Modelling of far-infrared irradiation in paddy drying process

Journal of Food Engineering 78 (2007) 1248–1258 www.elsevier.com/locate/jfoodeng Modelling of far-infrared irradiation in paddy drying process Naret Meeso b a,* , Adisak Nathakaranakule b, Thanid Madhiyanon c, Somchart Soponronnarit b a Department of Mechanical Engineering, North Eastern University, Khonkaen 40000, Thailand School of Energy and Materials, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand c Department of Mechanical Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand Received 27 August 2005; accepted 4 January 2006 Available online 2 March 2006 Abstract The set of coupled heat and mass transfer equations are developed to predict the effect of far-infrared irradiation in a series paddy drying process, comprising fluidized bed drying, transport of paddy, far-infrared irradiation, tempering and ambient air ventilation. Two layers inside a paddy grain, i.e. a penetrating layer and a conductive layer, were introduced in the development. Comparison results showed that the model predicted results agreed well with the experiments within the maximum differences in the average paddy moisture content and temperature of 2.5% d.b. and 5 C, respectively. Furthermore, the model was capable of reasonably predicting the temperature and moisture distributions inside a paddy grain.  2006 Elsevier Ltd. All rights reserved. Keywords: Drying process; Far-infrared irradiation; Fluidized bed; Modelling 1. Introduction Some paddy drying processes in Thai rice mills have been continuously developed over the past decade. A two-stage drying technique is widely used with various types of dryer, such as fluidized bed dryer, the Louisiana State University (LSU) dryer, cross-flow dryer, recirculation batch dryer, cooling bin and tempering bin (Meeso, Soponronnarit, & Wetchacama, 1999; Soponronnarit, 1995). This technique, however, is not completely effective because it still damages paddy qualities, such as head rice yield and whiteness. To improve the qualities, the suitable paddy drying process in some Thai rice mills is proposed by Soponronnarit, Wetchacama, Swasdisevi, and Poomsa-ad (1999) and Poomsa-ad, Soponronnarit, Prachayawarakron, and Terdyothin (2002), and it is proved to be successful in the commercial scale. The process is divided into two drying stages i.e. fast drying in the first stage using fluidized * Corresponding author. Tel./fax: +662 470 8663. E-mail address: [email protected] (N. Meeso). 0260-8774/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.01.003 bed dryer and slow drying in the second stage using ambient air ventilation with tempering between two drying stages. Under this paddy drying process, Poomsa-ad, Soponronnarit, Terdyothin, and Prachayawarakron (2001) suggested that the moisture content of paddy after the first drying stage should not be reduced lower than 22.5% dry basis and then followed by tempering for 30 min before ventilating with ambient air in order to maintain head rice yield. Due to the limitation of the moisture reduction of paddy in the first drying stage, the application of far-infrared radiation was introduced in the paddy drying process because this electromagnetic wave is capable of directly penetrating into the product and being absorbed by molecules of product. The absorbed energy activates interaction between molecules of the product causing heat generated inside (Ginzburg, 1969; Sandu, 1986; Sakai & Hanzawa, 1994). Meeso, Nathakaranakule, Madhiyanon, and Soponronnarit (2004) applied far-infrared irradiation in multi-stage paddy drying process, composing fluidized bed drying, far-infrared irradiation, tempering, and ambient air ventilation, respectively. Their results revealed that far-infrared 1249 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 Nomenclature A cp Deq D F hfg hm  hc k M Mw M qr,FIR qr,FIRg qleakage qloss q_ G r R R1 RH T Tabs v V surface area, m2 specific heat, J/kg K equivalent diameter of grain, m diffusion coefficient, m2/s view factor latent heat of vaporization, J/kg mass transfer coefficient, m/s heat transfer coefficient, W/m2 K thermal conductivity, W/m K moisture content, decimal d.b. moisture content, decimal w.b. average moisture content, decimal d.b. FIR transfer rate from FIR heater, W FIR transfer rate to grain, W energy leakage, W energy loss, W