TWO-DIMENSIONAL MATHEMATICAL MODEL FOR SIMULATION OF THE DRYING PROCESS OF THICK LAYERS OF NATURAL MATERIALS IN A CONVEYOR-BELT DRYER

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1 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp TWO-DIMENSIONAL MATHEMATICAL MODEL FOR SIMULATION OF THE DRYING PROCESS OF THICK LAYERS OF NATURAL MATERIALS IN A CONVEYOR-BELT DRYER by Duško R. SALEMOVIĆ a, Aleksandar Dj. DEDIĆ b*, and Nenad Lj. ĆUPRIĆ b a High Technical School, Departent of Mechanical Engineering, Zrenjanin, Serbia b Faculty of Forestry, University of Belgrade, Belgrade, Serbia Original scientific paper This paper presents the atheatical odel and nuerical analysis of the convective drying process of thick slices of colloidal capillary-porous aterials slowly oving through conveyor-belt dryer. A flow of hot oist air was used as drying agent. The drying process has been analyzed in the for of a 2-D atheatical odel, in two directions: along the conveyor and perpendicular on it. The atheatical odel consists of two non-linear differential equations and one equation with a transcendent character and it is based on the atheatical odel developed for drying process in a for of a 1-D thin layer. The appropriate boundary conditions were introduced. The presented odel is suitable for the autoated control of conveyor-belt dryers. The obtained results with analysis could be useful in predicting the drying kinetics of potato slices and siilar natural products. Key words: drying, thick layer, conveyor-belt dryer, odeling, autoatic control, siulation Introduction Drying as a ethod for the preservation of food has been used for centuries. Dried food retains its biological and nutritional values and is resistant to the influence of old and bacteria. The drying process of the group of colloidal capillary-porous aterials, where natural aterials belong, is one of the ost coplex processes to study. Natural agricultural products are dried by using different types of drying technologies. The transfer of huidity fro soe substance into drying agent, usually hot oist air, is a coplex process of heat necessary for that process and ass transfer. Many studies have been done on the transfer of heat and oisture during the drying process of natural aterials like wood, vegetables, fruits, edical herbs, etc. The review of the generally used 1-D analytical odels of drying agriculture products based on a thin-layer has been presented in [1-4]. A non-linear partial differential equation was solved nuerically [5, 6], and a linear correlation was considered between the thickness of the aterial and its oisture content. In [7, 8] the iportance of internal and external heat transfers in a contact dryer was highlighted. The 2-D odels were introduced in a case where the thickness of the dried aterials could not be neglected. In [9, 10] the finite-volue ethod was used to solve the nuerical * Corresponding author, e-ail: aleksandar.dedic@sfb.bg.ac.rs

2 1370 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp odel of a conveyor-dryer. In [11] the drying process of a packed bed of porous particles by using superheated stea and huid air is odeled by 1-D atheatical odel of heat and ass transfer. The governing partial differential equations, which were transfored into a non-siilar for by using a special transforation is presented in [12]. The resulting partial differential equations were solved nuerically by using an iplicit finite difference ethod. In [13] the industrial dryer used for the oisture reoval fro wet raisins was investigated and gave suggestion for the controller according to drying odel. A ethod of lines and without involving any adjustable paraeter or nuerically solving the dynaic 2-D odel for drying of ate leaves (Ilex paraguariensis) is presented in [14]. In [15] drying of corn grains in conveyor dryer was analyzed and nuerical solution using finite-volue ethod were presented. In