Coeficiente Convectivo Articulo
-
Upload
marlene-juarez -
Category
Documents
-
view
225 -
download
0
Transcript of Coeficiente Convectivo Articulo
-
8/13/2019 Coeficiente Convectivo Articulo
1/12
Heat transfer coefficients for forced-air cooling andfreezing of selected foods
Bryan R. Becker*, Brian A. FrickeMechanical Engineering, University of Missouri-Kansas City, 5100 Rockhill R oad, Kansas City, MO 64110-2499, USA
Received 1 April 2003; received in revised form 13 February 2004; accepted 19 February 2004
Abstract
To maximize the efficiency of cooling and freezing operations for foods, it is necessary to optimally design the refrigeration
equipment to fit the specific requirements of the particular cooling or freezing application. The design of food refrigeration
equipment requires estimation of the cooling and freezing times of foods, as well as the corresponding refrigeration loads. The
accuracy of these estimates, in turn, depends upon accurate estimates of the surface heat transfer coefficient for the cooling or
freezing operation. This project reviewed heat transfer data for the cooling and/or freezing of foods. A total of 777 cooling
curves for 295 food items were obtained from an industrial survey and a unique iterative algorithm, utilizing the concept of
equivalent heat transfer dimensionality, was developed to obtain heat transfer coefficients from these cooling curves. NineNusseltReynoldsPrandtl correlations were developed from a selection of the 777 heat transfer coefficients resulting from this
algorithm, as well as 144 heat transfer coefficients for 13 food items, collected from the literature. The data and correlations
resulting from this project will be used by designers of cooling and freezing systems for foods. This information will make
possible a more accurate determination of cooling and freezing times and corresponding refrigeration loads. Such information is
important in the design and operation of cooling and freezing facilities and will be of immediate usefulness to engineers
involved in the design and operation of such systems.
q 2004 Elsevier Ltd and IIR. All rights reserved.
Keywords:Cooling; Freezing; Food; Calculation; Cooling time; Freezing time; Heat transfer coefficient
Coefficients de transfert de chaleur de certains produits
alimentaires lors du refroidissement aair forceMots-cles:Refroidissement; Congelation; Produit alimentaire; Calcul; Temps de re frigeration; Temps de congelation; Coefficient de transfert
de chaleur
1. Introduction
In many food processing applications, including blast
cooling and freezing, transient convective heat transfer
occurs between a fluid medium and the solid food item [1].
Knowledge of the surface heat transfer coefficient is
required to design the equipment wherein convection heat
transfer is used to process foods. Newtons law of cooling
defines the surface heat transfer coefficient, h, as follows:
q hAts 2 tm 1
The surface heat transfer coefficient, h, is a lo ca l
phenomenon which depends upon the velocity of the
surrounding fluid, product geometry, orientation, surface
roughness and packaging, as well as other factors.Researchers have noted that the most significant factor
International Journal of Refrigeration 27 (2004) 540551
www.elsevier.com/locate/ijrefrig
0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved.
doi:10.1016/j.ijrefrig.2004.02.006
* Corresponding author. Tel.: 1-816-235-1255; fax: 1-816-
235-1260.
E-mail address:[email protected] (B.R. Becker).
http://www.elsevier.com/locate/ijrefrighttp://www.elsevier.com/locate/ijrefrig -
8/13/2019 Coeficiente Convectivo Articulo
2/12
-
8/13/2019 Coeficiente Convectivo Articulo
3/12
influencing the surface heat transfer coefficient is the
velocity of the fluid flowing past the product. Thus, it is
common to report the results of experimentally determined
surface heat transfer coefficients in terms of Nusselt
ReynoldsPrandtl correlations. These correlations give the
heat transfer coefficient as a function of product shape and
size as well as fluid velocity. Since the heat transfercoefficient is not constant over the surface of a body, the
value of the heat transfer coefficient reported by these
Nusselt Reynolds Prandtl correlations is actually the area
averaged value of the local heat transfer coefficient.
