Braz. J. Food Technol., Campinas, v. 13, n. 3, p. 219-225, jul./set. 2010
DOI: 10.4260/BJFT2010130300029
Thermophysical properties of umbu pulp
Propriedades termofísicas de polpa de umbu
Autores | Authors
Michelle Andrade SOUZA
Centro Federal de Educação
Tecnológica da Bahia
e-mail: [email protected]
Renata Cristina Ferreira
BONOMO
Universidade Estadual do
Sudoeste da Bahia (UESB)
Departamento de Tecnologia
Rural e Animal
Laboratório de Engenharia e Processo
Praça Primavera, 40
CEP: 45700-000
Itapetinga/BA - Brasil
e-mail: [email protected]
Rafael da Costa Ilhéu FONTAN
Universidade Estadual do
Sudoeste da Bahia (UESB)
Departamento de Tecnologia
Rural e Animal
Laboratório de Engenharia e Processo
e-mail: [email protected]
Luis Antonio MINIM
Jane Sélia dos Reis COIMBRA
Universidade Federal de Viçosa (UFV)
Departamento de Tecnologia de Alimentos
e-mail: [email protected]
[email protected]
Paulo BONOMO
Universidade Estadual do
Sudoeste da Bahia (UESB)
Departamento de Tecnologia
Rural e Animal
Laboratório de Engenharia e Processo
e-mail: [email protected]
Autor Correspondente | Corresponding Author
Recebido | Received: 22/12/2008
Aprovado | Approved: 05/07/2010
Summary
The effects of moisture content (between 65 and 95%) and temperature
(between 5 and 85 °C) on the specific mass, specific heat, thermal diffusivity and
thermal conductivity of umbu pulp were studied. The specific mass decreased
when the moisture content and temperature increased, and the thermal diffusivity
and thermal conductivity increased as the moisture content decreased and the
temperature increased as from 25 °C. There was also an increase in specific heat
as the moisture content increased. Models adequately describing the observed
experimental behaviour were adjusted by regression analysis, and the results will
be useful for the further development and adaptation of the equipment necessary
for umbu pulp processing.
Key words: Density; Specific heat; Thermal diffusivity.
Resumo
Neste trabalho, estudou-se o efeito do teor de umidade (entre 65 e 95%) e da
temperatura (entre 5 e 85 °C) nas propriedades massa específica, calor específico,
difusividade térmica e condutividade térmica da polpa de umbu. Verificou-se a
redução da massa específica com o aumento do teor de umidade e da temperatura,
e um aumento da difusividade térmica e da condutividade com a redução do teor
de umidade e o aumento da temperatura, a partir de 25 °C. Diferentemente, o
calor específico apresentou um aumento nos valores com o aumento do teor
de umidade. Por meio de análise de regressão, foram ajustados modelos que
descrevem adequadamente o comportamento experimental observado. Dessa
forma, as informações obtidas serão úteis para o desenvolvimento e a adaptação
de equipamentos para o processamento da polpa de umbu.
Palavras-chave: Densidade, calor específico, difusividade térmica.
www.ital.sp.gov.br/bj
Thermophysical properties of umbu pulp
SOUZA, M. A. et al.
1 Introduction
A great variety of tropical fruits, widely cultivated in
many countries, are exported and consumed around the
world, for example banana, guava, mango, papaya and
orange. However, some varieties of tropical fruits have not
yet been adequately studied, such as umbu (Spondias
tuberosa Arr. Cam.). Umbu fruits are oval drupes with a
diameter of 2-4 cm, mass of 10-20 g, glabrous or slightly
hairy. The peel is greeny-yellow and the pulp is whitishgreen, soft and juicy with a pleasant, bittersweet taste
(LIMA et al., 2003; FOLEGATTI, 2003).
Like other foodstuffs, fruit pulps are exposed
to heating and cooling during processing. Thermal
treatments are required to eliminate pathogenic and
deteriorative microorganisms, to inactivate enzymes and
to retard metabolic and microbiological processes during
storage. When the food is not immediately consumed,
processing, cooling or freezing is required to maintain
its characteristics (ARAÚJO et al., 2004). The effects
of temperature and solids (or moisture) content on the
thermophysical properties of juices and fruit pulps are
important for the industrial systems in which the processes
are applied, and these properties have been studied by
Choi and Okos (1983), Constenla et al. (1989), Alvarado
and Romero (1989), Telis-Romero et al. (1998), Cepeda
and Villarán (1999), Zuritz et al. (2005), Azoulbel et al.