this paper an original 2-D atheatical odel for defining the essential drying paraeters of a ovable layer of thick slices of colloidal capillary-porous aterials in a conveyor-belt dryer, using hot oist air as the drying agent, is presented. The background of this odel is presented in [1] where the drying process was analyzed in the for of a 1-D thin layer. It could be used for defining the drying kinetics of potatoes and siilar natural products. Obtained atheatical equations could be used for the autoated control of the drying process. Methodology and aterial Previously presented odels have structure which is not applicable for the autoated control of a convective drying process in industrial conveyor dryers. They are developed for drying aterial which does not ove through the stea of a drying agent. Also, deterination of drying kinetics curves of the whole layer by experients and defining dependences using the average values of the nuber of particles of the aterial and oisture content in the layer is insufficient to study the drying process of the thick layer of the natural aterials. The ain reason is that changes of paraeters values along the height of the thick layer have non-linear variation. The here presented ethod and odel for the deterination of drying kinetics curves is based on the experiental results obtained in the Vinča Institute of Nuclear Science, Belgrade, and have been presented in [16-19]. The ain iproveent of the odel is ade by introducing the corrective coefficient in balance equations of oisture and heat for the thick layer of drying aterial which is oving through strea of drying agent in the industrial conveyor dryers. The ethod of a thick layer of natural aterials is based on the odel and results obtained in the previous study of drying kinetics of a thin layer, presented in [1]. The thin layer height is sall enough and all the changes of the drying paraeter values along its height are linear and differentially sall. The thick layer is divided into a nuber of thin layers which influence each other. The previously defined odel [1] is now used for defining the changes of drying paraeters inside the thick layer by nuerically solving partial differential equations, obtained on the basis of aterial and heat balance of each of the thin layers. The following types of resistance are typical during the convective drying process: external resistance of oist convection fro the aterial surface to the drying agent, and internal resistance of oist conduction fro the inside of the aterial up to its surface. The theory of heat and ass transfer explained the first process in detail. The second one is uch ore coplex and it depends on any factors and requires a lot of experiental work for each natural product separately. Soe of results were presented in [16-18, 20-24]. The presented algorith was used for odeling the drying process of thick layers consists of sall potato cubes. Potato (Solanu tuberosu) was chosen because dried potato

3 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp has widespread use in the food industry. According to [25] approxiately 75% of all dried food in Russia belongs to dried potato products. In Serbia 80% of all annual production belongs to Desiree potato varieties. That potato variety was used for the experients in [16-18] and all necessary input data for here presented nuerical siulation are used fro those references. The atheatical odel The conveyor-belt dryer for natural products (vegetables, fruits, edical herbs, etc.), which is used for this analyze, consists of several segents. The scheatic view of the first segent is presented on fig. 1 [1, 19]. It consists of a belt conveyor which oves sall particles of oist aterial slowly through the flow of the drying agent. Sall particles of oist aterial have the approxiate shape as cubes with average thickness of h = 48. They ake porous thick layer of oisture aterial. The drying