Mathematical simulation of liquid food pasteurization using far

Journal of Food Engineering 107 (2011) 127–133
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Journal of Food Engineering
journal homepage: www.elsevier.com/locate/jfoodeng
Mathematical simulation of liquid food pasteurization using far infrared
radiation heating equipment
Weijie Mao a, Yuko Oshima b, Youko Yamanaka b, Mika Fukuoka b, Noboru Sakai b,⇑
a
b
College of Food Science and Technology, Guangdong Ocean University, East of Hu Guang Yan, Zhanjiang 524-088, China
Department of Food Science and Technology, Tokyo University of Marine Science and Technology, 4-5-7, Konan, Minato-ku, Tokyo 108-8477, Japan
a r t i c l e
i n f o
Article history:
Received 10 September 2010
Received in revised form 15 April 2011
Accepted 20 May 2011
Available online 31 May 2011
Keywords:
Far-infrared radiation
Liquid food
Pasteurization
Simulation
a b s t r a c t
In this study, pasteurization equipment using far-infrared radiation (FIR) was developed for liquid food.
The temperature was measured at various conditions to investigate the heating effect. With the liquid
food passing down an angled trough and FIR applied from above, the temperature changed with the radiation intensity (electricity supplied), the angle of the incline, and the flow rate. As the liquid film became
thinner, the temperature could be heated to nearly 80 °C. The pasteurization effect was verified using lactic acid bacteria as the target microorganism; the heat resistance of the bacteria was measured, the death
of bacteria was confirmed, and the effectiveness of the equipment was verified. Furthermore, a mathematical model for FIR pasteurization was developed using a heat transfer equation and thermal death
equation. The simulation could make predictions about temperature and the viable count of bacteria that
compared very well with the experimental results. Moreover, the model simulated the change of temperature and viable count of bacteria at different flow rates, and showed that it is possible to sterilize at low
temperatures with this equipment.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Pasteurization plays an important role in the food manufacturing process. At present, plate or tube type heat exchangers are
often used to pasteurize milk and other liquid foods. In these heat
exchangers, heat is transferred from a heat source such as steam or
hot water to the liquid food through thin stainless steel. For highly
viscous liquids, however, any scaling on the surface of the stainless
steel leads to microbe contamination and seriously harms the
quality of the product. Therefore, the cleanliness of the pasteurization equipment is very important. A lot of time and labor is required to clean the pasteurization equipment, and a large
quantity of wastewater is discharged, which is a major problem
for liquid food pasteurization. Therefore, a new type of equipment
needs to be developed, one that is not only effective in pasteurization, but easy to clean. Far-infrared radiation (FIR) is considered an
alternative heat source for pasteurization.
Infrared radiation consists of electromagnetic waves with
wavelengths of 0.78–100 lm. Infrared radiation is classified in
the wavelength range, with those longer than 3 lm being FIR
(Sakai and Mao, 2006). In many industrial and research settings,
applications of FIR are especially attractive due to its advantages,
including energy savings, simple apparatus, clean working environments and easy thermal control (Hashimoto et al., 1992).
⇑ Corresponding author. Tel./fax: +81 3 5463 0622.
E-mail address: [email protected] (N. Sakai).
0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2011.05.024
FIR is widely utilized in food processing. FIR is used to roast coffee (Kino, 1999) and tea (Takeo, 1999), to bake cookies, bread, fish
and kamaboko (Shibukawa, 1999), and to dry noodles (Yokouchi
et al., 1991) and potatoes (Masamura et al., 1988). Kamaboko is a
type of cured surimi, a Japanese processed seafood product, in
which various white fish are pureed, combined with additives,
formed into distinctive loaves, and then steamed until fully cooked
and firm. Pasteurization by FIR has been studied previously not
only for solid materials, but also for wet-solid and liquid foods.
Hamanaka et al. (2003b) reported that short-term infrared radiation (IR) was an effective method for reducing the viable counts
of microorganisms on the surface of wheat and soybeans.
Hamanaka et al. (2003a) studied the effect of IR on the inactivation
and injury of two kinds of bacterial spore suspensions, and found
that the inactivation of bacterial spores by IR was more intensive
than that by convection heating. For wet-solid food, the effect of
FIR on the pasteurization of Escherichia coli and Staphylococcus
aureus has been verified (Hashimoto et al., 1992). Sawai et al.
