Thermophysical Properties of Orange Juice

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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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    32

    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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    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

    35

    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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    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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