This paper presents heat transfer 3-D models of a passive refrigeration system, called Icepack, used to improve the shelf life and the quality of the perishable fruits. Passive refrigerator system uses the changing phase of a material to keep temperature close to the melting temperature.
A multi-step COMSOL Multiphysics (ver 4.2a) study was performed: 
-	a 3-D heat transfer model on the empty box;
-	a 3-D heat transfer model on the box containing a slab with apparent thermal properties obtained from the air and the fruit;
-	a 3-D heat transfer model on the box filled with randomized diameter spheres, simulating the fruits, created with an original MatLab\uae script and imported in COMSOL Multiphysics\uae (ver. 3.5a).
The temperature profile inside the box and the melting time of the ice slab were studied.
Results of the models agree with experimental data. The modeled melting time of the empty Icepack gives an error of about 7%. Modeled temperature profile inside the box filled with fruits reflects real temperature profile

E. FERRARI

R. CIVELLI

S.V. MARAI

AIR Universita degli studi di Milano

Post Harvest Cold Chain Optimization of Little Fruits 
 
 
Marai S.
*1
, Ferrari E.
1
, Civelli R.
1
 
1
DiSAA, Università degli Studi di Milano 
*Corresponding author: Via Celoria, 2, 20133, Milan, Italy - email: simone.marai@unimi.it 
 
 
Abstract: This paper presents heat transfer 3-D 
models of a passive refrigeration system, called 
Icepack, used to improve the shelf life and the 
quality of the perishable fruits. Passive 
refrigerator system uses the changing phase of a 
material to keep temperature close to the melting 
temperature. 
A multi-step COMSOL Multiphysics (ver 4.2a) 
study was performed:  
- a 3-D heat transfer model on the empty box; 
- a 3-D heat transfer model on the box 
containing a slab with apparent thermal 
properties obtained from the air and the 
fruit; 
- a 3-D heat transfer model on the box filled 
with randomized diameter spheres, 
simulating the fruits, created with an 
original MatLab® script and imported in 
COMSOL Multiphysics® (ver. 3.5a). 
The temperature profile inside the box and the 
melting time of the ice slab were studied. 
Results of the models agree with experimental 
data. The modeled melting time of the empty 
Icepack gives an error of about 7%. Modeled 
temperature profile inside the box filled with 
fruits reflects real temperature profile. 
 
Keywords: heat transfer, phase change, 
perishable fruits, passive refrigerator. 
 
 
1. Introduction 
 
Little fruits like blueberries, raspberries and 
blackberries need to be refrigerated as soon as 
possible after the harvest, to preserve the 
structural integrity and the nutritional and 
organoleptic properties. In fact, removing the 
field-heat, the respiration of these fruits 
decreases and so the shelf life of the product 
improves. 
Due to the fragility of these fruits means that 
the harvest must be done manually and the filling 
phase must be as gentle as possible. All the chain 
of transport from the field to the consumer 
should not cause further damages to the product 
and so the plastic case of sell that contain the 
fruits is the same that was used during the 
harvest. 
These plastic cases, containing about 250 g 
of fruits (inconvenient transport them one by 
one), are placed inside another bigger box, 
normally a wooden box, that contain 8 plastic 
little cases.  
The refrigeration can starts immediately after 
the harvesting with a passive refrigerator system, 
a special box, called Icepack.  
The Icepack is a polystyrene box (external 
dimension: 42.5x33.5x12 cm) with a plastic 
hermetic bag filled of water (about 1.0 kg) 
placed on the bottom. Inside the Icepack is 
possible to place 8 little plastic cases as normal 
wood box. The wall thickness is 2 cm and the 
height of the plastic bag is about 1.8 cm.  The 
bag is stored at -20 ° until the moment of the use. 
The heat flux from the outside is absorbed by the 
fusion of the ice keeping the temperature inside 
the Icepack almost constant, to 0°C, for a long 
period of time. 
Another advantage of this transport system is 
in the stackability of the Icepack, that optimize 
the space occupied and the exchange surfaces 
with the external environment. 
Experimental data were taken on blueberries 
taken in Ardenno (SO), Italy, in the Fojanini 
Foundation field. 
 
 
2. Governing Equation 
 
A mathematical model based on heat transfer 
in continuous media is used to model the cooling 
of blueberries. Temperature inside each material 
is considered uniform.  
Respiration of fruits and inside convection 
was neglected because of the little internal height 
of the box (about 6 cm with the empty box) and 
presence of the cool slab of ice at the bottom of 
the Icepack. When the box is filled with plastic 
boxes with fruits, the space is occupied by these, 
so the free space for the air circulation, and then 
for the internal convection is further limited. 
 2.1 Energy conservation equation 
 
Heat transfer occurs in three different form: 
conduction, convection (only external surface) 
and latent heat of fusion of water. 
 