(1997) reported that during the first few minutes of irradiation
by FIR, the number of colonies of spores of Bacillus subtilis increased and then gradually decreased. In addition, an increase in
irradiation power and a decrease in the depth of the spore suspension enhanced the pasteurization effect of FIR on spores. These results suggested that it would be possible to apply FIR irradiation to
the pasteurization of bacterial spores. Sawai (2000) evaluated the
pasteurization effect of FIR on E. coli suspended in saline solution.
FIR irradiation was more effective in pasteurizing bacterial cells
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W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
Nomenclature
D
Ea
DH
G
g
Kg
N
N0
Nl
Hl
H
P
Q
decimal reduction time (min)
activation energy (J kg1)
the latent heat (J kg1)
flow rate (m3 s1)
the acceleration of gravity (m s2)
film mass transfer coefficient (kg m2 s1 DH1)
the number of surviving bacteria ()
the initial number of bacteria ()
the evaporation rate
the saturated humidity ()
the saturated humidity of air ()
the saturated water vapor pressure (k Pa)
the amount of heat (J m2 s1)
than thermal conductive heating, and the death of E. coli by FIR
irradiation followed a first-order reaction model. For these studies,
the effect of pasteurization by FIR was verified, but for liquid food
the actual FIR equipment has not been positively utilized. In our
previous work (Sakai et al., 2008), we developed FIR pasteurization
equipment for thin liquid food. In the present work, we used lactic
acid bacteria as a target microorganism to verify the effect of FIR
irradiation on a liquid medium; additionally, we developed a
mathematical model, using the heat transfer equation and first-order reaction that predicts the change of temperature, the thermal
death of bacteria, and the optimal heating condition.
qr
qv
R
T
Th
Tl
eh
el
q
r
heat emitted (J m2 s1)
the amount of heat for evaporation (J m2 s1)
universal gas constant (mol1 K1)
time (min)
the temperature of the far-infrared irradiation heater
(K)
the temperature of the sample (K)
the emissivity of the far-infrared irradiation heater ()
the emissivity of the far-infrared irradiation heater ()
the density of the sample (kg m3)
Stefan–Boltzmann constant (J s1 m2 k4)
difference between the distance between A (the top of the trough
to the surface of the liquid) and B (the distance between the top
and bottom of the trough) is the liquid film thickness. At one condition, the thickness of the liquid film was measured for six times
and they were averaged for result. The thickness of the liquid layer
was measured with the change of the angle from 1° to 5°, and the
flow rate was changed from 200 to 1400 at 200 mm min1 intervals. The thickness of the liquid layer was measured 6 times. Based
on the results of the liquid layer thickness, the residence time was
calculated. The residence time was the time that the liquid
received the energy from the heater, namely the duration of the
sample’s passage through the heating line.
2. Experimental materials and methods
2.2. Pasteurization experiment
2.1. Heating experiment
2.1.1. Experiment equipment
Fig. 1 shows a schematic diagram of the equipment. The equipment is composed of five parts: the inlet of the sample, a tank, a heating line, a far-infrared radiation heater, and the angle regulator of the
heating line. The capacity of the tank is 2 l1. The width of the
trough-like heating line was 50 mm, the length was 855 mm and
the depth was 30 mm. The FIR heater was composed of five
120 mm square ceramic emitting surface (PLC 328, Noritake Co.
Ltd., Japan) as shown in Fig. 1b. The length of the heater is
600 mm, and the width 120 mm. The emissivity of the heater is
0.85. The distance between the far infrared radiation heater and
the heating line can be as close as 30 mm or as far as 300 mm. The
temperature of the far-infrared radiation heater can be changed by
adjusting the electric current from 10 to 20 A. The liquid sample
inflows from the inlet with a constant flow rate into the tank until
the tank overflows, then flows into the heating line naturally, in a
state of lamellar flow. The thickness and velocity of the flow can
be adjusted with the inflow volume and angle of the heating line.
2.1.2. Heating experiment
The temperature of the sample was measured with the change
of the angle from 1° to 5°. The supply electricity was fixed at
3.2 kW, and the distance between the heater and heating line
was set at 200 mm. The air space between the far-infrared radiation heater and the heating line was covered with aluminum foil
to prevent the scattering of radiation. The temperature of the heater surface was 650 °C.