A small number of studies have been performed to
measure or estimate the surface heat transfer coefficient
during cooling, freezing or heating of food items [1 34]. In
addition, a detailed literature survey has been compiled by
Arce and Sweat [35]. These studies present surface heat
transfer coefficient data and correlations for only a very
limited number of food items and process conditions. Hence,
the objective of this study was to determine the surface heat
transfer coefficients for a wide variety of foods during blast
cooling and freezing processes.
2. Review of existing techniques to determine the surface
heat transfer coefficients of foods
Techniques used to determine heat transfer coefficients
generally fall into three categories: steady-state temperature
measurement methods, transient temperature measurement
methods and surface heat flux measurement methods. Of
these three techniques, the most popular methods are the
transient temperature measurement techniques.
Transient methods for determining the surface heat
transfer coefficient involve the measurement of producttemperature with respect to time during cooling or freezing
processes. Two cases must be considered when performing
transient tests to determine the surface heat transfer
coefficient: low Biot number (Bi # 0.1) and large Biot
number (Bi . 0.1). The Biot number, Bi, is the ratio of
external heat transfer resistance to internal heat transfer
resistance and is defined as follows:
BihZ
k 2
A low Biot number indicates that the internal resistance to
heat transfer is negligible, and thus, the temperature within
the object is uniform at any given instant in time. A large
Biot number indicates that the internal resistance to heattransfer is not negligible, and thus, a temperature gradient
may exist within the object.
In typical blast cooling or freezing operations for foods,
the Biot number is large, ranging from 0.2 to 20[36]. Thus,
the internal resistance to heat transfer is generally not
negligible during food cooling and freezing and a
temperature gradient will exist within the food item.
One method for obtaining the surface heat transfer
coefficient of a food product with an internal temperature
gradient involves the use of cooling curves. For simple, one-
dimensional food geometries such as infinite slabs, infinite
circular cylinders or spheres, there exist empirical and
analytical solutions to the one-dimensional transient heat
equation. The slope of the cooling curve may be used inconjunction with these solutions to obtain the Biot number
for the cooling process. The heat transfer coefficient may
then be determined from the Biot number.
All cooling processes exhibit similar behavior. After an
initial lag, the temperature at the thermal center of the food
item decreases exponentially [36]. As shown in Fig. 1, a
cooling curve depicting this behavior can be obtained by
plotting, on semilogarithmic axes, the fractional unaccom-
plished temperature difference versus time. The fractional
unaccomplished temperature difference, Y, is defined as
follows:
Y tm 2 t
tm 2 ti
t2 tm
ti 2 tm3
The lag between the onset of cooling and the exponential
decrease in the temperature of the food item is measured
with thej factor, as shown inFig. 1.
FromFig. 1,it can be seen that the linear portion of the
cooling curve can be described as follows:
Y j exp2Cu 4
whereCis the cooling coefficient, which is minus the slope
of the linear portion of the cooling curve.
For simple geometrical shapes, such as infinite slabs,
infinite circular cylinders and spheres, analytical
expressions for cooling or freezing time may be derived.
To derive these expressions, the following assumptions are
made: (1) the thermophysical properties of the food item andthe cooling medium are constant, (2) the internal heat
Fig. 1. Typical cooling curve.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551542
-
8/13/2019 Coeficiente Convectivo Articulo
4/12
generation and moisture loss from the food item are
neglected, (3) the food item is homogeneous and isotropic,
(4) the initial temperature distribution within the food item
is uniform, (5) heat conduction occurs only in one
dimension, and (6) convective heat transfer occurs between
the surface of the food item and the cooling medium. With
these assumptions, the one-dimensional transient heatequation may be written as follows for infinite slabs, infinite
circular cylinders and spheres:
1
za
z
z
a f
z
1
a
f
u
5
The initial and boundary conditions are as follows:
fz; 0 ti 2 tm 6
zf0; u 0 7
2k
zfZ; u
hfZ; u 0 8
In order to non-dimensionalize the solutions of Eq. (5), twodimensionless parameters are introduced, namely, the Biot
number, defined in Eq. (2), and the Fourier number, defined
as follows:
Foau
Z2 9
3. Iterative technique to determine heat transfer
coefficients of irregularly shaped food items
The technique developed in this paper to determine heat
transfer coefficients from experimental cooling curves is
based upon the infinite series solution of Eq. (5), given byCarslaw and Jaeger [37], for the dimensionless center
temperature of a sphere:
YX1n1
AnBn 10
After the initial lag period has passed, in which case Fo $
0:2;thesecond andhigher terms of Eq.(10) are assumed to be
negligible[21].Thus, Eq. (10) can be simplified as follows:
YA1B1 11
whereA1andB1are given as follows:
A1 2Bisinm1
m1 2 sinm1cos m112
B1 exp2m21Fo 13
and m1is a parameter specified by a characteristic equation:
cotm1 12Bi
m114
The parameter, m1;may also be determined from the cooling
coefficient,C, defined in Eq. (4). By comparing Eqs. (4), (11)and (13), it can be seen that:
2Cu 2m21Fo 15
Since the Fourier number, Fo, of a cooling process can be
readily determined, and, provided that the value ofCcan be
determined from a cooling curve, the value of m1 can
be obtained by rearranging Eq. (15):
m1
ffiffiffiffiffiCu
Fo
r 16
Then, the Biot number,Bi, can be obtained from Eq. (14) and
the surface heat transfer coefficient, h, may be obtained
through algebraic manipulation of the definition of the Biotnumber, Eq. (2).
