An ASABE Meeting Presentation Paper Number: 131619320 Mathematical modeling and polysaccharide content of Ganoderma lucidum by hot air impingement drying Jun-Wen Bai, Hong-Wei Xiao, Zheng Lou, Zhen-Jiang Gao* College of Engineering, China Agricultural University, Beijing, China Written for presentation at the 2013 ASABE Annual International Meeting Sponsored by ASABE Kansas City, Missouri July 21 24, 2013 [Click here to mention other presentations of this paper (optional)] (The ASABE disclaimer is in a table which will print at the bottom of this page.) Abstract. Drying kinetics of Ganoderma lucidum was investigated in an air impingement dryer at the drying temperature of 55 70 o C with a constant air velocity of 15 m/s. The drying time decreased significantly with the increase of drying temperature. The experimental drying curves showed only a falling rate period. The experimental results were fitted to 10 thin-layer drying models and it was found that modified Page models best described the drying curves. The moisture effective diffusivity ranged from 1.96 10-9 to 6.01 10-9 m 2 /s calculated using the Fick s second law of diffusion. Activation energy for moisture diffusion of the Ganoderma lucidum samples was found to be 69.05 kj/mol. Ganoderma lucidum samples dried at 65 o C revealed the highest polysaccharide content than dried at other temperatures. Keywords. drying, Ganoderma lucidum, air impingement, Mathematical modeling, polysaccharide Introduction Ganoderma lucidum is known as a treasured fungus in most Eastern countries like China, Japan and Korea, for it is very rare in the wild. The fruiting bodies called Lingzhi or magic herb in China, and it has long been used as a folk or oriental medicine to cure various human diseases. Ganoderma lucidum have been proved to be effective in the treatment of chronic hepatopathy, hypertension hyperglycemia and neoplasia (Shi, Zhang and Yang, 2013; Wang et al., 1997). Ganoderma lucidum has been successfully domesticated in artificial culture, so a large amount of ganoderma lucidum will be harvested in a short time. Because it has high moisture content and high enzymatic activity such as peroxidase (POD), Ganoderma lucidum must be treated in one or two days in order to reduce economic losses. Drying is the most common methods for Ganoderma lucidum in order to prevent the reproduction of microorganisms, to prevent active components degradation (Mujumdar, 1997), and to lose weight for reducing transportation costs (Okos, Narsimhan, Singh and Witnauer, 1992; Doymaz, 2012). Drying Ganoderma The authors are solely responsible for the content of this meeting presentation. The presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Meeting presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author s Last Name, Initials. 2013. Title of Presentation. ASABE Paper No. ---. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a meeting presentation, please contact ASABE at rutter@asabe.org or 269-932-7004 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).
lucidum by natural sun drying is the most common methods in China as it is the simplest and most economical technique. But it also has disadvantages that the drying conditions cannot be controlled well so that the quality is usually not as good as expected. Besides, the final product may be contaminated by dust and insects, and it requires long drying time in lower temperature or rainy season (Ren and Mao, 2001). Air-impingement drying technology is an efficient drying process and has been used successfully in some agricultural materials such as grapes (Xiao, Pang, Wang, Bai, Yang and Gao, 2010), yam slices (Xiao, Yao, Lin, Yang, Meng and Gao, 2012), Hami melons (Zhang et al., 2011) and cherry tomatoes (Wang, Gao, Xiao, Lin and Gao, 2011). During air-impingement processing, the air impinges on the product surface at high velocity, removes the thermal boundary layers and increases the rate of heat transfer (Anderson and Singh, 2006). So hot air impingement drying may be suited to the Ganoderma lucidum dehydration and obtain a good quality. Drying is a complex