater wire, using a power supply (Tectrol TC 10/08, São Paulo, Brazil). The data acquisition system comprised a datalogger (Digi-Sense 92800-10, Vernon Hills, USA) and a personal computer with Scanlog data acquisition software (Figure 2). The thermocouple readings were recorded every four seconds for a period of 20 min. A digital multimeter (Minipa ET2700, São Paulo, Brazil) was used to check the current and voltage during data acquisition. A water bath, with temperature control and recirculating system, was used for controlling the temperature (Nova Técnica NT 281, Piracicaba, Brazil). Both the thermal conductivity and thermal diffusivity probes were placed in the samples in such a way that the probes’ lengths were fully covered. Each experiment was repeated three times. A linear regression line of ln (time) versus temperature was fitted to the experimental data and thermal conductivity was calculated according to Equation 1. The heat input Q (W/m) in this equation was calculated from the heater resistance and the electrical current by: Q = I 2R



(7)

where: I is the electrical current and R is the resistance.

Material pertencente a2.1 "Dados gráficos" com 0.6 de Stroke. 3.4 cm

olocar quadros em volta das legendas/gráficos

Fresh ripe papayas (Carica papaya L.) and cashew apples (Anacardium occidentale) were obtained in a local mento de barras pb devem ter 10% de preto quando houver texto e 50% quando não. market of Campinas, Brazil. Fruit sampling was based na tabela ou figura devem estar no mesmo idioma do artigo. on total soluble solids (10-12 °Brix) and damaged fruits a figura ou gráfico deve estar em "Sentence case". were eliminated. The main characteristics of the fruits s com stroke de 0.6, e com a cabeça no estilo 4 (arrowheads). are summarized in Table 2. Sample dimensions satisfy que representam figuras ex: Equation 5. a , devem estar no canto superior direito com 2 mm

mento de barras coloridas, seguir o padrão da Paleta de cores.

3.1 cm

Heater wire

ncia das extremidades da figura.

LETAR ESTA CAIXA APÓS O TÉRMINO DA FIGURA.

Table 2. Composition of papaya and cashew apple. wt % Papaya Cashew apple Moisture 87.7 ± 1.6 85.6 ± 1.1 Carbohydrate 10.2 ± 0.2 10.0 ± 0.2 Fibre 1.3 ± 0.4 1.7 ± 0.1 Fat 0.5 ± 0.1 0.2 ± 0.02 Ash 0.4 ± 0.05 0.3 ± 0.05 Proteins 0.3 ± 0.04 0.8 ± 0.05

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5.0 cm

The thermal conductivity and diffusivity were measured simultaneously for the temperature range of 20-40  °C for papaya and 25-45 °C for cashew respectively, using the linear heat-source probe. Figure 1 shows a scheme of the probes and Figure 2 shows a schematic diagram of the equipment. The probe encloses a heater wire (0.5 Ω/m) and a thermocouple junction, contained in

2.5 cm

2.2 Thermal properties

Thermocouple

Thermal conductivity probe

0.2 cm 0.1 cm

Thermal diffusivity probe

0.4 cm

Figure 1. Thermal conductivity and thermal diffusivity probes.

80

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

Data logger

temperature above freezing T (°C) and water content XW (kg H2O/kg wet material), utilizing literature data of fruits, vegetables and cereal foods. Some models are given by Equations 10, 11 and 12:

Power supply

Computer Thermocouple

Thermal conductivity probe

Heater circuit

Sample

k = −0.015 + 1.914 × 10 −3T + 0.590 XW



(10)

k = −0.022 + 1.924 × 10 −3T + 0.587 XW



(11)

k = −0.026 + 1.88 × 10 −3T + 0.618 XW

Thermal diffusivity probe

Figure 2. Thermal conductivity and thermal diffusivity measurement apparatus.

The thermal diffusivity was calculated according to Equations 2 to 4, using the non-linear regression procedure of the SAS software Version 6.11.



(12)

These equations are validated for the temperature range between 0 to 80 °C. Equations (10 and 11) and (12) are used for the moisture intervals 0 to 0.96 g water/g wet material and 0.05 to 0.85g water/g wet material, respectively. Equations 10, 11 and 12 are used to predict the thermal conductivity of fruits and vegetables, fruits, and apples, respectively.

For all the experiments, the probe was tested by determining thermal conductivity and thermal diffusivity of water, with 2% agar to avoid the effects of natural convection. Sweat (1986) suggested the addition of agar to water to turn it into gel when measuring thermal properties with the line heat source probe. It was estimated that agar would probably increase thermal conductivity by about 2%.

