International Journal of Materials, Mechanics and Manufacturing, Vol. 2, No.

4, November 2014

Mathematical Modeling of Food Freezing in Air-Blast

Freezer
Guiqiang Wang and Pinghua Zou

AbstractA mathematical model for simulating the heat II. MATHEMATICAL MODEL
transfer during food freezing was presented. The model consists
of three steps. First, the flow field inside the freezing chamber A. CFD Modeling of Flow Field in Freezing Chamber
was modeled using the CFD method, based on which the
The food products are always frozen to -15 in an air-blast
freezing condition, including the temperature and velocity
around the food, was calculated. Second, the heat transfer freezer in typical freezing process, in which air is cooled
coefficient between food and air was calculated in the CFD down and forced to circle by air cooler. The geometry of
model. Third, a finite-difference model was employed to freezer studied in this paper was show in Fig. 1. Food
simulate the heat transfer inside the food product. products were placed at the center of the freezer.
Measurements were conducted on different food products in
freezing chamber to verify the mathematical model. The effects
of process parameters on food freezing were also analyzed,
which concludes that the air temperature has more influence on
food freezing than the air velocity.

Index TermsAir-blast freezer, food freezing, package.

I. INTRODUCTION
Fig. 1. Geometry of air-blast freezer.
Cooling and freezing are effective ways to preserve food
products, among which air-blast is the most commonly used A steady state simulation was conducted on the air phase to
method. In air-blast freezer the temperature of product is model airflow patterns and the heat transfer with products
reduced by the heat conduction inside the product while inside the freezing chamber. The model was valid under the
convective heat transfer takes place at the product surface. assumption that the heat transfer coefficient was constant
Meanwhile water from inside diffuses towards the surface to during the freezing period. If the natural convection was taken
make up for evaporation which results from the convective into account in the above model, the heat transfer coefficient
moisture transfer to air if the product is unwrapped [1]. The would change with the airflow patterns. However, the effects
intensity of the phenomenon depends on air temperature, of natural convection could be ignored for the air velocity
relative humidity and flow field around the food product [2]. higher than 0.5 m/s, which is the fact in air-blast freezer [1].
Both heat and moisture transfer are affected by airflow The natural convection also tends to make the model slow to
characteristics, product shape and arrangement, which converge and sometimes unstable [6].
actually determine the heat and mass transfer coefficients. For The Fluent enhanced wall treatment was used on the
products with curved surface, flow separation occurs leading product side in order to calculate the heat transfer coefficient
to wake formation, in which case transfer coefficients cannot accurately. A non-uniform structured mesh was constructed
be calculated by analytical solutions, and numerical method with a higher resolution near the surface of product, where the
need to be used [3]. CFD appears as an powerful tool for mesh need to be fine enough to solve the heat transport
simulating the flow field and calculating the transfer equations down to the laminar sub-layer(y+=1).
coefficients around food product [4][6].
B. Heat Transfer Coefficient Calculation
The aim of the current work was to model the heat transfer
of food freezing and analyze the effects of freezing condition To model the heat transfer between food and air, the
on food freezing. The model was then validated using temperature of food surface was assumed to be constant,
freezing experiments on food products with different which has been proved to be an effective way. The
packages. temperature profile in the air control volume next to the
surface was used to calculate the surface heat flux qconv[1]:

qconv ka (Ts Tc ) / ds (1)

where ka is the thermal conductivity of air, Ts is the surface

Manuscript received February 17, 2014; revised April 5, 2014. This work temperature of food, and Tc is the temperature of air control
was supported in part by the Heilongjiang Municipal Natural Science volume next to the food surface.
Foundation. Then the convective heat flux qconv was used to calculate
Guiqiang Wang and Pinghua Zou are with the Harbin Institute of
Technology, Harbin, 150090 China (e-mail: wgq_hit@126.com). the local surface heat transfer coefficients ht as follows:

DOI: 10.7763/IJMMM.2014.V2.142 278

 International Journal of Materials, Mechanics and Manufacturing, Vol. 2, No. 4, November 2014

ht qconv / (Ts Ta ) (2) analyze the influence of air parameters on freezing time and
freezing speed. The freezing speed is the ratio between the
where Ta is the air temperature of main stream. minimum distance from the surface to the thermal center and
The local surface heat transfer coefficients along the air the time elapsed between the surface reaching 0 and the
blast direction were shown in Fig. 2. thermal center reaching 5 colder than the temperature of
initial ice formation at the thermal center, which was defined
by the International Institute of Refrigeration(IIR) [9].