Table 1
Geometric parameters and equations from Lin et al. [41]
Shape p1 p2 p3 Eo
Infinite slab b1 b2 1 0 0 0 1
Infinite rectangular rod (b1 $ 1: b2 1) 0.75 0 21 Eo 1 1
b1
1
b2
Brick (b1 $ 1: b2 $ b1) 0.75 0.75 21 Eo 1 1
b1
1
b2Infinite cylinder (b1 1: b2 1) 1.01 0 0 2
Infinite ellipse (b1 . 1: b2 1) 1.01 0 1 Eo 1
1
b1
1
b1 2 12b1 2
2
Squat cylinder (b1 b2; b1 $ 1) 1.01 0.75 21 Eo 1
1
b1
1
b2
Short cylinder (b1 1: b2 $ 1) 1.01 0.75 21 Eo 1 1
b1
1
b2Sphereb1 b2 1 1.01 1.24 0 3
Ellipsoid (b1 $ 1: b2 $ b1) 1.01 1.24 1 Eo 3b1 b2 b
211 b2 b
221 b1
2b1b21 b1 b22
b1 2 b220:4
15
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551 543
-
8/13/2019 Coeficiente Convectivo Articulo
5/12
Since the analytical method described thus far is only
applicable to spherical food items, an iterative technique
was developed to handle irregular shaped food items. Thisiterative technique utilizes a shape factor, called the
equivalent heat transfer dimensionality, to extend the
analytical method to irregularly shaped food items[3841].
This equivalent heat transfer dimensionality, E, compares
the total heat transfer to the heat transfer through the shortest
dimension.
The equivalent heat transfer dimensionality,E, is used to
modify the analytical solution, Eq. (13), as follows:
B1 exp 2m21Fo
E
3
17
resulting in the following modifications to Eqs. (15)
and (16):
2Cu 2m21Fo
E
3 18
m1
ffiffiffiffiffiffiffiffiffiCu
Fo
3
E
r 19
Lin et al. [3941] give the equivalent heat transfer
dimensionality,E, as a function of Biot number:
EBi4=3 1:85
Bi4=3
E1
1:85
Eo
20
Eo and E1are the equivalent heat transfer dimensionalities
for the limiting cases ofBi 0 and Bi !1, respectively.
For both two-dimensional and three-dimensional food
items, the general form for the equivalent heat transfer
dimensionality at Bi !1,E1, is given as:
E1 0:75p1fb1 p2fb2 21
where
fb 1
b2 0:01p3exp b2
b2
6
" # 22
The geometric parameters,p1,p2and p3, are given inTable
1for various geometries. The definition of the equivalentheat transfer dimensionality for Bi 0, Eo;is also given in
Table 1for various food geometries.
To determine the heat transfer coefficient of irregularly
shaped food items, the value ofm1 is obtained via Eq. (19)
and then the Biot number can be calculated from Eq. (14).
From the Biot number, the equivalent heat transfer
dimensionality can be obtained by using Eqs. (20)(22).
