Journal of Agricultural Sciences Dergi web sayfası: www.agri.ankara.edu.tr/dergi Journal homepage: www.agri.ankara.edu.tr/journal Tar. Bil. Der. Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves Tuncay GÜNHANa, Vedat DEMİRa, Abdülkadir YAĞCIOĞLUa a Ege University, Faculty of Agriculture, Department of Agricultural Machinery, 35100, Bornova, Izmir, TURKEY ARTICLE INFO Research Article Corresponding Author: Tuncay GÜNHAN, E-mail: [email protected], Tel: +90 (232) 311 26 62 Received: 11 February 2014, Received in Revised Form: 17 March 2014, Accepted: 18 March 2014 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-1) 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-1 while drying at an air velocity of 0.9 ms-1 took about 3.83, 1.60, 0.96 and 0.75 h. Increasing the drying air velocity up to 1.2 m s-1 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 (R2), root mean square error (RMSE), reduced chi-square (χ2) 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 ESER BİLGİSİ Araştırma Makalesi Sorumlu Yazar: Tuncay GÜNHAN, E-posta: [email protected], Tel: +90 (232) 311 26 62 Geliş Tarihi: 11 Şubat 2014, Düzeltmelerin Gelişi: 17 Mart 2014, Kabul: 18 Mart 2014 ÖZET 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 TARIM BİLİMLERİ DERGİSİ — JOURNAL OF AGRICULTURAL SCIENCES 20 (2014) 415-426 Tarım Bilimleri Dergisi Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al 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. Anahtar Kelimeler: Kurutma; Enginar; Modelleme © Ankara Üniversitesi Ziraat Fakültesi 1. Introduction The artichoke (Cynara scolymus L.) is a perennial vegetable that has a great production potential in Europe and in the continent of America and it received a great acceptance for the consumption in recent years in Turkey. Italy, Egypt, Spain, Peru and Argentina are the biggest artichoke producers in the World respectively while Turkey is ranked the 13th one and the production area of artichoke shows an increasing trend in Turkey (FAO 2013). Among the public, artichoke leaves are known to be useful in eliminating hepatitis and disorders related to hyperlipidemia. Artichoke leaf is also known as an herbal medicine for a long time and used for the treatment of hyperlipidemia and hepatitis in EU traditional folk medicine. Different studies about artichoke have demonstrated their health-protective potential. The artichoke leaves are characterized by the composition and high content in bitter phenolic acids, whose choleretic, hypocholerestemic and hepatoprotector activities are attributed (Alonso et al 2006). Antioxidant, hepatoprotective, anti-HIV, choleretic and inhibiting cholesterol biosynthesis activities of artichoke extracts are also reported by Zhu et al (2005). Shimoda et al (2003) reported that the methanolic extract of artichoke suppress the serum triglyceride in mice. Zhu et al (2005) reported that the artichoke leaves have a new potential application in the treatment of fungal infections. The composition of phytochemicals in artichoke leaves were well documented in the literature and medicinal values of artichoke leaves were found higher than flowers (Sanchez-Rabaneda et al 416 2003; Bundy et al 2008). Moreover, anti-oxidant, hepatoprotective, lowering blood cholesterol effects were mostly studied in the literature. Wang et al (2003) used three different artichoke varieties in order to determine the phenolic acid components. They dried the artichoke leaves and tissues in an oven at 70 °C and also in a freeze drier. After the drying, samples were kept in air tight bags at room temperatures for further analysis. Researchers determined the phenolic acid compounds and amounts by HPLC analysis for mature leaves, young and mature artichoke heads. According to the results obtained by Wang et al (2003) it was reported that the leaves have highest total phenols content than young artichoke heads as followed by mature artichoke heads. In terms of the method they used, they concluded that freeze drying and air assisted drying did not affect the amount of phenolic acid in artichoke. Fresh food materials cannot be stored for a long time. Therefore, products must be dried for a long-term storage. One of the most traditional and extensive technique used for the production of dehydrated fruits and vegetables is convection drying (Nicoleti et al 2001). It allows to reduce mass and volume, to store the products under ambient temperature and to minimize packaging, transportation and storage cost (Baysal et al 2003). Mathematical modelling in drying studies is one of the most significant step in drying technology and allows engineers to select the most suitable drying Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al conditions and to form a drying equipment at a proper scale (Strumillo & Kudra 1986; Hawlader et al 1997). 2. Material and Methods Scientific studies on the drying process of artichoke leaves in the literature is very limited and the most of them focused on determination of the chemical components of artichoke leaves and there is no study published on the determination of the drying characteristics of the artichoke leaves. Drying experiments were performed in a laboratory scale convective hot air dryer constructed in the Department of Agricultural Machinery, Faculty of Agriculture, Ege University, Izmir, Turkey. A schematic diagram of the laboratory dryer is illustrated in Figure 1. The drying system used in this study has been described in details by Demir et al (2007). The laboratory dryer includes; fan, cooler, heater, humidifier, drying unit and automatic control unit. The aim of the study was to determine the drying characteristics and to develop a mathematical model for predicting the kinetics of convection drying of artichoke leaves. 