FIR heat generation, W/m3 radial distance, m grain radius, m; thermal resistance, C/W; universal gas constant, kJ/kmol K grain radius of conductive layer; m relative humidity, decimal temperature, C absolute temperature, K air velocity, m/s volume of grain, m3 Dimensionless numbers Le Lewis number NuD Nusselt number Pr Prandtl number irradiation could further reduce the moisture content to 21% dry basis without affecting paddy qualities. In spite of the successful paddy drying process in Thai rice mills, a few studies on modelling of paddy drying process has been reported. Poomsa-ad et al. (2002) presented the simulation of multi-stage paddy drying process, including fluidized bed drying in the first stage, followed by ambient air ventilation or fluidized bed drying in the second stage and tempering between each stage, but their model did not include heat transfer equations. Similarly, a modelling of far-infrared drying of grains is rarely reported although the far-infrared drying is widely applied in the food processing industry. Ratti and Mujumdar (1995) proposed the modification of heat transfer equations for infrared drying of a single particle, while the mass transfer equations remained the same as that for purely convective drying. Fasina, Tyler, and Pickard (1998) developed the coupled heat and mass transfer models to describe the infrared heating of agricultural crops. Their model assumed that infrared energy impinged upon the product surface, and was converted to heat. This assumption contrasted with RaD ReD Rayleigh number Reynolds number Greeks a dp b q qb r e m l thermal diffusivity, m2/s penetration depth (R  R1), mm volumetric thermal expansion coefficient, 1/K density, kg/m3 bulk density, kg/m3 Stephan–Boltzman constant, W/m2 K4 emissivity; porosity value, decimal kinematic viscosity, m2/s dynamic viscosity, kg/m s Subscripts a drying air amb ambient air e equilibrium FC forced convection FIR FIR heater g grain in initial NC natural convection m mass, or moisture r radiation s surface side side wall top top wall w wall wi inside wall wo outside wall the published data of Ginzburg (1969), Sandu (1986), and Nindo, Kudo, and Bekki (1995) who reported that the penetration of infrared radiation into the most grains were just less than 1–2 mm. The latter assumption is applied in this study by assuming that infrared energy directly penetrates into the paddy grain, and heat is generated inside the grain. The specific objectives of this research were to develop the coupled heat and mass transfer models of far-infrared irradiation in multi-stage paddy drying process, and to test and validate the model predictions on different experimental data. 2. Model development The predicted paddy drying process, as shown in Fig. 1, consists in series of fluidized bed drying (FB), far-infrared Transport FB Transport Transport FIR TEM Fig. 1. Schematic diagram of paddy drying process. AAV 1250 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 irradiation (FIR), tempering (TEM) and ambient air ventilation (AAV), respectively. The transport of paddy from FB drying to FIR irradiation during the drying process is considered in this development because the high temperature paddy is pneumatically transported from the inside of fluidized bed drying chamber to ambient air immediately, and then is carried to FIR irradiation. This transport has a significant effect on the grain temperature, but the other transports (i.e. from FIR irradiation to TEM and from TEM to AAV) have negligible effect. The general assumptions of this paddy drying model are as follows: • Coupled heat and mass transfer models are used to describe drying process of a single paddy kernel. • A paddy grain is considered to be an isotropic sphere. • The shrinkage of the paddy grain during drying process is negligible. • The grain characteristics are constant during drying process. • Heat and mass transfers within the paddy grain simultaneously take place in the radial direction. • Temperature and moisture profiles of a paddy at the end of each stage are used as the initial conditions of the next stage except for the stage of FB drying has initially the uniformly distributed moisture and temperature. • Moisture evaporation takes place at the grain surface of paddy in each stage, except TEM stage. The specific assumptions of modelling for each stage in the paddy drying process are expressed as follows. 