agent is preheated oist air with exactly defined characteristics. The drying agent flows through the belt conveyor and through the gaps between slices of the oist aterial up fro the botto, perpendicularly to the oving direction of the oist aterial. Each segent has its own belt conveyor, fan and heater for the drying agent. The velocity of the belt conveyor in each segent is different, as well as the flow velocity and teperature of the drying agent. The atheatical odel of the convective drying process of thick ovable layer of oist aterial has the for of four non-linear partial differential equations with constant coefficients and with an algebraic equation of a transcendent character, additionally included. In accordance with [1] the following assuptions were accepted: the velocity of the drying agent in the direction of co-ordinate axes η is negligibly sall, the velocity of the drying agent in the direction of co-ordinate axes ν has a constant value, the total pressure of drying agent has a constant value, the oist aterial velocity in the oving direction (axes η) depends only on tie, which eans that the aterial oves along the conveyor without slipping, the velocity of the oist aterial in the oving direction (axes η) is negligibly sall, and the heat transfer (α) and oisture transfer (β) coefficients have constant values. The atheatical odel is presented as: xa ν β S ν Figure 1. Siplified schee of the convective conveyor-belt dryer [19] [ p R ρ x ( θ θ )] = wvs wv da a a + wa ρda θa αs = ( θa θ) ν wρ ( c + xc ) a da pda a pwv L = 1500 Drying agent flow x β S = [ pwvs R wvρdaxa ( θa + θ0) ] (3) η w ρd θ αs βs = ( θa θ ) [ pwvs R wvρdaxa ( θa + θ0)( ] r0 Krθ ) η w ρd ( cd + xc w) w ρd ( cd + xc w) (4) w a 0 w h = 48 η (1) (2)

4 1372 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp The syste of eqs. (1)-(5) defines the changes of huidity, x a, and the teperature of the drying agent oist air, θ a, as well as of the oisture, x, and teperature of the oisture aterial, θ, and the values of partial pressure of water vapor on the oisture aterial surface, p wvs, in dependence of two space co-ordinates, horizontal, η, and vertical, ν. For this syste of equations the boundary conditions are: h j = j = 1 j = 2 j = 1 j = 0 i = 0 i = 1 i = 2 i = n 3 i = n 2 i = n 1 i = n Figure 2. Boundary contour for the syste of eqs. (1)-(5) L 1 k ( θ + θ ) + k pwvs ln 1 p2θ a1 a2 p3 + θ 1 10 θ p βs k wvs wv da a a 2 0 θ0 k1( θ + θ0) ρd x A x = [ p R ρ x ( θ + θ0)] x (5) xa( ην, ) = ν 0 xa( η,0) = = xa0 (6) θa( η, ν) = ν 0 θa( η,0) = = θ (7) a0 x( ην, ) = η 0 x(0, ν) = = x (8) 0 θ( ην, ) = η 0 θ(0, ν) = = θ (9) 0 p ( ην, ) = = = p (0,0) = p (10) wvs η 0, ν 0 wvs wvs0 On fig. 2. the boundary contours presented. It is a rectangle with the length, L, equal to the length of the conveyor segent, and height, h, equal to the height of the thick layer on the conveyor (h = 48 ). The boundary contour is valued for the syste of eqs. (1)-(5), with boundary conditions (6)-(10). The coplete forulation of the atheatical odel, presented in this paper, with detailed clarification of physical eaning of all values given in eqs. (1)- (5), is given in details in [1]. The expressions used for heat transfer coefficient α [W 2 K 1 ] and ass (oisture) transfer coefficient β [kg 2 Pa 1 s 1 ] are taken fro literature [26, 27]. The syste of eqs. (1)-(5), with boundary conditions (6)-(10) can not be solved analytically. For that reason nuerical analysis was chosen as the ethod for solving the presented syste of equations. The following auxiliary values are introduced for the partially transforation of the syste of eqs. (1)-(5):