2.1. Experimental procedures Figure 1- Schematic diagram of the drying unit: 1, centrifugal fan; 2, cooling and condensing tower; 3, cold water tank and evaporator; 4,7,9, thermocouples (type T); 5, circulation pump; 6, cold water shower; 8, electric heaters; 10, mixing chamber and air channels; 11, steam tank; 12, solenoid valve; 13, temperature & humidity sensor; 14, balance; 15, computer with data acquisition and control cards; 16, artichoke leaves; 17, anemometer; 18, frequency converter Şekil 1- Kurutma ünitesinin şematik çizimi; 1, santrifüj fan; 2, soğutma ve yoğuşturma kulesi; 3, soğuk su tankı ve evaparatör; 4,7,9, termokupl (T tipi); 5, sirkülasyon pompası; 6, soğuk su duşu; 8, elektrikli ısıtıcı; 10, karışım odası ve hava kanalları; 11, buhar tankı; 12, solenoid valf; 13, sıcaklık ve nem sensörü; 14, terazi; 15, veri akış ve kontrol kartlı bilgisayar; 16, enginar yaprakları; 17, anemometre; 18, frekans dönüştürücü Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 417 Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al A personal computer equipped with A/D converters cards and data acquisition & control software called VisiDAQ (Advantech Automation Corp., USA) was used to control the drying temperature, relative humidity and the automation of the drying system. The artichoke leaves for the drying experiments were picked from the middle branches of the artichoke plants as they are located on the campus area of Ege University, between 8:30 and 9:00 a.m. During the experiments, the fresh leaves were collected daily in early-morning and unblemished ones were picked and used in the drying experiments. Some preliminary tests were carried out to examine the drying conditions from the point of test stand and some expected changes in artichoke leaves. In these tests, a homogeneous drying of the whole leaves was not obtained, especially the main vein of the leaves was found to be the last part that dried. In this situation, the tissues in the thinner part of the leaves were subjected to over drying and drying time significantly increased. For this reason, the leaves were divided into two parts along the main vein and then sliced perpendicularly to the main vein. The 4 or 5 mm wide slices were then used for the drying process. The experiments conducted in the lab had the objective to determine the effect of air temperature and drying airflow velocity on the drying constant were achieved at temperatures of 40, 50, 60 and 70 °C, and at velocity of 0.6, 0.9 and 1.2 m s-1 respectively. During the experiments, the relative humidity was maintained at 15 ± 2%. The drying system was run for at least one hour to maintain steady-state conditions before the experiments. Each drying experiment was performed with 20 g of leaves after steady state conditions of both temperature and air velocity was achieved in the dryer. The artichoke leaves were placed in a vertical drying channel equipped with fine sieves and weighed every three minutes in the first 15 minute drying process and then every 5 minutes until the drying process is completed. The drying experiments were ended when the mass of the samples does not change. The leaf samples were kept in an air-circulated oven for 24 hours at 105 ±2 °C in order to determine the initial moisture content. All of these experiments mentioned above were triplicated. 2.2. Mathematical modelling of the drying curves The experimental moisture ratio data of artichoke leaves were fitted to semi-empirical models in Table 1 to define the convection drying kinetics. The models in Table 1 were widely employed to describe the convection drying kinetics of vegetables. Table 1- Mathematical models widely used to describe the convection drying kinetics Çizelge 1- Konveksiyonla kuruma kinetiklerini belirlemede yaygın olarak kullanılan matematiksel modeler Model name Model equation References Lewis MR= exp(-kt) Yaldız & Ertekin (2001) Page MR= exp(-ktn) Modified Page MR= exp[-(kt) ] Artnaseaw et al (2010) Henderson and pabis MR= a exp(-kt) Figiel (2010) Logarithmic MR= a exp(-kt)+c Doymaz (2013) Midilli et al MR= a exp(-kt )+bt Silva et al (2011) Demir et al MR= a exp[-(kt) ]+b Demir et al (2007) Alibaş (2012) n n n MR, moisture ratio; a, b, c coefficients; n, drying exponent specific to each equation; k, drying coefficients specific to each equation; t, time 418 Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 The experimental moisture ratio data of artichoke leaves were fitted tosemi-empirical models in Table 1 Lewis MR= exp(-kt) Yaldız&Ertekin (2001) to define the convection drying kinetics. The models in Table 1 were widely employed to describe the Page MR= exp(-ktn) Alibaş (2012) convection drying kinetics of vegetables. n Artnaseaw et al (2010) Modified Page MR= exp[-(kt) ] Henderson and Pabis MR= a exp(-kt) (2010) drying kinetics Table 1- Mathematical models widely used to describe theFigiel convection Logarithmic MR= a exp(-kt)+c Doymaz (2013) modeler Çizelge 1- Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel Midilli et al MR= a exp(-ktn)+bt Silva et al (2011) The leave samples were kept an oven for at order n The leave Enginar samplesYapraklarının were Model kept(Cynara inequation an air-circulated air-circulated oven References for 24 24 hours at 105 105 ±2 ±2 C C in in Matematiksel order to to determine determine Model name Demir et al MR= ain exp[-(kt) ]+b L.) Konveksiyonel Demir ethours al (2007) scolymus Kuruma Karakteristiklerinin Modellenmesi, Günhan et al The leave samples were kept in an air-circulated oven for 24 hours at 105 ±2 C in order to determine the initial moisture content. All of theseexperiments mentioned above were triplicated. the initial All n, ofexp(-kt) theseexperiments above were triplicated. MR, moisturemoisture ratio; a, b,content. c coefficients; drying exponent specificmentioned to each equation; k, drying coefficients specific to each equation; Lewis MR= Yaldız&Ertekin (2001) the initial moisture content. All of theseexperiments mentioned above were triplicated. 