HOT-AIR DRYING AND MODELING THE DRYING KINETICS OF SUNFLOWER (HELIANTHUS ANNUS L.) PETALS
DOI:10.30825/5.EJPAU.190.2020.23.3

Amir Hossein Mirzabe¹, Gholam Reza Chegini^2
1 Department of Mechanical Engineering of Biosystems, College of Agriculture & Natural Resources, University of Tehran, Tehran, Iran
² Department of Mechanical Engineering of Biosystems, College of Aboureihan, University of Tehran, Tehran, Iran

ABSTRACT

Sunflower seeds and oil in food and agricultural processing are of great importance. Dried sunflower petals are the most important parts of the sunflower plant that have economic value. Thin-layer drying experiments were performed in a laboratory scale hot-air dryer. The results indicated that with increasing drying temperature and air velocity, time of drying reduces and in most cases, the logarithmic model had the best performance for modeling the drying kinetics. The calculated values of the effective moisture diffusivity varied from 3.16627 ×10^-13 to 1.32860 ×10^-12 m² s^-1 and the values of the activation energy for air velocities of 0.4 and 0.8 m s^-1 were equal to 51.21 and 42.3 kJ mol^-1, respectively. Also, to verify whether the production and sale of sunflower petals can be cost effective, economic analysis was done. This analysis showed that drying of sunflower petals is profitable process and the generated revenue can even surpass the revenue from the sale of sunflower seeds.

Key words: modeling, drying kinetics, moisture diffusivity, activation energy, thin-layer drying.

NOMENCLATURE

D0	Constant coefficient (Diffusion at reference temperature)	mi	Initial mass of the samples [g]
Deff	Effective moisture diffusivity [m2 s-1]	Mp	Mass of petal [g]
Ea	Activation energy [kJ mol-1]	MR	Moisture ratio
L	Thickness of [m]	Rg	Universal gas constant [J mol-1 K-1]
M	Moisture content at any time [%] (w.b.)	SH	Sunflower head
Meq	Equilibrium moisture content [%] (w.b.)	SHS	Sunflower heads
mf	Final mass of the samples [g]	t	Time [s]
Mi	Initial moisture content [%] (w.b.)	Tabs	Absolute air temperature [K]

INTRODUCTION

Sunflower (Helianthus annuus L.) is one of the most important oil crops in the World. Although food consumption of the seeds and oil extraction from the seeds are the main reasons for cultivation of sunflower, the other parts of the sunflower plant also have many applications; for example, no part of the sunflower is poisonous and the sunflower can be consumed wholly by ruminants.

Sunflower petals are often brightly colored or unusually shaped to attract pollinators and they are some of the most important parts of the sunflower that have several applications. The sunflower petals can be made into an infusion that can be used in the bath as soap. Sunflower petals are often used for their decorative element in products such as soap, wrapping paper, candle, and potpourri. They produce a dye that ranges in color from golden yellow to orange which is used as a natural fabric dye. Sunflower petals can be used for soups, salads or as a garnish for cakes and cookies to color and flavor to recipes. Also, dried sunflower petals are a great ingredient for herbal tea blending.

In order to consume the petals as a food additive, the petals must be dried; drying is a complex process and involves simultaneous mass and heat transfer, accompanied by physical and structural changes [21, 26]. Dehydration of agricultural products is one of the most important techniques in food processing; it is commonly done to keep the quality of products and to preserve the fruit for consumption during off seasons [16]. Some major disadvantages of traditional method of agricultural products drying (e.g., sun drying) are contamination of the products by dust, birds and insects, degradation or damage of a fraction of the processed material, loss of nutrients and total dependence of the method on favorable weather conditions.

Sunflower petals lose their shape and became brown if they dry by being exposed to air, but the use of a desiccant preserves the color of the petals and the shape of the flowers by sucking the moisture quickly from the sunflower. When properly dried, the petals retain their shape and appear dry and brittle. The implementing convective dryers in developing countries can reduce crop losses and improve the quality of the dried product significantly when compared to the traditional methods of drying; therefore, the simulation models are needed for the design and operation of dryers [2].

