Mathematical Modelling of Convection Drying Characteristics of Artichoke

12 Pages·2014·1.02 MB·English

Tarım Bilimleri Dergisi Journal of Agricultural Sciences
Tar. Bil. Der.
Dergi web sayfası: Journal homepage:
www.agri.ankara.edu.tr/dergi www.agri.ankara.edu.tr/journal
Mathematical Modelling of Convection Drying Characteristics of
Artichoke (Cynara scolymus L.) Leaves
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Tuncay GÜNHANa, Vedat DEMİRa, Abdülkadir YAĞCIOĞLUa 1
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aEge University, Faculty of Agriculture, Department of Agricultural Machinery, 35100, Bornova, Izmir, TURKEY 4)
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ARTICLE INFO (
Research Article 20
Corresponding Author: Tuncay GÜNHAN, E-mail: [email protected], Tel: [phone] S
Received: 11 February 2014, Received in Revised Form: 17 March 2014, Accepted: 18 March 2014 E
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ABSTRACT E
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This paper presents the results of a study on mathematical modelling of convection drying of artichoke (Cynara scolymus S
L.) leaves. Artichoke leaves used for drying experiments were picked from the agricultural faculty experimentation fields AL
on the campus area of Ege University. Chopped artichoke leaves were then used in the drying experiments performed R
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) U
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at constant relative humidity of 15±2%. Drying of artichoke leaves down to 10% wet based moisture content at air L
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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
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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 I
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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 G
0.71 h respectively. Different mathematical drying models published in the literature were used to compare based on the A
coefficient of multiple determination (R2), root mean square error (RMSE), reduced chi-square (χ2) and relative deviation F
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modulus (P). From the study conducted, it was concluded that the Midilli et al drying model could satisfactorily explain L
convection drying of artichoke (Cynara scolymus L.) leaves under the conditions studied. A
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Keywords: Drying; Artichoke; Modelling
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Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma İ
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Karakteristiklerinin Matematiksel Modellenmesi
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ESER BİLGİSİ İ
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Araştırma Makalesi E
Sorumlu Yazar: Tuncay GÜNHAN, E-posta: [email protected], Tel: [phone] ML
Geliş Tarihi: 11 Şubat 2014, Düzeltmelerin Gelişi: 17 Mart 2014, Kabul: 18 Mart 2014 İ
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ÖZET M
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Bu çalışmada enginar yapraklarının (Cynara scolymus L.) konveksiyonel kuruma karakteristiklerinin matematiksel R
A
modellenmesi sunulmuştur. Denemelerde kullanılan enginar yaprakları Ege Üniversitesi yerleşke alanı içerisindeki T
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
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 2003; Bundy et al 2008). Moreover, anti-oxidant,
hepatoprotective, lowering blood cholesterol
The artichoke (Cynara scolymus L.) is a perennial
effects were mostly studied in the literature.
vegetable that has a great production potential
in Europe and in the continent of America and it Wang et al (2003) used three different
received a great acceptance for the consumption in artichoke varieties in order to determine the
recent years in Turkey. Italy, Egypt, Spain, Peru and phenolic acid components. They dried the
Argentina are the biggest artichoke producers in the artichoke leaves and tissues in an oven at 70
World respectively while Turkey is ranked the 13th °C and also in a freeze drier. After the drying,
one and the production area of artichoke shows an samples were kept in air tight bags at room
increasing trend in Turkey (FAO 2013). temperatures for further analysis. Researchers
Among the public, artichoke leaves are known determined the phenolic acid compounds and
to be useful in eliminating hepatitis and disorders amounts by HPLC analysis for mature leaves,
related to hyperlipidemia. Artichoke leaf is also young and mature artichoke heads. According
known as an herbal medicine for a long time to the results obtained by Wang et al (2003) it
and used for the treatment of hyperlipidemia and was reported that the leaves have highest total
hepatitis in EU traditional folk medicine. Different phenols content than young artichoke heads as
studies about artichoke have demonstrated their followed by mature artichoke heads. In terms of
health-protective potential. The artichoke leaves the method they used, they concluded that freeze
are characterized by the composition and high drying and air assisted drying did not affect the
content in bitter phenolic acids, whose choleretic, amount of phenolic acid in artichoke.