2.2. Mathematical modelling modelling of of the the drying drying curves curves n t,2.2. timeMathematical Page MR= ) Alibaş (2012) 2.2. Mathematical modelling of exp(-kt the drying curves n of the equations The left hand side iset al a (2010) The better goodness of the fit means that the Artnaseaw Modified Page MR= exp[-(kt) ] TheThe experimental moisture ratio data of of artichoke leavesnumber were fitted fitted tosemi-empirical models in Table Table 1 left hand side of the ratio equations isknown aartichoke dimensionless known asvalue moisture it The experimental moisture data leaves were tosemi-empirical in 1 2 MRand of ratio Rmodels dimensionless number as moisture ratio MR should becould higher while the value of Henderson and Pabis MR= exp(-kt) Figiel The experimental moisture ratio akinetics. data of artichoke leaves were (2010) fitted tosemi-empirical models in Table 1 to the convection drying The in 11 were widely to describe the be written as follows: to define define the convection drying kinetics. The models models in Table Table were widely employed employed to describe the 2 and it could be written as follows: RMSE, χ and P should be lower. Selection of Logarithmic MR= a exp(-kt)+c Doymaz (2013) to define the convection kinetics. The models in Table 1 were widely employed to describe the convection drying kineticsdrying of vegetables. vegetables. convection drying kinetics of Midilli et al drying kinetics of MR= a exp(-ktn)+bt Silva et al (2011) the best suitable drying model was done using convection vegetables. MMR= Ma eexp[-(kt) t -widely Demir et al (1) (2007) Tableet11-alMathematical Mathematical models usedn]+b to describe describe the theDemir convection drying kinetics used this criteria. The drying constants (k) of the (1) Table widely to convection drying kinetics MR models Table 1-1models used to describe drying kineticsmodel modeler Çizelge Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel M 0 -widely M MR, moisture ratio; a, b, c coefficients; n, drying exponent specific tothe eachconvection equation; k, drying coefficients specific to each equation; modeler Çizelge 1-Mathematical Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel e chosen were then related t,Çizelge time 1- Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel modeler to the multiple The moisture ratio was calculated using equation combinations of the different equations as in the Model name name Model equation equation References Model Model References (1),side which simplified to equation number (2) by some of ratio linear, polynomial, logarithmic, power, The left hand of thewas equations is a dimensionless known asform moisture MRand it could Model name Model equation References Lewis MR= exp(-kt) Yaldız&Ertekin Lewis MR= exp(-kt) Yaldız&Ertekin (2001) (2001) M investigators (Menges & Ertekin, 2006; Midilli n exponential and Arrhenius. be written as follows: t Lewis Yaldız&Ertekin Page MR= exp(-kt Alibaş (2)exp(-kt) MR MR= Page MR= exp(-ktnn)) Alibaş (2012) (2012) (2001) & Kucuk 2003; Sacilik) nn]& Elicin 2006; Togrul Page MR= exp(-kt Alibaş (2012) Artnaseaw et&al al (2010) (2010) M Modified Page MR= exp[-(kt) Artnaseaw et o Modified Page MR= exp[-(kt)n] Artnaseaw et al (2010) Pehlivan 2003; Yaldiz et al 2001) because of the M M Modified Page MR= exp[-(kt) ] Henderson and and Pabis Pabis MR= a eexp(-kt) exp(-kt) Figiel (2010) (2010) t Henderson MR= a Figiel (1) MR MR=small 3. Results and Discussion is relatively comparedoftoFigiel M0drying and the M Henderson and Pabis (2010) MS Excel software was usedaaa exp(-kt) for when the calculation the constants and coefficients of semiLogarithmic MR= exp(-kt)+c Doymaz (2013) e MMR= Logarithmic Doymaz (2013) 0 -M eexp(-kt)+c 2 n Logarithmic a exp(-kt)+c Doymaz ) was considered as leaves the empirical models of in MR= Table Then)+bt coefficient of the multiple deviation the relative humidity of drying air Drying of the artichoke was performed in a Midilli et MR= a exp(-kt Silva et al (2011) Midilli et al al drying MR= a 1. exp(-kt )+bt Silva et determination(R al(2013) (2011) n n main criteria for selecting the best model to obtain the convection drying curves of artichoke leaves. Midilli et al MR= a exp(-kt )+bt Silva et al (2011) n]+b during the processes. convective drier and the experiments were carried Demir et al MR= a exp[-(kt) Demir et al (2007) Demir et al MR= a exp[-(kt) n]+b Demir et al (2007) other MR= statistical testswere achieved in equation; order evaluate how thespecific developed models Besides R2, some Demir et altheratio; exp[-(kt) ]+bspecific Demir et altok, (2007) MR, moisture moisture ratio; a, b, b, cc coefficients; coefficients; n,adrying drying exponent specific to each each equation; k, dryingout coefficients specific to each each equation; equation; at four different temperatures (40, 50, 60 and MR, a, n, exponent to drying coefficients to M t then, experiments. fit tomoisture the data from root mean square error(RMSE)and t, time time MR, ratio;obtained a, MR b, c coefficients; drying exponent Among specific tothese, each equation; k, drying coefficients specific to eachreduced equation; t, (2) (2) 70 °C), and three drying air velocities (0.6, 0.9 t, time et al 2002; -1Yaldiz&Ertekin chi-square (2)have a common M o use in drying related studies (Krokidaand 1.2 m s ) and constant air relative humidity The left left hand hand side side 2003; of the the Akgun&Doymaz equations is is aa dimensionless dimensionless numbertoknown known as moisture moisture ratio MRanddeviation it could could 2001;Midilli&Kucuk 2005).In addition these methods, mean relative The of equations number as ratio MRand it TheMRand average initial moisture content The left side of the iswas a dimensionless known moisture(Sacilik&Elicin ratio it 2006; could MS Excel software used thenumber calculation be written written ashand follows: modulus (P) value was alsoequations used to evaluate the for goodness of fit of theas(15±2%). models be as follows: MS Excel software was used for the calculation of the drying constants and coefficients of semibe written as follows: of the drying and coefficients of semiÖzdemir&Devres 1999). Theseconstants test functions used to determine the best fit of are the given below: leaves was 4.8964 kg water kg-1 2 artichoke empirical drying models in Table 1. The coefficient of multiple determination(R ) was considered as the dmcurves and the leaves was dried to the average final empirical drying