To the best of our knowledge, there are no published results on convective drying of the sunflower petals. The aims of the present study were to determine drying kinetics, effective moisture diffusivity, activation energy of the petals, and quantify the effects of the drying temperature and hot air velocity on drying characteristics. Also, this study aimed at modeling drying kinetics of the sunflower petals.

MATERIALS AND METHODS

1. Materials
The sunflower the Sirena variety, which is widely cultivated in Iran, was used as the experimental material. Sunflowers were planted in the research farm of the University of Tehran, located on Pakdasht, Tehran province, Iran. Drying experiments and data collection were carried out in early August, when sunflower petals were mature and yet fresh.

2. Drying set-up and procedure
The drying experiments were conducted in a laboratory-scale hot air dryer, under controlled temperature and superficial air velocity. A schematic diagram of the experimental hot air dryer, used to dry the petals, is shown in Figure 1. It consists of an electrical motor, fan, heater, drying compartment, and instruments for measurement. The air flow rate was adjusted by the fan speed control. The electric 1000 W heater was placed inside the air duct. The temperature in the drying compartment was adjusted by the heater power control. The experimental apparatus was constructed from stainless steel sheets as a rectangular tunnel of 1000 mm in length, 300 mm in width and 200 mm in height. The cylindrical drying section was 30 cm in diameter. In the measurements of temperatures, the J-type (iron-constantan) thermocouples were used with a manually controlled 20-channel automatic digital thermometer with reading accuracy of ±0.1°C. The velocity of air passing through the system was measured by an anemometer with accuracy of 0.05 m/s.

Fig. 1. Experimental hot air used to dry the sunflower petals.

In order to determine the initial moisture content of the Sirena’s petals, samples were dried for 12 h in a convective oven at 70°C. The initial (m_i) and final (m_f) mass of the samples were measured using a digital balance with an accuracy of 0.0001g. Then, the initial moisture content of the petals was calculated from the following equation:

(1)

Where: M_i is the initial moisture content (w.b.).

A factorial experiment was conducted (Completely Randomized Design). The factors included drying air temperature of 35, 45, 55 and 65°C and velocity of the hot air at 0.4 and 0.8 m s^-1 (some preliminary tests showed that these ranges of temperature and velocity are appropriate). For each test, 10 g sample of the petals was selected and placed on the grid-type tray inside the drying section. The average mass of a single petal was 0.150 g and its average projected area was 3.57 cm² [22]. Because the sample mass was equal to 10 g so the drying sample was formed from 65 to 70 petals and their surface area was about 250 cm². As the diameter of the circular sample holder was 30 cm giving the grid area of 706.84 cm² it means that the petals were loosely spread in a single layer over the entire surface of the grid. 

The drying started with original moisture content and was continued until the final moisture content of the samples reached approximately 0% (w.b.). To expose sunflower petals to the hot air flow, a sparse metal grid 64.63% of open area was used as the sample holder. The temporal mass of petals during drying experiment was periodically determined by weighting in a digital balance located close to the dryer. In preset time intervals, the metal grid with the sunflower petals on it, were quickly taken off the dryer and put on the digital balance to measure the momentary mass.  The weighting procedure lasted just 4–6 seconds and during weighting petals the flow of drying air was temporarily stopped. The mass data were recorded at 2 min intervals from 0 to 20 min; after which data were recorded at 5 min intervals from 20 to 60 min. Thereafter, data were recorded at 10 min intervals from 60 to 120 min; then data were recorded at 15 min intervals from 120 to 300 min; then data were recorded at 30 min intervals from 300 to 600 min; and after 600 min the data were recorded at 60 min intervals. Shorter time intervals at the beginning of the data recording were set because the higher rate of mass variations took place at the beginning of drying. Data obtained from time of 0 to 600 min were then used for mathematical modeling and other calculations.

3. Mathematical modeling
The moisture ratio of sunflower petals during the thin-layer drying experiments was calculated using Equation (2) [Akpinar et al. 2003, Darvishi et al. 2014]:

(2)

Where: MR is the moisture ratio, M_i is the initial moisture content (w.b.), M_eq is the equilibrium moisture content (w.b.), M (w.b.) is the moisture content at any time. Drying was continued until close to 0 moisture content so one can assume that:

(3)

Modeling the drying behavior of different agricultural products often requires the statistical methods of regression and correlation analysis [2]. Linear and non-linear regression models are important tools for finding the relationships between different variables, especially, those for which no established empirical relationship exists [2]. For mathematical modeling of the petals, the thin-layer drying equations specified in Table 1 were examined to select the best model for describing the drying curve of the petals.