The value ofm1 is then recalculated via Eq. (19), using the
updated value of equivalent heat transfer dimensionality.
This process is repeated until the value of the Biot number
converges. Finally, the heat transfer coefficient, h, may be
determined through algebraic manipulation of the definition
of the Biot number, Eq. (2).
Table 2
NusseltReynoldsPrandtl correlations for selected food items
Food type Reynolds number
range
Number of
data points
Level of
significance
(F-statistic)
Coefficient of
determination, r2NuRe Prcorrelation
Beef patties (Unpackaged) 2000 , Re , 7500 7 0.182 0.324 Nu 1.37Re 0.282Pr0.3
Cake (packaged and unpackaged) 4000, Re , 80 000 29 5.34 10212 0.833 Nu 0.00156Re 0.960Pr0.3
Cheese (packaged and unpackaged) 6000 , Re , 30 000 7 0.196 0.307 Nu 0.0987Re 0.560Pr0.3
Chicken breas t (unpackaged) 1000 , Re , 11 000 22 0.00115 0.418 Nu 0.0378Re 0.837Pr0.3
Fish fillets (packaged and unpackaged) 1000, Re , 25 000 28 1.27 1026 0.601 Nu 0.0154Re 0.818Pr0.3
Fried potato patties (unpackaged) 1000, Re , 6000 8 0.0143 0.660 Nu 0.00313Re 1.06Pr0.3
Pizza (packaged and unpackaged) 3000, Re , 12 000 12 0.00814 0.520 Nu 0.00517Re 0.981Pr0.3
Sausage (unpackaged) 4500,
Re,
25 000 14 0.314 0.0918 Nu 7.14Re
0.170
Pr
0.3
Trayed entrees (packaged) 5000 , Re , 20 000 42 0.213 0.0386 Nu 1.31Re 0.280Pr0.3
Fig. 2. Cooling curve for catfish.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551544
-
8/13/2019 Coeficiente Convectivo Articulo
6/12
4. Cooling curves
Members of the food refrigeration industry werecontacted
to collect cooling curves and surface heat transfer data for
various food items. These contacts included food refrigeration
equipment manufacturers, designers of food refrigeration
plants, and food processors. An effort was made to collect
information on as many food items as possible.
A total of 777 cooling curves for various food items were
collected from the following sources: (1) Advanced Food
Processing Equipment, Inc.; (2) Freezing Systems, Inc.; (3)
Frigoscandia Equipment, AB; and, (4) Technicold Services,
Fig. 3. NusseltReynoldsPrandtl correlation for unpackaged beef patties.
Fig. 4. NusseltReynoldsPrandtl correlation for packaged and unpackaged cake. If present, packaging consists of either an aluminum tray, or
an aluminum foil cover and a paper tray.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551 545
-
8/13/2019 Coeficiente Convectivo Articulo
7/12
Inc. These cooling were determined through the use ofthermocouples imbedded within the food items.
A typical cooling curve is shown in Fig. 2. These
collected cooling curves were digitized and a database was
developed which contains the digitized time-temperature
data obtained from these curves. The temperatures were
non-dimensionalized according to Eq. (3) and the natural
logarithm of these non-dimensional temperatures weretaken. The slopes of the linear portion(s) of the logarithmic
temperature versus time data were determined using the
linear least-squares-fit technique. These slopes were then
used in conjunction with the techniques described in Section
3 to determine the heat transfer coefficients for the food
items.
Fig. 5. NusseltReynoldsPrandtl correlation for packaged and unpackaged cheese. If present, packaging consists of either a pouch, a paper
tray with plastic lid, or a plastic box with lid.
Fig. 6. NusseltReynoldsPrandtl correlation for unpackaged chicken breast.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551546
-
8/13/2019 Coeficiente Convectivo Articulo
8/12
5. Calculated heat transfer coefficients
Using the iterative algorithm, 777 heat transfer
coefficients for foods were calculated from the database
of 777 cooling curves and tabulated with a description of
their packaging, dimensions, and weight, as well as the
air temperature and air velocity used to cool or freeze thefood items.
5.1. Effects of packaging
Packaging affects the heat transfer coefficients of food
Fig. 7. NusseltReynoldsPrandtl correlation for packaged and unpackaged fish fillets. If present, packaging consists of either a hard plastic
tray or a plastic pouch.