(2005), Shamsudin et al. (2005) and Muniz et al. (2006).
The processing of umbu pulp is still carried out
at a rudimentary, low technological level, and there
is a lack of knowledge concerning its thermophysical
characteristics, essential for the design of the industrial
processing equipment, such as pumps, heat exchangers,
evaporators and mixers.
Thus the objective of the present work was to
determine the specific mass, specific heat, thermal
diffusivity and thermal conductivity of umbu pulp as a
function of the moisture content and temperature.
2 Material and methods
2.1 Raw material and proximate analysis
The umbu pulp was prepared from fruits acquired
in the southwestern region of Bahia, Brazil, harvested
between December and March. In order to obtain the pulp,
the fruits were submitted to manual selection, washed with
fresh potable water, immersed in sodium hypochlorite
solution (50 ppm of residual chlorine) for 20 min and then
pulped in a pulper with a 1.5 mm sieve (model Bonina
0.25 DF, Itametal, Itabuna, Bahia, Brazil). The pulp was
filled into polyethylene bags and frozen at –18 °C in a
horizontal freezer, where it was stored until used.
In order to characterize the pulp, analyses of pH
(potentiometric method), total soluble solids (portable
Braz. J. Food Technol., Campinas, v. 13, n. 3, p. 219-225, jul./set. 2010
refractometer), total titratable acidity and proximate
analysis (ash, lipids, proteins, moisture and fibre) (IAL,
1985) were carried out, and the carbohydrate content
was obtained by difference.
To obtain the desired concentrations, the raw pulp
was concentrated in a rotary evaporator (Quimis, São
Paulo, Brazil) or diluted using distilled water.
2.2 Experimental design and analysis of the results
Experiments were planned using an entirely
randomized design, with treatments arranged in a 9 × 6
factorial scheme, with 3 repetitions in triplicate, giving a
total of 162 experimental points. Nine levels of temperature
(5, 15, 25, 35, 45, 55, 65, 75 and 85 °C) and six levels of
moisture content (70, 75, 80, 85, 90 and 95%, on a wet
basis) were tested, to determine of the specific mass of
the umbu pulp.
A similar experiment was carried out to determine
the thermal diffusivity, using only five levels of moisture
content (75, 80, 85, 90 and 95%, on a wet basis) instead
of six. Three repetitions in triplicate, giving a total of
135 experimental points, were carried out.
To determine specific heat, an entirely randomized
design with six levels for moisture content (the same
levels used for specific mass) was used, at an average
temperature between 40 and 45 °C. Three repetitions with
six replicates, giving a total of 18 experimental points
were carried out.
The thermal conductivity was determined from the
relationship between the specific mass, thermal diffusivity
and the specific heat proprieties (LEWIS, 1993).
The results were analyzed by the Analysis of
Variance (ANOVA) with 5% probability, and by the
Fisher test with a regression analysis for the significant
parameters (student test, p < 0.05), plus an analysis of the
residues and calculation of the coefficient of determination
(R²). All the statistical analyses were carried out using
the statistical package SAEG, v.8.1 (Ribeiro JÚNIOR,
2001).
2.3 Determination of specific mass
The picnometric method was used to determine the
specific mass at the chosen temperatures and moisture
contents (Coimbra et al., 2006). A 25 mL nominal
volume picnometer was calibrated with distilled water at
the temperatures under study using a thermostatic bath
(Q214S2 model, Quimis, São Paulo, Brazil, ±0.1 °C of
accuracy). Once calibrated, the picnometer was used to
determine the specific mass of the umbu pulp using an
analytical scale (AG200 model, Gehaka, São Paulo, Brazil,
±0.0001 g of accuracy).
220
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Thermophysical properties of umbu pulp
SOUZA, M. A. et al.
2.4 Specific heat determination
To determine the average specific heat of the umbu
pulp, the mixture calorimeter method was used (ARAÚJO
et al., 2004). The calorimeter consisted of a thermal
glass bottle with double insulated walls, an expanded
25 cm thick polystyrene layer and a cooper-constantan
thermocouple (Penta, São Paulo, Brazil, ±0.1 °C of
accuracy) inserted in its interior.