Based on literature data, Choi and Okos (1986) proposed the following general model to predict the thermal conductivity of foods for temperatures between 20 to 100 °C:

Therefore, correction factors f and h for the thermal conductivity and thermal diffusivity, respectively, were obtained:

The values of thermal conductivity (ki) of each pure constituent can be estimated from a linear function of temperature:

kac k exp α h = ac α exp

f =



(13)

where the subscript i refers to a particular pure component.

(8)

kW = 5.9075 × 10 −1 + 9.8601 × 10 −4T



(14)

(9)

k p = 1.8730 × 10 −1 + 7.8776 × 10 −4T



(15)

The correction factors are used to increase the precision of the k and α probe. It is determined by performing a test run at the same operation parameters, e.g. power input and test time, with a material of know thermal properties. It is calculated from the ratio between the published (actual value) and the measured (experimental value) for each thermal property of the calibration material (Equations 8 and 9). These values are then multiplied by the measured thermal properties values of the materials (fruits, in this study). The thermal conductivities of water are 0.606, 0.628 and 0.646 W/mK, at temperatures of 25, 35 and 45 °C, respectively, while the thermal diffusivities of water are 1.462 × 10-7, 1.508 × 10-7 and 1.554 × 10-7 at 25, 35 and 45 °C, respectively (CHOI and OKOS, 1986). 2.3 Analysis of the results The experimentally obtained values were compared with those obtained using mathematical models available in the literature. Vagenas et al. (1990) developed some models relating thermal conductivity k (W/m°C),

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k = ∑ ki X i

kf = 1.8022 × 10 −1 + 1.614 × 10 −4T



(16)

kc = 1.9306 × 10 −1 + 8.4997 × 10 −4T



(17)

ka = 1.2863 × 10 −1 + 3.9130 × 10 −4T



(18)

Some models used to predict thermal diffusivity of fruits, which include the water content XW (kg H2O/kg wet material), are given by Equations 19 and 20 (SINGH, 1982): α = 0.088 × 10 −6 + (αW − 0.088 × 10 −6 ) XW α = 0.057363 XW + 0.000288 × (T + 273 ) × 10 −6



(19)

(20)

where αW is the thermal diffusivity of water at the required temperature (m2/s). Choi and Okos (1986) proposed the following general model to estimate the thermal diffusivity of foods, based on literature, for temperatures between 20 to 100 °C: α = ∑ αi Xi



(21)

where the subscript i refers to a particular pure component. 81

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

αW = 1.3988 × 10 −1 + 3.0429 × 10 −4T −2



−4

α p = 8.7055 × 10 + 2.4021 × 10 T −1



−4

α f = 1.0306 × 10 + 1.5507 × 10 T



α c = 9.0371 × 10 −2 + 2.4548 × 10 −4T



α a = 8.3039 × 10 −2 + 1.1764 × 10 −4T



(22) (23) (24) (25) (26)

These equations show that thermal conductivity and thermal diffusivity depend strongly on the food component content and temperature. Empirical models as a function of temperature were obtained to predict accurately the thermal conductivity and thermal diffusivity of papaya and cashew apple. 2.4 Statistical analysis The proposed equations were analyzed by their average relative error E, calculated according to Equation 27. E (%) =

1 N VE − VP × 100 ∑ N i =1 VE



(27)

where VE is the experimental value, Vp is the predicted value and N is the population of experimental data.

(1996b), the correction factor is essentially due to factors that affect the slope of the linear portion of ln (time) versus temperature plots. One of these factors is the thermal mass ratio between calibration material and probe (M). In theory, M is not considered in the line-heat source equation. The thermal mass of the calibration material and the probe must be equal, but this is impractical in actual use, changing the slope of ln(time) versus temperature plots and affecting the calculated thermal properties’ values. 3.2 Thermal properties Results for the thermal conductivity (k) and thermal diffusivity (α) experiments at 20 to 40 °C for papaya and 25 to 45 °C for cashew apple are shown in Figures 3 to 6. In order to compare the experimental data of thermal conductivity and thermal diffusivity, mathematical models (Equations 10-13 and Equations 19-21) were used. Thermal conductivity (W/m °C)

The values of thermal diffusivity (αi) for each pure component can be estimated from a linear function of temperature, as follows:

0.64 0.62 0.60 0.58 0.56 0.54 0.52 15

3 Results and discussion

Table 3. Calibration factors f and h for cashew apple and papaya. Temperature (°C) f h Cashew apple 25 1.92 ± 0.03 0.91 ± 0.03 30 2.13 ± 0.03 0.67 ± 0.03 35 2.03 ± 0.11 0.69 ± 0.04 40 1.79 ± 0.07 0.96 ± 0.07 45 1.79 ± 0.07 0.95 ± 0.07 Papaya 20 1.78 ± 0.04 0.42 ± 0.02 25 1.69 ± 0.02 0.70 ± 0.03 30 1.87 ± 0.04 0.85 ± 0.05 35 1.90 ± 0.14 0.53 ± 0.07 40 1.79 ± 0.07 0.87 ± 0.07

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30 35 40 Temperature (°C)

45

50

Equation 12 Equation 13 Proposed model Equation 28

Figure 3. Thermal conductivity of papaya as a function of temperature.

