www.fmfi‐journal.org Focusing on Modern Food Industry (FMFI), Volume 5 2016 doi: 10.14355/fmfi.2016.05.003
Optimization of Microwave Drying of Celery Using Response Surface Method Zehra Yildiz*, Ayse Sarımeseli *Department of Energy Systems Engineering, Faculty of Technology, MEU, Mersin, Turkey *zyildiz@mersin.edu.tr Abstract In this article, a microwave system was used to dry the celery. Response surface methodology (RSM) was used to determine the influence of process variables and arrive at optimal processing conditions to reduce the moisture ratio of the celeries to a safe level based on a three‐level central composite design (CCRD) involving the variables A vegetable load (53.18‐86.82 g) (97.73‐ 602.27 W) X1, B microwave power X2 and C drying time (5.27‐18.73 min) X3, RSM for the moisture ratio and drying rate. In this study, a CCRD was created with 20 runs, 8 cube points, 4 center points per cube, 6 axial points, 2 center points per axial, and =1.68179. Data obtained from RSM on the moisture ratio and drying time of the celery were subjected to ANOVA and analyzed using a second‐order polynomial equations which resulted in the optimized process conditions. Keywords Microwave Drying, Celery, CCRD, RSM
Introduction It is a significant problem for the food sector that the rest of products after the consumption of fresh fruit and vegetables to be preserved for a long time. For the storage of fresh food not to be decomposed for a long time are various drying techniques. These include things such as hot air drying, vacuum drying, solar drying, microwave drying and freeze‐drying. They have some disadvantages like inability to handle large quantities to achieve consistent quality standards, contamination problems, and low energy efficiency, which is not a desirable situation for the food industry. Microwave drying is an alternative method because of its uniform energy and high thermal conductivity to the insides of the material, space utilization, energy savings, precise process control, and fast startup and shutdown conditions. It also reduces the drying time and prevents food from decomposing (Demirhan E. and Ozbek B., 2011, Decareau, 1985, 1992; Zhang et al., 2006, Askari G. R. et al., 2008, Cui Z. et al., 2008, Wu,G. et al., 2010) Response surface methodology combines mathematics with statistics for designing experiments, building models, evaluating the controlling factors and determining optimum processing conditions. In RSM, several factors are simultaneously varied. The multivariate approach reduces the number of experiments, improves statistical interpretation possibilities, and evaluates the relative significance of several affecting factors even in the presence of complex interactions. It is employed for multiple regression analysis using quantitative data obtained from properly designed experiments to solve multivariable equations simultaneously. There are several work which has been carried out on te optimization of vegetables by RSM method (Uddin et al., 2004; Corzo and Gomez, 2004; Eren and Ertekin 2007; Singh et al., 2007; Singh et al., 2008, Han,Q. et al., 2010, Alibas I. 2014 ). However, no information is found on the statistical modeling of celery drying by microwave system. Hence the present work aims to model the moisture ratio and drying rate as a function of the process variables and to find the optimum operating conditions that minimize the moisture ratio and drying rate using response surface methodology. Experimental Method Material and Drying Process Fresh organic celery samples were purchased from a local superstore, then thoroughly washed with water to remove adhering soil and other debris. They were stored at 4±0.5°C until the drying process. Microwave drying trials were performed in domestic digital microwave oven. The adjustment of microwave output power and
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processing time was done with the aid of a digital control panel located on the microwave oven. During drying experiments, each sample was put on the rotating glass, which was placed at the center of the microwave oven. Then, celery samples were removed from the microwave oven during the drying period, and the moisture loss and drying rate was determined by weighing the plate using a digital balance. Response Surface Methodology Modeling RSM was used to determine the optimum process parameters for microwave system which was used to dry the celery. CCRD for three independent variables was used. In this study, a CCRD was created with 20 runs, 8 cube points, 4 center points per cube, 6 axial points, 2 center points per axial, and =1.68179. The