in toTable 1. the Theconvection coefficientdrying Mthe Mmodels tt - best ee model main criteria for selecting obtain of artichoke leaves. MR M -1 (1) (R2) was considered as the M 2of multiple N (1) moisture content of 0.0662 determination t e other testswere achieved in order to evaluate how the developed models kg water kg dm until Besides the R , some 1 Mstatistical MR 2 0 -M ee (1) 0 RMSE for (MRthe Among MR (3) no changes in the mass of leaves were obtained. criteria selecting model the square fit to the data main obtained from theM experiments. root mean error(RMSE)and reduced pre,ibest exp,these, i )to obtain M 0 -N e i 1 in of )have a common use drying related studies (KrokidaThe et alcharacteristic 2002; Yaldiz&Ertekin chi-square (2convection drying curves were constructed drying curves artichoke leaves. Besides N Akgun&Doymaz 2005).In addition to these methods, mean relative deviation 2001;Midilli&Kucuk the R2,2003; some other statistical 2tests were achieved from the experimental data and indicated that M(MR modulus (P) value was also evaluate goodnessmodels of fit of modelsis(Sacilik&Elicin MR pre, tt used i -how only a falling2006; rate drying period for all (2)exp,to MR toMevaluate in order thei )the developed fitthe there t (2) Özdemir&Devres 1999). test functions used to determine the best fit are given below: 2 iThese M 1 o (2) MR changes in the moisture obtained χ data to the from the experiments. Among experimental cases. The(4) o Mo N - n 1 error (RMSE) and reduced ratio versus drying time and the drying rate versus these, root mean square N MS software the of the drying constants and coefficients of semi2 used 1MRfor MS Excel Excel chi-square software was was used for the calculation calculation ofdrying the drying constants and coefficients of semi2 drying time for temperatures and airflow velocity (χ ) have a common use in related - MR 22) was RMSE (MR iMRof (3) 100 exp, ithe MS Excel software was used 1. for calculation ofmultiple constants and coefficients of as semiconsidered as the empirical drying models inTable Table 1. The coefficient of multiple determination(R pre, i pre, exp, i )the drying ) was considered the empirical drying models in The coefficient determination(R 2 P studied is presented in Figure 2, and Figure 3 (5) studies (Krokida et al 2002; Yaldiz & Ertekin 2001; N i 1model ) was as the empirical drying in the Table 1. The coefficient multiple determination(R main criteria for selecting best to convection drying of artichoke main criteria for models selecting the best model to obtain obtainofthe the convection drying curves curves of considered artichoke leaves. leaves. MR 2Midilli &N exp, i respectively. Kucuk 2003; Akgun & Doymaz 2005). In 2 main criteria selecting best model to obtain the in convection drying curves artichoke models leaves. N the some other statistical testswere achieved in order to evaluate evaluate how the theofdeveloped developed models Besides the R R for ,, some other statistical testswere achieved order to how Besides the 2 2achieved Thebetter of the fit experiments. means the value ofinRorder should be higher whilethe value of reduced RMSE, , some other statistical evaluate thethese developed models Besides R2goodness addition to these methods, mean relative deviation fit data obtained from the these, root mean square error(RMSE)and (MR - testswere MRthat )Among fit2 to to the thethe data obtained from theexp, experiments. Among these, root to mean squarehow error(RMSE)and reduced From figures it is clear that the moisture i pre, i 2obtained chi-square P should be 2lower. Selection ofinthe bestAmong suitable drying done using this criteria.The fitand to the data from the experiments. rootmodel mean square error(RMSE)and reduced )have aa common use drying related studies (Krokida et al 2002; Yaldiz&Ertekin (( (P) was also used tothese, evaluate the was i 1 value 22modulus )have common use in drying related studies (Krokida et al 2002; Yaldiz&Ertekin chi-square ratio of artichoke leaves χ a (4)decreases continuously )have common use models in drying related studiesto (Krokida et al mean 2002;relative Yaldiz&Ertekin chi-square ( goodness 2001;Midilli&Kucuk 2003; Akgun&Doymaz 2005).In addition to2006; these methods, methods, mean relative deviation of fit of N the (Sacilik & Elicin 2001;Midilli&Kucuk 2003; Akgun&Doymaz 2005).In addition these deviation n with drying time. As seen from Figure 2, it is 1 2001;Midilli&Kucuk 2003; Akgun&Doymaz 2005).In addition these methods, relative deviation modulus was also used evaluate the goodness of of models (Sacilik&Elicin 2006; modulus (P) (P) value value was also used to to evaluate the test goodness oftofit fitused of the the modelsmean (Sacilik&Elicin 2006; Özdemir & Devres 1999). These functions obvious that the main factors effecting the drying modulus (P) value1999). was100 also used to evaluate the to of the fit best of the models 2006; Özdemir&Devres These test functions used determine fit given below: - MR MR Özdemir&Devres 1999). These test functions used togoodness determine the best fit are are given(Sacilik&Elicin below: exp, i are pre,i below: to determine the best fit given kinetics of artichoke leaves are the drying air Özdemir&Devres 1999). These test functions used to determine the best fit are given below: P ∑ ∑ ∑ ∑ ∑ (5) ∑ MR 4 N temperature and drying airflow velocity. Drying exp,i N N 1 means 2 N (MR timewhilethe went down drying air temperature and Thebetter goodness of the fit that the value of)22R(3) should be higher valueasofthe RMSE, RMSE MR (3) (3) 1∑ pre, exp, pre,ii exp,ii 2 2 N (MR MR ) (3) ∑ and P should beRMSE lower. Selection of the best suitable drying model was done using this criteria.The airflow velocity increases. Drying air temperature 1 ii pre, i exp, i N i 11 N N N ∑(MR ∑(MR was reported to be the most important factor 22 influencing drying rate by many researchers. exp,ii - MR pre, pre,ii )2 exp, MR ) 11 exp,i pre,i 22 increases drying ii (4) (4) Using higher drying temperatures χ 2 i 1 (4) 4 & van Boxtel 1999; χ rate significantly (Temple (4) N - n11 N - n1 Panchariya et al 2002). Drying of artichoke leaves - MR pre, MRexp, 100 exp,ii pre,ii down to 10% wet based(5) (5)moisture content at air P 100 ∑MRexp,i - MR pre,i (5) P N ∑ (5) and 70 °C lasted about temperatures of 40, 50, 60 MRexp, exp,ii N the fit means MRexp, i the value of R22should be higher whilethe value of RMSE, Thebetter goodness of that Thebetter goodness of the fit means that the value of R2should be higher whilethe value of RMSE, 2 Thebetter goodness of the fit means that the value of R should be higher whilethe value of RMSE, 22and and P P should should be be lower. lower. Selection Selection of of the the best best suitable suitable drying drying model model was was done done using using this this criteria.The criteria.The and P should be lower. Selection of the best suitable drying model was done using this criteria.The Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 4 4 419 Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al 1.0 1.0 40⁰C 0.6 m m/ss-1 0.9 40⁰C 1.2 m m/ss-1 0.7 0.6 0.5 0.4 0.3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Drying Time (h) 3.5 4.0 4.5 0.5 0.4 0.3 0.0 5.0 1.0 0.0 0.5 1.0 1.5 Drying Time (h) 2.0 2.5 3.0 1.0 60⁰C 0.6 m m/ss-1 0.9 0.6 0.5 0.4 0.3 70⁰C 0.9 m m/ss-1 0.8 Moisture Ratio (MR) 60⁰C 1.2 m m/ss-1 0.7 70⁰C 0.6 m m/ss-1 0.9 60⁰C 0.9 m m/ss-1 0.8 Moisture Ratio (MR) 0.6 0.1 0.1 0.2 70⁰C 1.2 m m/ss-1 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 50⁰C 1.2 m m/ss-1 0.7 0.2 0.2 0.0 50⁰C 0.9 m m/ss-1 0.8 Moisture Ratio (MR) Moisture Ratio (MR) 0.8 50⁰C 0.6 m m/ss-1 0.9 40⁰C 0.9 m m/ss -1 0.1 0.0 0.5 1.0 Drying Time (h) 1.5 0.0 2.0 0.0 0.5 1.0 Drying Time (h) 1.5 2.0 Figure 2- Variations of moisture ratio as a function of time for different air-drying temperatures and velocities Şekil 2- Kurutma havasının farklı sıcaklık ve hızlarında nem oranının zamana göre değişimleri 25.0 25.0 40⁰C 0.9 m m/ss-1 20.0 40⁰C 1.2 m m/ss-1 15.0 10.0 5.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Drying Time (h) 3.5 4.0 4.5 50⁰C 0.6 m m/ss-1 ΔM/Δt (kg water⋅kg-1 dm⋅h-1) ΔM/Δt (kg water⋅kg-1 dm⋅h-1) 40⁰C 0.6 m m/ss-1 25.0 50⁰C 1.2 m m/ss-1 15.0 10.0 5.0 0.0 5.0 50⁰C 0.9 m m/ss-1 20.0 0.0 0.5 1.0 1.5 Drying Time (h) 2.0 2.5 25.0 60⁰C 0.9 m m/ss-1 20.0 60⁰C 1.2 m m/ss-1 15.0 10.0 5.0 0.0 0.5 1.0 Drying Time (h) 1.5 2.0 70⁰C 0.6 m m/ss-1 ΔM/Δt (kg water⋅kg-1 dm⋅h-1) ΔM/Δt (kg water⋅kg-1 dm⋅h-1) 60⁰C 0.6 m m/ss-1 0.0 3.0 70⁰C 0.9 m m/ss-1 20.0 70⁰C 1.2 m m/ss-1 15.0 10.0 5.0 0.0 0.0 0.5 1.0 Drying Time (h) 1.5 2.0 Figure 3 - Variations of drying rate as a function of time for different air-drying temperatures and velocities Şekil 3 - Kurutma havasının farklı sıcaklık ve hızlarında kuruma hızının zamana göre değişimleri 420 Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s Predicted "k" 4.08, 2.29, 1.32 and 0.98 h respectively at a constant can be achieved the higher values than 0.99941 drying air velocity of 0.6 m s-1 while drying at an for R2, lower values than 0.00485 for RMSE, air velocity of 0.9 m s-1 took about 3.83, 1.60, 0.96 lower values than 0.00025 for χ2 and lower values and 0.75 h. Increasing the drying air velocity up than 7.202 for P. Therefore, the Midilli et al model to 1.2 m s-1 at air temperatures of 40, 50, 60 and was preferred because of its better fit to drying 70 °C reduced the drying time down to than 3.5, 0.00485 1.54, data. The Midilli et al model has theforfollowing for RMSE, lower values than 0.00025 2.and lower values tha 1.04 and 0.71 h respectively. From these findings and can reveal satisfactory order the Midilliet alform model was preferred because of itsresults better in fit to drying data. The M it could be stated that drying time for following artichoke form to predict experimental values of the moisture and canthe reveal satisfactory results in order to predict the exp leaves at 70 °C was 4.9 times shorter than that ofratio ratio moisture values for artichoke leaves.leaves. values for artichoke 40 °C. The experimental data showed that there is no constant drying rate period (Figure 3). The = ( ) + (6) drying process of artichoke leaves during all of the results as obtained bywere tabulated i tests took place in the falling rate period. As seen The statisticalThe basedstatistical results asbased obtained byMidilliet al model Midilli et al model were tabulated in Table 3. As table, from Figure 3, the drying rate increasesthe while thethe drying constant kincreases once the temperature of the drying ai from the table,a,n theand drying constant k increases while the model constants, b fluctuate. time is shortened as the drying air temperature andotherseen once the temperature of the drying air and velocity the velocity increases. The main factor that causes this is the temperature of the drying air as followed increases while the other model constants, a, n and Table Statistical analysis of drying models at various drying air temperatures b fluctuate. by velocity. The effect of either 1.2 or 0.9 m s−12-air Çizelge 2Kurutmahavasınınfarklısıcaklıkvehızlarıiçinkurumamodellerininistatistikse velocity in all of the drying tests was similar and Some other regression analysis were also made (Table 2:Ensondanalınıpburayayerleştrilecek) increasing the air velocity above 1.0 m s−1 did not in order to consider the effect of the drying air increase the drying rate too much. temperature and velocity variables on the drying The moisture content data obtained from the constant k (h-1) of the Midilli et al model. The experiments were converted to the moisture ratio drying constants (k) were correlated to the drying values and then curve fitting calculations were air temperature and velocity by considering the performed on the drying models as tabulated different combinations of the equations as in the in Table 1. These models and the results of the form of simple linear, polynomial, logarithmic, Some other regression analysis were also made in order to statistical analyses are shown in Table 2. power, exponential and Arrhenius typetheusing theconstant k (h-1) temperature and velocity variables on drying The