Thermal analysis of strawberry preservation by cooling and freezing
Adrian-Gabriel Ghiausa, Catalina Vasilescua
a
Technical University of Civil Engineering, Bucharest, Romania ([email protected])
ABSTRACT
Providing a healthy diet of the population requires a large consumption of fresh fruit and vegetables
throughout the year. Seasonal and perishable nature of these and especially of the strawberries, make them
difficult to commercialize outside the harvest period. Different conservation methods and techniques are used
to maintain the quality of the fresh product for the out of season. The cooling and freezing are the most
common methods used for strawberries conservation. The objective of this study is to investigate the
mechanisms through which different parameters affect the rate and uniformity of cooling. The thermal
behavior of the strawberries is analyzed along with the technology used for this process.
The evolution of temperature field inside the product is predicted for different operating conditions by
numerical simulation using the software package COMSOL Multiphysics based on finite element method.
The evolution of temperature in characteristic points of the considered domain is presented as function of
time. The temperature distribution in different sections is analyzed and the optimum cooling solution is
proposed for the specific case considered. The analysis and the interpretation of the results lead to the
functional parameters optimization and the choice of the cooling system to obtain a quality cooled product.
Keywords: strawberries, cooling, finite element method
INTRODUCTION
Healthy diet for the population requires large consumption of fresh fruit and vegetables throughout the year.
Their seasonal and perishable features, especially in the case of strawberries, make them difficult to
commercialize outside the harvest period. Therefore, different conservation methods and techniques are used
aiming to maintain, as much as possible, the properties of the fresh product and to achieve a high quality final
product for the out of the season. Cooling and freezing are the most common conservation methods used for
strawberries to enjoy their sweet taste all year round.
The objective of this study is to investigate the influence of the heat transfer mechanisms that affect the
cooling rate and uniformity of temperature distribution inside the cooling product. The temperature field
inside the strawberries is analyzed for cooling processes using natural and forced convection, conduction and
radiation.
MATERIALS & METHODS
The time depending temperature field inside the strawberry was numerically simulated using the COMSOL
Multiphysics commercial software package which is based on finite element method. The Heat Transfer
module was used to simulate different ways of heat transfer, e.g. conduction, convection and radiation as well
as combination between them.
The differential equation of the transient heat conduction is used for the calculation of the temperature
distribution in the product [1]:
∂t
k
2
=
∇ t
(1)
∂τ
ρ cp
where t is the temperature, τ is the time, k is thermal conductivity, ρ is the density and cp is the specific
heat. The solution of this differential equation is found based on finite element method.
Heat transfer from the product surface to the cooling room air is made by natural or forced convection and it
is based on the Newton law:
q& = hcv t p − t f
(2)
(
)
where
q& is the heat flux, hcv is the convection heat transfer coefficient, t p is the temperature of the
product surface and t f is the temperature of the cooling air.
When the radiation is used as additional source for cooling, the radiant heat flux is calculated based on the
Stefan-Boltzmann law:
q& pr = ε pr σ o ϕ pr S p T p − Tr
(3)
(
)
where ε pr is the reciprocal emissivity between the product and radiant surface, σ o is the constant of
Stefan-Boltzmann, ϕ pr is the form factor, T p and Tr are the absolute temperatures of the product and
radiant surface.
A 2D geometry of one piece strawberry fruit is created using the drawing tools from COMSOL Multiphysics.
Boundary conditions were imposed for each specific surface of the berry according to the analyzed cooling
system. A non-uniform mesh consisting of 2076 triangle elements has been generated.
The strawberries are arranged on trays that are placed on a support which
can be made by different materials.
Initially, the products are at the temperature of 20 °C and they are
introduced in a cooling room where the air temperature is maintained
constant at the value of 0 °C using a refrigerant that is evaporated.
It is assumed that the product is homogenous and the thermophysical
properties are constant: thermal conductivity, k is 1.1 W/m·K, density, ρ
is 800 kg/m3 and the specific heat, cp is 4000 J/kg·K [2].
The product is progressive cooled from its surface to the interior. Inside
the product, the heat is transferred by conduction and the heat is released
at the surface of the product, depending on the cooling system chosen,
Figure 1. Simulation grid
with natural or forced convection coupled with conduction or/and
radiation.
Depending on the heat transfer method, the following cases have been studied:
Case I: Cooling by natural convection
The product is placed on a support made by a good insulation material and no heat transfer occurs between
the support and the product. The cooling is done with natural convection with the ambient air with the
temperature of 0 ºC. At this level of temperature, the literature indicates the average value of the convection
heat transfer coefficient is equal to 5 W/m2K [2].