The heat capacity of the calorimeter was first
determined in order to determine the specific heat of the
samples. The calorimeter was half filled with cold distilled
water (~12 °C) and left at rest until thermal equilibrium
was reached. The calorimeter was then filled with warm
water (~45 °C), and left at rest again until thermal
equilibrium was again reached. This procedure was
carried out ten times and the heat capacity determined
using Equation 1a.
In order to determine the specific heat of the
samples, the calibrated calorimeter was filled with cold
water (~12 °C) and left at rest to reach thermal equilibrium.
The mass of sample (~45 g), contained in a polyethylene
bag, was then inserted into the calorimeter. Preliminary
tests showed that the mass of the bags could be ignored
in the calculations. The system was again left at rest until
thermal equilibrium was reached and the specific heat of
the sample determined using Equation 1b.
Ccal =
(
)
(T
)(T
eq
cp =
(
mh ⋅ c w ⋅ Th − Teq − mc ⋅ c w ⋅ Teq − Tc
(c w ⋅ mw + Ccal
(
eq
ms Ts − Teq
)
)
−T )
− Tc
)
0
model, Marconi, São Paulo, Brazil, ±0.1 °C of accuracy)
until thermal equilibrium between the bath and the cell
was reached. The bath was then heated at a constant
rate (1.1 °C /min) until the internal temperature of the
capsule reached at least 85 °C. The temperatures marked
by the two thermocouples were registered at one minute
intervals until the end of the experiment. The thermal
diffusivity of the encapsulated sample was calculated
using Equation 2:
α=
A ⋅ R2
4 (Text − Tint ) (2)
where: α is the thermal diffusivity (m2/s), A is the heating
rate of the bath (°C/min), R is the internal radius of the
cell (m), Text is the external temperature of the cell (°C)
and Tint is the internal temperature of the cell measured
at the centre of the cell (°C).
2.6 Determination of the thermal conductivity
Once the sample thermal diffusivity, specific heat
and specific mass values had been determined, the thermal
conductivity could be determined from the relationship
between these properties (Telis‑Romero et al., 1998).
3 Results and discussion
3.1 Proximate analysis
(1a)
(1b)
where: cw is the specific heat of water (kJ/kg.°C); mh is
the mass of the water at a high temperature (kg); mc is
mass of cold water (kg); Ccal is the heat capacity of the
calorimeter (kJ/°C); Th is the temperature of the hot water
(°C); Tc is the temperature of the cold water (°C) and Teq
is the temperature at equilibrium (°C); T0 is the initial
water+calorimeter temperature (°C), Ts is the initial sample
temperature (°C), ms is the sample mass (kg) and Cp is
the specific heat of the sample (kJ/kg.°C).
2.5 Determination of the thermal diffusivity
A method adapted from Dickerson (1965) was used
to determine thermal diffusivity. This method involved
the use of a stainless steel metallic capsule (3.8 cm
diameter; 25.5 cm height; 1.0 mm width) equipped with
two copper-constantan thermocouples (Penta, São Paulo,
Brazil ±0.1 °C of accuracy), one at the external surface
of the capsule, and the other at the central plane of the
capsule.
The metallic capsule was then filled with sample,
and immersed in a thermostatic bath at 2 °C (MA185
Braz. J. Food Technol., Campinas, v. 13, n. 3, p. 219-225, jul./set. 2010
The physical chemical characterization of the
umbu pulp is shown in Table 1. The values obtained
for the pH, soluble solids and titratable acidity and the
proximate composition were in agreement with the values
presented by Bispo (1989), except for the value for ash. A
comparison of the values obtained with those presented
by Mattietto (2005) also showed agreement, except for
the values for fiber and carbohydrate.
Table 1. Results for the proximate and physicochemical analyses
of umbu pulp.
Results
Analysis
Bispo
Mattietto
Experimental
(1989)
(2005)
pH
2.3 ± 0.00
2.45
2.75
Soluble solids (°Brix)
9.5 ± 0.00
10.00
9.59
Total titratable acidity
1.68 ± 0.00
1.23
1.39
(% citric acid)
Moisture content
89.70 ± 0.57
89.89
89.40
(% wt)
Carbohydrate (% wt)
7.96 ± 0.38
7.95
4.93
Proteins (% wt)
0.74 ± 0.08
0.52
0.75
Fat (% wt)
0.37 ± 0.01
0.35
0.30
Fibre (% wt)
0.24 ± 0.03
0.37
1.07
Ash (% wt)
0.99 ± 1.21
0.35
0.40
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Thermophysical properties of umbu pulp
SOUZA, M. A. et al.