2.1.3. The thickness of the liquid layer and the residence time
The distance between the liquid surface and stainless plate was
defined as the thickness of the liquid layer, as shown in Fig. 2. The
2.2.1. Choice of the target microorganism
The equipment is suitable for a wide variety of products in
small quantities. As a sample, we chose a soy sauce-based soup,
which is mainly contaminated by halotolerant microorganisms.
Generally, halotolerant microorganisms include halotolerant lactic
acid bacterium (Tetragenococcus halophilus), halotolerant yeast
(Zygosaccharomyces rouxii), and halotolerant lactic acid bacillus
(Lactobatillus plantarum). In this experiment, T. halophilus was
chosen for the pasteurization experiments.
2.2.2. Preparation of T. halophilus
T. halophilus that had frozen in 80 °C (glycerol stock) was
restored to a liquid medium, to culture. First, the glycerol stock
was slowly thawed at room temperature, and then 50 ll of glycerol
stock was inoculated into 3 ml of MRS liquid medium (MRS broth
52.5 g l1, Merck Ltd., JP; NaCl 100 g l1) for preculture at 30 °C for
2–3 days. For the main culture, 1 ml preculture liquid was inoculated to 100 ml of MRS liquid medium at 30 °C for 3–4 days. The
amount of culture was adjusted depending on the amount used
in the experiment.
2.2.3. Determination of viable count
When 1 ml of the original sample was added to 9 ml of sterile
water, it gave 1:10 or 101 dilution of original sample; similarly,
102, 103, 104, 105, and 106 dilutions of the original sample
were prepared. Finally, 0.1 ml aliquots of each dilution were added
to MRS agar culture (MRS broth 52.5 g l1, NaCl 100 g l1, CaCO3
5 g l1, agar 14 g l1), spread with a bacteria spreader and then
cultured at 30 °C, for 2–3 days.
In this study, the number of colonies remaining after incubation
was considered the number of survivors. Subsequently, the
W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
129
Fig. 1. Experimental apparatus. 1. Inlet of sample; 2. tank; 3. heating time; 4. far-infrared radiation heater; 5. angle regulator of heating time.
survival ratio (N/N0) was calculated, where N is the number of surviving bacteria and N0 the initial number of bacteria.
3. The mathematical model
3.1. Heat transfer model
2.2.4. Thermal resistance parameters
One milliliter of the culture liquid containing T. halophilus was
input into 100 ml of sterile soy sauce, and then sealed and
immersed in circulating water baths set at 48, 49, 51 or 54 °C. At
intervals, 1 ml of the samples were taken and removed to 9 ml
sterile water, then cooled on ice. Viable numbers were calculated
from the colony counts, and D values were evaluated at each temperature. The decimal reduction time D is widely used to indicate
the rate of inactivation in sterilization studies.
D¼
t2 t1
log N1 log N2
2.2.5. Thermal inactivation of bacteria
The sample containing T. halophilus flowed into the sample tank
and the flow rate and angle was adjusted to make the sample flow
naturally into the heating line. The heating conditions were as
follows: a flow rate of 240m1 min1, angle 1°, distance 60 mm,
and electricity supply of 2.8 kW. One-milliliter of samples were taken at the inlet, outlet and at 120 mm intervals in six positions
altogether; each was removed to 9 ml sterile water, then cooled
on ice. Viable numbers were calculated from the colony counts.
Fig. 2. The method for measuring the thickness of the liquid layer.
The mathematical models for heat transfer and microbial inactivation used in these studies can be summarized as follows. To
simplify the complexities of calculation, the following assumptions
were made: (1) The irradiation received from the far-infrared
heater is uniform from the inlet to the outlet. (2) The thickness
of the liquid layer is uniform, at any position. (3) The flow rate of
the liquid in the heating line is uniform.
Based on heat balances on a small distance, the following
equations were developed.