     
  
  
        
 
where  is the density, Cp is the specific heat and 
k is the thermal conductivity of the different 
material (see Table 1).  
Icepack contains the plastic bag filled with 
water in the phase change, so a modified specific 
heat was used. 
 
                                    
 
where the subscript w is water, lda is the latent 
heat of fusion, H is a smoothed step function of 
temperature from 0 to 1 and G is a Gaussian 
pulse centered in the fusion temperature. The 
pulse is necessary to simulate the latent heat of 
fusion (energy is absorbed while the temperature 
remains constant). The temperature range 
(defined by Gaussian pulse standard deviation) 
of the fusion is an approximation necessary 
because fusion at an exact temperature cannot be 
modeled numerically. 
Also  and k of the water are modified 
density and thermal conductivity equations, that 
consider the two phases of water: 
 
                      
 
                      
 
 
 
2.2 Boundaries conditions 
 
The boundaries conditions on air/polystyrene 
interface are: 
 
                       
 
where the subscript ext is external and h is the 
convective heat transfer coefficient 
 
2.3 Initial values and input parameters 
 
Initial temperatures are different for 
packaging material and fruits. Ice bags are put 
inside a polystyrene box to preserve their 
temperature. 
Input parameters and initial temperature are 
listed in Table 2. 
 
 
 blueberries air polystyrene ice water 
 - Density (kg/m3) 990 1.248 25 917 1000 
Cp -  Specific heat (J/kg K) 3786 1013 1200 2260 4186 
k - Thermal conductivity (W/m
 
K) 0.539 0.024 0.033 2.208 0.6 
   Table 1: characteristics of materials 
 
 
 
Parameters Value units 
Blueberries initial temperature 302.25 K 
Polystyrene initial temperature 295.15 K 
Air initial temperature 297.15 K 
Ice initial temperature 253.15 K 
lda - Latent heat of fusion 333 kJ/kg 
h - Convective heat transfer coefficient 8 W/m
2 
K 
Text - Ambient temperature 300.15 K 
Ice fusion temperature 273.15 K 
Percentage of blueberries in mixed slab 75 %  
       Table 2: initial temperatures and input parameters 
 
 3. Methods 
 
Two different type of experiment were 
performed, the first one in laboratory, on an 
empty Icepack, to study the passive refrigerator 
system in a controlled environment, the other 
one on field, to carry out operators manually 
harvest and the following trip to the collecting 
centre. 
Laboratory experiments were performed 
using T-thermocouples to monitor the 
temperature inside the Icepack in 5 different 
point: they were all put to detect the defrosting 
time of the ice slab. Icepack rests at monitored 
ambient temperature 20 hours on a table with 
inside the charge of ice. 
On field experiments were performed with 5 
stand alone temperature data logger, put under 
the ice slab, under the cover of the Icepack, 
inside the plastic case with blueberries at three 
different height: top, bottom and in the middle. 
Ice slab at 253.15K was put inside an Icepack in 
the collecting center, after about 30 minutes trip, 
on field, Icepack was filled with 8 plastic cases 
with manually harvesting fruits and then about 2 
hours trip to return to laboratory, where the box 
rests 15 hours. 
 
 
 
4. Numerical Model 
 
Three different numerical model was 
performed with COMSOL Multiphysics® (ver 
3.5a and 4.2a): 
 a 3D model of the empty Icepack to 
simulate the passive refrigerator system. 
The partial differential equations for heat transfer 
were solved using the Heat Transfer module, 
with a free time step by the solver MUMPS. The 
cooling simulation is 20 hours with a collecting 
time of 60 seconds. The mesh is automatically 
created with a normal refinement and is formed 
by 34568 elements. 
 a 3D symmetrical model of the Icepack 
filled with a 5 cm height slab with apparent 
thermal characteristics obtained from air and 
fruit. 
The partial differential equations for heat transfer 
were solved using the Heat Transfer module, 
with a free time step by the solver GMRES. The 
cooling simulation is 15 hours with a collecting 
time of 60 seconds. The mesh is automatically 
created with a normal refinement and it is 
formed by 14398 elements 
 a 3D symmetrical model of icepack filled 
with a randomize dispersion of fruits, created 
with a original Matlab® script and then imported 
in COMSOL Multiphysics®. 
The partial differential equations for heat 
transfer were solved using the Heat Transfer 
module, with a free time step by the solver 
GMRES. The cooling simulation is 15 hours 
with a collecting time of 60 seconds. The mesh is 
automatically created with a normal refinement 
and it is formed by 87271 elements 
 
 
 
