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ELSEVIER
Journal of Food Engineeri ng 38 (1998) 27-40
0 1998
Elsevier Science Limited. All rights reserved
Printed in Great Britain
0260-8774/98/$ - see front matter
PII: SO260-8774(98)00107-l
Thermophysical Properties of Brazilian Orange Juice as
Affected by Temperature and Water Content
J. Telis-Romero,“* V. R. N. Telis,” A. L. Gabas” & F. Yamashitah
“Departamento de Engenharia e Tecnologia de Alimentos, Universidade Estadual Paulista,
C.P. 136, S&oJose do Rio Preto, Sao Paulo, 15054-000, Brazil
“Departamento de Tecnologia de Alimentos e Medicamentos, Universidade Estadual de
Londrina, C.P. 6001, Londrina, ParanB, 86051-990, Brazil
(Received 25 August 1997; revised 7 July 1998; accepted 15 July 1998)
ABSTRACT
The specij ic heat, thermal conductivi ry, thermal di fSusivity and density of
Br azi l ian orange ju ice were determined between 0.34 and 0.73 w/w) water
content and with temperatures from 0.5 to 62°. The experimental data were
fi tted as functions of temperatur e and water content and all properti es showed
a linear dependenq with these variables. In the tested range, the water content
exhi bited a greater inf luence on the analyzed properti es than temperatur e. 0
1998 El sevier Science L imi ted. Al l r ights reserved.
NOTATION
A
G
I
Icp
4
ii
Ro
RI
R2
S
1
Heating rate (“C/s)
Specific heat (J/kg “C)
Specific heat of the cell material (J/kg “C)
Cell length (m)
Heat flux in the thermal resistance (W)
Radius (m)
External radius of thermal diffusivity cell (m)
Internal radius of the internal cylinder (m)
External radius of the internal cylinder (m)
Internal radius of the external cylinder (m)
Surface area of a cylinder of radius r (m”)
Time (s)
27
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J. Tel i s-Romero et al .
I’
Temperature (“C)
Temperature at the center of the thermal diffusivity cell (“C)
Steady state temperature at the internal cylinder (“C)
Steady state temperature in the thermostatic bath where the cell was
immersed (“C)
Temperature at the cell material (“C)
Temperature asymptotically attained at the end of cell heating (“C)
Temperature at the wall of the thermal diffusivity cell (“C)
Water content (w/w)
Experimental thermal diffusivity $m%)
Calculated thermal diffusivity (m /s)
Eigenvalues of space and time functions
Density (kg/m3)
Density of the cell material (kg/m3)
Thermal conductivity of the sample at the average temperature
T, +7’4/2
(W/m”(Z)
Thermal conductivity of the cell material (W/m“C)
INTRODUCTION
Concentrated orange juice is one of the most important commodities over the world
and Brazil is the major producer. In general, modeling, optimization and automa-
tion of food processes is difficult due to the complexity of the raw materials and
products involved, which affect thermophysical properties such as density, specific
heat and thermal conductivity. In addition, thermophysical properties of some foods
exhibit substantial changes with temperature and water content during processing,
and orange juice is an example of this kind of product. Mathematical models which
express the dependence of thermophysical properties on temperature and water
content are a very appealing alternative to experimentation, and an useful tool for
the implementation of computer-aided routines for equipment design and process
automation.
An extensive review of existing methods of measurement of thermophysical
properties of foods has been carried out by Reidy and Rippen (1971), Mohsenin
(1980) Singh (1982), and others. Sweat (1995) recommended methods and strat-
egies that can be employed to measure the thermal properties of food.
