CONVECTIVE HOT AIR DRYING KINETICS OF RED BEETROOT IN THIN LAYERS

The effect of air temperature on drying kinetics of red beetroot slices was investigated experimentally in a cabinet tray dryer. Drying was carried out at 70, 75, 80, and 85 °C with an air velocity 2 m/s and relative humidity 30 %. The drying data thus obtained were analyzed to get effective diffusivity values by applying the Fick’s diffusion model. Effective diffusivity increased with increasing temperature. An Arrhenius relation with an activation energy value of 35.59 kJ/mol expressed the effect of temperature on the diffusivity. Also, within the given operating range, the average heat transfer coefficient at the air-product interface is estimated. Experimental data were fitted to ten mathematical models available in the literature. The Midilli et al. and Wang & Singh models are given better prediction than the other models and satisfactorily described drying characteristics of red beetroot slices.


INTRODUCTION
In developing countries like India, post-harvest losses are more than 30% due to poor holding capacity, disorganised transport facilities and limited market access. If this high volume of losses is reduced, then it can address the food insecurity situation, a major threat being faced by many developing countries (Alizadeh and Allameh, 2013). Drying is one of the most preferable methods for reducing these post-harvest losses of agricultural products. A considerable amount of moisture content from the products can be removed by drying in order to minimise microbial spoilage and to maintain its desired levels of nutrients. Red beetroot (Beta vulgaris L.), which is used as a drying material in present work, is a root vegetable containing several essential nutrients and is a great source of fibre, manganese, potassium, iron, vitamin C and folate. Besides being used as a food, dried red beetroots find applications in food colorant and medicinal fields (Stintzing and Carle, 2004;Kaur and Kapoor, 2002). Traditionally, red beetroots are dried in open sun. But now-a-days a high volume of the total production of red beetroots is mechanically dried by forced convection. As it requires smaller investment and yields highquality end products (Gokhale and Lele, 2011). Generally, drying processes are modelled mathematically in order to optimise the existing drying systems or to include a novel process design (Xia andSun, 2002, Abhishek et al., 2018). Sometimes, drying data obtained experimentally is applied to existing drying equations to choose a sufficiently accurate drying model which is capable of predicting the moisture removal rates and elucidating the performance of drying process of each specific product under the general conditions employed in normal commercial relevant facilities (Sacilik and Elicin, 2006;Erbay and Icier, 2010). The model parameters like transfer coefficients, drying constants of modelling are directly related to the drying conditions i.e., 2 control unit, digital weighing balance and measuring instruments (temperature, humidity, and velocity) as shown in Fig. 1. Drying equipment has a drying capacity of 5 kg samples per batch, but only 500 g of beetroot samples are placed in dryer per batch for experimental purposes. Each sample weight is approximately 40 g, which is selected based on the size of the sample and size of the tray. The even distribution of the samples on the trays also plays a major role in the selection of the sample weights. The drying chamber consists of three trays, each about 340 × 260 mm size for holding product samples. The heating system consists of three electric heating coils of finned tubular elements consists of 80% Ni and 20% Cr, which is precisely centred in a stainless-steel Ubent tube for heating the ambient air to a required temperature. Air is drawn into the rectangular air duct through these heating coils by a motor driven axial flow induced fan of 2.77 m 3 s ⁄ capacity, which is inserted at the end of rectangular duct. The control unit is used for regulating the temperature and velocity of the air across the drying chamber. The digital weighing balance (Accurate electronics ATC-10W-Rear) is placed outside the dryer, which determines and displays sample weight loss continuously during the operation. Temperature of air at the entrance and exit of the drying chamber are measured using T-type thermocouples which are manually controlled by a six-channel temperature indicator with an accuracy of ± 0.1 °C. A digital anemometer (Beetech AM-4208) is used to measure the air velocity. Thermo hygrometer is employed to measure the humidity of air at various locations in the drying chamber. 1-Drying chamber; 2-Heating coils; 3-Induced draft fan; 4-Air duct; 5-control switches; 6-Digital weighing balance; 7-Measuring instruments

Experimental test procedure
First, drying equipment is operated under no-load conditions to obtain the losses. To study the influence of air temperature on drying kinetics of red beetroot samples, air velocity and humidity in the drying chamber are maintained to a constant value of 2 m s ⁄ and 30% respectively and air temperature is varied in the range of 70 ° to 85 °C. For each experiment, dryer should reach steady state condition. After the dryer has reached steady state conditions, 500 g of red beetroot slices are uniformly kept in the three trays provided inside the drying chamber. The sample weight loss is recorded during drying experiments at every 10 min intervals. This drying operation is continued until no change in the weight of the product is noticed for three successive readings. All experiments are repeated twice. Errors in the experiments can arise from instrument selection, condition, calibration, environment and human factors (Midilli, 2001b). During the measurements of the parameters, the uncertainties occurred were presented in Table 1.