coefficient of multiple determination (R2) software Datafit 6.0 (Oakdale Engineering). The constants (k) were correlated to the drying air temperature and indicating the goodness of the fit is over the values power model was assumed to beasthein appropriate combinations of the equations the form of simple line of 0.99395 in all drying conditions. Root mean model due toand theArrhenius easiness intype use using even though some Datafit 6.0 (Oa exponential the software square error (RMSE) which gives the deviation higher was assumed to be the appropriate model due to the easiness in order polynomial functions produced better between the predicted and experimental values predictions. polynomial functions produced better predictions. is in the range of 0.001413 and 0.021848 in the (7) = all drying conditions. The reduced chi-square (χ2) is in the range of 0.000002 and 0.001032 in all In In model, model, TT isistemperature temperature(°C), (C),VVisisthe thedrying drying air velocity ( drying conditions. The mean relative deviation -1 ), A, B and C are constants. The A, B and C was air velocity (m s modulus (P) values were found in the range of fitting to the above written model, the coefficients, fitting to the above written model, the coefficients, 1.495 and 39.388 in the all drying conditions. 0.563268, respectively with a coefficient of determination of 97.82 drying constant of the al model by use of the develope B and C was(k) found to Midilliet be 0.0002048, 2.408351 The statistical analysis results of experiments A, from0.563268, the comparison are depicted respectively with ina Figure4. coefficient of generally indicate high correlation coefficients and for the all drying models. The highest values of determination of 97.829%. The experimental and R2 and the lowest values of RMSE, χ2 and P can predicted drying constant (k)7.0of the Midilli et al be obtained by using the Demir et al and Midilli model by use of the developed model is compared 6.0 et al models in all drying air temperatures and and the findings from the comparison are depicted velocities. When the Midilli et al model used, it in Figure 4. 5.0 20 (2014) 415-426 4.0 3.0 2.0 1.0 421 422 Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s m s-1 R2 RMSE χ2 5.638 0.99988 0.002864 0.000008 0.6 7.237 0.99983 0.003197 0.000011 1.2 4.496 0.99990 0.002561 0.000007 0.6 4.899 0.99991 0.002426 0.000006 7.202 0.99982 0.003266 0.000011 1.2 0.9 4.351 0.99992 0.002272 0.000006 0.9 4.141 0.99991 0.002459 0.000006 0.6 0.6 18.099 0.99537 0.016748 0.000296 7.220 0.99890 0.008657 0.000079 1.2 1.2 27.499 0.99395 0.021064 0.000460 0.9 10.664 0.99811 0.011074 0.000129 25.533 0.99681 0.016758 0.000291 0.6 0.9 6.548 0.99982 0.003367 0.000012 18.473 0.99811 0.012933 0.000173 1.2 7.628 0.99984 0.003422 0.000012 6.548 0.99982 0.003367 0.000012 1.2 0.9 7.629 0.99984 0.003422 0.000012 0.9 5.638 0.99988 0.002864 0.000008 39.388 0.99530 0.031848 0.001032 1.2 0.6 33.291 0.99808 0.023750 0.000574 25.177 0.99888 0.019353 0.000381 P 40°C 0.9 0.6 Velocity R2 RMSE χ2 RMSE χ2 RMSE χ2 6.369 0.99980 0.002907 0.000009 6.678 0.99953 0.004047 0.000017 11.469 0.99923 0.005183 0.000028 6.037 0.99972 0.003518 0.000013 9.883 0.99944 0.004212 0.000018 6.369 0.99980 0.002907 0.000009 6.678 0.99953 0.004047 0.000017 11.469 0.99923 0.005183 0.000028 6.037 0.99972 0.003518 0.000013 6.059 0.99964 0.003669 0.000014 3.999 0.99969 0.003480 0.000013 3.555 0.99946 0.004995 0.000027 4.902 0.99969 0.003443 0.000013 3.322 0.99973 0.003291 0.000012 2.916 0.99949 0.004850 0.000025 5.289 0.99962 0.003762 0.000015 4.206 0.99969 0.003493 0.000013 4.065 0.99945 0.005052 0.000027 5.401 0.99806 0.008565 0.000076 1.693 0.99954 0.003839 0.000016 3.578 0.99958 0.003669 0.000014 2.140 0.99981 0.002668 0.000008 2.955 0.99956 0.003747 0.000015 2.524 0.99961 0.003563 0.000014 1.495 0.99983 0.002501 0.000007 5.207 0.99910 0.005356 0.000030 9.015 0.99902 0.005598 0.000033 1.939 0.99992 0.001413 0.000002 1.573 0.99939 0.004108 0.000018 1.884 0.99988 0.002046 0.000004 3.170 0.99987 0.001847 0.000004 1.705 0.99941 0.004038 0.000017 1.991 0.99987 0.002142 0.000005 2.242 0.99961 0.003157 0.000010 5.838 0.99899 0.005293 0.000029 7.436 0.99897 0.006238 0.000041 12.324 0.99820 0.007929 0.000066 9.725 0.99537 0.014316 0.000212 6.410 0.99900 0.005758 0.000034 10.542 0.99895 0.005570 0.000032 5.285 0.99893 0.006462 0.000043 9.589 0.99954 0.004607 0.000022 14.476 0.99894 0.006677 0.000046 6.608 0.99964 0.004024 0.000017 6.048 0.99941 0.005371 0.000030 9.035 0.99958 0.004143 0.000018 14.989 0.99912 0.006563 0.000045 10.924 0.99967 0.003860 0.000015 6.294 0.99963 0.003992 0.000016 5.725 0.99938 0.005479 0.000031 9.035 0.99958 0.004143 0.000018 14.989 0.99912 0.006563 0.000045 10.924 0.99967 0.003860 0.000015 6.294 0.99963 0.003992 0.000016 5.725 0.99938 0.005479 0.000031 R2 8.209 0.99815 0.011472 0.000134 P 70°C 6.596 0.99902 0.006048 0.000037 10.523 0.99892 0.005612 0.000032 5.599 0.99897 0.007478 0.000057 R2 60°C 9.952 0.99962 0.005548 0.000031 14.431 0.99890 0.006692 0.000046 6.820 0.99969 0.004546 0.000021 P Drying air temperature 6.257 0.99945 0.005927 0.000036 P 50°C P, mean relative percent error; R2, coefficient of determination; RMSE, root mean square error; χ2, reduced mean square of the deviation Demir et al Midilli et al Logarithmic Henderson and Pabis Modified Page Page Levis Model name Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al Table 2- Statistical analysis of drying models at various drying air temperatures and velocities Çizelge 2- Kurutma havasının farklı sıcaklık ve hızları için kuruma modellerinin istatistiksel analizi 20 (2014) 415-426 Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al 0.6 40 0.9 1.2 0.6 50 0.9 1.2 0.6 60 0.9 1.2 0.6 70 0.9 1.2 Replication Velocity m s-1 Temperature °C Table 3- Statistical results of the Midilli et al model and its constants and coefficients at different drying conditions Çizelge 3- Kurutma havasının farklı sıcaklık ve hızları için Midilli vd modelinin sabitleri, katsayıları ve istatistik analizi k a n b P R2 RMSE χ2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1.112265 