process in which unsteady heat and moisture transfer occur simultaneously (Sahin and Dincer, 2005), and the knowledge of this will be important for process design, energy consumption and product quality. Mathematical modeling has represented a good way to describe and predict drying process. Several different empirical, semi-empirical, and theoretical equations that can be widely used for describe for different material and drying conditions (). However, up to now, little or no information on modeling of the drying kinetics of Ganoderma lucidum. Polysaccharide is one of the most important biologically active components in Ganoderma lucidum, which was reported to play many special roles, such as it can promote the function of macrophages, B cells, T cell s as well as dendritic cells, include strong antioxidant activities and have anti-tumor activities (Shi, Zhang and Yang,2013; Shao, Dai, Xu, Lin and Gao, 2004). Besides, in Pharmacopoeia of China the polysaccharide content of the Ganoderma lucidum should be determined for evaluating the quality. So in this study the polysaccharide content was taken as an indicator of the product quality. Therefore, the current work was undertaken to: (1) Ganoderma lucidum was dried by hot air impingement drier at different temperature of 55 70 o C with a constant air velocity of 15 m/s; (2) model the drying process using 10 thin-layer models; (3) calculate moisture effective diffusivity and activation energy of the drying process; (4) analyze the content of polysaccharide to evaluate the product quality. Materials and Methods Materials Fresh Ganoderma lucidum were picked up from Ganoderma lucidum production base of Lishui of Zhengjiang province. To ensure the uniformity of the physical characteristics of experimental materials, the samples were carefully selected at the same size (average thickness, length and width is 2.52 cm, 16.8 cm, 14.3 cm, respectively). The initial moisture content of samples was determined as 1.516±0.004 kg water/kg dry matter (60.25±0.40%, w.b.). The samples were dried in no more than 24 h after hand-picking. Drying equipment and drying process Fig.1 Schematic diagram of equipment used for impingement drying 1, drying tray; 2, drying samples; 3, drying chamber 4, air velocity sensor 5, drying air distribute chamber 6, drying air channel 7, electric heater 8, centrifugal fan 9, drying air recycle channel 10, Temperature sensor 11, Proportional-Integral-Derivative controller. 2013 ASABE Annual International Meeting Paper Page 1
The schematic diagram of equipment used for drying process is shown in Fig. 1. In this study, the air velocity was at constant value of 15m/s. The drying temperature was at the range of 55-70 o C. When the dryer had reached steady state conditions for the set temperature, the Ganoderma lucidum samples were placed on the drying tray in one layer. At that time, the drying process was started. The weight of samples was measured by an electronic balance having a sensitivity of 0.01 g at 1 h intervals during drying. The samples were dried until they reached the desired final moisture content of 0.149 kg water/kg dry matter (13.0% w.b.). The experiments were repeated three times Mathematical modeling of drying curves The moisture ratio (MR) of the grapes was calculated using the following equation: (1) where M t, M 0 and M e are moisture content at any time of drying (kg water/kg dry matter), initial moisture content (kg water/kg dry matter) and equilibrium moisture content (kg water/kg dry matter), respectively. The drying rate of grape samples during drying experiments was computed using Eq. (2): (2) where t 1 and t 2 are the drying times in hours at different times during dying; M t1 and M t2 is the moisture content of grape samples at time t 1 and t 2, respectively expressed on a dry basis. Drying curves were fitted to 10 drying models, which are widely used in the scientific literature to describe the kinetics of the drying process. The selected thin-layer drying models are identified in Table 1. Table 1 Mathematical models applied for drying curves of Ganoderma lucidum Model