The amount of heat q (J m2s1) which the sample absorbed
equals the amount of heat qr (J m2s1) emitted from the heater
minus that for the latent heat of evaporation qv (J m2s1).
q ¼ qr qv ¼
G C p q dT
dx
h
ð1Þ
where G is the flow rate (m3 s1), Cp is the specific heat (J kg1 K), q
is the density (kg m3), h is the width of the heating line (m), T is the
temperature, and dT
is the thermal gradient in the direction of the
dx
flow.
The variable qr representing the radiant heat from a heater may
be defined by the Stefan–Boltzmann law.
qr ¼ C r T 4h T 4l
ð2Þ
1 1 1
¼ þ 1
C eh el
ð3Þ
where r = 5.7 108 (J s1 cm2 K4) is the Stefan–Boltzmann
constant. Th is the temperature of the far-infrared irradiation heater
(K), Tl is the temperature of the liquid sample at the l point (K). eh is
the emissivity of the far-infrared irradiation heater (), and el is the
emissivity of the liquid ().
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W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
By contrast, qv is the amount of heat for evaporation, which can
be represented by the latent heat of evaporation multiplied by the
evaporation rate.
ð4Þ
Nw ¼ kg ðHs HÞ
ps
;
Hs ¼ 0:620
101:3 ps
ð5Þ
p
H ¼ 0:620
101:3 p
ð6Þ
where DHL is the latent heat (J kg1), Nw is the evaporation rate
(kg s1), kg is the film mass transfer coefficient (m s1), HS is the
saturated humidity at the liquid temperature (), H is the humidity
of air () , pS is the saturated water vapor pressure at the liquid
temperature (kPa), and p is the water vapor pressure in air (kPa).
Inserting Eqs. (2)–(6) into Eq. (1), yields
dT
¼ f ðx; TÞ
dx
ð7Þ
Eq. (7) was integrated numerically using the Runge–Kutta–Gill
method.
The change in the inactivation of bacteria during far-infrared
irradiation over time can be described mathematically as:
ð8Þ
ð9Þ
where N is the number of bacteria at time t, N0 is the initial number of
bacteria and kd is the thermal death constant that can be presented by
the Arrhenius equation to describe temperature dependence.
Lnkd ¼ lnk0 Ea =RT
ð10Þ
where, Ea is the activation energy for inactivation of T. halophilus
(J kg mol K), and k0 is the frequency factor (s1).
Meanwhile, the flow speed of liquid u (m s1) is expressed as
follows.
u¼
G
dx
¼
hd dt
) dt ¼
dx
u
50
4°
5°
40
30
20
10
0
0
500
1000
Flow rate (ml/min)
1500
2000
Fig. 3. Relationship between flow rate of liquid and its increased temperature.
Initial liquid temperature: 18 °C, supplied electricity: 3.2 kW.
4.2. The relationship between the thickness of the liquid and the flow
rate
The relationship between the thickness of the liquid and the
flow rate is shown in Fig. 4. At the same flow rate, at a large angle
the liquid layer was thinner than at a small angle. However, when
the flow rate of the sample was changed, the tendency was different according to the angle. In other words, with an increase in the
flow rate, the thickness of the liquid layer increased when the
angle was large, while the thickness of the liquid layer did not
change when the angle was small.
When the fluid flows at a laminar flow state at the angle u,
where the horizontal is 0° the thickness of the liquid fluid, d (m)
can be represented by the following expression:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3lQ
3
d¼
q g cosð90 /Þ
ð11Þ
Substituting this relation into Eq. (9), the next expression is
obtained.
Z x
N
¼ exp kd udx
N0
0
2°
3°
were the important factors influencing the temperature of the
liquid.
3.2. Microbial inactivation model
dN
¼ kd N
dt
Z t
N
¼ exp kd dt
N0
0
0°
1°
60
Increased temperature (ºC)
qv ¼ DHL Nl
70
ð12Þ
where l is the coefficient of viscosity (Pa s), Q is the flow rate
(m3 s1), q is the density of the sample (kg m3), and g is the acceleration of gravity (m s2). From this equation, at the same flow rate,
with the angle increased, the liquid film becomes thinner, while at
the same angle, when the flow rate increased, the liquid layer becomes thicker. However, in fact, it was almost constant regardless
4. Results and discussion
As shown in Fig. 3, at any angle, with decreasing flow rate, the
temperature increased. It appeared that for lower flow rates, the
residence time of the sample in the heating line became longer,
and therefore the heating time became longer and the temperature
rose. Moreover, at the same flow rate, the larger the angle, the
higher the temperature rose. In other words, at the same flow rate,
the thinner the liquid layer, the larger the surface obtained, and the
more energy received. That is because even in the same volume
flow per second, the thinner the liquid layer, the larger the surface
area to receive energy becomes. Furthermore, even though the
temperature of the liquid increased greatly, the temperature of
the stainless steel heating line was 2–5 °C lower than that of liquid.