1.148662 1.094725 1.249831 1.329317 1.273962 1.356235 1.413097 1.320560 1.834230 1.913430 1.854856 2.512386 2.529225 2.465516 2.851674 2.859636 2.747172 2.881234 3.324264 2.854406 3.808960 4.264571 3.994963 4.171691 4.833548 4.123418 4.042290 4.367799 3.685662 5.579094 5.659406 5.200341 6.017516 6.342867 6.137372 0.994631 0.996646 0.996981 0.998437 1.002016 1.001094 0.998106 1.001369 0.998131 0.985748 0.987839 0.989230 0.992101 0.988270 0.992277 0.992316 0.989110 0.992062 0.990799 0.990232 0.992319 0.989667 0.990612 0.988930 0.994334 0.991000 0.991314 1.007230 1.004047 1.008259 0.993387 0.992359 0.994378 1.000903 1.001279 1.001025 0.883051 0.875175 0.899273 0.862140 0.851355 0.849801 0.788721 0.786712 0.796229 1.010571 1.019477 1.007723 1.005202 1.002063 1.004665 0.984463 0.981150 0.989060 1.108364 1.125468 1.083662 1.086432 1.080361 1.082727 1.065097 1.070963 1.037263 1.137207 1.163435 1.125381 1.061496 1.081631 1.032644 1.046930 1.052964 1.035744 0.000700 0.001010 0.000900 0.001325 0.001509 0.001481 -0.000587 -0.000040 -0.000756 0.002182 0.003203 0.003885 0.003502 0.002949 0.003752 0.002619 0.003525 0.003475 0.003324 0.005456 0.004832 0.003214 0.005065 0.002063 0.009271 0.008885 0.008903 0.000496 0.002166 0.007454 0.006544 0.007641 0.007303 0.007840 0.010255 0.008883 4.628 4.671 3.304 4.916 4.321 3.909 7.491 6.728 7.436 3.613 3.159 2.213 3.044 4.240 2.828 5.036 5.682 4.119 2.150 1.556 1.268 2.710 1.895 3.747 3.001 3.099 2.693 2.847 4.797 1.552 1.717 1.920 1.472 3.222 2.994 3.571 0.999894 0.999890 0.999919 0.999901 0.999920 0.999923 0.999824 0.999854 0.999665 0.999396 0.999450 0.999577 0.999823 0.999275 0.999833 0.999742 0.999515 0.999760 0.999805 0.999780 0.999844 0.999644 0.999582 0.999506 0.999719 0.999403 0.999487 0.999823 0.999929 0.999812 0.999348 0.999284 0.999568 0.999891 0.999821 0.999861 0.002674 0.002711 0.002364 0.002557 0.002272 0.002226 0.003269 0.002949 0.004546 0.005310 0.005069 0.004427 0.002656 0.005345 0.002581 0.003127 0.004261 0.003035 0.002744 0.002872 0.002423 0.003418 0.003628 0.003998 0.003044 0.004313 0.004050 0.002496 0.001577 0.002564 0.004244 0.004473 0.003447 0.001678 0.002136 0.001877 7.653E-06 7.865E-06 5.980E-06 7.020E-06 5.545E-06 5.324E-06 1.150E-05 9.353E-06 2.223E-05 3.018E-05 2.749E-05 2.097E-05 7.547E-06 3.057E-05 7.127E-06 1.046E-05 1.943E-05 9.858E-06 8.058E-06 8.829E-06 6.283E-06 1.250E-05 1.408E-05 1.710E-05 9.915E-06 1.991E-05 1.755E-05 6.667E-06 2.660E-06 7.033E-06 1.928E-05 2.141E-05 1.272E-05 3.013E-06 4.881E-06 3.769E-06 Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 20 (2014) 415-426 423 polynomial functions produced better predictions. = (7) In model, T is temperature (C), V is the drying air velocity (ms-1), A, B and C are constants. The Some otherabove regression analysis made in order to consider the effect of 0.0002048, the drying air fitting to the written model,were the also coefficients, A, B and C was found to be 2.408351 and MidillietThe al model. The drying temperature and velocity variables onofthethedrying constant k (h-1) of the 0.563268, respectively with a coefficient of determination 97.829%. experimental and predicted lysis were also made in order to consider the effect drying air Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al -1 constants (k) to al themodel. drying air drying temperature anddeveloped velocity bymodel considering the different ) of the The bles on the dryingdrying constant k (hwere constant (k)correlated of Midilliet the Midilliet al model by use of the is compared and the findings combinations of velocity the equations as in thetheform of simple linear, polynomial, logarithmic, power, to the drying air from temperature and considering different the comparison areby depicted in Figure4. Arrhenius type using the software Datafit 6.0 (Oakdale Engineering). The power model s as in the formexponential of simpleand linear, polynomial, logarithmic, power, depicted in Figure 5. As seen from this figure, the 7.0 was assumed to be theEngineering). appropriate model due to the easiness in use even though some higher order e using the software Datafit 6.0 (Oakdale The power model 7.0 predicted values generally accumulate around the polynomial functions bettersome predictions. priate model due to the easiness in useproduced even though higher order 6.0 straight line. This indicates how the developed better predictions. 6.0 = model fits to the data obtained (7) in the laboratory for 5.0 (7) the drying of artichoke leaves. -1 0 0 0.0 1.0 2.0 1.0 3.05.0 4.0 5.0 Experimental "k" Predicted "k" 0 6.0 0.7 2.0 4.0 0.0 0.0 6.0 1.0 7.0 2.0 Tahminlenen ANO değerleri 0.0 0 0 7.0 1.0 0 0 Predicted "k" Predicted "k" In model, T is temperature (C), 5.0 V is the drying air velocity (ms ), A, B and C are constants. The 1.0 4.0to the above written fitting theare coefficients, B and C was found to be 0.0002048, 2.408351 and B and C constants. A, The (C), V is the drying air velocity (ms-1), A, model, 0.563268, respectively with a coefficient of determination of 97.829%. The experimental and predicted del, the coefficients, A, B and C was found to be 0.0002048, 2.408351 and 4.0 0.9 3.0constant (k) of the Midilliet al model by use of the developed model is compared and the findings drying coefficient of determination of 97.829%. The experimental and predicted from the comparison are depicted in Figure4. 0.8 liet al model by use of the developed model is compared and the findings 3.0 2.0 ed in Figure4. 0.6 0.5 0.4 3.0 4.0 5.0 0.3"k" Experimental and 6.0 7.0 Figure 4- Comparison of the experimental 3.0 predicted drying constant (k) of the Midilli et al 0.2 model 2.0 Figure 4- Comparison of the experimental and predicted drying constant (k) of the Midilli et al model. 0.1 Şekil 4Midilli vd modelindeki kuruma katsayısının Şekil 4-Midillivdmodelindekikurumakatsayısının (k) (k) deneyselvetahminlenendeğerlerilekarşılaştırılması. 