Drying kinetics
The moisture transfer from red beetroot to surrounding hot air is mathematically analogous to the flow of heat from a hot body immersed in a cool fluid that is represented by Newton's law of cooling (Gokhale and Lele, 2011). Therefore, the drying rate is proportional to the difference in moisture content between the material being dried and the equilibrium moisture content ( ) which is dependent on the drying air conditions. The moisture ratio ∅ and drying rate DR of red beetroot slices during the thin-layer drying experiments were calculated using Eq. (1) and Eq.
(2) (Midilli, 2001a;Akpinar, 2002) Midilli model Drying curves were fitted to ten well-known thin-layer drying models in Table 2. to select the best suited model for describing the drying characteristics of red beetroot slices. Non-linear square regression analysis was performed using MATLAB 18.1 (MathWorks, Inc., 1984, Natick, USA) computer program. The goodness of the fit can be checked with different statistical indicators such as Correlation coefficient (R), Coefficient of determination (R 2 ), Chi-square (χ 2 ), Sum of Squares for Error (SSE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Mean Bias Error (MBE) respectively. But a minimum of two indicators are required to decide the goodness of the fit. Of all these statistical indicators, R 2 and RMSE are two regression parameters majorly employed by researchers. Hence, in the present work, the goodness of the fit was determined by using the coefficient of 3 determination ( 2 ) and root mean square error (RMSE) (Wang et al., 2007a, Vedavathi et al., 2019, Kiran et al., 2019, Midilli et al., 2002.
These parameters can be calculated by Eq. (3) & Eq. (4). The higher values of 2 and the lower values of are chosen as the criteria for the goodness of fit in the present study (Yaldiz et al., 2001, Wang et al., 2007b, Lahsasni et al., 2004.

Effective moisture diffusivity
It is the important drying parameter that represents the conductive term of all moisture transfer mechanisms (Srikiatden and Roberts, 2006). It gives the internal mass transfer in the red beetroot. Diffusion of moisture within the red beetroot during drying may occur as an amalgam of capillary flow, Knudsen flow, molecular diffusion, hydrodynamic flow and surface diffusion. Hence it is significant to compute effective moisture diffusivity. From the drying data analysis, it was recognized that the air-drying of red beetroot didn't consist of constant rate drying period. Hence, Fick's II law of unsteady state diffusion in Eq. (8) can be used to interpret the experimental results. For an infinite slab and uniform initial moisture concentration, Crank (1975) proposed analytical solution Eq. (9) for Eq. (8) with the following suitable boundary conditions Eq. (5) -Eq. (7).
D eff mainly varies with internal conditions like the product's temperature, the moisture content and the structure. By considering a very low thickness to width ratio, the sample was assumed to be infinite slab. For longer drying periods, the Eq. (9) can be reduced to Eq. (10). From Eq. (10), it is seen that the moisture ratio with respect to time data is provided.

Activation energy
The activation energy is another important drying parameter, that indicates the energy level of water molecules for moisture diffusion and evaporation (Chen et al., 2012). The dependency between and temperature can be indicated by an Arrhenius relationship Eq. (12).
The value of represents the sensibility of the diffusivity against temperature. The greater value of means more sensibility of to temperature (Kaymak-Ertekin, 2002). Here, Do is the pre-exponential factor of the Arrhenius equation (m 2 /s) that is generally defined as the reference diffusion coefficient at infinitely high temperature. Thus, the activation energy of red beetroot slices can be determined from the slope obtained by plotting ln( ) versus the reciprocal of absolute drying air temperature.

Heat transfer coefficient
The average convective heat coefficients ( ℎ ) at the interface of air-red beetroot slices are determined by Eq. (13)

Drying curves and drying rate curves
The drying of red beetroot slices is performed using convective tray dryer. The drying air temperatures considered are 70, 75, 80 and 85°C for a specified air velocity of 2 m s ⁄ , relative humidity 30 % and product thickness 4 mm. During the drying process, equilibrium moisture content of the beetroot with the drying air is said to be attained, where there is no further change in the weight of the red beetroot is noticed. For modelling, beetroot slices are assumed to be infinite slabs and the correlations for the moisture content are specified by Velic et al., (2004) are used. Beetroot slices of average initial moisture content 9.55 (kg w kg ds ⁄ ) is used and is dried to 0.03 (kg w kg ds ⁄ ). The variation of red beetroot moisture content and drying rate with time for different inlet air temperatures are plotted in Figs. 2 and 3. From Fig  2, it can be seen that moisture content decreases monotonically as a function of time. Also, it can be seen that as the inlet air temperature increases, the rate of decrease of moisture content is steep, which signifies the influence of the temperature. Drying time decreases from 420 min at 70°C air inlet temperature to 280 min at 85°C air inlet temperature. Rate of drying can be interpreted by plotting the drying rate as a function of moisture content of the sample given by Eq. (2). Fig. 3 illustrates the variation of drying rate (kg w min × m 2 ⁄ ) with moisture content for the sample at different temperatures. It can be seen that as the moisture content decreases the rate of drying also decreases and this variation doesn't follow a specific trend. For moderate temperatures, the rate of drying increases and then decreases as the moisture content decreases. At moderate temperatures, the reduction in the moisture content of the sample induces a moisture gradient between the surface and the sample interior core. As a result, the drying rate initially increases and then decreases due to lack of moisture on the surface of the beetroot. If the migration speed of molecules within the sample and the air are equal then the variation would have been linear. But due to the variation in the migration speeds of water molecules the trend is nonlinear. At higher temperatures drying rate decreases as the moisture content decreases.