Thermal conductivity (W/m °C)

There were differences between the real probe and the theoretical model. According to Murakami et al.

25

Experimental Equation 10 Equation 11

3.1 Probe calibration Calibration factors f and h were determined for all temperature experiments and can be seen in Table 3.

20

0.64 0.62 0.60 0.58 0.56 0.54 0.52

15

20

25

Experimental Equation 10 Equation 11

30 35 40 Temperature (°C)

45

50

Equation 12 Equation 13 Proposed model Equation 29

Figure 4. Thermal conductivity of cashew apple as a function of temperature.

82

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

These thermal properties were found to increase linearly with temperature. A similar behavior was observed by Hu and Mallikarjunan (2005) for oysters, by TelisRomero et al. (1998) for orange juice and by Singh and Goswami (2000) for cumin seed.

Thermal diffusivity (x 107 m2/s)

For cashew apple, thermal conductivity and thermal diffusivity values exhibited large errors probably due to high the temperature (at 45 °C). This fact caused a slight 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 15

20

25

30

35

40

45

50

Temperature (°C) Equation 20 Experimental Equation 21 Equation 19 Proposed model Equation 30

Thermal diffusivity (x 107 m2/s)

Figure 5. Thermal diffusivity of papaya as a function of temperature. 1.6 1.5 1.4 1.3 1.2

Krokida et al. (2001) made a thermal conductivity data compilation from the literature for different food materials. The experimental values of thermal conductivity obtained for papaya and cashew are close to the values reported for strawberry (0.63 W/m °C at 14 °C), beetroot (0.56 W/m °C at 20 °C), tomato (0.61 W/m °C at 21 °C) and cucumber (0.62 W/m °C at 22 °C). Two papers, one by Singh and Heldman (1993), and another by Sweat (1974a), have reported thermal diffusivity values for different fruits. The data we report are close to the values for banana (1.18 × 10-7 m2/s at 5 °C), lemon (1.07 × 10-7 m2/s at 28 °C) and strawberry (1.27 × 10-7 m2/s at 5 °C). The results showed the same trend as the mathematical models (Equations 10 to 13 and 19 to 21), by which the thermal properties increase with increasing temperatures (Figures 3 to 6). However, it can be noticed that these models were not valid for the data found in this study, because these models were obtained for a variety of foodstuffs and do not take into account the sample’s physicochemical characteristics. Therefore, the experimental data were fitted to a linear equation to predict the thermal properties of papaya and cashew, as showed in Table 4 The proposed equations afforded a good fit with low average relative error E and high determination coefficient values R2.

1.1 1.0 0.9 15

melting of agar (probe-agar interface), occurring convection currents on probe surface, thereby increasing the error. Moreover, thermal conductivity of cashew apple carried a high error for other temperatures. This could be explained considering the weak structure of the fruit. It is likely that as the probe is inserted in the sample, some tissue is ruptured and juice release occurs, causing convection currents on the probe surface.

20

25

30 35 Temperature (°C)

40

45

50

Experimental Equation 20 Equation 19 Equation 21 Proposed model Equation 31

Figure 6. Thermal diffusivity of cashew apple as a function of temperature.

4 Conclusions From this study, the use of a calibration factor was essential because the slope of the linear portion of ln(time) versus temperature is affected by the thermal mass of the calibration material. It was found that for papaya and cashew apple, the thermal conductivity and thermal diffusivity increase with temperature increasing. For temperature ranges from 20 to 40 °C and 25 to 45 °C,

Table 4. Equations fitted to predict thermal conductivity and thermal diffusivity for papaya and cashew apple. Equations R2 E (%) Temperature range 0.9923 0.26 20 < T < 40 °C k = 0.0024T + 0.523 papaya

(28)

kcashew = 0.0020T + 0.514

0.9900

0.24

25 < T < 45 °C

(29)

α papaya = (0.0062T + 1,0147) × 10 −7

0.9874

1.89

20 < T < 40 °C

(30)