From the above results, we considered that angle and thickness
Thickness of liquid layer (mm)
4.1. The temperature effect by the flow rate and angle
5
4
3
2
1
1°
0
0
400
800
Flow rate (ml/min)
2°
3°
1200
4°
5°
1600
Fig. 4. Relationship between flow rate of liquid and its thickness.
131
W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
70
60
Increased temperature(ºC)
of the flow rate when the angle was small. We considered that
when the angle is small, the fluid is not in a state of laminar flow.
Based on the result of thickness, the residence time was calculated. In the apparatus for this experiment, the heating line was
600 mm, and the residence time was the time it took for the liquid
sample to flow through the heating line. From Fig. 5, it can be seen
that the residence time was long at a smaller angle or lower flow
rate. Moreover, from Fig. 4, if the flow rate and angle are known,
the residence time can be calculated; therefore, the thickness of
the liquid layer of the experiment shown in Fig. 4 could be
obtained. Furthermore, a group of experiments with identical liquid layer thicknesses was conducted, and the relationship between residence and temperature increase in the group is shown
in Fig. 6. The temperature rose in proportion to the residence time,
because of the longer heating time. Additionally, given the same
residence time, the temperature of the thinner liquid films rose
higher.
50
40
30
20
10
0
0
5
10
4.5
4.0mm
3.5
3.0mm
3.0
2.5mm
2.0
1.5mm
1.5
1.0mm
15
20
25
Residence time (S)
30
35
Fig. 6. Relationship between residence time in the heating unit and increased
temperature of the liquid.
4.3. Thermal resistances of lactic acid bacteria
1
48.1ºC
0
49.7ºC
51.0ºC
53.3ºC
-1
log N/N0 (-)
The survival ratio of T. halophilus heated in 3%NaCl water is
shown in Fig. 7. The horizontal axis is the heating time t (min)
and the vertical axis is the logarithm of the survival ratio (N/N0).
The survival ratio fell linearly with the heating time, and at 48 °C
it was sterilized rather gradually. As the temperature increased,
however, the slope of this line became steep, which meant the
bacteria rapidly became extinct. Using Eq. (1), the D value can be
calculated from Fig. 7. In addition, a thermal death rate constant
kd was obtained from the expression: kd = 2.303/D, and the D and
kd values are shown in Table 1. Fig. 8 shows the relationship between kd and 1/T. The frequency factor k0 and the activation energy
Ea for thermal death were obtained from the results shown in
Fig. 8. According to Eq. (10), the intercept of the line is the value
of k0, 151.58, and the slope of the value of Ea/R is 4.91 104, in
which case the value of Ea is 4.07 105. Sawai et al. (2003) measured the Ea of E. coli and obtained a value of 4.05 105.
54.0ºC
-2
-3
-4
-5
-6
0
10
20
4.4. Pasteurization effect of FIR by experiment and simulation
Fig. 9 shows the viable count and temperature change of the
sample during FIR heating. The horizontal axis is the distance for
the liquid flow; the symbol of ‘‘N’’ is the experimental temperature
of the sample, which increased almost linearly as the liquid moved
downstream. The line is the calculated temperature, which shows
the same inclination as that of the experiment. In addition, the cal-
40
1°
35
2°
3°
Residence time(s)
30
30
40
Heating time (min)
50
60
70
Fig. 7. Survival curves of lactic acid bacteria in different temperature by water bath
heating.
Table 1
Thermal resistance of lactic acid bacteria D and kd Value of lactic acid bacteria in the
3% salt water.