independent variables selected for the optimization were the influence of process variables (microwave power, drying time and vegetable load) and arrived at optimal processing conditions to reduce the moisture ratio (MR) and drying time of the celery to a safe level. The dependent variable selected for this study was reduced the moisture ratio and drying rate (DR) of the celeries (YMR, YDR). Y is the predicted response; the independent variables chosen were A vegetable load (53.18‐86.82 g) X1, B microwave power (97.73‐602.27 W) X2 and C drying time (5.27‐18.73 min) X3. A mathematical model, describing the relationships among the process‐dependent variable and the independent variables in a second‐order equation, was developed. Coding of the variables was done according to the following equation: ∑
∑
∑
∑
(1)
where i and j are linear and quadratic coefficients, respectively, b is a regression coefficient, k is the number of factors studied and optimized in the experiment, and e is random error. The quality of fit of the second‐order equation was expressed by the coefficient of determination R2 and its statistical significance was determined by the F‐test. The coefficients of the equation were determined by employing DX6 software. Analysis of variance (ANOVA) for the final predictive equation was done using DX6 software. The response surface equation was optimized for maximum yield in the range of process variables using DX6 software. Table 1 shows the three independent variables (microwave power, drying time and vegetable load) at different coded and actual levels of the variables employed in the design matrix. TABLE 1. CODES AND ACTUAL LEVELS OF THE INDEPENDENT VARIABLES FOR DESIGN OF EXPERIMENT
Codes levels İnpendent Variables
Symbols ‐2
‐1
0
1
2
Vegetable load (gr)
X1
53.18
60
70
80
86.82
Microwave power (W)
X2
97.73
200
350
500
602.27
Drying time (min)
X3
5.27
8.00
12.00
16.00
18.73
X1=A‐70/10, X2=B‐350/150, X3=C‐12/4
Results and Discussion RSM Modeling The results of the different runs of reduction the moisture ratio and drying rate of the celeries (YMR, YDR) are shown in Table 2. An analysis of variance was conducted to determine the significant effects of process variables on each response. The P‐values were used as a tool to check the significance of each of the coefficients, which are necessary to understand the pattern of the mutual interactions between the independent variables. Values of P less than 0.0001 indicate that the model terms are significant. Table 2 shows that some process variables were found to be statistically significant for output data at P<0.0001. All process variables had a significant effect on the reducing the moisture content and drying rate of the celeries. The corresponding second‐order response models were assembled for each response. For example: 2
2
2
YMR =0.080+0.033 X1 ‐0.077 X2 ‐0.12 X3 +0.016 X1 +0.047 X2 +0.036 X3 (2) +0.0064 X1 X2 ‐0.019 X1 X3 +0.033 X2 X3
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2
2
2
YDR =0.37+0.044X1 ‐0.045X2 ‐0.30X3 +0.0045X1 +0.072X2 +0.056 X3 (3) +0.018X1 X2+0.013X1 X3 ‐0.020 X2 X3 Based on the experimental response, (YMR) produced by the moisture ratio ranged from 0.0025 to 0.44 and (YDR) produced by drying rate ranged from 0.12 to 0.99. Runs 5 and 18 had the maximum and minimum moisture ratio respectively. Runs 9 and 18 had the maximum and minimum drying rate respectively. The lowest yields of moisture content and drying rate were 0. 0025 and 0.12, respectively, and were obtained after 16 min drying at 350 W and 60 g. However, moisture ratio and drying rate increased to 44% and 0.99, respectively, when the vegetable load was increased from 70 to 80 g with the microwave power from 200 to 350 W and drying time from 5.27 to 8 min. TABLE 2. THREE‐LEVEL CCRD AND THE EXPERIMENTAL RESPONSES OF DEPENDENT VARIABLE
Microwave power (W)
Drying time (min)
Moisture ratio
Drying Rate (m/s)
X1
X2
X3
YMR
YDR
1
80.00(1)
500.00(1)
8.00(‐1)
0.288
0.831
2
70.00(0)
350.00(0)
12.00(0)
0.08
0.37
3
70.00(0)
350.00(0)
12.00(0)
0.081
0.38
4
80.00(0)
500.00(1)
16.00(1)
0.029
0.135
5
80.00(1)
200.00(‐1)
8.00(‐1)
0.44
0.795
6
70.00(0)
97.73(‐2)
12.00(0)
0.392
0.71
7
70.00(0)
350.00(0)
12.00(0)
0.082
0.34
8
60.00(‐1)
200.00(‐1)
8.00(‐1)
0.37
0.846
9
70.00(0)
350.00(0)
5.27(‐2)
0.34
0.99
10
60.00(‐1)
500.00(1)
8.00(‐1)
0.162
0.77
11
60.00(‐1)
500.00(1)
16.00(1)
0.009
0.061
12
80.00(1)
200.00(‐1)
16.00(1)
0.08
0.22
Run no
Vegetable load (g)
13
70.00(0)
602.27(2)
12.00(0)
0.038
0.49
14
60.00(‐1)
200.00(‐1)
16.00(1)
0.055
0.18
15
53.18(‐2)
350.00(0)
12.00(0)
0.064
0.27
16
70.00(0)
350.00(0)
12.00(0)
0.084
0.36
17
70.00(0)