α cashew = (0.0053T + 0.9478) × 10 −7

0.9612

3.02

25 < T < 45 °C

(31)

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www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

thermal conductivities varied from 0.58 to 0.62 W/m °C for papaya and from 0.57 to 0.61 W/m °C for cashew apple, respectively. Thermal diffusivities varied from 1.03 × 10-7 to 1.18 ×10-7 m2/s for papaya and 0.98 × 10-7 to 1.16 × 10-7  m2/s for cashew apple. The results were similar to those given in the literature for some other fruits, showing that the probe technique was efficient for adequate measurements of the studied thermal properties. However, literature models did not fit well our experimental results, since these models were obtained for a variety of foodstuffs. Therefore, empirical models based on a linear dependence of thermal properties on temperature provide very good predictive values for papaya and cashew apple, in the temperature range of 20 to 45 °C. The results of this work have direct application to fruit processes involving heat transfer. Acknowledgements The authors gratefully acknowledge the financial support of the State University of Campinas (UNICAMP), the São Paulo Research Foundation (FAPESP) and the National Council for Scientific and Technological Development (CNPq). References ASSUNÇÃO, R. B.; MERCADANTE, A. Z. Carotenoids and ascorbic acid from cashew apple (Anacardium occidentale L.): variety and geographic effects. Food Chemistry, Oxford, v. 81, n. 4, p. 495-502, 2003. CHANG, C. S. Thermal conductivity of wheat, corn, and grain sorghum as affected by bulk density and moisture content. Transactions of the ASAE, St. Joseph, v. 29, n. 5, p. 1446‑1450, 1986. CHOI, Y.; OKOS, M. R. The thermal properties of tomato juice concentrate. Transactions of the ASAE, St. Joseph, v. 26, n. 1, p. 305-311, 1983. CHOI, Y.; OKOS, M. R. Thermal properties of liquid foods – review. In: OKOS, M.R. (Ed). Physical and Chemical Properties of Food. St Joseph: American Society of Agricultural Engineers, 1986. p. 35-77. DE MOURA, S. C. S. R.; Germer, S. P. M.; Jardim, D. C. P.; Sadahira, M. S. Thermophysical properties of tropical fruit juices. Brazilian Journal of Food Technology, Campinas, v. 1, n. 1-2, p. 70-76, 1998.

HAMDAMI, N.; MONTEAU, J. Y.; BAIL, A. L. Thermophisical properties evolution of French partly baked bread during freezing. Food Research International, Amsterdam, v. 37,n. 7, p. 703-713, 2004. HU, X.; MALLIKARJUNAN, P. Thermal and dielectric properties of shucked oysters. Lebensmittel – Wissenschaft and Technologies, Zurich, v. 38, n. 5, p. 489-494, 2005. INGERSOLL, L. R.; ZOBEL, O. J.; INGERSOLL, A. C. Heat conduction with engineering, geological and other applications. New York: Mc Graw-Hill, 1954. 278 p. JASANSKY, A.; BILANSKI, W. K. Thermal conductivity of whole and ground soybeans. Transaction of the ASAE, St Joseph, v. 16, n. 1, p. 100-103, 1973. KROKIDA, M. K.; PANAGIOTOU, N. M.; MAROULIS, Z. B.; SARAVACOS, G. D. Thermal conductivity: Literature data compilation for foodstuffs. International Journal of Food Properties, Philadelphia, v. 4, n. 1, p. 111-137, 2001. MARTÍNEZ-MONZÓ, J.; BARAT, J. M.; GONZÁLEZ-MARTÍNEZ, C.; CHIRALT, A.; FITO, P. Changes in thermal properties of apple due to vacuum impregnation. Journal of Food Engineering, Oxford, v. 43, n. 4, p. 213-218, 2000. MOHSENIN, N. N. Thermal properties of foods and agricultural materials. New York: Gordon and Breach Science, Inc, 1980. 407 p. MURAKAMI, E. G.; SWEAT, V. E.; SASTRY, S. K.; HAYAKAWA, K.; DATTA, A. Recommended design parameters for thermal conductivity probes for nonfrozen food materials. Journal of Food Engineering, Oxford, v. 27, n. 2, p. 109-123, 1996a. MURAKAMI, E. G.; SWEAT, V. E.; SASTRY, S. K.; KOLBE, E. Analysis of various design and operating parameters of the thermal conductivity probe. Journal of Food Engineering, Oxford, v. 30, n. 1-2, p. 209-225, 1996b. NIX, G. H.; LOWERY, G. W.; VACHEN, R. I.; TANGER, G. E. Direct determination of thermal diffusivity and conductivity with a refined line-source technique. In: HELLER, G. R. (Ed). Progress in astronautics and aeronautics: Thermophysics of spacecraft and planetary. New York: Academic Press, 1967. p. 865-878. PARK, K. J.; MURR, F. E. X.; SALVADEGO, M. Construção de um sistema de medição da condutividade térmica pelo método da sonda. Ciência e Tecnologia de Alimentos, Campinas, v. 17, n. 3, p. 7-10, 1997.