Specific heat measurements are often made by means of a calorimeter (Riedel,
1951; Hwang and Hayakawa, 1979), which is a simple technique although requiring
a careful calibration as a result of the heat capacity of the apparatus. The differen-
tial scanning calorimeter is the best alternative for experimentally determining the
specific heat of foods, but has the disadvantage of being expensive (Constenla et al.,
1989; Sweat, 1995). _
Some empirical equations have been proposed for the estimation of specific heat
of various food products as a function of composition (Miles et al., 1983; Iamb,
1976). In these equations one can easily verify that specific heat of foods depends
strongly on the water content, since water has the highest specific heat of all food
components (Saravacos and Kostaropoulos, 1995). Experimental values of specific
heat are available for some food products and food processing materials (Lewis,
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Therr nophysi cal roperti es of orange ui ce
29
1987; Jowitt et al ., 1983) but most of them are restricted to a certain temperature
and/or water content.
Most works on thermal conductivity measurements of food products are con-
cerned with solid materials (Donsi
et al .,
1996; Lopez-Ramos
et al .,
1993; Pham and
Willix, 1989). Many measurement techniques have been described, such as the
guarded hot plate (ASTM Cl77 American National Standard Institute, 1970) or the
line heat source probe (Sweat and Haugh, 1974; Choi and Okos, 1983). In liquids,
the main source of experimental errors is convection during measurements. Sweat
(1995) recommends the addition of 0.5% agar to water when measuring its thermal
conductivity with a line heat source probe. For oils and water at high temperatures,
about 1% by weight of fiberglass ‘wool’ can be added to suppress convection. In
order to minimize uncertainties due to convection, Bellet
et al .
(1975) developed an
apparatus based on a cell made up of two coaxial cylinders, separated by an annular
space which is filled with the fluid sample. According to these authors, convection
can be avoided if the space between the cylinders is sufficiently small, and the
difference between wall temperatures is not very large. The thermal conductivity is
obtained from the equations describing heat transfer in steady-state conditions.
Mathematical modeling of unsteady-state operations allows for evaluation of the
specific heat of the fluid employing the same device, which constitutes the main
advantage of this method.
Thermal diffusivity can be estimated from the thermal conductivity, specific heat
and density of the product, according to its definition (given by eqn (1))
A
cl
--
Cal -
PCP
(1)
This method of evaluation has the inconvenience of adding up the experimental
errors involved in each one of these quantities. Alternatively, thermal diffusivity can
be measured directly using a transient heating technique developed by Dickerson
(1965). Singh (1982) discusses this and some other approaches used in determining
thermal diffusivity of foods, as well as the main sources of errors involved.
Thermophysical properties of orange juice are very scarce in the literature and
extensive work on temperature and water content dependence of this kind of
property has not yet been published. In an attempt to fill this gap, the objective of
this work was to measure the thermophysical properties (specific heat, thermal
conductivity, thermal diffusivity and density) of Brazilian orange juice as a function
of temperature and water content, and to obtain simple equations to correlate
experimental data.
MATERIALS AND METHODS
All the experimental measurements were made with samples prepared from the
same batch of concentrated orange juice (64.2”Brix and 10% (w/w) pulp), produced
with oranges cv. Pera-Rio in a six stage TASTE@ evaporator and stored at - 18°C.
In order to obtain different water contents, the concentrated juice was diluted with
distilled water.
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J. Telis-Romero et al.
Power supply
f--
Thermocouple
03
b0 ‘i’l
62 ‘k
I
\
Thermocouple (E)
Fig. 1. Cross section of the cell used for thermal conductivity and specific heat measure-
ments.
Thermal conductivity
Thermal conductivity at various temperatures and water contents, was measured
using the method described by Bellet et al. (1975) based on a cylindrical cell, where
the liquid whose properties are being determined fills the annular space between
two concentric cylinders. The equipment, shown in Fig. 1, presented the following
physical characteristics:
(1) two coaxial copper cylinders (A and B), 180 mm in length, separated by a
2 mm annular space, which was filled with the sample;
(2) 50 mm thick covers (C) made of a low thermal conductivity material
(0.225 W/m “C), to prevent axial heat transfer;
(3) inner cylinder (A) containing a heater (D) made with a constantan wire
(resistance 15 W), electrically insulated by a varnish and coiled around a
copper stick;
(4) two thermocouples type T (E) to measure temperature differences between
the two cylinders, located at the half-length of the cell. The wires were placed
inside 0.5 mm gaps, parallel to the cell axis.