Fig. 3. Geometry of products.

III. EXPERIMENTAL VERIFICATION

Fig. 2. Local surface heat transfer coefficients along the blow direction.
In order to verify the simulation, experiments were carried
To analyze the effects of freezing condition on food out in an air-blast freezer. During the freezing process, the
freezing, the average surface heat transfer coefficient was air-cooler fans were running all the time, and the air
taken into account. The average surface heat transfer temperature in the freezing chamber was kept between upper
coefficient can be calculated by the integration of local and lower limits. The air temperatures for the on/off control
surface heat transfer coefficients [7], and then applied in the algorithm were -26 compressor-on temperature and -16
food freezing model, as well as the air temperature calculated compressor-off temperature. Thermocouples were placed in
around the food. A series of simulations were carried out at the freezer to record the air temperature and relative humidity
different air velocities, the results of which were fitted into a every 5 minutes, which was shown in Fig. 4.
regression equation in terms of dimensionless numbers [6]:

Nu CRem Pr1/3Tu A (3)

where Nu is the Reynolds number, Pr is the Prandtl number,

Tu is the turbulence intensity of air around food. C, m, A are
empirical parameters.
C. Modeling of Food Freezing
Inside the food product, heat transfer happens throughout
the inner region of food, while only the surface region loses
water. The food products employed in the study were pork
cuts covered with plastic film inside cardboard box and iron
box. Because of the presence of film, the moisture transfer can Fig. 4. Air temperature and relative humidity in freezer.

be ignored in the simulation. The Fourier heat conduction The outlet velocity of fan was measured and averaged to be
equation applies in food product during freezing period [8]: 7.88 m/s using a hot-wire anemometer [10], which was shown
Tm in Fig. 5 and Table I.
m cm (kmTm ) qm (4)
t
where m is the density, cm is the specific capacity, and km is
the thermal conductivity of food. qm is the heat source term,
including the heat fluxes from boundaries.
To simplify the analysis, the food product was treated as
infinite slab, and an explicit finite difference scheme was used
to solve the model. Quasi-enthalpy method was used to deal
with the latent heat release, and the Kirchhoff transformation
was used to deal with the variable thermal conductivity. Full Fig. 5. The measurement points arrangement of cold fan.
details of calculation technique are given by Dawen Sun [8].
The geometry of food product can be seen in Fig. 3. At the TABLE I: THE OUTLET VELOCITY OF COLD FAN BY MEASUREMENT
presence of air layer between packaging and food, the Measure points 1 2 3 4 5 6 7
effective heat resistance of top surface of food is larger than Velocity(m/s) 12.9 5.3 3.3 5.6 9.3 9.7 4.2
its bottom surface, which was calculated based the type and Measure points 8 9 10 11 12 13
thickness of packaging. A series of simulations were Velocity(m/s) 4.4 9.7 6.9 12.0 11.1 8.1
conducted at different air velocities (from 0.5m/s to 4.5m/s) Average
7.88
velocity(m/s)
and different air temperatures(from -60 to -20) to

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 International Journal of Materials, Mechanics and Manufacturing, Vol. 2, No. 4, November 2014

The hot-wire anemometer was then placed at different iron box than that in carton box if 15 is considered to be the
locations in freezing chamber to measure the air velocity freezing completion temperature. Due to the control
magnitude, and was compared with the flow field predicted by algorithm, the air temperature shows a frequent fluctuation
the CFD methods. during freezing process. Little difference between supply and
Freezing experiments were performed on pork cuts packed return air temperature of air cooler is observed, which
in a rectangular carton and a cylindrical iron box to examine indicates the space uniformity of air temperature in freeing
the kinetics of food freezing. The pork cuts were wrapped in a chamber.
thin polyethylene, which has little impact on heat transfer, but Fig. 8(a) shows the effect of air parameters on freezing time,
prevents the moisture transfer. Thermocouples were placed while Fig. 8b shows that on freezing speed. As the air velocity
inside the products to measure the temperature in different increases, freezing time decreases relatively. That influence
depths, including the temperature of air gap, as shown in Fig. becomes slighter and slighter as the air velocity increases. The
3. The freezing process involves cooling down the food same trend can be seen on the influence of air temperature,
products from 10 to -15. During freezing process, which shows a more significant impact than air velocity. For
thermocouples were placed at different locations inside the the freezing speed, the air velocity has a reverse impact, as
food products, which was shown in Fig. 3. Temperatures was well as the air temperature. Except that the freezing speed
recorded every 10 minutes. decreases almost linearly as the air temperature increases,
which indicates that decreasing the air temperature has little
impact on freezing time when the air temperature is low
IV. RESULTS AND DISCUSSION enough, but is still meaningful to increase the freezing speed.
Fig. 6 shows the modeling result of flow field in the
air-blast freezer. The velocity magnitude shows a good
agreement with measured data. The flow field shows a large
circumfluence with small velocity in the center of the flow
field, and may lower the freezing speed of food. The velocity
magnitude ranges from 0.5m/s to 5m/s, which may causes
local differences of freezing process when there are numbers
of food products in the freezing chamber.