1.0 deneysel ve tahminlenen değerler ile karşılaştırılması 0.0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Deneysel ANO değerleri (R2=0.97829) (8) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Figure 5- Comparison of the experimental and The drying drying constant, kk was was employed employed in in model model developed Experimental "k" The constant, bymoisture Midillietratio alandfor predictions weremodel made. predicted the developed developed by Midilli et al and predictions weredrying For this purpose, regression analysis were made and the predicted results were correlated with the Figure 4- Comparison of the experimental and predicted constant (k) of the Midilli et al model. Şekil 5- Deneysel ve geliştirilen model yardımıyla made. For this purpose, regression analysis while reducing the RMSE and 2and the values of a, n and experimental in order R2were Şekil 4-Midillivdmodelindekikurumakatsayısının (k) deneyselvetahminlenendeğerlerilekarşılaştırılması. perimental and predicted drying data constant (k) of to theobtain Midilliaethigher al model. tahminlenen nem oranı değerlerinin karşılaştırılması wereand found be 0.983970, and 0.0074083 made the to predicted results1.039708 were correlated with respectively. makatsayısının (k) b deneyselvetahminlenendeğerlerilekarşılaştırılması. Midilli et2.408351 al model as atofunction the temperature of drying air2 and velocity in order to use for the The experimental data in order obtain aofhigher R2 0.563268 = 0.0002048 (R =0.97829) (8) 2 4. Conclusions artichoke drying has the following form: while reducing the RMSE and2 χ and the values of a, 63268 (R =0.97829) (8) n and were constant, found tok be 1.039708 and Inby this study, drying were behavior Thebdrying was0.983970, employed in model developed Midilliet alandthe predictions 2 made. of artichoke 2.408351 0.563268 ) 1.039708 ] investigated. + were 0.0074083(R =0.992995)(9) = 0.983970exp[(0.0002048 Fordeveloped this purpose, regression werewere made and the predicted results correlated with the 0.0074083 respectively. leaves was Drying artichoke leaves employed in model by Midilliet alandanalysis predictions made. 2 2 while reducing the RMSE and and the values of a, nvelocity and experimental data in order to obtain a higher R -1 nalysis were made and the predicted results were correlated with the at constant 1.2 m s drying air down to Thefound Midilli et aldrying model as a isand function of the 2 model The generalised valid under the following conditions of air temperature (T) and air b were to be 0.983970, 0.0074083 reducing the RMSE and 1.039708 and the values of a, n andrespectively. btain a higher R2 while approximately 10% (wet basis) moisture content at temperature velocity in temperature order to of drying air and velocity in order to use for The Midilli al modelair as and a function of the velocity (V). ofet drying 039708 and 0.0074083 respectively. air temperature of 40, 50, 60 and 70 °C in the dryer artichoke drying hasdrying the following use for artichoke has theform: following function of the temperature of drying air and velocity in order toform: use for about 1.04 and 0.71 h respectively. ng form: 1.23.50, ms-11.54, 40°C T 70°C 0.6lasted ms-1 V 2 2.408351 0.563268 ) 1.039708 ] + 0.0074083(R =0.992995)(9) data there is no = 0.983970exp[(0.0002048 It is evident from the experimental 2 (9) from ) 1.039708 ] + 0.0074083(R 2048 2.408351 0.563268 constant rate dryingdata period. The dimensionless moisture=0.992995)(9) ratio values found experimental and predicted models are The generalised drying model is valid under the following conditions of air temperature (T) and air depicted in Figure 5. As seen from this figure, the predicted values generally accumulate the (V). For describing the drying behavior around of artichoke del is valid under velocity the The following conditions of airmodel temperature (T)under and air generalised drying is valid the seven models were applied to the drying following conditions of air temperature (T) and air leaves, -1 1.2 msThe 40°C T 70°C 0.6 ms-1 V process. different mathematical drying models (V). V 1.2 ms-1 40°C T 70°C velocity 0.6 ms-1 considered in this study were evaluated according The ratio -1 values found -1from experimental data and predicted models are 40 °Cdimensionless ≤ T ≤ 70°C moisture 0.6 ms ≤ V ≤ 1.2 ms 2 2 to the R , RMSE, χ and P to estimate drying curves. depicted Figure 5. Asdata seenand from this figure, theare predicted values generally accumulate around the ure ratio values found frominexperimental predicted models The dimensionless moisture ratio values found The correlation coefficients of all of the models from this figure, the predicted values generally accumulate around the 9 from experimental data and predicted models are considered in this study was found to be close to 0 0.0 1.0(R2=0.97829) 2.0 3.0 (8)4.0 = 0.0002048 2.408351 0.563268 5.0 6.0 7.0 Experimental "k" 424 Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s 9 20 (2014) 415-426 9 Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al each other while the RMSE, χ2 and P values were the smallest once the Midilli et al model was used. Based on these findings the Midilli et al model was selected and a drying constant model of k as a function of the temperature of drying air and airflow velocity was developed and a final model was proposed. The drying model explains the drying of artichoke leaves the air temperature T range of 40 °C ≤ T ≤ 70 °C and 0.6 m s-1 ≤ V ≤ 1.2 m s-1 drying airflow velocity. The predictions by the Midilli et al model were found to be in good agreement with the data obtained in the laboratory. Wang et al (2003) found that the phenolic content of artichokes did not significantly change during the drying at a temperature of 70 °C and freeze-drying. Using this argument, it can be stated that artichoke leaves can be dried at either 60 or 70 °C if a faster drying is needed. Acknowledgements The authors would like to acknowledge the financial support provided by the Ege University Research Fund. References Akgun N A & Doymaz I (2005). Modelling of olive cake thin-layer drying process. 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# Mathematical Modelling of Convection Drying Characteristics of