To keep the external temperature constant, the cell was immersed in a thermo-
static bath (MK70, MLW, Dresden, Germany) containing water. The power input to
the heater resistance was made by means of a microprocessed, stabilized source
(ETB-252, Entelbra, Sao Paulo, Brazil), which allowed the adjustment of the current
with a stability of 0.05%. A HP data logger model 75.000-B, an interface HP-IB and
a HP PC running a data acquisition program written in IBASIC monitored tempera-
tures with an accuracy of 0.6”C.
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Thermophysical properties of orange juice
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In the steady state, conduction inside the cell was described by the Fourier
equation in cylindrical coordinates, with boundary conditions corresponding to heat
transfer between two concentric cylindrical surfaces kept at constant temperatures,
as given by eqns (2)-(4) and shown in Fig. 2.
a4
- = -A(T):
as
(2)
T(r=R,)=T,
(3)
T r = R,) = T2
Equation (2) was integrated in the form:
4)
which permitted the calculation of the sample thermal conductivity, A.
(5)
Specific heat
The apparatus described above was also used to measure specific heat. Considering
unsteady heat conduction through an isotropic, homogeneous medium allows the
equation of energy conservation to be written as:
-=-
- - -
I
(6)
Equation (6) must be solved to give the time and space temperature distribution in
the annular space between two infinite length coaxial cylinders. The following initial
and boundary conditions apply to the system:
T r,O) = T2 (isothermal system at t = 0)
7)
T R,,t) = TZ, V t (system kept in the thermostatic bath during the measurements) (8)
aT
i-1
4
=--
&-
R,,
271R& ’
V t (constant and uniform heat flux at the heater)
(9)
?‘ R,,t) = T R,,t) (equality of temperatures at the sample/cell interface)
(IO)
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R,,=
R =
R*=
RE=
J. Telis-Romero et al.
-f-VW)
WW)=T2
t ?
:
i
5mm
IOmm
12mm
17mm
Fig. 2. Geometric characteristics of thermal conductivity and specific heat cell.
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Thermophy sical propert i es of orange j ui ce
33
AfaT
ar (Rd=A ar
T (I?,,@ (equality of fluxes at the sample/cell interface)
(11)
The solution is presented in detail by Bellet et al. (1975). Nevertheless, a summary
of the equations needed to determine specific heat is given as follows.
The experimental procedure consisted of measuring the evolution of the tempera-
ture at R, from the beginning of the heating process. At this position, temperature
is given by:
W,,t) = TcAR,) - T(R,,t) =
& I[
o(
MG)]exp()
(12)
Equation (12) implies that a plot of the log of the temperature difference,
O(R,,t)
versus time is a straight line with a slope:
(13)
In eqn P), ~WJ(PJG)~
s an expression written in terms of zero-order Bessel
functions. The parameter /? represents the eigenvalues of the problem, and must
satisfy the equation:
cL(p)= 1 JI (~R,)Y ) - Jo(PRdY,(PR,) _
P’CP’ RI
P J”(PR,)Y,(PR,)-JJ~(PR*>Y,(PR,) PCP 2
14)
where
p’
and C P’ are, respectively, the density and specific heat of the cell material.
Combining eqns (13) and (14):
kh@>=P
J,(PR,WdPRd - Jo(PRdY,(PRi>
P,P’CP’ RI
J,(PR ,db’R,) JoWW=O (PRI ) =
1, y
(15)
Since thermal conductivity, 1, was already determined by steady-state experiments,
all terms on the right-hand side of eqn (15) are known, which allows for the
calculation of ,u,@). On the other hand, by adopting arbitrary values of /I, it is
~os$$ to construct a plot of fir(p)
versus fi characteristic of the experimental cell
kherefore, calculation of CP involved determining the slope P,
from the plot
log[B(R,,t)]
versus time and calculating p,(p) using eqn (15). Figure 3 was then used
to evaluate p, which could be substituted in eqn (13) to give the specific heat.
