Abbasnezhad Et Al-2015-Food Science Nutrition
Abbasnezhad Et Al-2015-Food Science Nutrition
Abbasnezhad Et Al-2015-Food Science Nutrition
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Keywords Abstract
Egg, heat transfer, numerical modeling,
pasteurization, Salmonella enteritidis, Thermal Pasteurization of Eggs, as a widely used nutritive food, has been simu-
thermophysical properties lated. A three-dimensional numerical model, computational fluid dynamics codes
of heat transfer equations using heat natural convection, and conduction mecha-
Correspondence nisms, based on finite element method, was developed to study the effect of
Behzad Abbasnezhad, Department of
air cell size and eggshell thickness. The model, confirmed by comparing experi-
Food Science and Technology, Faculty of
Agriculture, Isfahan University of Technology,
mental and numerical results, was able to predict the temperature profiles, the
Isfahan 84156-83111, Iran. slowest heating zone, and the required heating time during pasteurization of
Tel: +983133913428; Fax: +983133912254; intact eggs. The results showed that the air cell acted as a heat insulator. In-
E-mail: B.abasnezhad@ag.iut.ac.ir creasing the air cell volume resulted in decreasing of the heat transfer rate, and
the increasing the required time of pasteurization (up to 14%). The findings
Funding Information show that the effect on thermal pasteurization of the eggshell thickness was not
No funding information provided.
considerable in comparison to the air cell volume.
Received: 6 January 2015; Revised: 8 June
2015; Accepted: 17 June 2015
doi: 10.1002/fsn3.257
© 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc. 1
This is an open access article under the terms of the Creative Commons Attribution License, which permits use,
distribution and reproduction in any medium, provided the original work is properly cited.
Numerical Modeling of Heat Transfer and Pasteurizing B. Abbasnezhad et al.
using analytical and numerical solutions of partial dif- shown in Figure 1. The meshing was done in the
ferential equations governing the process (Kızıltaş et al. “Uniform” trigonal type. The total count of trigonal
2010). For realistic and more complicated heat transfer elements was 288186.
problems usually no analytic solution is available, and
a numerical solution becomes mandatory (Ruiz-Cabrera
Assumptions of the model
et al. 2014).
Thermal pasteurization of intact eggs has been studied The egg is placed into a water bath and its surface
vastly to decrease microbial population and to increase directly exposed to hot water, and heated by natural
the shelf life, in recent years (Hou et al. 1996; Coimbra convection. The heating of the surface creates a tem-
et al. 2006; Denys et al. 2004; Ferreira et al. 1997; perature gradient, which is the origin of the driving force
Koen et al. 2007). Computational fluid dynamics (CFD) behind the heat transfer in the egg toward the center.
has been used to study heat transfer in various food Heat transfer inside the shell can be treated as heat
processes (Koen et al. 2007; Barbosa- Cánovas et al. conduction.
2011; Erdogdu et al. 2007; Ghani et al. 2001; Juliano In order to simplify the problem, the following
et al. 2011; Mahesh and Kannan 2006; Norton and assumptions were considered:
Sun 2006). Denys studied heat transfer and velocity
profiles of egg shells filled with viscous liquids. The 1. Egg white and yolk are homogeneous and isotropic dur-
slowest heating point (SHP) was reported to be about ing pasteurization.
the geometrical center of the samples (Denys et al. 2. The initial temperature is constant and same in all
2004). Denys developed a model based on CFD and eggs.
experimental estimation tools to calculate surface heat 3. Thermophysical properties were used as functions of
transfer coefficient of eggs (Denys et al. 2003). temperature, excluding the volumetric thermal expansion
Ramachandaran developed a three-dimensional model coefficient and specific heat.
to simulate the thermal pasteurization of eggs in sta- 4. Viscous dissipation was neglected because of low shear
tionary and rotational conditions of heat treatment. rates.
The results showed that rotation of eggs highly de- 5. No-slip boundary condition was assumed for velocity
creased the time needed for thermal treatment components relative to boundaries.
(Ramachandran et al. 2011). Fabbri studied thermal 6. The natural convectional flow of fluid was assumed in
pasteurization of eggs in hot air currents, using CFD the gravitational direction.
modeling. They also included the air cell of eggs in 7. The moisture transfer was neglected during the
the model. The results showed that air cells have heat process.
resistant characteristics (Fabbri et al. 2012). However,
to our knowledge, no previous researchers have
developed a general model for eggs pasteurization
Model Development
2 © 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc.
B. Abbasnezhad et al. Numerical Modeling of Heat Transfer and Pasteurizing
Governing equations Ts is the water bath temperature that was 333 for heat-
ing part.
Partial differential equations, related to governing natural
Initially the egg yolk and white were at rest and at a
convection motion of fluids (Navier stokes equations),
uniform temperature
and heat transfer phenomenon (energy equation) in a
three-dimensional x, y, and z coordinate system, are pre- T = Ti , u = 0, v = 0 at 0 ≤ r ≤ R, 0 ≤ z ≤ H. (9)
sented as (Ramachandran et al. 2011; Denys et al. 2003):
The yolk wall was given as a coupled wall to the egg
Continuity equation:
white for uniform heating.