350.00(0)
12.00(0)
0.077
0.38
18
70.00(0)
350.00(0)
18.73(2)
0.0025
0.12
19
86.82(2)
350.00(0)
12.00(0)
0.19
0.55
20
70.00(0)
350.00(0)
12.00(0)
0.078
0.37
This was due to the fact that the higher vegetable load contained higher water mass than the lower vegetable load did and it affects the reduction of moisture ratio and drying rate in the final dried celeries at the same operating conditions of microwave power and drying time. Moisture ratio decreased from 44 to 0.25 % and drying rate decreased from 0.12 to 0.99 when microwave power was increased from 97.73 to 602.27 W in the same operating conditions of drying time (16 min) and vegetable load (60 kg). It indicated that microwave power had a great influence on accelerating the reduction of moisture ratio and drying rate of the celeries. This phenomenon can be interpreted as the high microwave energy being absorbed by the dipole molecules available in the celeries and the high absorbed microwave energy generating heat to increase the drying rate and mass transfer being dominated by vaporization [20]. The results also show that the drying time played an effective role in reducing the moisture ratio and drying rate of the celeries. When drying time increased from 5.27 to 18.73 min in the drying operation of microwave power (350 W) and vegetable load (60 g), the moisture ratio and drying rate of the celeries decreased 0.0025‐0.44 and 0.12–0.99, respectively. Overall observations of the results show that the moisture content and drying rate generally decreased with the microwave power and drying time and were inversely related to vegetable load in the microwave drying process of celeries. The ANOVA result of the quadratic regression model for YMR‐YDR is described in Table 3. ANOVA of the regression model for YMR‐YDR yield demonstrated that the model
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was significant due to an F‐value of 11.09 and a very low probability value (P model >F‐0.001). ANOVA (F‐test) for the model explained the response of the dependent variable YDR and YMR. Table 3 also shows that the experimental yields fitted the second‐order polynomial equation well as indicated by high R2 values (0.9605‐0.9678). TABLE 3. ANOVA OF THE REGRESSION PARAMETERS FOR RSM FOR MICROWAVE DRYING OF CELERIES
Response
Regression
df
Type 1 sum of squares
R‐square (R2)
F value
Pr F
Moisture content
Linear
3
0.029
0.7963
20.85
0.0001
Cross‐product
3
0.012
0.8291
0.830
0.5008
Quadratic
3
0.047
0.9605
11.09
0.0016
Residual
6
0.00004
Total
20
0.800
Drying rate
Linear
3
1.29
0.8876
42.12
0.0001
Cross‐product
3
0.0074
0.8927
0.21
0.8911
Quadratic
3
0.11
0.9678
7.78
0.0057
Residual
6
0.0095
Total
20
5.66
The plots of the experimental values of moisture ratio yield versus predicted values (Eq. (2)) and the experimental values of drying rate yield versus predicted values (Eq. (3)) are shown in Figs. 1 and 2. The plots showed a close fit of the observed values with the predicted ones. Thus, a statistically significant multiple regression relationship between the independent variables (X1, X2, and X3) and the YMR and YDR can be established. The second‐order polynomial model showed a good fit and effectively represented the relationship among the parameters selected. An F‐ value several times greater than the tabulated F‐value shows that the model predicts the experimental results well and the estimated factors effects were real.
Experimental and predicted mouisture content
0.5 Predicted value
0.4
Experimental value 0.3 0.2 0.1 0 1
3
5
7
9
11
13
15
17
19
21
Treatment number FIG. 1. COMPARİSON BETWEEN EXPERİMENTAL AND PREDİCTED YİELDS OF MOİSTURE RATİO OF DRİED CELERİES.
The regression coefficients, along with the corresponding P‐values, for the model of production moisture content and drying rate are described in Table 4. It shows that the regression coefficients of all the linear terms and all quadratic coefficients of X1, X2 and X3 were significant at<1% level and interaction coefficients of X1X2, X1X3 and X2X3 were less significant. ANOVA suggests the model to be significant at P<0.0001. The P‐values used as a tool to check the significance of each of the coefficients in turn indicate the pattern of interactions between the variables. A smaller value of P was more significant to the corresponding coefficient. The contour plots based on independent variables were obtained using the same software package (Figures 1–3), indicating that a local optimum exists in the area experimentally investigated. The optimal levels in coded values for vegetable load, microwave power and drying time lie between 0‐1, and for YMR and YDR between 0‐1.