2.1. FB drying In development of the modelling in this stage, heat is transferred to a paddy grain via forced convection, and transferred into the interior of a grain via conduction. Nevertheless, moisture is diffused from the interior of a grain to the surface, and loses into the drying air. Therefore, the equations of heat and mass transfer are given as follows: Mass transfer  2  oM o M 2 oM ¼ Dm þ for 0 6 r 6 R ot or2 r or Heat transfer  2  oT o T 2 oT ¼a þ ot or2 r or for 0 6 r 6 R T ¼ T in at t ¼ 0; 06r6R 06r6R r¼R ð6Þ ð7Þ ð8Þ 2.2. Transport from FB drying to FIR irradiation During transporting of paddy, the heat used for moisture evaporation at the surface of grain is derived from the heat stored inside grain. Both heat and moisture of a paddy grain lose to the ambient air are assumed by natural convective transfer. The equations of heat and mass transfer are obtained from Eqs. (1) and (2), respectively. The initial and boundary conditions for this stage are given as follows: Initial conditions M ¼ MðrÞ at t ¼ 0; T ¼ T ðrÞ at t ¼ 0; 06r6R 06r6R Boundary conditions oM ¼ 0 at t > 0; r ¼ 0 or dM D ¼ hm ðM s  M e Þ at t > 0; r ¼ R dr s oT ¼ 0 at t > 0; r ¼ 0 or oT oM ¼ hNC Ag ðT amb  T s Þ þ qg V g hfg  k g Ag or s ot at t > 0; r¼R ð9Þ ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ 2.3. FIR irradiation ð2Þ Initial conditions at t ¼ 0; at t > 0; ð5Þ ð1Þ The initial and the boundary conditions are as follows: M ¼ M in Boundary conditions oM ¼ 0 at t > 0; r ¼ 0 or dM D ¼ hm ðM s  M e Þ at t > 0; r ¼ R dr s oT ¼ 0 at t > 0; r ¼ 0 or oT oM  k g Ag ¼ hFC Ag ðT a  T s Þ þ qg V g hfg or s ot ð3Þ ð4Þ According to the theory of FIR irradiation (Sandu, 1986), FIR energy from heaters suddenly impinges upon a grain surface, and directly penetrates into the grain, approximately 1 mm under the surface (Ginzburg, 1969; Nindo et al., 1995), as show in Fig. 2. Therefore, all of FIR Energy is completely absorbed from the grain surface into the depth of 1 mm, so called the penetrating layer. This layer is considered the location of the heat-conversion. The interior of the grain from the depth of 1 mm through to the grain core is called the conductive layer, which heat is transferred by conduction. On the contrary, moisture inside the paddy grain is transferred from the core to the grain surface. Besides, heat and moisture at the grain 1251 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 FIR Heater Natural convection Moisture Conduction r=0 Penetrating layer Conductive layer R1 R The second term in the right-hand side of Eq. (16) is FIR heat generation. This is simply assumed that the spatial distribution of FIR energy absorption is an exponential decay from the surface into the inside of a spherical grain according to Lambert’s law (Eric Weisstein’s World of Physics, 2005). The FIR heat generation is calculated from the energy delivered to the paddy grain per unit volume of the penetrating layer. As shown in Fig. 4, the mechanism of FIR irradiation in a box-type FIR dryer is assumed that the quantity of FIR energy irradiated from the FIR heater is equal to the sum of the quantity of FIR energy delivered to the paddy grain and the quantity of energy loss from the inside of radiative chamber to the environment, so that energy balance for FIR irradiation is as follows: qr;FIR ¼ qr;FIRg þ qloss ð25Þ Fig. 2. Far-infrared irradiation of a paddy grain in the spherical geometry. where qr;FIR ¼ eFIR rAFIR T 4FIR . The quantity of FIR energy delivered to the paddy grain is from the FIR heaters directly and the walls of radiative chamber, which is written as follows: surface lose into the air within the radiative chamber by natural convection. The equations of heat and mass transfer are written for each layer as follows: qr;FIRg ¼ For the penetrating layer  2  oM o M 2 oM ¼ Dm þ for R1 6 r 6 R ot or2 r or    2  oT o T 2 oT 1 Rr ¼a þ þ q_ G exp  ot or2 r or k dp for R1 6 r 6 R For the conductive layer  2  oM o M 2 oM ¼ Dm þ for 0 6 r < R1 ot or2 r or  2  oT o T 2 oT ¼a þ for 0 6 r < R1 ot or2 r or ð15Þ ð16Þ ð17Þ ð18Þ Initial conditions T ¼ T ðrÞ at t ¼ 0; at t ¼ 0; 06r6R 06r6R at t > 0; r¼R where the values of eFIR and eg are 0.9 from the manufacturer (Sang Chai Meter Co., Ltd., Thailand, 2004) and 0.7 (Arinze, Schoenau, & Bigsby, 1987), respectively. Moreover, the