Fig. 8. NusseltReynoldsPrandtl correlation for unpackaged fried potato patties.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551 547
-
8/13/2019 Coeficiente Convectivo Articulo
9/12
items in several ways. It insulates the food item by
presenting a barrier to the transfer of energy from the
food, thus lowering the heat transfer coefficient. Packagingmay also create air-filled voids around the food item which
further insulates the food and lowers the heat transfer
coefficient.
Furthermore, the algorithm developed in Section 3
makes use of a density for the food item which includes
the packaging. In the algorithm, this density is calculated
from the outside dimensions of the package around the fooditem and the mass of the food item plus the packaging. Thus,
the density used to calculate the heat transfer coefficient is
affected by the packaging, resulting in a heat transfer
coefficient for the food item within its packaging.
Fig. 9. NusseltReynoldsPrandtl correlation for packaged and unpackaged pizza. If present, packaging consists of either a cardboard backing
or a cardboard backing and shrink wrap.
Fig. 10. NusseltReynoldsPrandtl correlation for unpackaged sausage.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551548
-
8/13/2019 Coeficiente Convectivo Articulo
10/12
5.2. NusseltReynoldsPrandtl correlations
Non-dimensional analyses were performed to develop
Nusselt Reynolds Prandtl correlations for selected food
items. The Nusselt number is a dimensionless heat transfer
coefficient defined as:
Nuhd
km23
Physical reasoning indicates a dependence of the heat
transfer process on the flow field, and hence on the Reynolds
number,Re:
RermUd
mm
24
The relative rates of diffusion of heat and momentum are
related by the Prandtl number, Pr, and hence, the Prandtl
number is expected to be a significant parameter in the
determination of heat transfer coefficients:
Prmmcm
km25
An exponential function is commonly used to relate the
Nusselt number, Nu, to the Reynolds and Prandtl numbers:
Nu CRem
Prn
26
where C, m and n are constants determined from
experimental data.
To obtain Nusselt Reynolds Prandtl correlations forfoods, in the form given by Eq. (26), the Reynolds, Prandtl
and Nusselt numbers were determined for each coolingcurve using Eqs. (24)(26) in conjunction with the reported
air temperature and commodity size. Based on information
from the heat transfer literature[42], the exponent,n, in Eq.
(26), was set at 0.3. Using the Data Analysis TookPak
available in the Microsoft Excel software package [43],
regression analysis was performed on the collective
logNuPr20:3 vs. log(Re) data for a particular food item.
This regression analysis yielded the constant C and the
exponentm in Eq. (26).
The resulting Nusselt Reynolds Prandtl correlations
are summarized inTable 2and plotted inFigs. 3 11.Table
2 also gives the level of significance, F-statistic, and the
coefficient of determination, r2, for the correlations.
Generally, a significance level less than 0.05 indicates thatthe correlation represents the data significantly better than
the mean. The coefficient of determination,r2, indicates the
proportion of variation in log(NuPr20.3) explained by the
variation in log(Re).
6. Conclusions
This study was initiated to resolve deficiencies in heat
transfer coefficient data for food cooling and/or freezing
processes. Members of the food refrigeration industry were
contacted to collect cooling curves and surface heat transfer
data. In addition, a literature search was performed to collectcooling curves as well as surface heat transfer data for
Fig. 11. NusseltReynoldsPrandtl correlation for packaged trayed entrees. Packaging consists of either an aluminum tray, a plastic tray, an
aluminum tray with paper lid, a plastic tray with film lid, a paper tray with paper lid, or a paper tray with plastic lid.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551 549
-
8/13/2019 Coeficiente Convectivo Articulo
11/12
various food items. Techniques to determine surface heat
transfer coefficients from cooling curves were also collected
and reviewed.
A unique iterative algorithm was developed to estimate
the surface heat transfer coefficients of irregularly shaped
food items based upon their cooling curves. This algorithm
utilizes the concept of equivalent heat transfer dimension-
ality to extend to irregularly shaped food items existing
techniques for the calculation of the surface heat transfer
coefficient, previously applicable to only regularly shaped
food items.