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Experimental and predicted drying rate
Predicted value
1.00
Experimental value
0.80 0.60 0.40 0.20 0.00 0
5
10
15
20
25
Treatment number FIG. 2. COMPARİSON BETWEEN EXPERİMENTAL AND PREDİCTED YİELDS OF DRYİNG RATE OF DRİED CELERİES.
The significance of each coefficient and their interactions was shown in table 4. The linear terms of vegetable load (X1), microwave power (X2), and drying time (X3); the second‐order term of X22 and X32 gave significant effects on the yields of moisture content and drying rate of the celeries, and the cross‐product term (X2X3) between drying time and vegetable load gave significant effects on the yields of moisture ratio (at p value <0.05 and degrees of freedom=9). The second‐order terms of X12 and cross‐product terms of X1X2 and X1X3 did not show a highly significant effect on the yields of moisture ratio and drying rate. Analysis of variance (ANOVA) results of the models is shown in Table 3, indicating a good model performance (with an R2 value of 0.9605 and an F value of 11.09 for drying rate yield and with an R2 value of 0.9678 and an F value of 40.27 for moisture ratio yield) among linear, quadratic, cross‐product, and total model. Interactions among the variables are not negligible. The R2 is one of the measures of degree of fit of a model. The model R2 values of 0.97 (for drying rate yield) and 0.96 (for moisture ratio yield) imply that the variations of 97% for drying rate yield and 96% for moisture content yield of microwave drying can be attributed to the independent variables of microwave power, drying time and vegetable load. TABLE 4. ANOVA FOR THE QUADRATIC POLYNOMIAL MODEL ON MOISTURE CONTENT AND DRYING RATE
Moisture Ratio Factor
Sum of Squares
df
F Value
Sum of Squares
df
F Value
p‐value Prob > F
Model
0.35
9
27.01
< 0.0001
1.41
9
33.41
< 0.0001
x1
0.015
1
10.53
0.0088
0.026
1
5.54
0.0404
x2
0.081
1
56.85
< 0.0001
0.028
1
5.90
0.0355
x3
0.19
1
134.18
< 0.0001
1.24
1
264.33
< 0.0001
x1 x2
0.0003
1
0.23
0.6433
0.0027
1
0.57
0.4678
x1 x3
0.0028
1
2.00
0.1879
0.0013
1
0.29
0.6026
x2 x3
0.0086
1
6.06
0.0336
0.0034
1
0.72
0.4164
x12 x22
0.0038
1
2.65
0.1346
0.0003
1
0.062
0.8082
0.032
1
22.61
0.0008
0.074
1
15.82
0.0026
x32
0.018
1
12.96
0.0048
0.045
1
9.58
0.0113
Residual
0.014
10
0.047
10
Lack of Fit
0.014
5
426.93
< 0.0001
0.046
5
40.27
0.0005
Pure Error
0.00003
5
0.0013
5
Cor Total
0.36
19
1.45
19
R2 = 0.9605
20
Drying Rate p‐value Prob > F
R2 = 0.9678
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Response Surface Analysis The three‐dimensional plots of the response surfaces are presented in Figs. 3‐7 by presenting the response as function of two factors and keeping the third constant. Figures 3 and 5 reveal the effects of microwave power and vegetable load on moisture ratio yield and drying rate yield of microwave drying of celeries.
0.45 0.37 Moisture ratio
0.29 0.21 0.13
500.00 80.00 425.00 75.00 350.00 B: Microwave power
70.00
275.00
65.00
A: Vegetable load
200.00 60.00
FIG. 3. RESPONSE SURFACE PLOT OF THE MİCROWAVE DRYİNG OF CELERİES FOR THE EFFECTS OF MİCROWAVE POWER (W) AND VEGETABLE LOAD (G) ON MOİSTURE RATİO.
A linear effect of microwave power and an inversely linear effect of vegetable load on the responses were found. Figures 4 and 6 show the effects of drying time and vegetable load on moisture content yield and drying rate yield of microwave drying of celeries. The results indicate that the drying time has a linear effect, whereas the vegetable load has an inversely linear effect on moisture ratio and drying rate of microwave dried celeries. Therefore, the moisture ratio and drying rate of celeries decreased with the increase of both the microwave power and the drying time, whereas the vegetable load had a negative effect on the reduction of moisture ratio and drying rate of celeries during the microwave drying of the vegetables. The response surfaces show a similar trend for both of moisture ratio and drying rate, which indicates a correlation between moisture ratio and drying rate. Figures 7 show the effects of microwave power and vegetable load on drying rate yield of microwave drying of celeries. The results indicate that the microwave power has a linear effect, whereas the vegetable load has an inversely linear effect on moisture ratio and drying rate of microwave dried celeries.