hypocholerestemic and hepatoprotector activities
Fresh food materials cannot be stored for a
are attributed (Alonso et al 2006). Antioxidant,
long time. Therefore, products must be dried for
hepatoprotective, anti-HIV, choleretic and
a long-term storage. One of the most traditional
inhibiting cholesterol biosynthesis activities of
and extensive technique used for the production
artichoke extracts are also reported by Zhu et al
of dehydrated fruits and vegetables is convection
(2005). Shimoda et al (2003) reported that the
drying (Nicoleti et al 2001). It allows to reduce
methanolic extract of artichoke suppress the serum
mass and volume, to store the products under
triglyceride in mice. Zhu et al (2005) reported
ambient temperature and to minimize packaging,
that the artichoke leaves have a new potential
transportation and storage cost (Baysal et al
application in the treatment of fungal infections.
2003).
The composition of phytochemicals in artichoke
leaves were well documented in the literature and Mathematical modelling in drying studies is one
medicinal values of artichoke leaves were found of the most significant step in drying technology and
higher than flowers (Sanchez-Rabaneda et al allows engineers to select the most suitable drying
416 Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 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 2. Material and Methods
proper scale (Strumillo & Kudra 1986; Hawlader et
al 1997). 2.1. Experimental procedures
Scientific studies on the drying process of Drying experiments were performed in a laboratory
artichoke leaves in the literature is very limited and scale convective hot air dryer constructed in the
the most of them focused on determination of the Department of Agricultural Machinery, Faculty
chemical components of artichoke leaves and there of Agriculture, Ege University, Izmir, Turkey.
is no study published on the determination of the A schematic diagram of the laboratory dryer is
drying characteristics of the artichoke leaves. illustrated in Figure 1. The drying system used in
The aim of the study was to determine the drying this study has been described in details by Demir et
characteristics and to develop a mathematical model al (2007). The laboratory dryer includes; fan, cooler,
for predicting the kinetics of convection drying of heater, humidifier, drying unit and automatic control
artichoke leaves. unit.
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
Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 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 and drying airflow velocity on the drying constant
converters cards and data acquisition & control were achieved at temperatures of 40, 50, 60 and
software called VisiDAQ (Advantech Automation 70 °C, and at velocity of 0.6, 0.9 and 1.2 m s-1
Corp., USA) was used to control the drying respectively. During the experiments, the relative
temperature, relative humidity and the automation humidity was maintained at 15 ± 2%. The drying
of the drying system. system was run for at least one hour to maintain
The artichoke leaves for the drying experiments steady-state conditions before the experiments.
were picked from the middle branches of the Each drying experiment was performed with 20
artichoke plants as they are located on the campus g of leaves after steady state conditions of both
area of Ege University, between 8:30 and 9:00 temperature and air velocity was achieved in
a.m. During the experiments, the fresh leaves were the dryer. The artichoke leaves were placed in a
collected daily in early-morning and unblemished vertical drying channel equipped with fine sieves
ones were picked and used in the drying experiments. and weighed every three minutes in the first 15
minute drying process and then every 5 minutes
Some preliminary tests were carried out to
until the drying process is completed. The drying
examine the drying conditions from the point of
experiments were ended when the mass of the
test stand and some expected changes in artichoke
samples does not change.
leaves. In these tests, a homogeneous drying of the
whole leaves was not obtained, especially the main The leaf samples were kept in an air-circulated
vein of the leaves was found to be the last part that oven for 24 hours at 105 ±2 °C in order to determine
dried. In this situation, the tissues in the thinner the initial moisture content. All of these experiments
part of the leaves were subjected to over drying and mentioned above were triplicated.
drying time significantly increased. For this reason,
the leaves were divided into two parts along the 2.2. Mathematical modelling of the drying curves
main vein and then sliced perpendicularly to the
The experimental moisture ratio data of artichoke
main vein. The 4 or 5 mm wide slices were then
leaves were fitted to semi-empirical models in Table
used for the drying process.