Making use of this algorithm, 777 heat transfer
coefficients for 295 different food items were calculatedfrom the cooling curves collected during the industrial
survey. An additional 144 surface heat transfer coefficients
were collected from the literature for 13 different food
items. Nine Nusselt Reynolds Prandtl correlations were
developed from a selection of this data. As shown by their
level of significance and coefficient of determination,
reported in Table 2, these nine correlations satisfactorily
represent the experimental data. The NusseltReynolds
Prandtl correlations given for cake, chicken breast, fish
fillets, fried potato patties and pizza were found to be more
representative of the data than the correlations given for beef
patties, cheese, sausage and trayed entrees.
The data and correlations resulting from this project will
be used by designers of cooling and freezing systems for
foods. This information will make possible a more accurate
determination of cooling and freezing times and correspond-
ing refrigeration loads. Such information is important in the
design and operation of cooling and freezing facilities and
will be of immediate usefulness to engineers involved in the
design and operation of such systems.
References
[1] Dincer I. Heat-transfer coefficients in hydrocooling of
spherical and cylindrical food products. Energy 1993;18(4):
33540.
[2] Alhamdan A, Sastry SK, Blaisdell JL. Natural convection heat
transfer between water and an irregular-shaped particle. Trans
ASAE 1990;33(2):6204.
[3] Ansari FA. A simple and accurate method of measuring
surface film conductance for spherical bodies. Int Commun
Heat Mass Transfer 1987;14(2):22936.
[4] Chen SL, Yeh AI, Wu JSB. Effects of particle radius, fluid
viscosity and relative velocity on the surface heat transfer
coefficient of spherical particles at low Reynolds numbers.
J Food Engng 1997;31(4):47384.
[5] Clary BL, Nelson GL, Smith RE. Heat transfer from hams
during freezing by low-temperature air. Trans ASAE 1968;
11(4):4969.
[6] Cleland AC, Earle RL. A new method for prediction of surface
heat transfer coefficients in freezing. Bull De LInstitut Int Du
Froid 1976;1:3618.
[7] Daudin JD, Swain MVL. Heat and mass transfer in chilling
and storage of meat. J Food Engng 1990;12(2):95115.
[8] Dincer I. A simple model for estimation of the film coefficients
during cooling of certain spherical foodstuffs with water. Int
Commun Heat Mass Transfer 1991;18(4):43143.
[9] Dincer I, Yildiz M, Loker M, Gun H. Process parameters for
hydrocooling apricots, plums, and peaches. Int J Food Sci
Technol 1992;27(3):34752.
[10] Dincer I. Heat transfer coefficients for slab shaped products
subjected to heating. Int Commun Heat Mass Transfer 1994;
21(2):30714.
[11] Dincer I. Development of new effective Nusselt Reynolds
correlations for air-cooling of spherical and cylindrical
products. Int J Heat Mass Transfer 1994;37(17):27817.[12] Dincer I. Surface heat transfer coefficients of cylindrical food
products cooled with water. Trans ASME, J Heat Transfer
1994;116(3):7647.
[13] Dincer I, Genceli OF. Cooling process and heat transfer
parameters of cylindrical products cooled both in water and in
air. Int J Heat Mass Transfer 1994;37(4):62533.
[14] Dincer I. An effective method for analysing precooling
process parameters. Int J Energy Res 1995;19(2):95102.
[15] Dincer I. Effective heat transfer coefficients for individual
spherical products during hydrocooling. Int J Energy Res
1995;19(3):199204.
[16] Dincer I. Development of new correlations for forced
convection heat transfer during cooling of products. Int J
Energy Res 1995;19(9):791801.
[17] Dincer I. Determination of heat transfer coefficients forspherical objects in immersing experiments using temperature
measurements. In: Zabaras N, Woodbury KA, Raynaud M,
editors. Inverse problems in engineering: theory and practice.
New York: American Society of Mechanical Engineers; 1995.
p. 23741.
[18] Dincer I, Genceli OF. Cooling of spherical products: part 1
effective process parameters. Int J Energy Res 1995;19(3):
20518.
[19] Dincer I, Genceli OF. Cooling of spherical products: part 2
heat transfer parameters. Int J Energy Res 1995;19(3):21925.