Temperature (°C)
D value (min)
Thermal death rate constant kd (min1)
48.1
49.7
51.0
53.3
54.0
7.53
4.20
2.13
0.64
0.54
0.31
0.55
1.08
3.61
4.25
4°
25
5°
20
15
10
5
0
0
200
400
600
800 1000 1200 1400 1600
Flow rate (ml/min)
Fig. 5. Relationship between flow rate of liquid and its residence time in heating
unit.
culated temperature was in good agreement with that of the
experiment.
The symbol ‘‘s’’ represents the viable count of T. halophilus. The
initial number of bacteria was about 1 106 CFU ml1, and the
viable bacterial count had not begun to decrease at the position
of 120 mm, when the temperature of the sample was over 40C,
the viable bacterial count decreased quickly. In addition, at a later
position, no bacteria were detected. At temperatures over 50C, the
bacteria were killed at once. The curved line in Fig. 9 represents the
calculated results of the viable bacterial count, and shows the same
tendency as the experiment. Therefore, the model can be used in
simulations to determine the optimum heating condition.
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W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
2
120
120ml/min
1.5
100
1
240ml/min
Temperature (°C)
lnkd
0.5
0
-0.5
lnkd = 151.58-4.91*104/T
-1
80
360ml/min
60
600ml/min
720ml/min
480ml/min
40
960ml/min 1080ml/min
840ml/min
-1.5
3.05
3.06
3.07
3.08
3.09
3.1
3.11
3.12
20
1/T *103(K-1)
Fig. 8. Relationship between kd and 1/T.
0
120
240
360
Distant(mm)
480
600
Fig. 10. The calculated temperature at different flow rates.
100
7
0
90
6
80
1.0E+07
70
50
3
40
30
2
20
1.0E+06
120ml/min
240ml/min
1.0E+05
1.0E+04
480ml/min
600ml/min
1.0E+03
1
1080ml/min
360ml/min
logN
60
4
Temperature(°C )
LogN
5
840ml/min
10
720ml/min
N.D
0
120
240
360
Distant(mm)
480
0
600
960ml/min
1.0E+02
1.0E+01
Fig. 9. The viable count and temperature change during the heating process in the
case of Tetragenococcus halophilus. (s: viable count, N: temperature) Angle of the
heating unit: 1°, the straight line is the calculated temperature, the curve is the
calculated viable count.
1.0E+00
0
120
240
360
Distant(mm)
480
600
Fig. 11. The calculated viable count of bacteria at different flow rates.
Fig. 10 shows the simulation results of temperature at different
flow rates when the angle was 1°. It can be seen that at a low flow
rate, the temperature of the sample rose greatly, while at a high
flow rate, the temperature increased slowly, at 960 mm min1,
with the highest temperature reaching only about 40C. As mentioned previously, the thickness of the liquid layer doesn’t change
with the flow rate at a small angle. When the flow rate is low, the
residence time is long, and then the temperature increases quickly.
and then the temperature increases quickly. Fig. 11 shows the simulation results of the viable bacterial count at different flow rates.
At a low flow rate the bacteria will be extinguished before reaching
the position of 120 mm, and when the flow rate is 960 mm min1,
the bacteria will be extinguished at a distance of about 600 mm.
This result suggests that the pasteurization will be incomplete if
the flow rate is greater than 960 mm min1.
The proposed model compares very well with the experimental
tests, and simulates the change of temperature and the death of the
bacteria under various conditions. Using this equipment, liquid
foods can be pasteurized effectively.
5. Conclusion
A pasteurization system using FIR was developed, and then its
heating characteristics were examined. A soy sauce-based soup
was used as a food model, and T. halophilus was chosen as the target bacteria. The pasteurization of T. halophilus was performed.
Furthermore, the thermal resistance of T. halophilus was examined,
and a mathematical model was developed to simulate the change
in the temperature of the sample and the viable bacterial count
at different heating conditions. The following results were obtained: (1) Because the liquid food is irradiated by FIR originating
above the liquid food, the temperature on the stainless steel trough
is lower than that of the sample; (2) The rate of the increase in
temperature of the liquid food can be changed by adjusting the angle and flow rate; (3) The FIR system is effective in the pasteurization of liquid food; and (4) the results predicted by our model agree
well with the experimental results. The validity of the model was
W. Mao et al. / Journal of Food Engineering 107 (2011) 127–133
verified. It appears that our FIR system can be used for low-temperature pasteurization.
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