Evaluation of transport properties during drying
Non-linear regression analysis is performed using least square methods in MATLAB-2018 to fit the experimental data to pre-existing models from the literature described in Table 2. The coefficients RMSE and R 2 are evaluated and tabulated in Table 3. The model with lowest RMSE and highest R 2 describes the drying process of beetroot. From  (Gokhale andLele, 2011, Doymaz, 2007). In the present work, Figs. 4-5, describes the variation of ln(∅) with time. The best suitable models that describe the drying process i.e., models 8 & 10 in Table 2, are plotted. The plots obtained are in accordance with that of Gokhale andLele, (2011) andDoymaz, (2007). Drying time is influenced by the internal mass transfer rate when the rate of drying decreases with a decrease in moisture content as shown in Fig.  3. The falling rate drying processes is analysed by Fick's law of diffusion. The general solution for the present geometry of the beetroot is given by Crank (1975) as stated in Eq. (9). The general solution as such is an infinite series that requires a series convergence study, but for a higher  drying time equation can be simplified by considering the first term in the series as stated in Senadeera et al., (2003). The simplified expression is given by Eq. (10). From Figs. 4 & 5, it can be seen that variation of ln( ) with time is not linear which concludes that effective diffusivity D eff is not constant and has to be obtained from Eq. (10), which is a typical feature observed in porous materials. The variation of the effective diffusivity D eff with moisture ratio is shown in Fig. 6. It can be seen that D eff increases with a decrease in moisture ratio and further, it can be seen that D eff increases with an increase in drying air temperature. The dependence of the D eff on moisture content is due to the complex phenomenon that governs the transport of moisture during drying. The average effective moisture diffusivity D eff are found to be 3.11 × 10 −8 , 3.89 × 10 −8 , 4.03 × 10 −8 & 5.48 × 10 −8 m 2 min ⁄ for 70, 75, 80 and 85°C respectively. With an assumption that the temperature distribution within the beetroot is uniform, the convective heat transfer coefficient between air and beetroot was calculated using Eq. (13). Fig. 7. illustrates the variation of effective diffusivity D eff and the heat transfer coefficient with temperature. It can be seen that the heat transfer coefficient decreases with an increase in drying temperature and variation is vice versa for D eff viz., moisture effective diffusivity increases with an increase in drying temperature. Since the moisture evaporation rate at all drying temperature is similar, therefore change in heat transfer coefficient is small at all drying temperatures. It can be concluded that D eff is directly proportional to beetroot temperature, which in turn depends on the drying air temperature.

5
The temperature dependence of D eff can be described by Arrhenius-type of the relationship as given in Eq. (12). The activation energy E a is calculated from the slope of the plot on ln(D eff ) vs 1 T ⁄ in Fig. 8. Calculations for E a & D o are shown below. Slope from the plot Fig. 8 is, m = −E a R ⁄ = −4258 Therefore, E a = 4258 × 8.314 J mol ⁄ = 35.59 kJ mol ⁄ From the curve fitting, (R 2 = 0.9216) we get ln(D o ) = −4.878 ⇒ = 7.61 × 10 −3 2 ⁄ D o which is pre-exponential factor of Arrhenius equation, represents the diffusivity value for infinite moisture content in the product. The value of is found to be 35.6 kJ/mol. The value obtained in this study is in close range of 15 − 40 kJ/mol with various foods reported by Rizvi (1995).

CONCLUSIONS
The drying kinetics of beetroot slices are investigated in an induced draft convective tray dryer, at constant air velocity of 2.0 m s ⁄ and at 70, 75, 80 and 85°C air temperatures respectively. The following conclusions can be drawn from this work.
(1) Heat transfer coefficient and average effective diffusion coefficient at all considered temperatures are obtained.
(2) During beetroot drying, only initial and falling rate periods are occurred, with the absence of a constant-rate period, like most agricultural products. (3) The effective moisture diffusivity values calculated for drying of beetroot in temperature 70 − 85 ° are ranged from 3.11 × 10 −8 m 2 min ⁄ to 5.48 × 10 −8 m 2 min ⁄ . (4) It is found that higher drying temperatures are corresponds with shorter drying time. (5) The results also suggest that with increase in air temperature, heat transfer coefficient decreases and effective diffusivity coefficient increases.