𝜕ux 𝜕uy 𝜕uz
+ + =0 (1) Pasteurizing value (F) calculation
𝜕x 𝜕y 𝜕z
Momentum equation: The purpose of this calculations is to arrive at an appropri-
ate process time under a given set of heating conditions to
( )
𝜕𝜌V result in a given process lethality, or alternately to estimate
+ ▿.𝜌V ⊗ V = ▿.(−p𝛿 + 𝜇(▿V + (▿V)t )) + SM (2)
𝜎t the process lethality of a given process. In order to charac-
Energy equation: terize the effect of temperature evolution on micro-organism
( ) destruction at a given location during pasteurization, the
𝜕T 𝜕T 𝜕T 𝜕T 𝜕2 T 𝜕2 T 𝜕2 T so-called pasteurizing value (F) can be calculated:
+ ux + uy + uz =∝ + + (3)
𝜕t 𝜕x 𝜕y 𝜕z 𝜕x2 𝜕y2 𝜕z2 t
∫0
where u (m/s) is the velocity, p (Pa) is pressure, ρ (kg/ F= 10(T−Tref )∕Z dt (10)
m3) is the density, μ (m2/s) is the kinematic viscosity of
the fluid, and g (m/s2) is the gravitational acceleration where Tref is 60°C and Z is 4.08°C, based on the thermal
acting in the negative z-direction, and α (m2/s) is the resistance of Salmonella enteritidis. A 5D inactivation of
thermal diffusivity. To consider buoyancy, the force driv- the mentioned microorganism (Dvalue = 0.17) is assumed
ing the convective motion of the egg white is the gravi- to be a good thermal process (Hema 2011; American Egg
tational force comprised in the equations, and the variation Board, 2012).
of the density with temperature is expressed using the
Boussinesq approximation that was very accurate to model Model parameters
the natural convection during thermal processing of egg The inputs of the mathematical model are as follows: the
bodies. water bath temperature was constant, product dimensions,
SM = 𝜌g (4) density, component mass fractions, surface heat transfer
coefficient of egg, initial product temperature, number of
𝜌 = 𝜌ref [1 − 𝛽(T − Tref )] (5) nodes in the space, heating and cooling, and time of
where Tref (°C) and ρref (kg/m3)
are the reference tem- pasteurization. Based on these inputs, the model will de-
perature and corresponding density, respectively, and β termine values of temperature at each node for each time
(1/K) is the volumetric thermal expansion coefficient of step. The thermophysical properties used in the model
the liquid. are shown in Table 1.
The dimensionless Rayleigh number, which measures
Numerical solution of the model
the strength of buoyancy driven flows, was calculated. The
Rayleigh number was lower than 108 and showed laminar In this study, the resulting system of the above partial
flow behavior during the process. (Erdogdu et al. 2007). differential equations were solved by the “finite element”
method by COMSOL Multiphysics 3.5a (COMSOL Inc.,
Burlington, MA). The solution of the equations was obtained
Initial and boundary conditions in the “Direct UMFPACK” mode and time intervals were
Yolk and white interface, set with the help of the algorithm present in the software.
T = Ts , u = 0, v = 0 for 0 ≤ r ≤ R. (6) The total process time was 2000 s and time step was 1 s.
Maximum relative error of 10−3 was selected as the criterion
Outside of eggshell, for convergence relative to the tolerance window.
= 0 v = 0 for 0 ≤ z ≤ H.
𝜕T 𝜕u
= 0, (7)
𝜕r 𝜕r
Inside of eggshell, Experimental Methodology
= 0, u = 0 v = 0 for 0 ≤ r ≤ R.
𝜕T
(8) The experiments were carried out on intact fresh eggs.
𝜕r Eggs, not older than 3 days, bought from local stores
© 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc. 3
Numerical Modeling of Heat Transfer and Pasteurizing B. Abbasnezhad et al.
Table 1. Thermal properties of egg white, yolk, and egg shell, used in the modeling.
Value r2 Source
4 © 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc.
B. Abbasnezhad et al. Numerical Modeling of Heat Transfer and Pasteurizing
(A) (B)
(C) (D)
Figure 3. Temperature distribution of eggs having different air cell locations, during pasteurization process. (A) The air cells located at the bottom (B)
Absence of air cell (C) two air cells, on top and bottom (D) The air cells located at the top.
concluded that the assumptions applied to develop the shell, was between the geometric center of the sample
model (conductive–convective and conductive heat transfer and upper zone of the air cell, as shown in Figure 3A.
in the white and yolk, respectively, and other assumptions) Assuming the absence of air cell, the SHZ would locate
describe the heat transfer mechanisms well during egg pas- in the geometric center zone (Fig. 3B). The SHZ of the
teurization (Ramachandran et al. 2011; Denys et al. 2004). eggs with two air cells, on top and bottom, was in the
geometric center (Fig. 3C). The air cells located at the
top of the egg resulted in the displacement of the SHZ
Effect of air cell on the slowest heating zone
toward the center of the yolk (Fig. 3D).