5 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp w β S 1 = (11) aρda αs 2 = (12) wa ρda β S 3 = (13) w ρd αs Nuerical algorith for solving the atheatical odel 4 = (14) w ρd The coplete algorith of nuerical solution of the syste of eqs. (1)-(4), with boundary conditions (6)-(10) and boundary contour given on fig. 2 is developed by using the Euler ethod of siple definite differences. For additional algebraic eq. (5) the Newton ethod of tangent is applied. In the process of nuerical integration the correct selection of the value for integration step, Δ, is extreely iportant since the stability of a solution depends on it significantly. As a natural and logical solution for the value of the integration step, the ean equivalent diaeter of a particle, d e, has been accepted, = d e. The first step of the algorith of nuerical integration is to define the network by dividing the boundary contour, fig. 2, into equal segents with sae width and height as the adopted integration step, Δ. Now, it is possible to define the coplete algorith for nuerical solution of syste of equations with boundary contour given on fig. 2. Before solving equations of the coplete boundary contour it is necessary to solve the equations in the nodes on the very edges of the boundary contour. The values of x a and θ a are defined by boundary conditions (6) and (7), while the values of x and θ are calculated by eans of algorith having in ind eqs. (3) and (4) and auxiliary values (13) and (14). It is obtained: x θ = x (15) ai,0 a0 = θ (16) ai,0 a0 x = x [ p R ρ x ( θ + θ )] (17) i,0 i1,0 3 wvsi1,0 wv da a0 a0 0 θ = θ + ( θ θ ) 4 i,0 i1,0 a0 i1,0 cd + x c i1,0 w [ p R ρ x ( θ θ )]( r K θ ) 3 wvs i 1,0 wv da a0 a r i1,0 cd + x c i1,0 w (18) This algorith is valid for i = 0-p, j = 0. The values of x a and θ a are calculated by eans of algorith having in ind the eqs. (1) and (2), and auxiliary values (11) and (12). The values x and θ are defined by the boundary conditions (8) and (9), as:

6 1374 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp x = x + [ p R ρ x ( θ + θ )] (19) a0, j a0, j1 1 wvs0, j1 wv da a0, j1 a0, j1 0 θ θ 2 = ( θ θ ) a0, j a0, j1 a0, j1 0 cpda + xa c 0, j1 pwv (20) x θ = x (21) 0, j 0 = θ (22) 0, j 0 This algorith is valid for i = 0, j = 0-q. After solving those equations it is possible to start solving of the equations in nodes within the boundary contour. For all points for which the next conditions are valid: i = 1 p, j = 1 q (23) the values of x a, θ a, x, θ, and p wvs, are obtained by the following algorith: xa = x,, 1 1[ R (, 1, 1, 1 0)] i j a + p i j wvs i j wvρdaxa θ i j a + θ i j (24) 2 θ = θ ( θ θ ) ai, j ai, j1 ai, j1 i, j1 cpda + xa c i, j1 pwv (25) x = x, 1, 3[ R ( 1, 1, 1, 0)] i j p i j wvs i j wvρdaxa θ i j a + θ i j (26) θ = θ + ( θ + θ ) 4 i, j i1, j ai1, j i1, j cd + x c i1, j w [ p R ρ x ( θ θ )]( r K θ ) 3 wvs i 1, j wv da ai 1, j a + i 1, j 0 0 r i1, j cd + x c i1, j w Discussion of the results of the nuerical siulation In order to exaine the stability of the nuerical solution of the syste of four non-linear partial differential equations of the convective drying process of natural aterials, the boundary conditions have been varied. The boundary conditions in essence are the input paraeters of the atheatical odel. Initial values for huidity of drying agent, x a, and its teperature, θ a, were adopted in accordance with [1, 16, 17] and there are in the zone above the line of saturation. The influence of the drying agent huidity was analyzed for values between x a ={0.06 and 0.08} kg wv /kg da and teperature in interval between θ a ={100 and 120} ºC. Presented results are obtained using values for initial oisture content and ass (oisture) transfer coefficient obtained experientally for potato (Solanu tuberosu) as drying aterial, given in [16, 17]. The belt conveyor length was L = 1.5 and the velocity of the conveyor was w = /s. The potato pieces had the for of a cube, with the edge d e = 6. The length of the edge of the potato cube, = d e, was chosen for the step of nueric integration, foring 2-D net with 2259 nodes at the boundary contour, 251 steps in the direction of the η-axes and 9 steps in the direction of the ν-axes, fig. 2. The product layer on the belt conveyor had the height of h = 48 and it was porous with the gaps between the cubes. The value of initial huidity and teperature for oist potato cubes were: x 0 = kg w /kg d, θ 0 = 20 C. All calculations were ade in EXCEL. (27)

