## THERMAL SCIENCE

International Scientific Journal

### MATHEMATICAL MODELLING OF FAR-INFRARED VACUUM DRYING OF APPLE SLICES

**ABSTRACT**

In this study, a mathematical model of far-infrared vacuum drying of shrinkage body is presented. The system of two coupled PDE for heat and mass transfer with appropriate initial and boundary conditions are solved numerically with used of the finite difference method. On the basis of the numerical solutions a computer program for calculation of temperature profiles, transient moisture content, mid-plane temperature, and the volume averaged moisture content changes for different drying regime was developed. For verification of a mathematical model a series of numerical calculations were carried out with experimental conditions similar to those in the realized experiments of far-infrared vacuum drying of apple slices. Very good agreement between the experimental and numerical temperature and moisture content changes during the drying was obtained.

**KEYWORDS**

PAPER SUBMITTED: 2018-02-05

PAPER REVISED: 2018-04-17

PAPER ACCEPTED: 2018-04-18

PUBLISHED ONLINE: 2018-05-12

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**1**, PAGES [393 - 400]

- Mitrevski, V., et al., Evaluation of some thin-layer drying models, J. Process. Energy in Agr., 17 (2013) 1, pp.1-6.
- Mitrevski, V., et al., Statistical evaluation of thin-layer models of banana, Journal of Hygenic Eng.&Des., 8 (2014) 1, pp. 145-152.
- Lutovska, M., et al., Mathematical modelling of thin layer drying of pear, Chem. Ind.&Chem.Eng. Q., 22 (2016) 2, pp.191-199.
- Karathanos, V.T., et al., Comparison of two methods of estimation of the effective moisture diffusivity from drying data, J. Food Sci., 55 (1990) 1, pp. 218- 223.
- da Silva, C.K.F., et al., Determination of the diffusion coefficient of dry mushrooms using the inverse method, J. Food Eng., 95 (2009) 1, pp. 1-10.
- Daud, W.R.W., et al., Parameter estimation of Fick's law drying equation, Drying Technol., 15 (1997) 6&8, pp. 1673-1686.
- Park, K.J., et al., Effective diffusivity determination considering shrinkage by means of explicit finite difference method, Drying Technol., 25 (2007) 7&8, pp. 1313-1319.
- Zogzas, N.P., Maroulis, Z.B., Effective moisture diffusivity estimation from drying data. A comparison between various methods of analysis, Drying Technol., 14 (1996) 7&8, pp. 1543-1573.
- Kanevce, G., et al., Inverse approaches to drying with and without shrinkage, Proceedings, 15th International Drying Symposium Budapest, Hungary, 2006, pp. 576-583.
- Kanevce, G., et al., Inverse approaches to drying of thin bodies with significant shrinkage effects, Int. J. Heat and Mass Transfer, 129 (2007) 3, pp. 379-386.
- Kanevce, G., et al., Application of inverse concepts to drying, Thermal Science, 9 (2005) 2, pp. 31-44.
- Mitrevski, V., et al., Estimation of moisture diffusivity of banana, J. Process. Energy in Agr., 13 (2009) 1&2, pp. 102-106.
- Salemovic, D., et al., A mathematical model and simulation of the drying processes of thin layers of potatoes in a conveyor-belt dryer, Thermal Science, 19 (2015), 3, pp. 1107-1118.
- Afolabi, T.J., Agarry, S.E., Mathematical modeling and simulation of the mass and heat transfer of batch convective air drying of tropical fruits, Chem. Process Eng. Res., 23 (2014) 1, pp. 9-19.
- Yamsaengsung, R., Moreira, R.G., Modeling the transport phenomena and structural changes during deep fat frying. Part I: model development, J. Food Eng., 53 (2002) 1, pp. 1-10.
- Dinčov, D.D., et al., Heat and mass transfer in two-phase porous materials under intensive microwave heating, J. Food Eng., 65 (2004) 3, pp. 403-412.
- Ousegui, A., et al., Porous multiphase approach for baking process-explicit formulation of evaporation rate, J. Food Eng., 100 (2010) 3, pp. 535- 544.
- Halder, A., et al., Water transport in cellular tissues during thermal processing, AIChE Journal, 57 (2011) 9, pp. 2574-2588.
- Mitrevski, V., et al., Vacuum far-infrared drying of apple, J. Process. Energy in Agr, 20 (2016) 1, pp.1-3.
- Mitrevski, V., Investigation of the drying processes by inverse methods, Ph. D. thesis, University of Bitola, Bitola, Macedonia, 2005.
- Bundalevski, S., Modelling of far-infrared vacuum drying processes by applying inverse approach, Ph. D. thesis, University of Bitola, Bitola, Macedonia, 2015.
- Niesteruk, R., Changes of thermal properties of fruits and vegetables during drying, Drying Technol., 14 (1996) 2, pp. 415-422.
- Donsi, G., et al., Experimental determination of thermal conductivity of apple and potato at different moisture contents, J. Food Eng., 30 (1996) 3&4, pp. 263-268.