No. Model equation Model equation References 1 MR exp Lewis (Newton) Lewis, 1921 2 MR exp Page Page, 1949 3 MR exp Modified Page Overhultset al., 1973 4 MR aexp Henderson & Pabis Henderson & Pabis, 1961 5 MR aexp Logarithmic Yagcioglu, 1999 6 MR aexp bexp Two-term Henderson, 1974 7 MR aexp 1 exp Two-term expotential Sharaf-Eldeenet al., 1980 8 MR 1 at bt Wang & Singh Wang & Singh, 1978 9 MR aexp 1 exp Vermaet al. Vermaet al., 1985 10 MR exp / Modified Page II Diamente & Munro, 1993 The parameters of the model were estimated using non-linear regression analysis by PASW Statistics 18. Three criteria of statistical analysis have been used to evaluate the fitting of the experimental data to the different models: the coefficient of determination (R 2 ), reduced chi-square (χ 2 ) and root mean square error (RMSE). The higher the R 2 value and the lower the χ 2 and RMSE values, the better is the goodness of fit. These parameters can be calculated as: 1,,, (3),, (4)., Where MR exp,i is the ith experimental moisture ratio, MR pre,i is the ith predicted moisture ratio, N is the number of observation and z is the number of measured data. (5) 2013 ASABE Annual International Meeting Paper Page 2
2.6 Determination of moisture effective diffusivity(d eff ) Fick s second law of diffusion equation (Eq. 6) has been widely used to describe the drying process during the falling rate period for agricultural materials. (6) The solution of diffusion equation (Eq. 3) for infinite slab was sloved by Crank (1975), and supposed uniform initial moisture distribution, negligible external resistance, constant diffusivity, and negligible shrinkage, is (Falade and Solademi, 2010; Doymaz,2009; Goyal, Kingsly, Manikantan and Ilyas, 2006): (7) Where, D eff is the moisture effective diffusivity (m 2 /s); L is the half thickness of Ganoderma lucidum samples, with 1.26 10-2 m as its value; t is the drying time expressed in second (s); and n is positive integer. For long time drying times, Eq. 7 can be further simplified to a limiting form of the diffusion equation and expressed in a logarithmic form: (8) The D eff is obtained by plotting the experimental drying data in term s of lnmr versus time. From Eq. (8), a plot of lnmr versus time gives a straight line with a slope of (9) 2.7 Calculation of activation energy The dependence of the effective moisture diffusivity on drying temperature is generally described by the Arrhenius equation (Duc, Han and Keum, 2011; Meziane, 2011; Jokkumar and Pandey, 2012):. (10) Where D 0 is the pre-exponential factor of Arrhenius equation in m 2 /s; Ea is the activation energy in kj/mol; R is the universal gas constant in kj/mol K; T is temperature in o C. The Eq. 10 can be expressed in a logarithmic form (Eq.11). (11). So the activation energy (Ea) can be calculated from the slope of lnd eff versus the reciprocal of the temperature (1/ (T+273.15)). Polysaccharide content The dried Ganoderma lucidum samples were ground into power and take about 2g to use for analysis. The method followed the Pharmacopoeia of China 2005 edition. The content was expressed as g/110g dry product. Results and Discussion Drying kinetics The moisture ratio of the Ganoderma lucidum as a funtionof drying time at different drying temperature of 55-70 o C is shown in Fig. 2. At all drying temperatures, the moisture ratio of the samples was decreased continuously with the drying time. The drying time needed to reduce the moisture from initial moisture content of about 60.2% (w.b.) to desired moisture 13% (w.b.) in the final product was 20, 14, 10 and 7 h at the drying temperature of 55, 60, 65 and 70 o C, respectively. So it is clear that the drying temperature a significant effect on drying time. This might be because higher air temperature can increase the heat transfer between the air and the Ganoderma lucidum samples and accelerate water migration and transfer (Falade and Solademi, 2010). This result was in agreement with previous literature studies on drying of foods such as Monukka seedless grapes (Xiao et al., 2010), pumpkin (Tunde-Akintunde ang Ogunlakin, 2011), apricot (Toğrul and Pehlivan) and kiwifruit (Orikasa, Wu, Shiina and Tagawa, 2008). 2013 ASABE Annual International Meeting Paper Page 3