7 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp The obtained results, presented on the following figures, clearly show that the here presented atheatical odel is very stable without any noticeable eleents of the divergence of nuerical results. On figs. 3 and 4 changes of the absolute huidity of the drying agent are presented for the two different starting values of drying agent teperature, θ a, and the drying agent huidity, x a. In the beginning of the drying process, the drying agent becoes saturated just after it passed the first layer of the cubes because of the intensive heat transfer to potato cubes, which is presented on figs. 5 and 6. The drying agent teperature drop down is presented on fig. 7. At the sae tie the high initial huidity of drying agent and the difference between the teperatures of potatoes cubes and drying agent is enough to cause condensation on layers of the cubes. Condensation has a positive effect because the water vapor fro the drying agent, during the condensation, releases the latent heat of the phase change and heats the drying aterial. Those two reasons caused that in the beginning the potato cubes did not lose any oisture fro their boundary layer surface at all, which is presented on fig. 8. By the tie, the teperature of the potato cubes rises, fig. 9, the heat transfer fro the drying agent becoes less, which causes the drop of drying agent teperature to becoe saller, as well as the teperature difference between potato cube and the drying agent. The drying agent becoes unsaturated and the process of oisture transfer trough the boundary lay- Absolute huidity of drying agent [kg wv kg da 1 ] [θ a = 100 C] [x a = 0.06] [ν = 12] [] Position and tie spent in the dryer Figure 3. Changes of the relative huidity of the drying agent x a = 0.06 kg wv /kg da, θ a = 100 C [x a = 0.06] 1.3 [θ a = 100 C] [ν = 12] [] Position and tie spent in the dryer Figure 5. Changes of the relative huidity of the drying agent x a = 0.06 kg wv /kg da, θ a = 100 C [ ] Relative huidity of drying agent Absolute huidity of drying agent [kg wv kg da 1 ] [θ a = 120 C] [x a = 0.08] [ν = 12] [] Position and tie spent in the dryer Figure 4. Changes of the relative huidity of the drying agent x a = 0.08 kg wv /kg da, θ a = 120 C [ ] Relative huidity of drying agent [x a = 0.08] 1.3 [θ a = 120 ºC] [ν = 12] [] Position and tie spent in the dryer Figure 6. Changes of the relative huidity of the drying agent x a = 0.08 kg wv /kg da, θ a = 120 C

8 1376 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp Teperature of drying agent [ C] [ν = 12] 20 [θ a = 100 C] [x a = 0.06] [] Position and tie spent in the dryer Figure 7. Changes of the teperature of the drying agent x a = 0.06 kg wv /kg da, θ a = 100 C Moisture content of drying aterial [kg w kgd 1 ] [x a = 0.06] [θ a = 100 C] [] Position and tie spent in the dryer Figure 8. Changes of the oisture content of drying aterial [ν = 12] Teperature of drying aterial [ C] [ν = 12] 20 [θ a = 100 C] [x a = 0.06] Position and tie spent in the dryer Figure 9. Changes of the teperature of drying aterial [] [s] er of potato cubes begins, firstly on the lower layers of potato cubes and in tie in the iddle and upper layers. For the top ost layer, fig. 5, ν = 48, θ a = 100 ºC, and x a = 0.06 kg wv /kg da, the period when the drying agent is saturated lasts 159 seconds. It becoes shorter for the higher drying agent teperatures and the drying agent huidity. For the sae layer, it lasts 36 seconds for θ a = 120 ºC, and x a = 0.08 kg wv /kg da, fig. 6. It is also obvious that the oisture transfer is higher at the beginning of the process and on the layers which first have