1 to define the convection drying kinetics. The
The experiments conducted in the lab had the models in Table 1 were widely employed to describe
objective to determine the effect of air temperature 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) Alibaş (2012)
Modified Page MR= exp[-(kt)n] 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(-ktn)+bt Silva et al (2011)
Demir et al MR= a exp[-(kt) n]+b Demir et al (2007)
MR, moisture ratio; a, b, c coefficients; n, drying exponent specific to each equation; k, drying coefficients specific to each equation;
t, time
418 Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426
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.
2.2. Mathematical modelling of the drying curves

The experimental moisture ratio data of artichoke leaves were fitted tosemi-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.

The leave samples were kept in an air-circulated oven for 24 hours at 105 ±2 C in order to determine
Table 1- Mathematical models widely used to describe the convection drying kinetics
the initial moisture content. All of theseexperiments mentioned above were triplicated.
Çizelge 1- Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel modeler
2.2. Mathematical modelling of the drying curves

Model name Model equation References
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.
Modified Page MR= exp[-(kt)n] Artnaseaw et al (2010)

HTeanbdleer s1o-n M anadt hPeambisa tical modMelRs =w iad eexlyp (u-kste)d to describe theF cigoinelv (e2c0ti1o0n) d rying kinetics
LÇoigzaerligthem 1i-c K onveksiyonlakuruMmRa=ki nae etxikpl(e-rkitn)+ibce lirlemedeyaygDınooylmaraazk (k2u0l1la3n) ı lanmatematiksel modeler
M idilli et al MR= a exp(-ktn)+bt Silva et al (2011)
MDeomdeTTirl hhneeeta amlllee eaa vvee Essaanmmginppallree Yssa wwpreearrkeela MMkkrıneeoRıppd=ntte (laCii nne yeq nxaauapnnar[a t-aai s(oiikcrrnot--) lcc yniim]rr+ccuuubs llL aa.tt)ee Kddo noovvveeeknnsi RDyffoeooenfrrmee r22ile rK44 neu cthhr euaoosmluu (rra2ss 0K aa0att7r a)11k 00te55r i±±st22ik leCCrin iiinnn Moorraddteeemrr attooti kddseeettl eeMrrmmodiiennlleee nmesi, Günhan et al
tthhee Tiinnhiitteii aallle ammvooeii sssttauumrreep lcceoosnn wtteeennrtte.. AAkellllp too ffi ntt hhaeenss eeaeeirxx-ppceeirrrciimmuleeanntettssd mmoveeennnttii oofonnree dd2 4aa bbhooovvueer sww aeetrr 1ee 0tt5rrii pp±ll2iicc aaCttee ddin.. order to determine
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HbTttooeehn edddw eeeerrffixsiitonntpeneeen ratt inahhmdsee e Pfccndoaootlibalmnniolsvv w emeenscco:tts iiiisoootnnun rlddeerr sMyyrsaiiRnn tnigg=ou akkmd iiaennbtxeeapett (riio-cc kfkss t..)na rTTotiwhhceehn omm akoosedd mleeellaossv iiiesnnts u FTTwrieaagebb irerllelaee (t f2i11iot0 t1 ewwM0dee) rrRt eeo swwemiiddviee-allelyymu eeepmm iroppicflla oolRyy mee2dd os hdttooeo ludds eelidssncc rrTbiibbaeeeb lhetthhi g1ee her while the value of