[20] Dincer I. Development of a new number (the dincer number)
for forced-convection heat transfer in heating and cooling
applications. Int J Energy Res 1996;20(5):41922.
[21] Dincer I, DostS. New correlations for heat transfer coefficients
during direct coolingof products.Int J Energy Res 1996;20(7):58794.
[22] Dincer I. New effective Nusselt Reynolds correlations for
food-cooling applications. J Food Engng 1997;31(1):5967.
[23] Flores ES, Mascheroni RH. Determination of heat transfer
coefficients for continuous belt freezers. J Food Sci 1988;
53(6):18726.
[24] Frederick RL, Comunian F. Air-cooling characteristics of
simulated grape packages. Int Commun Heat Mass Transfer
1994;21(3):44758.
[25] Khairullah A, Singh RP. Optimization of fixed and fluidized
bed freezing processes. Int J Refrigeration 1991;14(3):
17681.
[26] Kondjoyan A, Daudin JD. Heat and mass transfer coefficients
at the surface of a pork hindquarter. J Food Engng 1997;32(2):
22540.
[27] Kopelman I, Blaisdell JL, Pflug IJ. Influence of fruit size and
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551550
-
8/13/2019 Coeficiente Convectivo Articulo
12/12
coolant velocity on the cooling of jonathan apples in water and
air. ASHRAE Trans 1966;72(1):20916.
[28] Mankad S, Nixon KM, Fryer PJ. Measurements of particle
liquid heat transfer in systems of varied solids fraction. J Food
Engng 1997;31(1):933.
[29] Smith RE, Bennett AH, Vacinek AA. Convection film
coefficients related to geometry for anomalous shapes. Trans
ASAE 1971;14(1):447. see also p. 51.
[30] Stewart WE, Becker BR, Greer ME, Stickler LA. An
experimental method of approximating effective heat transfer
coefficients for food products. ASHRAE Trans 1990;96(2):
1427.
[31] Vazquez A, Calvelo A. Gas particle heat transfer coefficient in
fluidized pea beds. J Food Process Engng 1980;4(1):5370.[32] Vazquez A, Calvelo A. Gas-particle heat transfer coefficient
for the fluidization of different shaped foods. J Food Sci 1983;
48(1):1148.
[33] Verboven P, NicolaBM, Scheerlink N, De Baerdemaeker J.
The local surface heat transfer coefficient in thermal food
process calculations: a cfd approach. J Food Engng 1997;
33(1):1535.
[34] Zuritz CA, McCoy SC, Sastry SK. Convective heat transfer
coefficients for irregular particles immersed in non-Newtonian
fluid during tube flow. J Food Engng 1990;11(2):15974.
[35] Arce J, Sweat VE. Survey of published heat transfer
coefficients encountered in food refrigeration processes.
ASHRAE Trans 1980;86(2):23560.
[36] Cleland AC. Food refrigeration processes: analysis, design and
simulation. London: Elsevier Science; 1990.
[37] Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed.
London: Oxford University Press; 1980.
[38] Cleland AC, Earle RL. A simple method for prediction of
heating and cooling rates in solids of various shapes. Int J
Refrigeration 1982;5(2):98106.
[39] Lin Z, Cleland AC, Serrallach GF, Cleland DJ. Prediction of
chilling times for objects of regular multi-dimensional shapes
using a general geometric factor. Refrigeration Sci Technol
1993;3:25967.
[40] Lin Z, Cleland AC, Cleland DJ, Serrallach GF. A simplemethod for prediction of chilling times for objects of two-
dimensional irregular shape. Int J Refrigeration 1996;19(2):
95106.
[41] Lin Z, Cleland AC, Cleland DJ, Serrallach GF. A simple
method for prediction of chilling times: extension to three-
dimensional irregular shapes. Int J Refrigeration 1996;19(2):
10714.
[42] Holman JP. Heat transfer, 8th ed. New York: McGraw Hill;
1997.
[43] Microsoft Corporation, Excel Software, One Microsoft Way,
Redmond, WA 98052-6399, USA.
B.R. Becker, B.A. Fricke / International Journal of Refrigeration 27 (2004) 540551 551