Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves

Abstract

This paper presents the results of a study on mathematical modelling of convection drying of artichoke (Cynara scolymus L.) leaves. Artichoke leaves used for drying experiments were picked from the agricultural faculty experimentation fields on the campus area of Ege University. Chopped artichoke leaves were then used in the drying experiments performed in the laboratory at different air temperatures (40, 50, 60 and 70 °C) and airflow velocities (0.6, 0.9 and 1.2 m s) at constant relative humidity of 15±2%. Drying of artichoke leaves down to 10% wet based moisture content at air temperatures of 40, 50, 60 and 70 °C lasted about 4.08, 2.29, 1.32 and 0.98 h respectively at a constant drying air velocity of 0.6 m s while drying at an air velocity of 0.9 ms took about 3.83, 1.60, 0.96 and 0.75 h. Increasing the drying air velocity up to 1.2 m s at air temperatures of 40, 50, 60 and 70 °C reduced the drying time down to 3.5, 1.54, 1.04 and 0.71 h respectively. Different mathematical drying models published in the literature were used to compare based on the coefficient of multiple determination (R), root mean square error (RMSE), reduced chi-square (χ) and relative deviation modulus (P). From the study conducted, it was concluded that the Midilli et al drying model could satisfactorily explain convection drying of artichoke (Cynara scolymus L.) leaves under the conditions studied.

Keywords

• Drying
• Artichoke
• Modelling

Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi

Abstract

Bu çalışmada enginar yapraklarının (Cynara scolymus L.) konveksiyonel kuruma karakteristiklerinin matematiksel modellenmesi sunulmuştur. Denemelerde kullanılan enginar yaprakları Ege Üniversitesi yerleşke alanı içerisindeki Ziraat Fakültesi deneme parsellerinden toplanmıştır. Doğranmış enginar yaprakları, laboratuvarda çeşitli sıcaklıklarda (40, 50, 60 ve 70 °C) ve hava hızlarında (0.6, 0.9 ve 1.2 m s-1) sabit bağıl nem değerinde (% 15±2) kurutma denemelerinde kullanılmıştır. Enginar yapraklarının 40, 50, 60 ve 70 °C sıcaklıklarda % 10 nem içeriğine (yb) ulaşmaları 0.6 m s-1 sabit hava hızında sırasıyla yaklaşık olarak 4.08, 2.29, 1.32 ve 0.98 h sürerken, 0.9 m s-1 sabit hava hızında yaklaşık olarak 3.83, 1.60, 0.96 ve 0.75 h sürmüştür. 40, 50, 60 ve 70 °C sıcaklıklarda kurutma havası hızını 1.2 m s-1’ye kadar artırmak kuruma süresini sırasıyla 3.5, 1.54, 1.04 ve 0.71 h’e kadar düşürmüştür. Literatürde yer alan çeşitli kuruma modelleri, belirtme katsayısı (R2), ortalama hata kareleri karekökü (RMSE), khi-kare (χ2) ve mutlak bağıl hata (P) değerleri kullanılarak karşılaştırılmıştır. Yapılan çalışma sonunda denemelerin yapıldığı koşullar altında enginar yapraklarının kurumasını en iyi Midilli vd. kuruma modelinin açıkladığı belirlenmiştir.

Keywords

• Kurutma
• Enginar
• Modelleme

References

1. Lewis MR= exp(-kt) Yaldız & Ertekin (2001)
2. Page MR= exp(-kt n ) Alibaş (2012)
3. Modified Page MR= exp[-(kt) n ] Artnaseaw et al (2010)
4. Henderson and Pabis MR= a exp(-kt) Figiel (2010)
5. Logarithmic MR= a exp(-kt)+c Doymaz (2013)
6. Midilli et al MR= a exp(-kt n )+bt Silva et al (2011)
7. Demir et al MR= a exp[-(kt) n ]+b Demir et al (2007)
8. MR, moisture ratio; a, b, c coefficients; n, drying exponent specific to each equation; k, drying coefficients specific to each equation; t, time 419 4 4 4 The better goodness of the fit means that the value of R 2 should be higher while the value of RMSE, χ 2 and P should be lower. Selection of the best suitable drying model was done using this criteria. The drying constants (k) of the chosen model were then related to the multiple combinations of the different equations as in the form of linear, polynomial, logarithmic, power, exponential and Arrhenius. Results and Discussion Drying of the artichoke leaves was performed in a convective drier and the experiments were carried out at four different temperatures (40, 50, 60 and 70 °C), and three drying air velocities (0.6, 0.9 and 2 m s -1 ) and constant air relative humidity (15±2%). The average initial moisture content of the artichoke leaves was 4.8964 kg water kg -1 dm and the leaves was dried to the average final moisture content of 0.0662 kg water kg -1 dm until no changes in the mass of leaves were obtained.