L cctoooog nnadvvreieetfhccinmttiieooi cnnt h dderr yycaiionnnndggv kkeitcii nntcieeoottuniicc lssdd roo Mbyffi eRnvv gee=wgg akreei ittetnaatxbbeeptlln(iee-c sskas..t. s) + Tfcoh lel omwosd:els in DToaybmlea z1 (2w0e1r3e) w idReMly SeEm, plχo2y eadn dto Pd esschroibuel dth eb e lower. Selection of
Mc oidnilvlie cett iaoln drying kineticsM oMf Rv-e=Mg ae teaxbpl(e-sk.t n )+bt Silva et al (2011) the best suitable drying model was done using
DTT eaambbillree e 11t --a lMM aatthheemmaaMttiiccRaall mmooddMeetllRss =ww iiadd eeeexll (yyp 1[ uu-)( sskeetdd) n ]ttoo+ bdd ee ssccrriibbee tthheeD cceoomnnivvr eeecct ttaiiloo ((nn12 0dd)0rr7yy)ii nntggh ikksii nneecttriiccitsse ria. The drying constants (k) of the
MÇÇTRiiazzb,ee mllleggo eei1s -t11u --Mr eKK arooattnnhiovve;ee makk,ssa biityy,i cooc anncolll aaemfkkfuuioMcrrdiuueenmm0ltssaa-; wkkMnii,inn ddeeerettyiilikkynll geeu rresxiiennpdiiobb nteeeolln iitdrr slleeepsemmccreeifiddibcee etyyo aat ehyyaggec ııhcnn oeooqnlluaavarretaaicokktnkki;ouu knll,ll daadrnnryııiyllnaaignnn ccgmmho ekaaofittfsneeicemmeinetaani ctttiismskk ssspoeeelldc immefilcoo tddwoee elleaeecrrrhe eqtuhaetinon ;r elated to the multiple
t Ç, tiizmeelg e 1- KonveksTiyhoen lmakouirsutmuareki rnaettiikol ewriansib cealilrcluemlaetdeedy auysginıngo leaqraukaktuiollnan ılancmoamtebminataiktisoeln ms oodfe ltehre different equations as in the
MLPMLPML b aaeeeoooeggwww dddeewiiieeeT ssslllr h innnteaaat emmmleneeef at sh af(ionn1ldlv)o ,se wMiswdsteRi:h g oiacft htoh Mrwes MMMMMMMM eatqoRRoRRoRs((Muddd =====2seeea )llliteeeeee mixxxxxeeenoqppqppqpngp(((((uuus-----elaaakkkkk istttitttttfiiiis)))nn ooo)) ennn a&d d timoE erentqesukioainntli,eo sn2s 0n(RYARYARY02ueeellaaa6)miiffflllbb eeeddd;bbaarrr ıııeeeşşzzzeyMnnn &&&r(( ccc22 sEEEkeeei00osssdrrrn11ttt mioeee22lkkkw))le iiiinnnn (((a222s000fe 000mox111rop)))m ios ntueornef trilaaitnli oea anMrd,R Aapnrodrl hyiten cnooimuulsid.a l, logarithmic, power,
MMP aoogddeii ffiieedd PPaaggee & Kucuk 2M0MMM0oRRR3===; eeeSxxxapppc[[(---ik((lkktinttk))) nn ]]& Elicin 2006AAA;rrl ittTbnnaaaoşssg ee(aar2uww0l1 ee2tt&) aa ll ((22001100))
HHM eeonndddieefirressdoo nnP aaagnnedd PPPaaebbiihssMl ivRan 2M00MMMt3RRR-;=== MY aaeax eeeplxxd[(pp-i1(((zk--) kk t)tten))]t al 2001) becFFAaiiruggtniiseeaells ((e22oa00fw11 00teh))t ea l (20310. ) R esults and Discussion
LMLMHL eoooemiigggnddaaapdiiMllrrreilliiiriirttt Sihhhseecommm tta nEaaliii ll cccax d ncrdey lPi dMnasgeboe vif msiti swao tradieroeellna s wt oiiMvnaf se MMMMMMT tl0huyaRRRRRR-seb ======seM lm edraaaaaae 1aeleeeeeefa.oxxxxxxl ltpppppprT i ((((((wv------htkkkkkkheehtttttte ))))nne+++)) ch ++nocucccabb e mclttf cfoiiumdcliaiepttyniaot r noeo fdfo tmfth oDSDSFDtue hiiil Mooollgetdvvyyyii peaar0mmmd l ylee aeraaa(itty 2nzzz ndaai 0d(((nglle1222 g(( t0000t22ea h)11100rci e333m r11o ))) 11n i ))ns atatDinotrnsy (iRann2g)d wocfao set hfcfeoic naiserintditescr heoodf kasese mltehiea- ves was performed in a
