MATHEMATICAL MODELS TO DETERMINE OF THIN LAYER DRYING KINETIC OF GINGER SLICES

In the present work, the effects of some parametric values on the thin layer drying process of ginger slices were investigated. Drying was done in the laboratory by using cyclone type convective dryer. The drying air temperature was varied as 40, 50, 60 and 70 ̊C and the air velocity is 0.8, 1.5 and 3 m/s. All drying experiments had only falling rate period. The drying data were fitted to the twelve mathematical models and performance of these models was investigated by comparing the determination of coefficient (R), reduced chi-square (χ) and root mean square error (RMSE) between the observed and predicted moisture ratios. Among these models, drying model developed by Midilli et al. model showed good agreement with the data obtained from the experiments. From the Midilli et al. model for ginger slices, R, and RMSE were determined between 0.99587 and 0.99971, 0.0006156 and 0.00003721 and, 0.019792 and 0.005597, respectively. Using regression analysis, the relationship between the coefficients of Midilli et al. model with drying air temperature and velocity was investigated.

Drying of materials having high moisture content is a complicated process involving simultaneous heat and mass transfer [2]. The materials are dried by thin layer drying due to faster drying with minimum loss of nutrients. Thin-layer drying describes the process of drying in a single layer of sample particles. Three types of thin-layer drying models are used to describe the drying phenomenon of farm product. The theoretical model considers only the internal resistance to moisture transfer between product and heating air whereas semi-theoretical and empirical models consider only the external resistance [3][4]. Theoretical model needs assumptions of geometry of a typical food, its mass diffusivity and conductivity [5][6]; empirical model neglects the fundamentals of drying process and presents a direct relationship between average moisture and drying time by means of regression analysis [7][8], and semi-theoretical model is a tradeoff between the theoretical and empirical ones, derived from simplification of Fick's second law of diffusion or modification of the simplified model, which are widely used, such as the Lewis, Page, Modified Page, Henderson and Pabis, Logarithmic, Two term, Two term exponential, Diffusion approach, Modified Henderson and Pabis, Verma and Midilli et al. models [9][10]. Recently, very little studies have been conducted on the investigation of drying behavior of ginger using different drying methods and systems [1,[11][12][13][14][15][16][17][18]. Determination of drying kinetics and convective heat transfer coefficients of ginger slices was introduced in the literature in a previous work by authors [17][18]. The main objective of this study was to describe the thin layer drying kinetics of ginger at each experimental condition, using twelve empirical models. Relations between experimental conditions with coefficients of the selected model were to investigate. Figure 1 illustrates the schematic diagram of the cyclone type dryer, developed for experimental work [19]. The system was introduced in the literature [20]. Briefly, it consists of fan, resistance and heating control systems, air-duct, drying chamber in cyclone type, and measurement instruments.

Experimental set up
In the measurements of temperatures, J type iron-constantan thermocouples were used with a manually controlled 20-channel automatic digital thermometer (Elimko 6400, Ankara, Turkey), with reading accuracy of 0.1 C. A thermo hygrometer (Extech 444731, Shenzhen, China) was used to measure humidity levels at various locations in the system. Moisture loss was recorded at 20-minute intervals during drying by means of a digital balance (Bel, Mark 3100, Monza, Italy) an accuracy of 0.01 g (Fig. 1).

Experimental procedure
Fresh ginger slices were used in the experiments. Before the drying process, the gingers were cut into slices of 4 mm thickness and 30 mm in diameter with a mechanical cutter. After the dryer had reached steady state temperature conditions for operation, 150 g ginger slices are put on the tray of dryer and dried there. The initial and final moisture contents of the ginger slices were determined at 80 C using an infrared moisture analyzer (Mettler LJ16, Greifensee, Switzerland).
Drying experiments were carried out at 40, 50, 60, and 70C drying air temperatures and 0.8, 1.5 and 3 m/s air velocities. Drying was continued until the average final moisture content (0.06 g water/g dry matter) from the average initial moisture content (4.8 g water/g dry matter). During the experiments, ambient temperature and relative humidity, and the inlet and outlet temperatures of the drying air in the dryer chamber were recorded.

3. Mathematical modelling of drying curves
The moisture ratio (MR) of the ginger slices during the thin layer drying experiments was calculated using the following equation: where Mt, Mo and Me are the anytime, the initial and equilibrium moisture contents (% dry basis) respectively [21].  [3] The experimental moisture ratio data of ginger obtained were fitted to the 12 commonly used thin-layer drying models in Tab. 1 [8,[22][23][24][25][26][27][28][29][30]. Non-linear least square regression analysis was performed using Levenberg-Marquardt procedure in Statistica 6.0 computer program. The goodness of fit of the selected mathematical models to the experimental data was evaluated with the correlation coefficient (R 2 ), the reduced chi-square (χ 2 ) and the root mean square error (RMSE). The goodness of fit will be better, if R 2 values are higher and χ 2 and RMSE values are lower. These can be calculated as: where, MRexp,i is the ith experimentally observed moisture ratio, MRpre,i the ith predicted moisture ratio, N the number of observations and n is the number constants [7,31,32].

Results and discussion
The times to reach the final moisture content from the initial moisture content at the various drying air temperature and velocity of the ginger slices were found to be between 8700 and 24900 seconds. The temperature is the major effect on the drying process, and, air velocity has less important effect on the drying of ginger slices. In order to normalize the drying curves, the data involving dry basis moisture content versus time were transformed to a dimensionless parameter called as moisture ratio versus time (Fig. 2). The moisture content data at the different experimental mode were converted to the most useful moisture ratio expression and then curve fitting computations with the drying time were   Tab. 1. The regression analysis was used to set up the relations between these parameters with the temperatures and velocities. Thus, the regression equations of these parameters against drying temperature, T (°C) and V (m/s) for accepted model using linear equation are as follows: T V 97 -0.0000004 b 19 10

Conclusions
The influence of drying air temperature and velocity on modeling of drying of ginger slices was investigated in this study. Drying of ginger slices occurred in falling rate period; no constant rate period of drying was observed for the present study, which implies that moisture removal from the material was governed by diffusion phenomenon. In order to explain the drying behaviour and to develop the mathematical modeling of ginger slices, 12 models were applied to thin layer forced drying processes.