Journal of Food Engineering 107 (2011) 127–133 Contents lists available at ScienceDirect 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 128 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 (). 130 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. 132 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. References Hamanaka, N., Uchino, T., Hu, W.Z., Yasunaga, E., 2003a. Effects of infrared radiation on inactivation of Bacillus subtilis spore and Aspergillus niger spore. Journal of the Japanese Society of Agriculture Machinery 50 (2), 51–56. Hamanaka, N., Uchino, T., Hu, W.Z., Yasunaga, E., 2003b. 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