DDM meeiadmmiiiinlrrl i eecettrt aaiatllel r ia dfourr isnegle cthtien gp rtMMMohcRRRe e===bs aaaess eeeetsxxx .pppm[[(---ok((dkktntte)))l+ nn ]]bt++ot bbo btain the DDScieeolvmmnavii rree teec ttat liaa oll( 2n((220 100d100ry77) ))i ncgo ncuvrevcetsi voef darritiecrh oakned ltehaev eesx. periments were carried
DBMMeeRRms,, iimmrd ooeeiitsss attuutlhrr eee rr aaRttii2oo,;; saao,, bbm,, cce ccoooeethffffeiiMccrii eeMsnntttRass;;t= inns ,,at ddi cerryyaxiilpnn [ggt-e ee(skxxttpps)oo wnnn]eee+nnrbtte ss ppaeeccchiiffiiiecc vttooe deeaa Dccinhhe eemoqqruuirdaa tteeiitoor nnat;;lo kk( ,,2e dd0vrr0yya7iilnnu)gg ao cctuooeee tffh ffaiiocctwii eefnn otttssh usseppr ee dccdeiiffiviifccef ltteooor peeeaaenccdhht eemtqqeuuomaadttiiepoolnnes;; ratures (40, 50, 60 and
fMtt,,i tttR iimm,t omee othisetu rde artaati oo; ba,t aMbi,n cRe cdo effrfiocmien tttsh (; 2en) , edxrypinegr iemxpeonntesn.t Aspmeciofincg to t ehaecshe e,q uroatoiotn ;m (k2e, ad)rny isnqg7 uc0oaer fef° iCceire)rn,ot sr a(sRpnedMci fSitcEh t)roae eneadc h dr eerqyduuiantciogend ; air velocities (0.6, 0.9
c t,h tiim-seq uare (2)have a coMmmon use in drying related studies (Krokida et al 2002; Yaldiz&Ertekin
2 00TT1;hhMee illdeeifflttl ihh&aannKddu cssiiuddkee 2oo0ff 0tt3hhee; Aeeoqqkuugaauttniioo&nnDss oiissy aam ddaiizmm 2ee0nn0ss5iioo).nnIllnee ssassd nnduuitmmiobbnee trro kk tnnhooewwsenn m aassea tmmhnodoodii sss1tt,uu .m2rree e marraan tt iisrooe- 1lMM)a tRRiavnaaennd ddd eciivtto iccnaootsiuutoallnddn t air relative humidity
mbbeeo wwdTurrhliittuett seel enn(f Paat ss)h affvoonalldllluoo seMwwi dsswSe:: a oEsf xtahclseeo le qsuuoseaftdtwi otnaors e ei svw aala udsai mtuese etnhdsei o fgnoolreo stdshn ene uscsma lbocefu rfl iakttn iooofwn t nh ea s(m m1o5od±ies2ltus% r(e)S .ra actTiiolhi kMe& REaalvnicedir niat g2ce0o 0u6lidn; itial moisture content
MS Excel software was used for the calculation of the drying constants and coefficients of semi-
eÖ bmez dpweirrmiitctiaerl&n dDarsye fivonorgflel som tw1ho9esd9: e9dl)sr. y iTninh Tegs aebc ltoeen s1ts .tf auTnnhtcset iocaonnesd fuf iscceiodee ntfotfi odcfei etmenrutmslt iinpoelfe t hdseee tmbeerims-t ifnita toairofe n t(ghRiev2 e) anwr btaiescl ohcwoonk: seid leeraedv eass twhea s 4.8964 kg water kg-1
mcBf ihtea isit-noisdq etcuhsrae irtt ehed reai (atRa 22feomco,)omo fhbsra na omtpiavvsnRMMMmiieeuer nMcl eiclRRReecrt atcdiioSai ptt otleiEcfhl nnrerodegio MMMMMM mradr dm y rtsefmhyittt 000totntaeieo---rh---nt gr Nnie1MMMsbMMMgms eetm eiculs∑icixeeeeeeenNutsoa pc1eardl(((met v(t111ietriMineo)))eoiln msssdgn R t e ose itdl(nwhnpf rRr etytaeesoT2 ,irri.b)n aet eiogA wbcasb lmhMctaetr aohesm oiR il1knneaco.e egtvo xde tT elpnhdete,dihehs la i e)esitvd2csnot eeeouc soo,rdno e.rbvir eeddBoetfsea ocfie aritts cnsi (toiKm i odtetnh hreen eoeeasdtvkn rai ydlsuiaqnadmnT ugtemoeah ot rc e he iuc sa aorhcetlnwvu rhaedr2 rnaoste 0rhg rt a0(oehecRc2 fseod Mt; naeeilrYSrvtneteieEi asacnlt)tvlohhdtaiep ocnieozsek d d& dfe m w rr0Emeylaae.dri0osatsnuesdv6 cgk (dee6e3io lsrnd2cs).fi u e kldregv a etvwose awtsht eeewrr eeak rvgcee-o 1r onadbsgmtterau iufincntneetdaidll.