Table 1. Mathematical models tested for fit to drying curves.

Model name	Model function	Reference
Newton or Lewis		[9]
Page		[14]
Modi?ed page		[3]
Henderson and Pabis		[7]
Logarithmic		[32]
Two term		[13]
Wang and Singh		[31]
Polynomial (Parabolic)		[23]
Approximation of di?usion		[33]
Verma et al.		[30]

The regression analysis was performed using the MATLAB 2009a software package. The coefficient of determination was the primary criterion for selecting the best equation to describe the drying curve [2, 12]. In addition, the reduced chi-square (R²), sum of squares error (SSE) and root mean square error analysis (RMSE) were used to determine the best fit. The RMSE and SSE parameters can be calculated as follows [8]:

(4)

(5)

(6)

Where: MR_exp,i is the ith experimentally observed moisture ratio, MR_pred,i is the i^th predicted moisture ratio, N is the number of observations [25].

In the present study, the relationships of the constants of the best suitable model with the drying temperature and air velocity were also determined using the Parabolic Polynomial, Henderson and Pabis, Wang and Singh, Two-Term and Logarithmic models (these are the most customary models and using more models spotted in published papers would make the paper lengthy).

4. Effective moisture diffusivity
The Fick’s second law of the unsteady state diffusion, resulting by neglecting the effects of temperature and total pressure gradients, can be used to describe the transport of water during the food dehydration process that takes place in the falling rate period [4, 6].

In order to determine the effective moisture diffusion coefficient, the following assumptions were taken into account: the moisture is initially distributed uniformly throughout the mass of a sample, mass transfer is symmetric with respect to the center, surface moisture content of the sample instantaneously reaches equilibrium with the conditions of surrounding hot air, resistance to the mass transfer at the surface is negligible compared to internal resistance of the sample, diffusion coefficient is constant and independent of moisture concentration, shrinkage is negligible (in short time intervals, it is ignorable), and mass transfer occurs by diffusion only [5, 28, 29].

(7)

Where: M is the moisture content at any time, n = 1, 2, 3 … is the number of terms taken into consideration, t is the time of drying in seconds, D_eff is the effective moisture diffusivity in m² s^-1 and L is the thickness of the plate in meters. Only the first term of Equation (7) is used – for long drying times [18]; the drying of these flowers can be regarded as long enough, hence:

(8)

The slope (K) is calculated by plotting Ln (MR) versus time according to Equation (9):

(9)

5. Activation energy
For given moisture content, the correlation between the drying temperature and the values of the effective diffusivity can adequately be expressed by the Arrhenius equation [4, 15, 19, 20]:

(10)

Where: D₀ is the effective diffusivity at the reference temperature, E_a is the activation energy, T_abs is the absolute air temperature, and R_g is the universal gas constant (8.3143 J mol^-1 K^-1). Equation (10) can be linearized by applying logarithms thus leading to the following equation:

(11)

From this equation the E_a can easily be obtained by plotting on Ln (D_eff) versus T_abs^-1 diagram. The D₀ and E_a parameters can be subsequently related to the drying conditions by applying the regression analysis techniques.

RESULTS AND DISCUSSIONS

1. Drying curves
Several researchers have suggested that since the equilibrium moisture content is significantly less than the initial moisture content or due to fluctuating relative humidity during drying, the equilibrium moisture content can be assumed to be 0 g/g dry solid [24, 33]. In the case of low-temperature drying of sunflower petals it is also acceptable to assume M_eq = 0% (w.b.) for single pass (no recirculation) of ambient air. The initial moisture content of sunflower petals of the Sirena variety was determined as 80.82 ± 0.15% (w.b.). The drying curves of all drying tests are presented in Figures 2 and 3. The momentary moisture content of the dried samples was calculated depending on the basis of weight changes of the samples. The momentary moisture content ranged from 79.90 ± 0.08 to 0.000 ± 0.001% (w.b.). For all conditions, a falling rate period was characterized by a rapid decrement of the drying rate with time. This indicates that the main mechanism of water transport is by diffusion so the diffusion equation may be used for analysis of drying data [5, 18].