view factors are obtained from the following relation for the paddy and the cylindrical FIR heater (Obert & Young, 1962). The values of FFIRg, FFIRw and Fgw are approximately 0.258, 0.742 and 0.945, respectively. The quantity of energy loss from the inside of radiative chamber to the environment includes the losses from the side surface and the top surface of chamber walls, ignoring the bottom surface due to a box-type FIR dryer set on a table, and from the leakage though the vents. The energy balance for energy loss is written as follows:   1 1 qloss ¼ ð27Þ þ ðT a  T amb Þ þ qleakage Rw;side Rw;top ð19Þ where ð20Þ 1 L 1 Rw;side ¼  þ þ hwi;side Aw;side k w;side Aw;side hwo;side Aw;side 1 L 1 þ þ Rw;top ¼  hwi;top Aw;top k w;top Aw;top hwo;top Aw;top Boundary conditions oM ¼ 0 at t > 0; r ¼ 0 or dM D ¼ hm ðM s  M e Þ at t > 0; r ¼ R dr s oT ¼ 0 at t > 0; r ¼ 0 or oT oM  k g Ag ¼ hNC Ag ðT a  T s Þ þ qg V g hfg or s ot 1e 1 þ Ag egg þ 1=ð1=AFIR F FIRg Þþ1=ðð1=A FIR F FIRw Þþð1=Ag F gw ÞÞ ð26Þ The initial and the boundary conditions are as follows: M ¼ MðrÞ rðT 4FIR  T 4s Þ 1eFIR AFIR eFIR ð21Þ ð22Þ ð23Þ Thus, the air temperature inside the radiative chamber can be calculated from Eq. (27), and the energy leakage is estimated from the energy loss. 2.4. TEM ð24Þ In the paddy TEM, the average temperature of paddy grain is equal to the TEM temperature. The moisture inside 1252 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 a paddy grain is diffused to the grain surface, but the evaporation and the convection of moisture dose not take place at the grain surface. The heat and mass transfer equations are obtained from Eqs. (1) and (2) with the new initial and boundary conditions as follows: Initial conditions M ¼ MðrÞ T ¼ T ðrÞ at t ¼ 0; at t ¼ 0; The convective heat transfer coefficient can be divided into two modes, namely, natural and forced convection heat transfer coefficients. These coefficients are obtained from the following relation (Holman, 1997; Incropera & DeWitt, 1996): N uD k a or hFC ¼ Deq hNC 06r6R 06r6R ð28Þ ð29Þ For the natural convection heat transfer coefficient Boundary conditions oM ¼ 0 at t > 0; r ¼ 0 or oM ¼ 0 at t > 0; r ¼ R or s oT ¼ 0 at t > 0; r ¼ 0 or oT ¼ 0 at t > 0; r ¼ R or s 1=4 ð30Þ ð31Þ ð32Þ ð33Þ 0:589RaD
9=16 i4=9 1 þ 0:469 Pr and, the forced convection heat transfer coefficient !1=4 l N uD ¼ 2 þ ð0:4Re1=2 þ 0:06Re2=3 ÞPr0:4 a lg la cpa ka gbðT s  T a ÞD3eq RaD ¼ aa m a qa va Deq ReD ¼ la Pr ¼ The grain temperature, after TEM, is much higher than the ambient air temperature. This results in the moisture evaporation on the grain surface during AAV. The heat and mass transfer equations used in this stage are similar to the stage of FB drying. The initial and boundary conditions for this stage are as follows: Initial conditions T ¼ T ðrÞ N uD ¼ 2 þ h at t ¼ 0; at t ¼ 0; 06r6R 06r6R ð34Þ ð35Þ Boundary conditions oM ¼ 0 at t > 0; r ¼ 0 or dM D ¼ hm ðM s  M e Þ at t > 0; r ¼ R dr s oT ¼ 0 at t > 0; r ¼ 0 or oT oM  k g Ag ¼ hFC Ag ðT amb  T s Þ þ qg V g hfg or s ot r¼R ð43Þ ð44Þ where 2.5. AAV M ¼ MðrÞ ð42Þ ð36Þ ð37Þ ð38Þ at t > 0; ð39Þ The convective mass transfer coefficients are obtained from the heat and mass transfer analogy as follows (Incropera & DeWitt, 1996): hc ¼ qa cpa Le2=3 ð40Þ hm where c = NC: natural convection; FC: forced convection; r: radiation. aa Le ¼ ð41Þ Dm ð45Þ ð46Þ ð47Þ Above physical properties of air are obtained from Pakowski, Bartczak, Strumilo, and Stenstrom (1991). The radiative heat transfer coefficient is calculated from the following equation: hr ¼ qr;FIRg AFIR ðT FIR  T s Þ ð48Þ where the value of qr,FIRg in Eq. (48) is obtained from Eq. (26). The moisture diffusion coefficient for all stages, which is based on the Arrhenius type equation, are obtained from the diffusion equation of paddy drying in the wide drying temperature range as follows (Tirawanichakul, Prachayawarakorn, Varanyanond, & Soponronnarit, 2003):   37099:99 Dm ¼ 2100 exp ð49Þ RT abs Equilibrium moisture content of paddy for each stage can be calculated from Laithong (1987) h i 1  RH ¼ exp 4:723  106 T a ð100M e Þ2:386 ð50Þ On the other hand, equilibrium moisture content in the stage of FIR irradiation is estimated to be zero because the surface burning of paddy grain occurs when paddy is irradiated to FIR for longer times. This is in line with the studies of Abe and