(SHZ) and flow patterns
Figure 4 shows that the fluid in eggs is warmed up and
After validation, the developed model was used to deter- flows upward in the boundary layer near the lateral eggshell.
mine the SHZ of the egg during pasteurization. Figure 3 The warm liquid coming from the boundary layer almost
represents the results of the simulation for the intact eggs, stagnates at the top of egg. In fact, according to the mass
without and with the air cell in three different positions, balance terms, it flows slowly inward and downward. The
heated in a water bath at 60°C. As can be seen, the air area with downward flow is much greater than the area
cell is capable of influencing the heat transfer during with the upward flow as can be seen on the horizontal
thermal pasteurization of the intact eggs. The SHZ of the cross section (Figure 4). As the liquid descends, its tem-
eggs with an air cell, be located in the bottom of the perature decreases because of conduction and mixing with
© 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc. 5
Numerical Modeling of Heat Transfer and Pasteurizing B. Abbasnezhad et al.
Figure 4. White flow pattern of eggs having different positions of air cells at 50 s of the thermal process in 60°C.
6 © 2015 The Authors. Food Science & Nutrition published by Wiley Periodicals, Inc.
B. Abbasnezhad et al. Numerical Modeling of Heat Transfer and Pasteurizing
air cell volume in egg was 1680, 1770, and 1920 s, Barbosa-Cánovas, G. V., A. Ghani Albaali, P. Juliano, and
respectively. The SHP of the eggs with a medium air K. Knoerzer. 2011. Introduction to innovative food
cell was between the geometric center of the sample processing technologies: background, advantages, issues,
and the upper zone of the air cell. SHP of the eggs and need for multiphysics modeling. in Innovative food
with a minimum percent of air cell, the SHP located processing technologies: advances in multiphysics
in the geometric center zone, and the SHP of the eggs simulation. Blackwell Publishing Ltd.
with a maximum air cell volume were the upper zones Chen, C. R., and H. S. Ramaswamy. 2002. Modeling and
of the air cell. optimization of constant retort temperature (CRT)
The heating times to obtain an equal pasteurization thermal processing using coupled neural networks and
value (F60°C = 2.85 min) with different egg shell thick- genetic algorithms. J. Food Process Eng. 25:351–379.
nesses were simulated. For thicknesses of 0.175, 0.4, and Coimbra, J. S. R., A. L. Gabas, L. A. Minim, E. E. Garcia
0.25 mm, the required times were 1670, 1695, and 1710 s, Rojas, V. R. N. Telis, and J. Telis-Romero. 2006. Density,
respectively. This shows that an increase in shell thickness heat capacity and thermal conductivity of liquid egg
leads to a reduction in heat transfer and consequently products. J. Food Eng. 74:186–190.
an increase in the required heating time to achieve a Denys, S., J. G. Pieters, and K. Dewettinck. 2003. Combined
satisfactory F-value. CFD and experimental approach for determination of the
surface heat transfer coefficient during thermal processing
of eggs. J. Food Sci. 68:943–951.
Conclusions Denys, S., J. G. Pieters, and K. Dewettinck. 2004.
Computational fluid dynamics analysis of combined
A numerical model was developed to simulate 3D heat
conductive and convective heat transfer in model eggs. J.
transfer in the intact egg to predict the local temperature
Food Eng. 63:281–290.
and Fvalue during pasteurization. The model accommodates
Denys, S., J. G. Pieters, and K. Dewettinck. 2005.
the effects of air cell volume and temperature- dependent
Computational fluid dynamics analysis for process impact
variables such as density and thermal conductivity. The model
assessment during thermal pasteurization of intact eggs. J.
was validated by comparison of the experimental temperature
Food Prot. 68:366–374.
profiles during pasteurization of the egg with the predicted
Erdogdu, F., M. Ferrua, S. K. Singh, and R. Paul Singh. 2007.
values. The main results that can be drawn from this study Air-impingement cooling of boiled eggs: analysis of flow
are the following: (1) the position and size of air cells affect visualization and heat transfer. J. Food Eng. 79:920–928.
the heat transfer patterns and characteristics during egg pas- Fabbri, A., C. Cevoli, and A. Giunchi. 2012. Validation of a
teurization; (2) the thickness of the eggshell affects the re- simplified numerical model for hot-air treatment of egg
quired pasteurization time; (3) the effect of eggshell thickness shell surface. J. Food Process Eng. 35:695–700.
on the required pasteurization time was less than the air Ferreira, M., C. Hofer, and A. Raemy. 1997. A calorimetric
cell volume; and (4) the model is useful to describe the study of egg white proteins. J. Therm. Anal. 48:683–690.
heat transfer phenomenon during egg pasteurization. Ghani, A. G. A., M. M. Farid, X. Chen, and P. Richards. 2001.
Thermal sterilization of canned food in a 3-D pouch using
Conflict of Interest computational fluid dynamics. J. Food Eng. 48:147–156.
Hema, A. L. A. 2011. Effect of different pasteurization
The authors do not have any conflict of interest. methods of egg in shell on survival of Salmonella
enteritidis, in Foreign Agricultural Relations (FAR): Egypt.
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