The value of moisture ratio decreases rapidly, with consequent increase of the drying rate, when air temperature increases. The initial values of drying rate almost doubled when the air temperature increased from 35 to 65°C. This predominant direct effect of air temperature on the drying rate, as clearly are shown in the Figures 2 and 3 for all temperature levels.

Fig. 2. Air temperature effect on the drying curves when air velocity is 0.4 m s-1.

Fig. 3. Air temperature effect on the drying curves when air velocity is 0.8 m s-1.

Results showed that with increasing air temperature and air velocity, time of the drying shortens. The same results were obtained for solid waste from pressing of olives [11], corn [9], Riesling seeds, cab Franc seeds and concord seeds [24]. That with increasing air velocity and temperature, time decrease is usual in agricultural products, and for different products, with identical temperature and air velocity, the only things that can differ are time length and curves slope. If any different behavior is observed, it is specific to that situation. Also, with elapsing time, the curves slope decrease, and this is also usual, for at the beginning, the moisture is high, but with passing time, the moisture decreases.

2. Modeling drying data
The statistical analysis results applied to these models, by taking into consideration different temperatures and 0.4 and 0.8 m s^-1 values, are given in Tables 2 to 6. The best model describing the drying characteristics of the petals was chosen to be the one with the highest r-square and the lowest RMSE and SSE values.

Constant coefficients and capability of the polynomial (Parabolic) model to fit the data of drying are shown in Table 2. Results indicated that in all temperatures, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE decreased, increased and increased, respectively; therefore, the polynomial (Parabolic) model with 0.4 m s^-1 air velocity had the best performance.

Table 2. Constant coefficients and capability of polynomial (Parabolic) model to fit the data on drying of petals of Sirena variety.

Drying temperature [°C]	Air velocity [m s-1]	a	b	c	R2	SSE	RSME
35	0.4	1.571 × 10-6	-0.0024	0.9249	0.9937	0.0328	0.0261
	0.8	2.158 × 10-6	-0.0028	0.9112	0.9903	0.0518	0.0332
45	0.4	2.128 × 10-6	-0.0028	0.9387	0.9959	0.0206	0.0214
	0.8	3.466 × 10-6	-0.0036	0.9241	0.9923	0.0402	0.0302
55	0.4	5.976 × 10-6	-0.0046	0.9006	0.9892	0.0442	0.0341
	0.8	8.754 × 10-6	-0.0055	0.8788	0.9710	0.1113	0.0556
65	0.4	2.004 × 10-5	-0.0090	1.0160	0.9993	0.0025	0.0095
	0.8	3.322 × 10-5	-0.0111	0.9372	0.9867	0.0424	0.0396

Constant coefficients and capability of the Henderson and Pabis model to fit the data of drying are shown in Table 3. Results indicated that in all temperatures, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE increased, decreased and decreased, respectively; therefore, the Henderson and Pabis model with 0.8 m s^-1 air velocity had the best performance to model the data.

Table 3. Constant coefficients and capability of Henderson and Pabis model to fit the data on drying of petals of Sirena variety.

Drying temperature [°C]	Air velocity [m s-1]	a	b	R2	SSE	RSME
35	0.4	0.9597	-0.0035	0.9926	0.0380	0.0279
	0.8	0.9560	-0.0044	0.9952	0.0251	0.0229
45	0.4	0.9728	-0.0041	0.9884	0.0576	0.0354
	0.8	0.9702	-0.0056	0.9954	0.0240	0.0231
55	0.4	0.9446	-0.0072	0.9898	0.0393	0.0326
	0.8	0.9372	-0.0093	0.9920	0.0330	0.0291
65	0.4	1.0600	-0.0121	0.9878	0.0443	0.0391
	0.8	0.9999	-0.0173	0.9985	0.0047	0.0130

Constant coefficients and capability of the two-term model to fit the drying data are shown in Table 4. Results indicated that the two-term model cannot fit to the data when the temperature equals to 35°C and hot air velocity equals to 0.4 m s^-1.  For 45 and 65°C temperatures, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE decreased, increased and increased, respectively; therefore, the two-term mode

Table 4. Constant coefficients and capability of two-term model to fit the data on drying of petals of Sirena variety.