1.0 Moisture Ratio 0.8 0.6 0.4 55 o C 60 o C 65 o C 70 o C 0.2 0.0 0 2 4 6 8 10 12 14 16 18 20 22 Drying time (h) Fig.2 Effect of drying temperature on drying kinetics of Ganoderma lucidum Fig. 3 shows the effect of drying air temperature on the drying rate of Ganoderma lucidum at 55, 60, 65 and 70 o C. It can be found that the drying rate decreased continuously with drying time, and the entire drying process occurred in the falling rate period like most food products, which illustrated that moisture diffusion controlled the drying process. The absence of constant rate period might be because of that at initial stages of drying the material could not provide a constant supply of moisture for an appreciable period of time (Toğrul and Pehlivan, 2003; Singh and Gupta, 2007). 0.6 Drying rate (g water/g solid hour) 0.5 0.4 0.3 0.2 70 o C 65 o C 60 o C 55 o C 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Moisture content (kg/kg) Fig. 3 Effect of drying temperature on drying rate of Ganoderma lucidum Moisture effective diffusivity and activation energy As the drying rate curves in Fig. 3, the drying process occurred in one falling rate period, so the Fick s second law of diffusion can be used to describe the drying process. The experimental drying data in terms of ln (MR) versus drying time is given in Fig. 4. And the slope can be given from the linear regression of lnmr versus time curves, so the effective diffusion coefficients can be determined as shown in Tab. 2. In Tab. 2, it was found that the D eff was at the range of 1.9625 10-9 m 2 s -1 to 6.0095 10-9 m 2 s -1 under the drying temperature of 55-70 o C, These values lie within the general range from 10-11 to 10-9 m 2 /s for food materials (Madamba, Driscoll and Buckl, 1996).The D eff significantly increased with the increase of drying temperature, it may due to that in the higher drying temperature the water molecules moved faster so that the moisture can be easier to migrate in the environment. 2013 ASABE Annual International Meeting Paper Page 4
0.0-0.5-1.0 55 o C 60 o C 65 o C 70 o C ln MR -1.5-2.0-2.5 0 10 20 30 40 50 60 70 80 Drying time ( 1000s) Fig. 4 lnmr versus drying time of Ganoderma lucidum under different drying temperatures Table 2 Moisture effective diffusion coefficients of Ganoderma lucidum under different drying temperature Drying temperature Linear regression equation R 2 D eff /(10-9 m 2 s -1 ) 55 o C lnmr = -3.05 10-5 t-0.1120 0.9975 1.9625 60 o C lnmr = -4.54 10-5 -0.0663 0.9980 2.9212 65 o C lnmr = -6.32 10-5 t-0.0692 0.9979 4.0664 70 o C lnmr = -9.34 10-5 t-0.0838 0.9937 6.0095 The activation energy is a very important value for indicate the lowest energy to start to remove moisture from inside to the outside of the drying product. The activation energy (Ea) for Ganoderma lucidum was 69.05 kj/mol which can be calculated from the slope of the Arrhenius plot presented in Fig. 5. Some published Ea values of agricultural materials were presented in Table 3. It can be found that Ea for Ganoderma lucidum was similar with the Monukka seedless grape, higher than Carrot, coconut and green peas, lower than Pumpkin. The difference may come from that activation energy for drying process may effect by the components, variety, tissue structures of the samples, drying method and pretreatment. -18.8-19.0-19.2 ln D eff = -8.3058/(T+273.15)+ 5.2645 R 2 = 0.9987-19.4 lnd eff -19.6-19.8-20.0-20.2 2.90 2.95 3.00 3.05 1/(T+273.15 ) ( 10 3 ) 2013 ASABE Annual International Meeting Paper Page 5