3.2 Specific mass
The experimental results obtained for the specific
mass of the umbu pulp at the temperatures and moisture
contents studied were submitted to ANOVA and a
regression analysis. Both variables showed a significant
effect (p < 0.05), and the model chosen (Equation 3) was
based on the significant parameters (p < 0.05), analysis
of the residues, and the coefficient of determination.
A quadratic model for both variables was fitted, with
a coefficient of determination of 0.97, as presented in
Equation 3.
ρ = 2891.520 – 39.558 Xa + 0.209 Xa2 + 0.135T – 0.010T 2 (3)
where: ρ is the specific mass (kg/m3), Xa is the moisture
content (%m/m, wet basis) and T the temperature (°C).
Figure 1 shows the experimental and predicted
values for specific mass as a function of temperature and
moisture content for the umbu pulp. The specific mass
decreased as the temperature and moisture content
increased. This behaviour had been previously mentioned
by other authors who worked with fruit products, such as
apple juice (CEPEDA; VILLARÁN, 1999); peach juice and
puree (RAMOS and IBARZ, 1998) and clarified apple juice
(CONSTENLA et al., 1989).
3.3 Specific heat
According to the average experimental values
presented in Figure 2, there was a minimum specific
heat of 3.66 kJ/kg.°C and maximum specific heat of
4.18 kJ/kg.°C for umbu pulp in the range of moisture
contents and temperatures studied. The specific heat
presented by Choi and Okos (1986) for fruit juices was
between 3.00-4.00 kJ/kg.°C. Other researchers reported
values for the specific heat in the same ranges of moisture
content and temperature, such as 3.346 kJ/kg.°C for açai
pulp (PEREIRA et al., 2002), 3.616 kJ/kg.°C for bakuri pulp
(MUNIZ et al., 2006) and 2.962 kJ/kg.°C for banana pulp
(ALVARADO, 1994).
Lima et al. (2003) also studied the thermophysical
properties of umbu pulp, evaluating the influence of
soluble solids at the concentrations of 10, 20 and 30 °Brix.
They found specific heat values of respectively 3.67, 3.48
and 3.21 kJ/kg.°C, which were lower than the values found
in the present experiment.
In order to explain the relationship between
moisture content and specific heat, a simple linear model,
which presented significant parameters (p < 0.05) and a
high coefficient of determination (R2 = 0.99) was fitted.
The fitted model is presented in Equation 4.
c p = 2.192 + 0.021Xa where: c p is the specific heat (kJ/kg.°C) and X a is the
moisture content (%m/m, wet basis).
The influence of moisture content on the specific
heat can be observed from an analysis of the results in
Figure 2. The relationship was directly proportional, since
the highest values for cp were found for the samples with
the highest moisture contents. This result agrees with the
studies carried out by Choi and Okos (1986), Constela,
Lozano and Crapiste (1989), Simões (1997) and Silva
(1997).
3.4 Thermal diffusivity
From the statistical analysis of the experimental
results, it was shown that the moisture content and
temperature had a significant effect (p < 0.05) on the
thermal diffusivity of umbu pulp. A multiple polynomial
model was fitted from the regression analysis, with
1120
4,4
1100
4,2
1080
Cp (kJ/kg°C)
1060
ρ (kg/m3)
(4)
1040
1020
1000
980
4,0
3,8
3,6
3,4
960
940
3,2
0
20
40
60
80
100
Temperature (°C)
75%
95%
80%
85%
Predicted
65
70
75
80
85
90
95
100
Moisture content (%m/m)
90%
Figure 1. Effect of temperature and moisture content on the
specific mass of umbu pulp.
Braz. J. Food Technol., Campinas, v. 13, n. 3, p. 219-225, jul./set. 2010
Experimental
Predicted
Figure 2. Variation of specific heat with moisture content for
umbu pulp.
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Thermophysical properties of umbu pulp
SOUZA, M. A. et al.
a coefficient of determination (R 2) equal to 0.97 and
significant parameters. Equation 5 shows the fitted
model.