Drying temperature [°C]	Air velocity [m s-1]	a	b	c	d	R2	SSE	RSME
35	0.4	–	–	–	–	–	–	–
	0.8	0.9547	-0.0045	0	-0.0045	0.9952	0.0254	0.0235
45	0.4	0.9935	-0.0045	0	-0.0045	0.9848	0.0758	0.0415
	0.8	10550	-0.0078	-10550	-0.0078	0.9964	0.0187	0.0208
55	0.4	0.9555	-0.0076	0	-0.0076	0.9911	0.0364	0.0314
	0.8	-0.00002	0.0187	0.9353	-0.0092	0.9902	0.0376	0.0328
65	0.4	0.8604	-0.0056	0	-0.0056	0.7943	0.7444	0.1660
	0.8	-0.0002	0.0243	0.997	-0.0170	0.9991	0.0029	0.0106

Constant coefficients and capability of the logarithmic model to fit the data on drying are shown in Table 5.  For 35, 45 and 65°C temperatures, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE increased, decreased and decreased, respectively; but for 55°C temperature, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE decreased, increased and increased, respectively; therefore, for 35, 45 and 65°C temperatures, the logarithmic model, at 0.8 m s^-1 air velocity had the best performance to model the data; while, when the value of temperature equals to 55°C,  the logarithmic model, at 0.4 m s^-1 air velocity had the best performance to model the data.

Table 5. Constant coefficients and capability of logarithmic model to fit the data of drying of petals of Sirena variety.

Drying temperature [°C]	Air velocity [m s-1]	a	b	c	R2	SSE	RSME
35	0.4	1.0420	0.0029	-0.0950	0.9960	0.0205	0.0207
	0.8	0.9997	0.0039	-0.0525	0.9969	0.0165	0.0187
45	0.4	1.1240	0.0030	-0.1702	0.9959	0.0203	0.0212
	0.8	1.0200	0.0048	-0.0606	0.9976	0.0127	0.0170
55	0.4	1.0030	0.0061	-0.0714	0.9943	0.0236	0.0249
	0.8	0.9324	0.0095	0.0065	0.9898	0.0392	0.0330
65	0.4	1.2550	0.0082	-0.2249	0.9982	0.0064	0.0152
	0.8	1.0160	0.0164	-0.0216	0.9989	0.0036	0.0116

Constant coefficients and capability of polynomial (Parabolic) model to fit the drying data are shown in Table 6. Results indicated that in all temperatures, with increasing air velocity from 0.4 to 0.8 m s^-1 the values of r-square, RMSE and SSE decreased, increased and increased, respectively; therefore, the Wang and Singh model at 0.4 m s^-1 air velocity had the best performance to model the data.

Table 6. Constant coefficients and capability of Wang and Singh model to fit the data of drying of petals of Sirena variety.

Drying temperature [°C]	Air velocity [m s-1]	a	b	R2	SSE	RSME
35	0.4	1.997 × 10-6	-0.0028	0.9744	0.1324	0.0520
	0.8	2.737 × 10-6	-0.0033	0.9649	0.1868	0.0624
45	0.4	2.673 × 10-6	-0.0032	0.9839	0.0804	0.0418
	0.8	4.259× 10-6	-0.0041	0.9756	0.1282	0.0534
55	0.4	8.120× 10-6	-0.0057	0.9584	0.1708	0.0662
	0.8	1.235× 10-5	-0.0070	0.9258	0.2854	0.0878
65	0.4	1.861× 10-5	-0.0086	0.9987	0.0048	0.0129
	0.8	3.956 × 10-5	-0.0126	0.9765	0.0749	0.0517

A comparison between the polynomial, Henderson and Pabis, two-term, logarithmic and Wang and Singh models indicated that when the temperature equals to 35°C, the logarithmic model had the best performance to model the data. Results indicated that when temperature equals to 45°C, the logarithmic and Wang and Singh models had respectively the best and the worst performance to model the data.