Fig. 5 Arrhenius-type relationship between moisture effective diffusivity and drying temperature of Ganoderma lucidum Table 3.Activation energies of Ganoderma lucidum and other agricultural materials Products Ea ( kj/mol) References Ganoderma lucidum 69.05 Present study Seedless grape 67.29 Xiao et al.(2010) Carrot 23.00 Kaya et al.(2009) Pumpkin 78.93 Doymaz (2007) green peas 28.40 Simal et al.(1996) coconut 25.93 Madhiyanon et al.(2009) Mathematical modeling of Drying Curves Table 4 statistical results of mathematical modeling the drying curves Model No. Temperature Model parameters R 2 χ 2 RMSE 55 k=0.1266 0.9869 8.4191 10-4 0.0283 1 60 k=0.1774 0.9927 5.3061 10-4 0.0222 65 k=0.2492 0.9963 3.0435 10-4 0.0167 70 k=0.3762 0.9973 2.6441 10-4 0.0152 55 k=0.1802 n=0.8385 0.9997 1.9581 10-5 0.0042 2 60 k=0.22184 n=0.8792 0.9988 9.7750 10-5 0.0092 65 k=0.2900 n=0.8998 0.9999 7.3770 10-6 0.0024 70 k=0.4173 n=0.9080 0.9997 3.4899 10-5 0.0051 55 k=12.565 n=.83846 0.9997 1.9581 10-5 0.0042 3 60 k=0.1804 n=0.8792 0.9988 9.7748 10-5 0.0092 65 k=0.2526 n=0.8998 0.9999 7.377 10-6 0.0024 70 k=0.3819 n=0.9080 0.9997 3.4899 10-5 0.0055 55 k=0.1180 a=0.9399 0.9936 4.3111 10-4 0.0198 4 60 k=0.1692 a=0.9580 0.9960 31621 10-4 0.0166 65 k=0.2425 a=0.9752 0.9975 23412 10-4 0.0138 70 k=0.3793 a=0.9851 0.9977 26239 10-5 0.014 55 k=0.1429 a=0.8996 b=0.0654 0.9971 2.1102 10-4 0.0134 5 60 k=0.1870 a=0.9328 b=0.0370 0.9969 2.6473 10-4 0.0014 65 k=0.2764 a=0.9410 b=0.0483 0.9992 8.3623 10-5 0.0078 70 k=0.4233 a=0.9485 b=0.0488 0.9998 2.3822 10-5 0.0038 55 k 1 =0.1048 k 2 =0.6848 a=0.8344 b=0.1656 0.9999 3.9461 10-6 0.0018 6 60 65 k 1 =0.1792 k 2 =0.1798 k 1 =0.2176 k 2 =0.9336 a=11.8414 b=- 10.8688 a=0.8646 b=0.1353 0.9955 4.1499 10-4 0.1746 0.9999 9,2061 10-6 0.0024 70 k 1 =0.1735 k 2 =0.4856 a=0.2319 b=0.7669 0.9999 2.2993 10-5 0.0034 7 55 k=0.6289 a=0.1669 0.9999 6.3707 10-6 0.0024 2013 ASABE Annual International Meeting Paper Page 6
60 k=1.5730 a=0.10061 0.9996 3.0511 10-5 0.0005 65 k=0.4489 a=0.3991 0.9997 3.0405 10-5 0.0050 70 k=0.6265 a=0.4316 0.9998 1.9023 10-5 0.0038 55 a=-0.1047 b=0.0031 0.9669 2.2501 10-5 0.0452 8 60 a=-0.1452 b=0.0060 0.9765 1.8456 10-3 0.0340 65 a=-0.2042 b=0.1186 0.9839 1.4852 10-3 0.0348 70 a=-0.3025 b=0.0255 0.9872 1.4760 10-3 0.0333 55 a=0.8344 k=0.1048 g=0.6849 0.9999 3.7269 10-6 0.0018 9 60 a=0.90286 k=0.1587 g=1.9428 0.9996 3.1013 10-5 0.0050 65 a=0.13526 k=0.9353 g=0.2176 0.9999 8.0573 10-6 0.0024 70 a=0.5000 k=0.3762 g=0.3762 0.9973 37017 10-4 0.0152 55 k=12.565 n=0.8385 0.9997 1.9581 10-5 0.0042 10 60 k=19.0156 n=0.8792 0.9988 9.7748 10-5 0.0092 65 k=27.5845 n=0.8998 0.9999 7.3773 10-6 0.0024 70 k=41.3807 n=0.9080 0.9997 3.4899 10-5 0.0051 The experimental data of Moisture ratio (MR) were fitted to the 10 drying models in Table 1. Non-linear regression was used to obtain each parameter value of every model. The Model parameters and statistical results including and R 2, χ2 and RSME is in table 4. For Ganoderma lucidum drying, the 10 drying models shown that statistical results were 0.9765-0.9999 for R 2, 3.7269 10-6 -1.8456 10-3 for χ2 and 0.0005-0.0452 for RSME. Compare with the 10 models, the modified Page have the higher R 2, lower χ 2 and RSME, so the modified page models can be used for predict and control the drying process. Polysaccharide content of the dried product 1.4 1.2 Polysaccharide content (g/100g) 1.0 0.8 0.6 0.4 0.2 0.0 55 60 65 70 Drying temperature ( o C) Fig. 6 Polysaccharide content of the dried Ganoderma lucidum at different drying temperature Polysaccharide content of the dried Ganoderma lucidum at different drying temperature is presented in Fig. 6. It was indicated that polysaccharide content was increased when the drying temperature was increased from 55 o C to 65 o C. However, it decreased when the drying temperature was in 70 o C. The polysaccharide content may be influenced by the peroxidase, temperature and drying time. In lower temperature of 55 o C, it need about 20 h to decreased moisture to the required moisture content, the polysaccharide content may degraded by the peroxidase in that long drying time. In the high temperature of 70 o C, although the drying time was short, the polysaccharide can be easily disintegrated in high temperature. So the highest polysaccharide content was obtained at air temperature of 65 o C. 2013 ASABE Annual International Meeting Paper Page 7