α = 0.675x10 −8 – 0.129x10 −7 T + 0.111 x10 −9 T 2 +
0.335 x10 −8 Xa + 0.649 x10 −10 TXa
(5)
where: α is the thermal diffusivity (m2/s), Xa is the moisture
content (%m/m, wet basis) and T is the temperature
(°C).
Figure 3 shows the experimental and predicted
values for thermal diffusivity under the ranges of
temperature and moisture content studied.
It was shown that as the moisture content increased,
so the thermal diffusivity also increased. Similar results
were found by Moura et al. (2003) for simulated juice
models, Azoubel et al. (2005) for cashew juice and
Muniz et al. (2006) for bakuri pulp. This behaviour shows
that as the solids concentration increased (or the moisture
content reduced), so the propagation of heat or speed of
diffusion through the pulp slowed down, as represented
by the thermal diffusivity (HUBINGER; BARONI, 2001).
As in the case of moisture content the temperature also
affected the values obtained for thermal diffusivity.
In general these two variables are proportional: as
the temperature increases, the diffusivity also increases.
This fact was observed by Choi and Okos (1983) studying
concentrated tomato juice in a wide range of temperatures
(20 to 150 °C), and by Telis-Romero et al. (1998), working
with orange juice at temperatures between 0.5 and 62 °C.
The results obtained for thermal diffusivity in the present
study were similar to those obtained by the above authors
for temperatures up to 20 °C. A small reduction in thermal
diffusivity was shown at temperatures between 5 and
25 °C.
3.5 Thermal conductivity
The thermal conductivity values for umbu pulp were
calculated using the experimental specific mass, specific
heat and thermal diffusivity data. From the statistical
analysis of the experimental results, it was shown that both
the moisture content and temperature had a significant
effect (p < 0.05) on the thermal conductivity of umbu
pulp. In order to find the relationship between thermal
conductivity, temperature and moisture content, a multiple
polynomial model was fitted by regression analysis.
The model presented a coefficient of determination (R2)
equal to 0.96 and good fit for the parameters. Equation 6
presents the fitted model.
k = −0.706 – 0.277 × 10 −1T + 0.434x10 −3 T 2 + 0.228x10 −1 Xa (6)
where: k is the thermal conductivity (W/m.°C), X a the
moisture content (%m/m, wet basis) and T the temperature
(°C).
Figure 4 shows the thermal conductivity of umbu
pulp as a function of temperature and moisture content. It
was shown that the thermal conductivity increased as the
moisture content increased. This behaviour was expected
since this property is affected by the composition of the
food, water being the most influential component. Most
foods are bad heat conductors, and foods with higher
moisture contents present higher thermal conductivity
values (LEWIS, 1993).
Donsì et al. (1996) determined the thermal
conductivity of apple and tomato pulps with various
moisture contents at 30 °C. They showed the same
tendency for the thermal conductivity to increase with
increasing moisture content. Identical behaviour was
also observed for guava juice at concentrations of 10 to
40 °Brix at a temperature of 30 °C (SHAMSUDIN et al.,
2005).
7,00 e –7
3,0
6,00 e –7
2,5
k (W/°C.m)
α (m2/s)
5,00 e –7
4,00 e –7
3,00 e –7
2,00 e –7
2,0
1,5
1,0
0,5
1,00 e –7
0,00
0,0
0
20
40
60
80
100
0
20
40
Temperature (°C)
75%
95%
80%
85%
Predicted
60
80
100
Temperature (°C)
90%
Figure 3. Thermal diffusivity of umbu pulp as a function of
temperature and moisture content.
Braz. J. Food Technol., Campinas, v. 13, n. 3, p. 219-225, jul./set. 2010
75%
95%
80%
85%
Predicted
90%
Figure 4. Thermal conductivity of umbu pulp as a function of
temperature and moisture content.
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Thermophysical properties of umbu pulp
SOUZA, M. A. et al.
4 Conclusion
The temperature and moisture content of umbu pulp
affected its thermophysical properties. Simple models
satisfactorily fitted (p < 0.05) and adequately described
the experimental behaviour. With this information,
equipment for processing umbu pulp could be developed
and adapted.
Acknowledgements
To the Fundação de Amparo à Pesquisa do Estado
da Bahia – FAPESB and to CNPq for their financial
support.
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