Also results indicated that when the air velocity equals to 0.4 m s^-1 and drying temperature equals to 55 and 65°C, the logarithmic and polynomial models had the best performance to model the data; whereas when the air velocity equals to 0.8 m s^-1, Henderson and Pabis and two-term models had the best performance to model the experimental data.

3. Effective moisture diffusivity
Drying of most food materials occurs in the falling rate period [24], and moisture transfer during drying is controlled by internal diffusion [25]. The Fick’s second law of diffusion has been widely used to describe the drying process during the falling rate period for most biological materials [24, 25]. The drying data were plotted on the Ln (MR) versus time t (in seconds) diagrams, resulting in a straight line according to the linear form of Equation (11). The slope of the line determines the drying coefficient K. Figure 4 shows the family of lines obtained on a logarithmic plot for different air temperatures and for air velocity of 0.4 m s^-1. The other diagram (Fig. 5) for air velocity of 0.8 m s^-1 shows similar trends for all temperatures.

Fig. 4. Ln(MR) versus time when air velocity is 0.4 m s-1 for thin-layer drying of sunflower petal.

Fig. 5. Ln(MR) versus time when air velocity is 0.8 m s-1 for thin-layer drying of sunflower petal.

The values of D_eff presented in Table 7 show the changes of effective moisture diffusivity caused by temperatures and air velocities. The higher drying temperature and air velocity can accelerate the water molecules present in the sunflower petal to evaporate faster, thus providing a faster decrease of the material moisture content and the corresponding higher value of effective moisture diffusivity. A comparison between the temperature and air velocity indicated that the temperature is more efficient on the effective moisture diffusivity then air velocity is.

Table 7. Air temperature and air velocity effects on the effective moisture diffusivity in sunflower petal.

Temperature [°C]	Effective moisture diffusivity [m2 s-1]
	Vair = 0.4 m s-1	Vair = 0.8 m s-1
35	3.16627 × 10-13	3.93149 × 10-13
45	4.02269 × 10-13	5.18795 × 10-13
55	6.33903 × 10-13	7.19828 × 10-13
65	1.11987 × 10-12	1.32860 × 10-12

The values of effective moisture diffusivity of all experiments ranged from 3.16627×10^-13 to 1.32860 ×10^-12 m² s^-1 being dependent on the temperatures and air velocities. These values are comparable with the values reported in the topical papers [10, 17, 20, 27] for drying other foods in the temperature range from 40 to 80°C; in other words, these values fell within the normally expected range of effective moisture diffusivity for dehydrated foods.

4. Activation energy
In Figure 6, the value of Ln (D_eff) versus T_abs-1 is plotted and the value of E_a is obtained using Equation (13). The value of E_a for air velocities of 0.4 and 0.8 m s^-1 was calculated as equal to 51.21 and 42.3 kJ mol^-1, respectively. Plotted curves show that the increase in temperature values increases the slope of straight line; in other words, the effective moisture diffusivity increases, whereas the effect of air velocity on the slope is adverse. The values are comparable to results obtained by other researchers for drying other foods and the same trends were reported for drying other foods [1].

Fig. 6. Ln(Deff) versus 1/Tabs different levels of air velocities for thin-layer drying of sunflower petal.

5. Economic issue
One important aspect of each agricultural product and its manufacturing process is the issue of economics. To understand whether the production and sale of sunflower petals can be cost effective, in this section we give an example of the magnitude of production and price for edible (not oily) sunflower seeds and petals per hectare.

In Iran, the current price of sunflower seeds per kilogram, depending on the variety and quality, is between 2 and 3 dollars, and at the best less than 3.5 dollars. On the other hand, the yield of harvested seeds can vary from 1 to 2.5 tons per hectare. If we consider a good growing condition in which 2 tons of seeds are harvested per hectare with the price of $ 3 per kilogram, the revenue arising from the planting seeds per hectare will be equal to $ 6,000.

As you see, this revenue is considerable and even more than the revenue from the sale of seeds, themselves. This fact justifies the production, drying and selling sunflower petals, as well as research on medicinal and chemical properties of sunflower petals and also on methods of drying them.