(a) Effects of air parameters on freezing time.

Fig. 6. Flow field predicted by CFD model.

(b) Effects of air parameters on freezing speed.

Fig. 8. Effects of air parameters on food freezing.

V. CONCLUSIONS
A modeling on flow field in freezing chamber was achieved
using CFD code, which fits well with the experimental results.
The surface heat transfer coefficient was calculated and fitted
into a regression equation. Finally the simulation on food
freezing was conducted, which shows a significant effect of
Fig. 7. Comparison of measured and simulated temperature. packaging material. The influences of air temperature and
velocity on freezing were analyzed. Air velocity has less
The measured and simulated center temperatures of food effect on freezing as the velocity increases. The effect of air
with two types of packaging are plotted in Fig. 7, which show temperature on freezing time displays a similar trend, while
that both simulations fit the experimental results well. The the freezing speed increases almost linearly with the air
freezing curves in Fig. 7 illustrate a typical pattern of food temperature decreasing. For lower air temperature, it is still
freezing. Because of different geometries and packaging meaningful to decrease air temperature in order to achieve
material, it took 17 hours less to freeze the food packaged in higher freezing speed.

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REFERENCES [7] P. Verboven, B. M. Nicola, N. Scheerlinck, and J. de Baerdemaeker,

The local surface heat transfer coefficient in thermal food process
[1] F. J. Trujillo and Q. T. Pham, A computational fluid dynamic model calculations: A CFD approach, Journal of food engineering, vol. 33,
of the heat and moisture transfer during beef chilling, International no. 1, pp. 1535, 1997.
Journal of Refrigeration, vol. 29, no. 6, pp. 9981009, Sep. 2006. [8] D. W. Sun, Handbook of Frozen Food Processing and Packaging.
[2] P.-S. Mirade, A. Kondjoyan, and J.-D. Daudin, Three-dimensional CRC Press, 2012.
CFD calculations for designing large food chillers, Computers and [9] I. international du froid, Recommendations for the Processing and
Electronics in Agriculture, vol. 34, no. 13, pp. 6788, 2002. Handling of Frozen Foods., IIF = IIR, 2006.
[3] A. Kondjoyan, A review on surface heat and mass transfer [10] J. Xie, X. H. Qu, J. Y. Shi, and D. W. Sun, Effects of design
coefficients during air chilling and storage of food products, parameters on flow and temperature fields of a cold store by CFD
International Journal of Refrigeration, vol. 29, no. 6, pp. 863875, simulation, Journal of Food Engineering, vol. 77, no. 2, pp. 355363,
Sep. 2006. Nov. 2006.
[4] D.-W. Sun and Z. Hu, CFD predicting the effects of various
parameters on core temperature and weight loss profiles of cooked
Guiqiang Wang was born in 1983 in Dalian, China. He
meat during vacuum cooling, Computers and Electronics in
received his B.E degree in heating, ventilating and air
Agriculture, vol. 34, no. 13, pp. 111127, May 2002.
conditioning from Harbin Institute of Technology,
[5] Z. Hu and D. W. Sun, CFD simulation of heat and moisture transfer
China during 2003-2007, and M.E degree during
for predicting cooling rate and weight loss of cooked ham during
2007-2009 from the same University. He is currently
air-blast chilling process, Journal of Food Engineering, vol. 46, no. 3,
pursuing his Ph.D degree in Harbin Institute of
pp. 189197, Nov. 2000.
Technology, China.
[6] Q. T. Pham, F. J. Trujillo, and N. McPhail, Finite element model for
.
beef chilling using CFD-generated heat transfer coefficients,
International Journal of Refrigeration, vol. 32, no. 1, pp. 102113,
Jan. 2009.

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