contact with drying agent, fig. 7. The ain reason is that transfer of oisture fro the boundary layer surface, of the wet aterial to the drying agent needs uch less energy and tie than the transfer of oisture fro the inside of the drying aterial to the surface. The obtained results of nuerical siulation clearly showed good agreeent with experiental results presented in [16, 17]. Conclusions The presented original atheatical odel describes changes in thick layers of natural aterials and it treats heat and ass transfer on the surface and inside the aterial as one continuu, but with specific differences. It is suitable for the siulation of the drying process of thick aterials and for application in autoated control of belt conveyer dryers. The presented results, obtained using potato cubes as drying aterial, show the differences of the drying kinetic on different layers of the thick drying aterial, following the changes of the drying agent oisture and teperature as well as the oisture and teperature of drying aterial. The nuerical solution of the atheatical odel gives very stable results. It is clearly shown that the increase of enthalpy of the drying agent caused increase of the dry-

9 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp ing agent absorbing capacity of oisture fro drying aterial. With the increase of enthalpy the heat transfer on to drying aterial becoes ore intensive and the period during which the drying agent is saturated, becoes shorter. Acknowledgent This aterial is based upon work partly supported by the Ministry of Education, Science and Technological Developent of the Republic of Serbia. Also, the authors would like to thank the anonyous reviewers for their useful coents. Noenclature A constants, [ ] c d specific heat capacity of dry aterial, [Jkg 1 K 1 ] c pda specific heat of dry air, [Jkg 1 K 1 ] c pwv specific heat of water vapor, [Jkg 1 K 1 ] c w specific heat capacity of water, [Jkg 1 K 1 ] d e equivalent diaeter of a particle, [] h height of oist aterial on belt transporter, [] K r constant, [ ] k 1, k 2 constants, [ ] k 3, k 4 constants, [ ] L length of belt conveyor, [] 1, 2 constants, [ ] 3, 4 constants, [ ] p wv partial pressure of water vapor of drying agent, [Pa] p wvs partial pressure of water vapor on surface of oist aterial, [Pa] p 1, p 2 constants, [ ] p 3 constants, [ ] R wv gas constant of water vapor, [Jkg 1 K 1 ] r 0 latent heat of evaporation of water at 0 C, [Jkg 1 ] S specific surface of layer of oist aterial, [ 2 3 ] w a velocity of draying agent, [s 1 ] w velocity of oist aterial, [s 1 ] x a absolute huidity of drying agent oist 1 air, [kg wv kg da ] x oisture content of drying 1 aterial, [kg w kg d ] Greek sybols α heat transfer coefficient, [W 2 K 1 ] β ass (oisture) transfer coefficient, [kg 2 Pa 1 s 1 ] step of nuerical integration, [ ] η,ν space co-ordinate, [] θ a teperature of drying agent oist air, [ C] θ teperature of drying aterial, [ C] θ 0 constant (θ 0 = ), [K] ρ da partial density of dry air, [kg da 3 a] ρ d partial density of dry aterial, [kg d 3 ] References [1] Saleović, D. R., et al., A Matheatical Model and Siulation of the Drying Process of Thin Layers of Potatoes in a Conveyor-Belt Dryer, Theral Science, 19 (2015), 3, pp [2] Xanthopoulos, G, et al., Applicability of a Single-Layer Drying Model to Predict the Drying Rate of Whole Figs, Journal of Food Engineering, 81 (2007), 3, pp [3] Aghbashlo, M., et al., Energy and Exergy Analyses of Thin-Layer Drying of Potato Slices in a Sei-Industrial Continuous Band Dryer, Drying Technology, 26 (2008), 12, 4, pp [4] Srikiatden, J., Roberts, J. S., Predicting Moisture Profiles in Potato and Carrot During Convective Hot Air Drying Using Isotherally Measured Effective Diffusivity, Journal of Food Engineering, 84 (2008), 4, pp [5] Batista, M. L., et al., Thin Layer Drying of Chitosan Considering the Material Shrinkage, Proceedings, 14 th International