CONCLUSIONS

To dry sunflower petals, temperature of drying was set at 35, 45, 55 and 65°C and velocity of the hot air was adjusted at 0.4 and 0.8 m s^-1. The results showed that with increasing air temperature and air velocity, time of drying decreased and with passing time, the curves slope decrease, which is usual for agricultural products. A comparison between air velocity and air temperature showed that air temperature is more effective than air velocity for shortening time of drying.

The values of effective moisture diffusivity varied from 3.16627 ×10^-13 to 1.32860 ×10^-12 m² s^-1 for sunflower petal in present study. The increase in air temperature at constant air velocity increased the value of D_eff, and the increase in air velocity at constant air temperature also increased the value of D_eff. The activation energy E_a calculated for sunflower petal in drying experiments varied from 42.30 to 51.21 KJ mol^-1 and this range corresponded with the activation energy of other food products in a general range reported by several researchers.

Finally, economic analysis showed that drying of sunflower petals is an economically attractive process because of added value so the generated revenue can exceed the revenue from the sale of sunflower seeds. Therefore, an economic analysis justifies the production, drying and selling sunflower petals, as well as research on medicinal and chemical properties of sunflower petals and also on methods of drying them.

Acknowledgements

The authors would like to thank the University of Tehran for providing technical support for this work. The authors would also like to thank Dr. Mohammad Hassan Torabi, Ms. Zohre Torki, and Ms. Fateme Jafari for their technical help and support while doing this research.

