## THERMAL SCIENCE

International Scientific Journal

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

**ABSTRACT**

This paper presents the mathematical model and numerical analysis of the convective drying process of thick slices of colloidal capillary-porous materials slowly moving through conveyor-belt dryer. A flow of hot moist air was used as drying agent. The drying process has been analyzed in the form of a 2-D mathematical model, in two directions: along the conveyor and perpendicular on it. The mathematical model consists of two non-linear differential equations and one equation with a transcendent character and it is based on the mathematical model developed for drying process in a form of a 1-D thin layer. The appropriate boundary conditions were introduced. The presented model is suitable for the automated control of conveyor-belt dryers. The obtained results with analysis could be useful in predicting the drying kinetics of potato slices and similar natural products.

**KEYWORDS**

PAPER SUBMITTED: 2016-03-08

PAPER REVISED: 2016-07-29

PAPER ACCEPTED: 2016-10-03

PUBLISHED ONLINE: 2016-11-06

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Issue 3**, PAGES [1369 - 1378]

- Salemović, D. R., et al., A Mathematical Model and Simulation of the Drying Process of Thin Layers of Potatoes in a Conveyor-Belt Dryer, Thermal Science, 19 (2015), 3, pp. 1107-1118
- 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. 553-559
- Aghbashlo, M., et al., Energy and Exergy Analyses of Thin-Layer Drying of Potato Slices in a Semi-Industrial Continuous Band Dryer, Drying Technology, 26 (2008), 12, 4, pp. 1501-1508
- Srikiatden, J., Roberts, J. S., Predicting Moisture Profiles in Potato and Carrot During Convective Hot Air Drying Using Isothermally Measured Effective Diffusivity, Journal of Food Engineering, 84 (2008), 4, pp. 516-525
- Batista, M. L., et al., Thin Layer Drying of Chitosan Considering the Material Shrinkage, Proceedings, 14th International Drying Symposium, Sao Paulo, Brazil, 2004, Vol. C, pp. 407-413
- Pinto, A. A., Tobinaga, S., Diffusive Model with Shrinkage in the Thin-Layer Drying of Fish Muscles, Drying Technology, 24 (2006), 4, pp. 509-516
- Lecomte, D., et al., Method for the Design of a Contact Dryer-Application to Sludge Treatment in Thin Film Boiling, Drying Technology, 22 (2004), 9, pp. 2151-2172
- Midilli, A., et al., A New Model for Single-Layer Drying, Drying Technology, 20 (2002), 7, pp. 1503-1513
- Khankari, K. K., Patankar, S. V., Performance Analysis of a Double-Deck Conveyor Dryer – a Computational Approach, Drying Technology, 17 (1999), 10, pp. 2055-2067
- Dong, C., et al., Numerical Modeling of Contaminant Transport in Fractured Porous Media Using Mixed Finite-Element and Finite Volume Methods, Journal of Porous Media, 14 (2011), 3, pp. 219-242
- Souad, M., et al., Mathematical Modeling of a Packed Bed Drying with Humid Air and Superheated Steam, Journal of Porous Media, 14 (2011), 2, pp. 169-177
- Damseh, R. A., Duwairi, H. M., Thermo-Phoresis Particle Deposition: Natural Convection Interaction from Vertical Permeable Surfaces Embedded in a Porous Medium, Journal of Porous Media, 12 (2009), 1, pp. 79-88
- Kiranoudis, C. T., et al., Dynamic Simulation and Control of Conveyor-Belt Dryers, Drying Technology, 12 (1994), 7, p. 1575-1603
- Koop, L., et al., A Dynamic Two-Dimensional 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. 185-193
- Pereira de Farias, R., et al., Drying of Grains in Conveyor Dryer and Cross Flow: A Numerical Solution Using Finite-Volume Method, Revista Brasileira de ProdutosAgroindustriais, Campina Grande, 6 (2004), 1, pp.1-16
- 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
- Raković, A., Analysis of Drying Kinetics of Natural Products (in Serbian), M. Sc. thesis, University of Belgrade, Belgrade, Serbia, 1987
- Stakić, B. M, Numerical Study on Hygroscopic Capillary-Porous Material Drying in Packed Bed, Thermal Science, 4 (2000), 2, pp. 89-100
- Salemović, D., Mathematical Modeling, Simulation and Identification of Drying Process of Natural Products in Striped Drying Chamber (in Serbian), Ph. D. thesis, University of Belgrade, Belgrade, Serbia, 1999
- Dedić, A., Simplifying Convective Heat and Mass Transfer in Moisture Desorption of Oak Wood by Introducing Characteristic Transfer Coefficients, HolzalsRoh und Werkstoff, 58 (2000), 1-2, pp. 96-101
- Dedić, A., et al., A Three Dimensional Model for Heat and Mass Transfer in Convective Wood Drying, Drying Technology Journal, 21 (2003), 1, pp. 1-15
- Dedić, A., et al., Modelling the Process of Desorption of Water in Oak [QuercusRobur] Wood, Holzforschung, 58 (2004), 3, pp. 268-273
- Dedić, A., Determination 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. 75-82
- 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
- Filonenko, K. А., et al, Sushka Pishchevikov Rustitel’nykh Materialov (Drying Plants for Vegetables – in Russian), Pishchevaya promyshlenost, Moscow, 1971
- Pakowski, Z., Mujumdar, A. S., Basic Process Calculations and Simulations in Drying, in: Handbook of Industrial Drying (Ed. A. S. Mujumdar), CRC Press, New York, USA, 2007, pp. 54-179
- Eckert, E. R. G., Drake, R. M., Analisys of Heat and Mass Transfer, McGraw-Hill, New York, USA, 1972