Drying Syposiu, Sao Paulo, Brazil, 2004, Vol. C, pp [6] Pinto, A. A., Tobinaga, S., Diffusive Model with Shrinkage in the Thin-Layer Drying of Fish Muscles, Drying Technology, 24 (2006), 4, pp [7] Lecote, D., et al., Method for the Design of a Contact Dryer-Application to Sludge Treatent in Thin Fil Boiling, Drying Technology, 22 (2004), 9, pp [8] Midilli, A., et al., A New Model for Single-Layer Drying, Drying Technology, 20 (2002), 7, pp [9] Khankari, K. K., Patankar, S. V., Perforance Analysis of a Double-Deck Conveyor Dryer a Coputational Approach, Drying Technology, 17 (1999), 10, pp

10 1378 THERMAL SCIENCE: Year 2017, Vol. 21, No. 3, pp [10] Dong, C., et al., Nuerical Modeling of Containant Transport in Fractured Porous Media Using Mixed Finite-Eleent and Finite Volue Methods, Journal of Porous Media, 14 (2011), 3, pp [11] Souad, M., et al., Matheatical Modeling of a Packed Bed Drying with Huid Air and Superheated Stea, Journal of Porous Media, 14 (2011), 2, pp [12] Daseh, R. A., Duwairi, H. M., Thero-Phoresis Particle Deposition: Natural Convection Interaction fro Vertical Pereable Surfaces Ebedded in a Porous Mediu, Journal of Porous Media, 12 (2009), 1, pp [13] Kiranoudis, C. T., et al., Dynaic Siulation and Control of Conveyor-Belt Dryers, Drying Technology, 12 (1994), 7, p [14] Koop, L., et al., A Dynaic Two-Diensional Model for Deep-Bed Drying of Mate Leaves (Ilex paraguariensis) in a Single-Pass/Single-Zone Conveyor-Belt Dryer, Drying Technology, 33 (2015), 2, pp [15] Pereira de Farias, R., et al., Drying of Grains in Conveyor Dryer and Cross Flow: A Nuerical Solution Using Finite-Volue Method, Revista Brasileira de ProdutosAgroindustriais, Capina Grande, 6 (2004), 1, pp.1-16 [16] Milojević, D., Analysis of Heat and Mass Transfer of Convective Drying Process of Natural Products (in Serbian), M. Sc. thesis, University of Belgrade, Belgrade, Serbia, 1979 [17] Raković, A., Analysis of Drying Kinetics of Natural Products (in Serbian), M. Sc. thesis, University of Belgrade, Belgrade, Serbia, 1987 [18] Stakić, B. M, Nuerical Study on Hygroscopic Capillary-Porous Material Drying in Packed Bed, Theral Science, 4 (2000), 2, pp [19] Saleović, D., Matheatical Modeling, Siulation and Identification of Drying Process of Natural Products in Striped Drying Chaber (in Serbian), Ph. D. thesis, University of Belgrade, Belgrade, Serbia, 1999 [20] Dedić, A., Siplifying Convective Heat and Mass Transfer in Moisture Desorption of Oak Wood by Introducing Characteristic Transfer Coefficients, HolzalsRoh und Werkstoff, 58 (2000), 1-2, pp [21] Dedić, A., et al., A Three Diensional Model for Heat and Mass Transfer in Convective Wood Drying, Drying Technology Journal, 21 (2003), 1, pp [22] Dedić, A., et al., Modelling the Process of Desorption of Water in Oak [QuercusRobur] Wood, Holzforschung, 58 (2004), 3, pp [23] Dedić, A., Deterination of Coefficients in the Analytical Solution of Coupled Differential Equations of Heat and Mass Transfer During Convective Drying of Heat-treated Wood, Journal of Porous Media, 15 (2012), 1, pp [24] Dedić, A., Genić, S., Modelling of the Coupled Process of Heat and Mass Transfer During Convective Drying of Capillary-Porous Anisotropic Materials (in Serbian), Monograph, University of Belgrade, Belgrade, Serbia, 2015 [25] Filonenko, K. А., et al, Sushka Pishchevikov Rustitel nykh Materialov (Drying Plants for Vegetables in Russian), Pishchevaya proyshlenost, Moscow, 1971 [26] Pakowski, Z., Mujudar, A. S., Basic Process Calculations and Siulations in Drying, in: Handbook of Industrial Drying (Ed. A. S. Mujudar), CRC Press, New York, USA, 2007, pp [27] Eckert, E. R. G., Drake, R. M., Analisys of Heat and Mass Transfer, McGraw-Hill, New York, USA, 1972 Paper subitted: March 8, 2016 Paper revised: July 29, 2016 Paper accepted: October 3, Society of Theral Engineers of Serbia Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 ters and conditions