REFERENCES

1. Aghbashlo M., Samimi-Akhijahani H., 2008. Influence of drying conditions on the effective moisture diffusivity, energy of activation and energy consumption during the thin-layer drying of berberis fruit (Berberidaceae). Energy Convers Manag., 49(10), 2865–2871.
2. Akpinar E.K., Bicer Y., Yildiz C., 2003. Thin layer drying of red pepper. J. Food Eng., 59(1), 99–104.
3. Arslan D., Özcan M.M., 2010. Study the effect of sun, oven and microwave drying on quality of onion slices. LWT-Food Sci. Technol., 43(7), 1121–1127.
4. Babalis S.J., Belessiotis V.G., 2004. Influence of the drying conditions on the drying constants and moisture diffusivity during the thin-layer drying of figs. J. Food Eng., 65(3), 449–458.
5. Corzo O., Bracho N., Alvarez C., 2008. Water effective diffusion coefficient of mango slices at different maturity stages during air drying. J. Food Eng., 87(4), 479–484.
6. Crank J., 1979. The Mathematics of Diffusion. Oxford University Press.
7. Da Silva W.P., e Silva C.M., Gama F.J.A., Gomes J.P., 2014. Mathematical models to describe thin-layer drying and to determine drying rate of whole bananas. J. Saudi Soc. Agric. Sci., 13(1), 67–74.
8. Darvishi H., Asl A.R., Asghari A., Azadbakht M., Najafi G., Khodaei J., 2014. Study of the drying kinetics of pepper. J. Saudi Soc. Agric. Sci., 13(2), 130–138.
9. Doymaz I., Ismail O., 2011. Drying characteristics of sweet cherry. Food Bioprod. Process., 89(1), 31–38.
10. Gely M.C., Santalla E.M., 2007. Moisture diffusivity in quinoa (Chenopodium quinoa Willd.) seeds: Effect of air temperature and initial moisture content of seeds. J. Food Eng., 78(3), 1029–1033.
11. Gögüş F., Maskan M., 2006. Air drying characteristics of solid waste (pomace) of olive oil processing. J. Food Eng., 72(4), 378–382.
12. Guarte R.C., 1996. Modelling the drying behaviour of copra and development of a natural convection dryer for production of high quality copra in the Philippines.
13. Henderson S.M., 1974. Progress in developing the thin layer drying equation. Trans ASAE., 17(6), 1167–1168.
14. Jangam S.V., Joshi V.S., Mujumdar A.S., Thorat B.N., 2008. Studies on dehydration of sapota (Achras zapota). Dry Technol., 26(3), 369–377.
15. Karatas S., 1997. Determination of moisture diffusivity of lentil seed during drying. Dry Technol., 15(1), 183–199.
16. Lin T.M., Durance T.D., Scaman C.H., 1998. Characterization of vacuum microwave, air and freeze dried carrot slices. Food Res. Int., 31(2), 111–117.
17. Lomauro C.J., Bakshi A.S., Labuza T.P., 1985. Moisture transfer properties of dry and semimoist foods. J. Food Sci., 50 (2), 397–400.
18. Lopez A., Iguaz A., Esnoz A., Virseda P., 2000. Thin-layer drying behaviour of vegetable wastes from wholesale market. Dry Technol., 18(4–5), 995–1006.
19. Madamba P.S., Driscoll R.H., Buckle K.A., 1996. The thin-layer drying characteristics of garlic slices. J. Food Eng., 29(1), 75–97.
20. Maskan A., Kaya S., Maskan M., 2002. Hot air and sun drying of grape leather (pestil). J. Food Eng., 54(1), 81–88.
21. Medeiros G.L., Sereno A.M., 1994. Physical and transport properties of peas during warm air drying. J. Food Eng., 21(3), 355–363.
22. Mirzabe A.H., Chegini G.R., Khazaei J., 2018. Sunflower petals: Some physical properties and modeling distribution of their number, dimensions, and mass. Inf. Process Agric., 5(2),  doi:10.1016/j.inpa.2018.03.002.
23. Özdemir M., Devres Y.O., 1999. The thin layer drying characteristics of hazelnuts during roasting. J. Food Eng., 42(4), 225–233.
24. Roberts J.S., Kidd D.R., Padilla-Zakour O., 2008. Drying kinetics of grape seeds. J. Food Eng., 89(4), 460–465.
25. Saravacos G.D., Charm S.E., 1962. Effect of surface-active agents on dehydration of fruits and vegetables. Food Technol., 16(1), 91.
26. Senadeera W., Bhandari B.R., Young G., Wijesinghe B., 2000. Physical property changes of fruits and vegetables during hot air drying. Dry. Technol. Agric. Food Sci., Science Publishers, 149–166.
27. Seth D., Sarkar A., 2004. A lumped parameter model for effective moisture diffusivity in air drying of foods. Food Bioprod. Process., 82(3), 183–192.
28. Taheri-Garavand A., Rafiee S., Keyhani A., 2011a. Effective moisture diffusivity and activation energy of tomato in thin layer dryer during hot air drying. Int. Trans. J. Eng. Manag. Appl. Sci. Technol., 2(2), 239–248.
29. Taheri-Garavand A., Rafiee S., Keyhani A., 2011b. Study on effective moisture diffusivity, activation energy and mathematical modeling of thin layer drying kinetics of bell pepper. Aust. J. Crop. Sci., 5(2), 128.
30. Verma L.R., Bucklin R.A., Endan J.B., Wratten F.T., 1985. Effects of drying air parameters on rice drying models. Trans. ASAE, 28(1), 296–301.
31. Wang Z., Sun J., Chen F., Liao X., Hu X., 2007. Mathematical modelling on thin layer microwave drying of apple pomace with and without hot air pre-drying. J. Food Eng., 80(2), 536–544.
32. Yagcioglu A., 1999. Drying characteristic of laurel leaves under different conditions. Proc. 7th Int. Congr. Agric. Mech. Energy, Faculty of Agriculture, Cukurova University, 565–569.
33. Yaldýz O., Ertekýn C., 2001. Thin layer solar drying of some vegetables. Dry Technol., 19(3–4), 583–597.

Received: 21.05.2020
Reviewed: 14.09.2020
Accepted: 22.09.2020

---

Amir Hossein Mirzabe
Department of Mechanical Engineering of Biosystems, College of Agriculture & Natural Resources, University of Tehran, Tehran, Iran
Telephone: 098 3153239185
Cell phone: 0989399442161
a_h_mirzabe@yahoo.com
email: a_h_mirzabe@alumni.ut.ac.ir

Gholam Reza Chegini
Department of Mechanical Engineering of Biosystems, College of Aboureihan, University of Tehran, Tehran, Iran
Telephone: 098 21 360 406 14
Cell phone: 0989126356329
email: chegini@ut.ac.ir

---

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.

---

Main  -  Issues  -  How to Submit  -  From the Publisher  -  Search  -  Subscription