9. The characteristic drying curves were constructed from the experimental data and indicated that there is only a falling rate drying period for all experimental cases. The changes in the moisture ratio versus drying time and the drying rate versus drying time for temperatures and airflow velocity studied is presented in Figure 2, and Figure 3 respectively. From these figures it is clear that the moisture ratio of artichoke leaves decreases continuously with drying time. As seen from Figure 2, it is obvious that the main factors effecting the drying kinetics of artichoke leaves are the drying air temperature and drying airflow velocity. Drying time went down as the drying air temperature and airflow velocity increases. Drying air temperature was reported to be the most important factor influencing drying rate by many researchers. Using higher drying temperatures increases drying rate significantly (Temple & van Boxtel 1999;
10. Panchariya et al 2002). Drying of artichoke leaves down to 10% wet based moisture content at air temperatures of 40, 50, 60 and 70 °C lasted about 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.0 0.5 0 5 0 5 0 5 0 5 0 Drying Time (h) M ois tu re R atio ( M R) Drying Time (h) 50⁰C 0.6 m/s 50⁰C 0.9 m/s 50⁰C 1.2 m/s 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.0 0.5 0 5 0 Drying Time (h) M ois tu re R atio ( M R) Drying Time (h) 70⁰C 0.6 m/s 70⁰C 0.9 m/s 70⁰C 1.2 m/s Drying Time (h) ΔM /Δt (k g w at er ⋅kg -1 dm ⋅h -1 ) Drying Time (h) 50⁰C 0.6 m/s 50⁰C 0.9 m/s 50⁰C 1.2 m/s 0.0 0 0 0 0 0 0.0 0.5 0 5 0 Drying Time (h) ΔM /Δt (k g w at er ⋅kg -1 dm ⋅h -1 ) Drying Time (h) 70⁰C 0.6 m/s 70⁰C 0.9 m/s 70⁰C 1.2 m/s 421 can be achieved the higher values than 0.99941 for R 2 , lower values than 0.00485 for RMSE, lower values than 0.00025 for χ 2 and lower values than 202 for P. Therefore, the Midilli et al model was preferred because of its better fit to drying data. The Midilli et al model has the following form and can reveal satisfactory results in order to predict the experimental values of the moisture ratio values for artichoke leaves. 7 (6)
11. The statistical based results as obtained by Midilli et al model were tabulated in Table 3. As seen from the table, the drying constant k increases once the temperature of the drying air and velocity increases while the other model constants, a, n and b fluctuate. Some other regression analysis were also made in order to consider the effect of the drying air temperature and velocity variables on the drying constant k (h -1 ) of the Midilli et al model. The drying constants (k) were correlated to the drying air temperature and velocity by considering the different combinations of the equations as in the form of simple linear, polynomial, logarithmic, power, exponential and Arrhenius type using the software Datafit 6.0 (Oakdale Engineering). The power model was assumed to be the appropriate model due to the easiness in use even though some higher order polynomial functions produced better predictions. 9 Some other regression analysis were also made in order to consider the effect of the drying air temperature and velocity variables on the drying constant k (h -1 ) of the Midilliet al model. The drying constants (k) were correlated to the drying air temperature and velocity by considering the different combinations of the equations as in the form of simple linear, polynomial, logarithmic, power, exponential and Arrhenius type using the software Datafit 6.0 (Oakdale Engineering). The power model was assumed to be the appropriate model due to the easiness in use even though some higher order polynomial functions produced better predictions.