Conclusion Ganoderma lucidum was dried in an air impingement dryer at the drying temperature of 55 70 o C with a constant air velocity of 15 m/s. Drying temperature had a significant effect on drying time. The experimental drying curves showed only a falling rate period. The moisture effective diffusivity ranged from 1.96 10-9 to 6.01 10-9 m 2 /s calculated using the Fick s second law of diffusion. Activation energy for moisture diffusion of the Ganoderma lucidum samples was found to be 69.05 kj/mol. The experimental results were fitted to 10 thinlayer drying models and it was found that modified Page models best described the drying curves.ganoderma lucidum samples dried at 65 o C revealed the highest polysaccharide content than dried at other temperatures. This research provides technical basis for applying the air impingement drying technology to Ganoderma lucidum drying. Acknowledgements Project supported by the National Natural Science Foundation of China (Grant No. 31201436). References Anderson, B. A., Singh, R. P., 2006. Modeling the thawing of frozen foods using air impingement technology. International Journal of Refrigeration, 29(2), 294 304. Crank, J., 1975. The Mathematics of Diffusion (second Ed). Oxford University Press, London, UK. Doymaz, I., 2007. The kinetics of forced convective air-drying of pumpkin slices. Journal of Food Engineering, 79(1), 243-248. Doymaz, I., 2009. An Experimental Study on Drying of Green Apples. Drying Technology, 27(3), 478-485. Doymaz, I., 2012. Sun drying of seedless and seeded grapes. Journal of Food Science and Technology-Mysore, 49(2), 214-220. Diamente, L.M. & Munro, P.A., 1993. Mathematical modelling of the thin layer solar drying of sweet potato slices. Solar Energy, 51, 271 276. Duc, L. A., Han, J. W., & Keum, D. H., 2011. Thin layer drying characteristics of rapeseed (Brassica napus L.). Journal of Stored Products Research, 47(1), 32-38. Falade, K. O., & Solademi, O. J., 2010. Modelling of air drying of fresh and blanched sweet potato slices. International Journal of Food Science & Technology, 45(2), 278-288. Goyal, R. K., Kingsly, A. R. P., Manikantan, M. R., & Ilyas, S. M., 2006. Thin-layer Drying Kinetics of Raw Mango Slices. Biosystems Engineering, 95(1), 43-49. Henderson, S.M. & Pabis, S., 1961. Grain drying theory. Temperature effect on drying coefficient. Journal of Agricultural Engineering Research, 6, 169 174. Joykumar Singh, N., & Pandey, R. K., 2012. Convective air drying characteristics of sweet potato cube (Ipomoea batatas L.). Food And Bioproducts Processing, 90(2), 317-322. Kaya, A., Aydın, O., & Demirtaş, C., 2009. Experimental and theoretical analysis of drying carrots. Desalination, 237(1 3), 285-295. Lewis, W.K., 1921. The rate of drying of solid materials. Industrial Engineering Chemistry, 13, 427 432. Madamba, P.S., Driscoll, R.H. & Buckle, K.A., 1996. The thin-layer drying characteristics of garlic slices. Journal of Food Engineering, 29, 75 97. Madhiyanon, T., Phila, A., & Soponronnarit, S., 2009. Models of fluidized bed drying for thin-layer chopped coconut. Applied Thermal Engineering, 29(14-15), 2849-2854. Meziane, S., 2011. Drying kinetics of olive pomace in a fluidized bed dryer. Energy Conversion and Management, 52(3), 1644-1649. Mujumdar, A.S., 1997. Drying fundamentals. In Industrial Drying of Foods (C.G.J. Baker, Ed.) Chapman and Hall, London. Okos, M.R., Narsimhan, G., Singh, R.K. & Witnauer, A.C., 1992. Food dehydration. In: Handbook of food engineering. Heldman DR, Lund DB (ed), Marcel Dekker, New York. Orikasa, T., Wu, L., Shiina, T., & Tagawa, A., 2008. Drying characteristics of kiwifruit during hot air drying. Journal of Food Engineering, 85(2), 303-308. Overhults, D.G., White, H.E., Hamilton, H.E. & Ross, I.J., 1973. Drying soybean with heated air. Transactions of ASAE, 16, 112 113. Page, G.E., 1949. Factors influencing the maximum rates of air drying shelled corn in thin layers. MSc Thesis, Purdue University. Ren, D.F. and Mao, Z.H., 2001. Present situation and developing trend on drying of Chinese herbs. Trans. CSAE 17, 5 8 (in Chinese with English abstract). Sahin, A. Z., & Dincer, I., 2005. Prediction of drying times for irregular shaped multi-dimensional moist solids. Journal of 2013 ASABE Annual International Meeting Paper Page 8
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