Afzal (1997) and Fasina et al. (1998). N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 3. Materials and methods 3.1. Experimental apparatus Multi-stage paddy drying process developed earlier (Meeso et al., 2004) was used in this study. It was operated in series by the devices as follows: a batch-type FB dryer, a box-type FIR dryer, a tempering glass bottle and an ambient air ventilator, respectively. The batch-type FB dryer (Fig. 3) comprised a cylindrical drying chamber, a 12-kW electrical heater, and a centrifugal fan driven by 1.5-kW motor. A drying temperature was controlled by a PID controller with an accuracy of ±1 C. The box-type FIR dryer (Fig. 4) comprised a radiative chamber, a ceramic infrared heater (1.7 cm in diameter, 60 cm in length and 800 W maximum power), a surface temperature of infrared heater controlled by ON–OFF controller, an acrylic sample tray 50 · 60 · 1.5 cm in dimensions. The tempering glass bottle had a diameter and a height of 12 and 10 cm, respectively. outlet air recycle air paddy inlet drying chamber φ 20 cm paddy outlet inlet air 1253 The last device, the ambient air ventilator, comprised a cylindrical ventilation chamber, a centrifugal fan, and a sample tray made of wire mesh (20 cm in diameter and 3 cm in height). The temperatures of paddy grain, drying air and ambient air were measured by K-type thermocouples connected to a data logger (accuracy of ±1 C). Besides, air velocity was measured by hot-wire anemometer (accuracy of ±0.1 m/s). 3.2. Experimental procedure Fresh Supanburi 1 paddy with high moisture content (25.0–29.0% d.b.) was harvested from Pathumtani Rice Research Center. They were then rewetted to about 30.0– 33.0% d.b. and kept in a cooling room at 3–5 C for 7 days. Paddy was allowed to stabilize at ambient air temperature before the drying experiments. The drying experiments were divided into three conditions as shown in Table 1. In operating the drying process, paddy was dried by a FB dryer at 150 C for 1–2 min. Then, it was transported from a FB dryer into the sample tray as a single-grain layer and irradiated by a FIR dryer at intensities of 0.30 and 0.70 W/cm2 for 0.5–1 min. After that, it was put into a glass bottle, which was closed completely and kept in a hot-air oven at temperature equal to the grain temperature after FIR irradiation for 20 min. Lastly, it was transported into ambient air ventilator and was ventilated by ambient air with velocity of 0.15 m/s for 30 min. During operation, paddy samples were taken after each stage of the drying process for measuring moisture content. The moisture contents of paddy were determined by drying triplicate samples in a hot-air oven at 103 C for 72 h (AACC, 1995), and were calculated on dry basis (d.b.). distributor 3.3. Solution methodology fan heater Fig. 3. Schematic diagram of a batch-type FB dryer. Air vents Sample tray 30 cm 15 cm FIR heater 800 W and reflector To solve these heat and mass transfer equations, the simple explicit method of finite-difference scheme was applied to discrete all heat and mass transfer equations with boundary conditions in the spherical symmetry (Ozisik, 1990). Then, the sets of equation were written in computer program. The average moisture contents and temperatures for a paddy grain were calculated with Simpson’s rule (Chapra & Canale, 1990) MðtÞ ¼ T ðtÞ ¼ 60 cm 80 cm Fig. 4. Schematic diagram of a box-type FIR dryer. 4p Vg Z 4p Vg Z R r2 Mðr; tÞdr ð51Þ r2 T ðr; tÞdr ð52Þ 0 R 0 The thermo-physical properties of a paddy grain used in the model were as follows (Brooker, Bakker-Arkema, & Hall, 1992; Laithong, 1987): 1254 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 Table 1 The experimental conditions of the paddy drying process The drying process The conditional numbers A B C D 150 9.5 2.6 1 150 9.5 2.6 1 150 9.5 2.6 1.5 150 9.5 2.6 1.5 0.5 0.5 0.5 0.5 0.310 * 15 1 0.700 * 15 1 0.310 * 15 0.5 0.700 * 15 0.5 Time (min) 20 20 20 20 Bed thickness (cm)a Air velocity (m/s)a Time (min) 3 0.15 30 3 0.15 30 3 0.15 30 3 0.15 30 FB Air temp. (C)a Bed thickness (cm)a Air velocity (m/s)a Time (min) Transport Time (min) FIR Average radiative intensity (W/cm2) Bed thickness Distance between heater-paddy (cm)b Time (min) TEM AAV * a b A single layer of grain. Recommended by Poomsa-ad et al. (2001). Recommended by Afzal, Abe, and Hikida (1999). cg ¼ 1110 þ 44:8M w ; k g ¼ 0:0863 þ 0:00134M w ; qg ¼ qb =ð1  eÞ; qb ¼ 552 þ 282M; e ¼ 0:623  0:25M; R ¼ 1:75  103 m; R1 ¼ 0:75  103 m 4. Results and discussion 4.1. Moisture distribution of a paddy grain The comparison of predicted and experimental average moisture contents of paddy during drying processes shown in Figs. 5–8 exhibited the change of average moisture content with processing time. Figs. 5 and 6 showed the predicted and experimental average moisture contents during Fig. 6. Comparison of predicted and experimental average moisture contents of paddy at condition B: FB (150 C, 1 min), transport (0.5 min), FIR (0.7 W/cm2, 1 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). Fig. 5. Comparison of predicted and experimental average moisture contents of paddy at condition A: FB (150 C, 1 min), transport (0.5 min), FIR (0.310 W/cm2, 1 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). the drying conditions A and B. Both drying conditions were similar except for FIR intensity was different (Table 1). It can be seen from FIR irradiation stage that FIR intensity helped the removing of moisture in a paddy grain, which still had high moisture content after FB drying and transport of paddy, approximately above 24.0% d.b. This result indicated that the average moisture content of paddy was significantly reduced with an increase in FIR intensity. However, it resembled that FIR intensity slightly affected on moisture reduction after FB drying and transport of paddy if moisture content was lower than about 24% d.b. even at applying high FIR intensity as shown in Figs. 7 and 8 because when a paddy grain enriched with water, N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 1255 gave a higher rate of moisture reduction during the onset of AAV stage. However, the TEM time in this study was 20 min in order to reduce the time of the experiments. Figs. 5–8 indicated a good agreement between the predicted and experimental average moisture contents of paddy during the drying processes. The maximum difference in moisture content was less than 2.5% d.b. at the end of FB drying stage. To understand the moisture distribution inside a paddy grain, the predicted moisture inside a paddy grain of the drying condition B were presented in two figures, i.e. Fig. 9 presented during the stage of FB drying to FIR irradiation, and Fig. 10 presented for overall stages. It could be seen that the moisture content, at the superficial layer Fig. 7. Comparison of predicted and experimental average moisture contents of paddy at condition C: FB (150 C, 1.5 min), Transport (0.5 min), FIR (0.310 W/cm2, 0.5 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). Fig. 9. Predicted moisture profiles inside a paddy grain of drying condition B during fluidized bed drying stage to FIR irradiation stage. Fig. 8. Comparison of predicted and experimental average moisture contents of paddy at condition D: FB (150 C, 1.5 min), transport (0.5 min), FIR (0.7 W/cm2, 0.5 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). FIR energy was mainly absorbed by water molecules inside the grain rather than organic compounds (i.e. proteins and starches). In exposure to AAV after TEM stage, it was noted that the average moisture contents progressively dropped in the first 5 min, and further reduced gradually during the rest of ventilation stage as shown in Figs. 5–8. In fact, if the TEM time was 35 min, according to the recommendation of Poomsa-ad et al. (2002), the curve of moisture content in the first 5 min of AAV stage was sharply less than these moisture curves in this study, because a longer TEM time Fig. 10. Predicted moisture profiles inside a paddy grain of drying condition B during overall stages. 1256 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 under the grain surface, fast approached the equilibrium moisture content (approximately below 5% d.b.) during the stage of FB drying (lines 2 and 3 in Fig. 9). This was mainly because of high mass transfer between the air and the grain due to high air velocity (2.6 m/s). Thereafter, the moisture changes in the deeper layer of a paddy grain were slow during the stages of paddy transport and FIR irradiation (lines 4–6 in Fig. 9), respectively. Tempering paddy for longer than 35 min caused moisture gradient (line 8 in Fig. 10) equalize between the center and surface of the paddy grain. 