4.1 Geometry   
 
The geometry of the first model consist of 3 
blocks put in the right position, that describe the 
Icepack system, the air inside the icepack and the 
ice slab. All the real geometry was drawn. 
The second geometry consist of 4 blocks put 
in the right position. These blocks describe the 
Icepack system, the air, the slab of blueberries 
and the ice. Only a quarter of the real geometry 
was drawn because of the symmetry of the 
system. 
The third geometry is created like the first 
one, but the fruits are simulated and imported 
from Matlab®. The original script consist in a 
randomized Gaussian distribution diameter of 
the fruits (sphere) experimentally determined. It 
is hypothesized that the set sizes of the plastic 
case, that contains blueberries is the resulting of 
the intersection of 5 sphere with infinite 
diameter. Each fruit have to touch three points of 
the geometry to be in equilibrium. The sphere 
that must be positioning will be placed in the 
point with less absolute potential energy. No 
overlapping between spheres is allowed. The 
loop ends when all the spheres have been 
positioned. Also in this case only a quarter of the 
real geometry was drawn because of the 
symmetry of the system. The sequence of 
randomized distribution of fruits was repeated 
two times because in a quarter of Icepack there 
are 2 plastic cases. 
 
 
5. Results and discussions 
 
The model of the empty Icepack was focused 
on the melting time of the ice slab. After a fast 
decrease of the inside temperature from ambient 
temperature due to the insertion of the ice slab in 
the box, there is an increase until it reaches the 
fusion temperature of the ice, with a constant 
value of about 273.15. The total thawing time of 
the ice slab is after 15.8 hours, and then the 
temperature rises again. The model gives about 
17 hours as thawing time, with a relative 
percentage error, calculated as 
 
  
               
    
 
 
where the subscript exp is experimental and mod 
modeled, equal to 7.6%. 
Figure 1 is the graph of compared 
temperatures (modeled and experimental) of the 
ice slab. 
 
 
Figure 1: temperature of ice slab of empty Icepack 
 
 
The model with the mixed air/blueberries 
slab was focused on thawing time of the ice slab 
and on the temperature in the warmer point 
inside the blueberries mass (the sensor in the 
middle). There is a quickly decrease of the 
measured temperature of the ice, followed by an 
increase until a plateau is reached at melting 
temperature of the ice. Total melting is about 
after 10.6 hours from the filling of the Icepack. 
The measured temperature between the 
blueberries presents a decreasing till about 283 K 
and after a slow increasing. The model simulate 
the total thawing of the ice at about 9.7 hours, 
with a relative percentage error (e) equal to 
8.5%. The quality of the simulation is given by 
the mean relative error, which is defined as: 
 
      
   
 
  
           
    
 
 
 
   
 
 
where n is the number of experimental 
observations. The calculated em of the central 
probe is 1.06%. Figure 2 shows the graph of 
temperatures (modeled and experimental) of the 
ice slab and of the blueberries  
 
 
Figure 2: temperature profiles of ice and blueberries in 
the slab model 
 
 
The model simulating fruits with sphere was 
focused on melting time of the ice slab and on 
the temperature distribution inside the 
blueberries mass, improving the slab model 
results. 
The simulated melting time is very close to 
the real thawing time, with a relative percentage 
error close to 0. The mean relative error (em) of 
the central probe (blueberries mass) is 0.43%, 
about half of the error from the slab model. 
Figure 3 shows the temperature profiles of 
simulated fruits model and experimental data 
 
 
Figure 3:temperature profiles of ice and blueberries in 
the simulated fruits model 
 
260 
270 
280 
290 
300 
310 
0 5 10 15 20 
T
em
p
er
at
u
re
 (
K
) 
 
Time (h) 
Experimental data Model 
260 
270 
280 
290 
300 
310 
0 5 10 15 
T
em
p
er
at
u
re
 (
K
) 
Time (h) 
model ice  
model blueberries 
experimental ice 
experimental blueberries 
260 
270 
280 
290 
300 
310 
0 5 10 15 
T
em
p
er
at
u
re
 (
K
) 
Time (h) 
model ice  
model blueberries 
experimental ice 
experimental blueberries 
  
 
 
 
6. Conclusions 
 
The finite element models were developed to 
investigate the temperature profile inside the 
Icepack and the cooling of blueberries from 
immediately after harvest to 15 hours later. The 
models predictions were validated with 
experimental measurements. 
Future improvement of this models is under 
way, which will deal with the optimization of the 
geometry of the Icepack. The time from the 
harvest on field to the collecting center with the 
refrigerated rooms is about 6 hours, so it is 
possible to reduce the weight of the packaging 
reducing the ice slab height. Stackability of 
Icepack is also studied, to improve melting time 
of ice slab. 
 
 
 
7. Acknowledgements 
 
The authors thank Miss Valentina 
Giovenzana and Mr Roberto Beghi for their 
contribution to this study. 
 


POST HARVEST COLD CHAIN OPTIMIZATION OF LITTLE FRUITS

https://air.unimi.it/retrieve/handle/2434/235474/314234/paper%20Post%20harvest.pdf

POST HARVEST COLD CHAIN OPTIMIZATION OF LITTLE FRUITS

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