DICKERSON, R. W. An apparatus for the measurement of thermal difusivity of foods. Food Technology, Chicago, v. 19, n. 5, p. 198-204, 1965.

RAHMAN, M. S.; CHEN, X. D.; PERERA, C. O. An improved thermal conductivity prediction model for fruits and vegetables as a function of temperature, water content and porosity. Journal of Food Engineering, Oxford, v. 31, n. 2, p. 163-170, 1997.

FAO. Food and Agriculture Organization of the United Nations. FAOSTAT: FAO Statistical Database. Disponível em: . Acesso em: 13 ago. 2007.

REIDY, G. A.; RIPPEN, A. L. Methods for determining thermal conductivity in foods. Transactions of the ASAE, St. Joseph, v. 15, n. 2, p. 248-254, 1971.

Braz. J. Food Technol., v. 11, n. 1, p. 78-85, jan./mar. 2008

84

www.ital.sp.gov.br/bj Thermal conductivity and thermal diffusivity of papaya (Carica papaya L.) and cashew apple (Anacardium occidentale L.) KUROZAWA, L. E. et al.

SHAMSUDIN, R.; MOHAMED, I. O.; YAMAN, N. K. M. Thermophysical properties of Thai seedless guava juice as affected by temperature and concentration. Journal of Food Engineering, Oxford, v. 66, n. 3, p. 395-399, 2005. SINGH, K. K.; GOSWAMI, T. K. Thermal properties of cumin seed. Journal of Food Engineering, Oxford, v. 45, n. 4, p. 181-187, 2000. SINGH, R. P. Thermal diffusivity in food processing. Food Technology, Chicago, v. 36, n. 2, p. 87-91, 1982. Singh, R. P.; Heldman, D. R. Introduction to food engineering. 2.ed. San Diego: Academic Press, 1993. 499 p. SWEAT, V. E. Experimental values of thermal conductivity of selected fruits and vegetables. Journal of Food Science, Chicago, v. 39, n. 6, p. 1080-1083, 1974a. SWEAT, V. E. Experimental values of thermal conductivity probe for small food samples. Transaction of the ASAE, St. Joseph, v. 17, n. 1, p. 56-58, 1974b. SWEAT, V. E. Thermal properties of foods. In: RAO, M. A.; RIZVI, S. S. H. (Eds.). Engineering properties of foods. New York, Basel: M. Dekker, 1986. cap. 3, p. 99-138. TELIS-ROMERO, J.; TELIS, V. R. N.; GABAS, A. L.; YAMASHITA, F. Thermophysival properties of brazilian orange juice as

Braz. J. Food Technol., v. 11, n. 1, p. 78-85, jan./mar. 2008

affected by temperature and water content. Journal of Food Engineering, Oxford, v. 38, n. 1, p. 27-40, 1998. URBICAIN, M. J.; LOZANO, J. E. Definition, measurement, and prediction of thermophysical and reological properties. In: Valentas, K. J.; Robstein, E.; Singh, R. P. Handbook of food engineering practice. Boca Raton: CRC Press, 1997. cap. 11, p. 427-486. VAGENAS, G. K.; DROUZAS, A. E.; MARINOS-KOURIS, D. Predictive equations for thermophysical properties of plant foods. In: Spiess, W.E.; Schubert, H. Engineering and food, Vol.1, Physical properties and process control. London and New York: Elsevier Applied Science, 1990. p. 399-407. VAN DER HELD, E. F. M.; VAN DRUNEN, F. G. A method of measuring the thermal conductivity of liquids. Physica, v. 15, n. 10, p. 865-881, 1949. VOUDOURIS, N.; HAYAKAWA, K. Simultaneous determination of thermal conductivity and diffusivity of foods using a point heat source probe: a theorical analysis. Lebensmittel, Wissenschaft and Technologie, Zurich, v. 27, n. 6, p. 522-532, 1994. WALL, M. M. Ascorbic acid, vitamin A, and mineral composition of banana (Musa sp.) and papaya (Carica papaya) cultivars grown in Hawaii. Journal of Food Composition and Analysis, San Diego, v. 19, n. 5, p. 434-445, 2006.

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