2m 0o0d1u;lMusi d(iPll)i& vitKnhal euuo ceMMurR dkw2RRe ,2a rs 0s t0o∑aoN3mlMMM s;e o(eAvM ttuako((Rlsg22tueuh))edaxn ept &re,ti o D-s hteoMoavywtaiRmsl utaptiarhzcet eae,i2 l)0 td2h0teee5v s)get.Islon oo pwaddenedderi setsmi o aonocf d thoefii letts vh oeefifsd tet hme eftmthrhooeodmrdees l ,s imt sh( eSeoaa nnce ilrlxyeikp la&aet irEvifmelai cldelieinnnv tgi2aa 0lt ir0oa6dnt;ae t ad raynindg ipnedriicoadte fdo rt haaltl
Ö zdemir&Devttrohe ests h1Meχe9,2 R9rd9oa)o.t iatT MMM 1mhoebeoootstaea(n 2ite n)Nss etqd fu- uafnnrrc1oet mieo rnrtsho uer s (eeRdx MptoeS rdEiem)te eranmntdisn. erA ethdmeu ocbneegdst fit aerarxetpi goei rvviemenr esbnuetslao dlw r:cy aisnegs .t imThee (a 4nc)hd a tnhgee ds ryinin tgh era tme oviesrtsuures
mm eeemmmaaiipppMMMnniii rrrSSSiiicccccrr aaaiiEEEttlllee xxxdddrrccciirrraaeeeyyy llliii csffnnnsssoothggguooorri fffd-mmmtttssRPsiwwweeqeoooMllaaasudddeerrr eeeccaSeee(1lllttrK sssiiEeNnn0www r iiigg0(nnnoaaa χ sssk∑ttTTT2 hhi)uuudaaa eehsssbbba Neee1aMlllbb eeedddevee t∑ssRe111i fffNtt a...ooo 1e aMxlmmrrrTTT(p Mc2,hhhiootttRhhho0eeedd-Reeem 0eeMccc ll2pooocccm r;aaaReeette oolll,offfYicccfffp niiiuuuraooccce llllbb,iiiuiaaadMeeetttttsaainnniii ezoooiiRtttnn nnniooo&e nxfffttpooohh ,dmmmifffEee r) rtttuuuy2cchhhtllleiooeeettt niiiknn pppgdddivvllln eeerrreeryyy cce2dddiiittlnnnii0eeeaoogggttt0teeenn e1rrr cccdmmm;ddooo rrnnniiiyynnnsssiiaaatttnnaaatttdsggiiinnntooor utttynnnsssccd i(((uunRRRiaaarrennngvv222d)))dddee tsswwwiccc imaaaoosooosss ffeeee fffpccc aaffffoooriiirrcccoettnnniiiiisrssscceee eiiihhnnndddtnoottteeeessstkkmrrr eeeeeeooodd d dpfffll eeeaaasssiraassseeenavv mmm tttt((eehhhu35Fiiisseee))---r..i egsu aren d2 a, iraflnodw F vigeulorcei t3y
mBBBffiitteeea sssittTnooiiiddd heeettcehhsssrbee itttet hhhetddtreeeaaei attrRRRaa 222gMafoo,,,ood bbsssroid ooodttdaaismmmitniielinnlloeeeeieees n cddooos& t tttitoffhhhn ∑orrKNfeeegoo rrr mmtut (hthssscMh ettteuttaaae hhsttt Rfkeiiieeibsss t ettt2 eeiiimms0cccxxtaaa0 ppeelll-matee3 htttrrnM;oeeeiio smmAsssd dRttteetssseexkshlpwwwnn, ga, ittteeetussmo rrr..nt eeeh)eoAA 2ea&aaabmm nccctv ahhh ooDaiiiirnnnleeeeou ggvvvleyta eeeh ttmdddthhoei v eefaiii cssnnnezReeo ooo,,n2d2 srrrvrre0hdddooev0oeeeoocirrr5uttta i l)tttotmmd.oooi n o Ieeb eeennaadevvv nn raaa yhlllssuuuiiqqngaaaruughttteeeeaa es rrcrphhhee Fu eooowrreecwwwvohrrterr imioosltttvehhh rr et((oeeethRRl fheyddd MMe .aeeevsrSSvvveateeeEEil clllu))fiooohaaepppgonn eeekoudddddefr rremmmReelseddM oooauuidddvtScc eeeeeeEilllsddssss,. clear that the moisture