The cell was calibrated with distilled water and silicone oil. This permitted the
calculation of p’ and C
r’, the properties of the cell material, introduced in eqn (15).
Density
Density of orange juice at different temperatures and concentrations was deter-
mined in triplicate by weighing, in an analytical balance, the juice contained in a
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34
J. Telis-Romero
et al.
standard volumetric pycnometer (Constenla et al., 1989). Sample temperature was
varied by equilibration on a thermostatic bath. The pycnometer of 25 ml was pre-
viously calibrated with distilled water at each temperature.
Thermal diffusivity
Thermal diffusivity was determined using the method proposed by Dickerson
(1965). The experimental apparatus consisted of a cylindrical cell (24.75 x 10e3 m
internal radius and 248.5 x 1O-3 m length) made of chromium plated brass with two
nylon covers with thermal diffusivity of 1.09 x lop7 m%, which is similar to most
liquid food products. Two thermocouples of type T were fixed at the center and on
the external surface of the cell. The cell was immersed in a well agitated thermo-
static bath (MK70, MLW, Dresden, Germany) heated at a constant rate, and the
evolution of temperatures at the wall and at the center of the cell was monitored.
Temperatures were monitored by employing the same data acquisition system as
used in thermal conductivity and specific heat measurements.
Fig. 3. Characteristic function of the thermal conductivity and specific heat cell.
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Themophysical properties of orange juice
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The calculations were based on the solution of the equation of energy conserva-
tion, considering unsteady state,
constant unidimensional (radial) heat flux,
subjected to the following boundary conditions:
T=T,=At, t>O, r=R
(16)
aT
- =O, t>O, r=O
at
(17)
The value of a,,,, is given by:
(TR-To)= g
(18)
=P
where (TR - T,) is the temperature difference between the center and the surface of
the sample, and
A
is the constant heating rate. For each experiment it was con-
I
I
I I
I
I
H
T=Q%
0 T=@C
A
T=ltf’C
7’
T=6?‘C
I
I I
I
I I I
a3 a4 Q5
Q6
Q7 Q6
abet )(NwN
Fig. 4. Experimental specific heat of orange juice as a function of water content and tempera-
ture. (-
) Predictions of eqn (19); (. . -) apple juice 30°C (Constenla et al., 1989); (- . -)
orange juice 25°C (Moresi and Spinosi, 1980).
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36
J. Tel -Romero et al.
strutted a plot of
TR
and
T,,
versus time. The heating rate was obtained from the
slope of the
TR
versus
t
curve, and
(TR-To)
was evaluated from the difference
between the
TR
and
To
curves after eliminating the initial transient.
Data analysis
All statistical analysis was performed using the GLM procedure while fitted func-
tions were obtained by using the REG procedure from the SAS statistical package
(SAS Institute Inc., 1985). The suitability of the fitted functions was evaluated by the
coefficient of determination (R*), the level of significance Cp) and residual analysis.
RESULTS AND DISCUSSION
Specific heat, thermal conductivity, thermal diffusivity and density of Brazilian
orange juice with 0.34, 0.40, 0.44, 0.50, 0.55, 0.59, 0.63, 0.69 and 0.73 (w/w) water
content were determined at
0.5, 8.0, 18.0, 27.0, 35.0, 47.0, 53.0 and 62.O”C, adding
T=QS’C
T=@C
T= l&Z
T=27+‘C
T=X#‘C
T=@C
T=@C
T=6?C
I
I I
I
I
I
03 Q4
Q5 Q6 Q7 06
=aJ-t9 +/ wW
Fig. 5.
Experimental thermal conductivity of orange juice as a function of water content and
temperature. (- ) Predictions of eqn (20); (. . *) apple juice 20°C (Constenla et al., 1989).