0.25 0.18 0.12 Moisture ratio 0.06 -0.01
16.00 80.00 14.00 75.00 12.00 C: Drying time
70.00
10.00
65.00
A: Vegetable load
8.00 60.00
FIG. 4. RESPONSE SURFACE PLOT OF THE MİCROWAVE DRYİNG OF CELERİES FOR THE EFFECTS OF DRYİNG TİME (MİN) AND VEGETABLE LOAD (G) ON MOİSTURE RATİO.
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0.81 0.62 0.43 Drying rate 0.24 0.05
16.00 500.00 14.00 425.00 12.00 C: Drying time
350.00
10.00
275.00
B: Microwave power
8.00 200.00
FIG. 5. RESPONSE SURFACE PLOT OF THE MİCROWAVE DRYİNG OF CELERİES FOR THE EFFECTS OF MİCROWAVE POWER (W) AND DRYİNG TİME (MİN) ON DRYİNG RATE.
0.83 0.63 0.44 Drying rate 0.25 0.06
16.00 80.00 14.00 75.00 12.00
70.00
C: Drying time 10.00
65.00
A: Vegetable load
8.00 60.00
FIG. 6. RESPONSE SURFACE PLOT OF THE MİCROWAVE DRYİNG OF CELERİES FOR THE EFFECTS OF DRYİNG TİME (MİN) AND VEGETABLE LOAD (G) ON DRYİNG RATE.
0.84 0.80 0.77 Drying rate 0.73 0.69
500.00 80.00 425.00 75.00 350.00 B: Microwave power
70.00
275.00
65.00
A: Vegetable load
200.00 60.00
FIG. 7. RESPONSE SURFACE PLOT OF THE MİCROWAVE DRYİNG OF CELERİES FOR THE EFFECTS OF MİCROWAVE POWER (W) AND VEGETABLE LOAD (G) ON DRYİNG RATE.
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Conclusion Regression model Eq. (2) was used to determine the optimum processing conditions for moisture ratio yield of microwave drying of celeries. The values of independent variables (X1, X2, X3) were determined and response was calculated at the optimum point. In order to get these optimum values, first the partial derivatives of the regression Eq. (2‐3) were obtained with respect to X1, X2, and X3, respectively, and they were set to zero to get the three equations given below: 0.032 X1+0.0064 X2‐0.019 X3= ‐0.033 (4) 0.0064 X1 +0.094 X2 +0.033 X3= 0.077 (5) ‐0.019 X1+0.033 X2+0.072 X3= 0.12 (6) 0.009 X1+0.018 X2+0.013 X3=‐0.044 (7) 0.018 X1+0.144 X2 ‐0.020 X3=0.045 (8) 0.013 X1‐0.020 X2+0.112 X3 =0.30 (9) By solving Eqs. (4), (5), and (6), the optimum drying point, called the stationary point, was obtained for the moisture ratio yield, and the corresponding values of independent variables at this point in coded form were X1=‐ 1.655, X2=0.596, and X3=0.957 the corresponding experimental parametric values were 439,38 W (optimum microwave power), 15,823 min (optimum drying time), and 53,45 g (optimum vegetable load), respectively; and the predicted moisture ratio yield at the optimum point was 0,0001. By solving Eqs. (7), (8), and (9), the optimum drying point was obtained for the drying rate yield, and the corresponding values of independent variables at this point in coded form were X1=‐1,088, X2=0.859, and X3=2,958; the corresponding experimental parametric values were 478,91 W (optimum microwave power), 23,83 min (optimum drying time), and 59,119 g (optimum vegetable load). REFERENCES
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[12] Han,Q., Yin,L., Li,S., Yang,B.and Ma J., 2010, Optimization of Process Parameters for Microwave Vacuum Drying of Apple Slices Using Response Surface Method, Drying Technology, 28: 523–532. [13] Alibas I., 2014, Mathematical modeling of microwave dried celery leaves and determination of the effective moisture diffusivities and activation energy, Food Sci. Technol, Campinas, 34(2): 394‐401.
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