4.2. Temperature distribution of a paddy grain Figs. 11–14 showed the comparison of predicted and experimental grain temperatures of paddy during drying processes. In order to clarify the effect of FIR intensity, the grain temperature in FIR irradiation stage of conditions A and B were examined for two levels of the FIR intensities of 0.310 and 0.700 W/cm2 as shown in Figs. 11 and 12, respectively. It was evident that the grain temperatures were considerably increased with higher FIR intensity. A similar trend was also observed when the average moisture content after FB drying and transport lower than Fig. 11. Comparison of predicted and experimental grain temperatures of paddy at condition A: FB (150 C, 1 min), transport (0.5 min), FIR (0.310 W/cm2, 1 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). Fig. 13. Comparison of predicted and experimental grain temperatures of paddy at condition C: FB (150 C, 1.5 min), transport (0.5 min), FIR (0.310 W/cm2, 0.5 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). Fig. 12. Comparison of predicted and experimental grain temperatures of paddy at condition B: FB (150 C, 1 min), transport (0.5 min), FIR (0.7 W/cm2, 1 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). Fig. 14. Comparison of predicted and experimental grain temperatures of paddy at condition D: FB (150 C, 1.5 min), transport (0.5 min), FIR (0.7 W/cm2, 0.5 min), TEM (20 min) and AAV (30 min, ambient air condition: 30 C, 70% RH). N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 24% d.b. as shown in Figs. 13 and 14 accordance with conditions C and D, respectively, but the temperature difference between both conditions (C and D) was less than that of A and B’s conditions. This result was due to less water molecules to absorb FIR energy in conditions C and D. The grain temperature after TEM stage suddenly dropped to ambient air temperature (approximately 30 C), and was maintained throughout the AAV period. From Figs. 11–14, it can be seen that the predicted grain temperatures was in good agreement with the experimental grain temperatures during paddy drying processes. The maximum difference in the grain temperatures between the predictions and the experiments did not exceed 5 C at the first 5 min of AAV stage. Figs. 15 and 16 showed the predicted temperature profiles inside a paddy grain in drying condition B during 1257 FB drying stage to FIR irradiation stage and overall stages, respectively. After the changes in grain temperature profile during FB drying and transport of paddy (lines 2–4 in Fig. 15), it can be seen that when exposure to FIR irradiation resulted in an immediate increase in grain temperature within the penetrating layer (line 5 in Fig. 15) until temperature gradient inside a paddy grain almost approached to zero (line 6 in Fig. 15). This phenomenon was because FIR energy directly penetrates into a paddy grain, and induces the mechanism of changes in molecular vibration state, resulting in heating within the penetrating layer of a paddy grain. The grain temperature profile was maintained during the TEM stage (line 7 in Fig. 16), and then it was immediately reduced close to ambient air temperature during AAV stage (lines 8–11 in Fig. 16). Fig. 15. Predicted temperature profiles inside a paddy grain of drying condition B during fluidized bed drying stage to FIR irradiation stage. Fig. 16. Predicted temperature profiles inside a paddy grain of drying condition B during overall stages. 1258 N. Meeso et al. / Journal of Food Engineering 78 (2007) 1248–1258 5. Conclusions Simultaneous heat and mass transfer equations were solved using the finite-difference scheme to predict the changes in paddy moisture content and temperature in a series drying process, comprising fluidized bed drying, transport of paddy, far-infrared irradiation, tempering and ambient air ventilation. The predicted results agreed well with the experimental data. The maximum difference was 2.5% d.b. for average moisture content at the end of fluidized bed drying and 5 C for the grain temperature at the first 5 min of ambient air ventilation. The model indicated that far-infrared irradiation was more effective in moisture reduction of wet paddy than dry paddy, and temperature inside a paddy grain within the penetrating layer was also increased with FIR intensity level. 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