Case II: Cooling by forced convection
The product is cooled by a horizontal cooling air flow and no heat transfer occurs between the support and
the product. The air velocity is increased and makes the value of the convection heat transfer coefficient to
rise to 9 W/m2K.
Case III: Cooling by natural convection and radiation
The product is cooled by the ambient air from the cooling room and by a superior radiant panel.
Case IV: Cooling by conduction and natural convection
The product is cooled by the air from the cooling room supplementary by the support. In this case, there is a
heat transfer between the support and the product. The support is cooled by a cooling fluid with the
temperature of -3 °C.
Case V: Cooling by conduction, natural convection and radiation
The product is cooled by the air from the cooling room and also by the support and by a superior radiant
panel.
Case VI: Cooling by conduction, forced convection and radiation
The product is cooled by a horizontal cooling air flow and also by the support and by a superior radiant
panel.
RESULTS & DISCUSSION
The temperature distribution in the product during the cooling process of product is presented below. The
variation of temperature during the cooling process is presented in two characteristics points, A and B: at the
surface of the top of the product and in the middle of the product, respectively.
The temperature distribution in the cooled product after 4 hours and 10 minutes is presented in Figures 2-4. It
can be seen that the surface temperature is lower at the top and increases slightly to the bottom.
Figure 2 presents the distribution of the temperature in the product for the cooling by the natural convection.
The temperature distribution is symmetrical and temperature difference between the lowest temperature and
the highest temperature of the product is 0.3 K. The distribution of the temperature in the product cooled by
forced convection is unsymmetrical (Figure 3). When the radiation is supplementary introduced with the
natural convection, after the same time period, the average temperature of the product is with cca. 1.9 K
smaller than in the simple case with natural convection.
A
A
A
B
B
B
Figure 2. Temperature distribution in
case I
Figure 3. Temperature distribution in
case II
Figure 4. Temperature distribution in
case III
B
B
B
A
A
Figure 5. Temperature variation for
natural convection cooling
Figure 6. Temperature variation for
forced convection cooling
A
Figure 7. Temperature variation for
natural convection and radiation cooling
Figure 8 presents the distribution of temperature in the case of cooling with conduction and natural
convection after 2 hours, 46 minutes and 40 seconds. In this situation, the temperature difference between the
top and the bottom is 0.7 K. It can be seen that, in contrast to the first cases, the surface temperature is higher
at the top and decreases slightly to the bottom.
Figures 9-10 present the cooling of the product when all the mechanisms of heat transfer are used after 1
hour. It can be observed that the distribution of the temperature in Figure 9 is symmetrical because of the
natural convection. In Figure 10 the distribution of temperature is unsymmetrical because of the presence of
the forced convection.
Figures 11-13 indicates temperature variation during the cooling time. In contrast with the first cooling cases
that don’t use conduction, the cooling time is reduced and the temperature in middle of the product becomes
slightly lower than the temperature at the top of the product surface. After 1 hours of cooling the average
temperature of the product is around the 0 °C.
A
A
A
B
B
B
Figure 8. Temperature distribution
in case IV
Figure 9. Temperature distribution
in case V
A
A
B
B
Figure 11. Temperature variation for
conduction and natural convection
cooling
Figure 10. Temperature distribution
in case VI
Figure 12. Temperature variation for
conduction, natural convection and
radiation cooling
A
B
Figure 13. Temperature variation for
conduction, forced convection and
radiation cooling
The analysis of the temperature distribution at different time intervals leads to the optimization of the
operating parameters and the choice of the cooling system in order to obtain high quality cooled product.
CONCLUSION
A simulation of the cooling process of strawberry was performed with the software package COMSOL
Multiphysics that is based on finite element method. The cooling of the product was studied when different
heat transfer mechanisms are used: conduction, convection and radiation.
The results revealed that a significant influence has the cooling by conduction. When this mechanism of heat
transfer is presented, the cooling time is significantly reduced and the temperature in middle of the product is
slightly lower than the temperature at the top of the product.
REFERENCES
[1] Ghiaus A.-G., 2003, Heat Transfer, Editura Conspress, Bucharest
[2] ASHRAE, 2006, Refrigeration
[3] Ghiaus A.-G., Vasilescu C., 2010, The analysis of strawberries freezing methods and systems with numeric
simulations, The Conference of the Building Services Faculty, 18-19 March
[4] Ferrua M. J., Singh R. P., 2009, Design guidelines for the forced-air cooling process of strawberries, International
Journal of Refrigeration 32, 1932-1943,
[5] Guemes D. R:, Pirovani M. E., Di Pentima J. H., 1989, Heat transfer characteristics during air precooling of
strawberries, International Journal of Refrigeration, Vol. 12, May.