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Therrnophysical roperti es of orange uice
37
up to 72 experimental values. of each thermal property. Polynomial functions simul-
taneously dependent upon temperature and water content were fitted to the data
and the results are expressed by eqns (19)-(22). All fitted functions had R .97
and p < 0.001 and the residual analysis showed adequacy of the models.
Cp = 1424.34+2673. 19Xw+2.446T
(19)
;1. 0.0797+0.5238Xw+0.000580T
(20)
c(
+,=7.9683 x 10-*+5.9839x 10-8Xw+0.02510 x lo-‘T
(21)
p =
1428.5-454.9Xw-0.231T
(22)
Figures 4-7 present the experimental values obtained, as well as the predictions of
eqn (19)-(22).
In the tested range, water content exhibited a greater influence on the analyzed
properties than temperature.
Q8
Fig 6 Experimental thermal diffusivity of orange juice as a function of water content and
temperature. (-
) Predictions of eqn (21).
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38 J. Tel i s-Romero et al .
Specific heat increased in a linear manner as water content was elevated from
0.34 to 0.73. Temperature rising was also responsible for higher values of Cp.
Empirical correlations obtained for clarified orange juice at 25°C (Moresi and
Spinosi, 1980) and apple juice at 30°C (Constenla ef al., 1989) are represented in
Fig. 4 to allow for comparison. Results from Moresi and Spinosi (1980) showed a
similar dependence on water content and a reasonable agreement in relation to
temperature. On the other hand, the correlation of Constenla et al. (1989) produced
higher values of Cp and a smaller dependence on water content when compared
with the present work. The same behavior can be observed when comparing thermal
conductivity results obtained in this work with the correlation proposed by Con-
stenla et al. (1989), as shown in Fig. 5. One of the reasons for these discrepancies
may be the fact that the orange juice studied in this work was not clarified, present-
ing a certain amount of insoluble solids. Observing that the deviations between
clarified and non-clarified juices increase with solid concentration reinforces this
explanation.
1380
I I I I
1
l J x -
c-f7
lm-
E
2
.g
1200-
i
8
llsl-
llCQ-
T=Q ?C
0 T=@C
A T=l6’C
v T=@‘C
+ T=6@C
+ T=@C
*.
. .
. .
X T=53’C
*.
‘\ . .
-\
# T=@‘C
. .
I
I
I I I
I 1
Q3 a4
cl5 06 Q7 06
Wter content,+Jwhv)
Fig. 7. Experimental density of orange juice as a function of water content and temperature.
(--- ) Predictions of eqn (22); (*.
.)
apple juice 20°C (Constenla et al., 1989);
(- .
-)
orange juice 21°C (Moresi and Spinosi, 1980).
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Thermophy si cal propert i es of orange jui ce 39
The agreement between experimental thermal diffusivities and the predictions of
eqn (21) was not as good as was observed with specific heat and thermal con-
ductivity, mainly at 0.5, 8 and 62°C (Fig. 6). However, in order to improve simplicity
the same correlation was adopted for the entire range of temperatures analyzed.
Experimental values of density presented a very strong dependence on water
content but were less affected by temperature (Fig. 7). Comparison with correlations
proposed for clarified orange juice at 21°C (Moresi and Spinosi, 1980) and apple
juice at 20°C (Constenla
et al.,
1989),
indicates that data obtained in this work
increased less rapidly with solids than those of clarified juices, which can be attri-
buted to the presence of insoluble solids.
Calculated thermal diffusivity
Thermal diffusivities were calculated according the definition (eqn (l)), using 72
experimental data for each thermophysical property and a polynomial function was
fitted (eqn (23)). The fitted function had
R* >
0.96
and p
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40
J. Tel i s-Romero et al.
Lewis, M. J. (1987). Physi cal Properti es of Foods and Food P rocessi ng M at eri al s. Ellis Hor-
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