ccc22fihhh002ta iii00t---no11sssdqqq ;; MMtuuuhPaaaeii rrrdd seeediih llallo(((iitu&&al 222mgdKKo)))ohhh bouuboaaatdccavvvedχuuui eeennkk2ll oeeu aaa22wsds s00 eccc f00(oirroooP33.of 1mmm;; m)S fi AAmmme tvlt kkoooehoaggnnncefluutu e iNtxennoeuuuhpx&&,n sssiepeee- w DDe omnrafooiiiinnn osmyyt dhmmedddaeenpaarrrl lrstyyyzzsbeso iii,ei.22(nnn sS00gggAtu a00 mssc55rrr eueeei))odlilll..tinIIaaa aknngtttbteee o&aaldddte ddh eeddEsssdsviitttrttleuuuayiii,dddoocli uniiinnireeenog assstto too 2emt (((0 ttKKKmhho0theedrrre6ososoeea;eekkkl n iii mmwdddsaaaqaeerw uttsahh eeeaitoodtttrti eddhooaaa ssn elll,,ed ormm r222rfuoy 000eesraaia000i(nnRnnr222ggt M;;;rri ceetYYYSllhthaaiEiaaaomtts)iilll kvvdddaeceneeiiir.zzz d idd&&&t lAeeereEEErevvasidrrriia vaatttu.eeeTstteciikkk(esoohe4iiie nnnnned)nd ecfrroemas eFs igcuornet in2u, oiuts liys
mm20oo0dd1uu;llMuussi d((iPPll))i& vvÖKaazlluuudceeeu mkww 2iaarss0 &0aa3ll ss;D ooA euukvssgreeueddns &tt1ooD9 ee9o1vv9yaa)mll.uu aTaaztth ee2e 0ttshh0eee5 t)egg.Isoontoo afddudnnndeeicsstsstiio ooonnff tsoff ii uttt hsooeeffsd e tt hhmee emmthooodddeesll,ss m ((eSSaaancc iirlleiikkla&&tiEEvellii ccdiiennv i22a00ti00o66n;;
mÖ Ö Özzzoddddeeeummmluiiisrrr &&&(PDDD)eee vvvvtorrraeeel sssud ePe111 t999ew999ra999m1s))) ...i0 anTTT0leshhh o∑eeet hsssueeees MtttebeeedesssR ttts ttfffeo uuuxfi pnnne,ticcc va-tttaiiirMoooleunnn aRgssst ieuuupv rssseteeeeh,niddde b tttooogeo ldddooeeewdttteeen:rrremmmssiii nnnoeeef ttthhhfieeet bbboeeefsss tttt hfffeiiittt okaaamrrrbieeeonv degggietoiiiilvvvsuceee ssnnn( S tbbboaheeecfalll ioootl iwwwaktrh:::&t eiEc mhliocaiknine 2 f0lae0(ca564t)v;o erss eafrfee cttihneg dthrye indgry ianigr
N MR temperature and drying airflow velocity. Drying
2anTdh ePb esthteoru lgdo obdeRRRn MMMleoswsSSS eEEEorf. tSheel efNNNc111itt iom∑∑∑iiNNNne11 ao(((nMMMf st RRRehtxheppppa ,irrrbteee ,,,iiietshte MMMsvuaiRRRtlaueeebxxxepppl ,,,eiiio )))fd 222rRy 2isnhgo umldo( d3be)el hwiagtashii merdrfloe own wweh ie ulvenstiethn ledgo ocvtwihatilynsu eica nrosict fert herRiaeaMs .TdeS(((rhsE333y.e))), i Dngry ainirg t eamir pteermatpuerrea taunrde
∑∑∑NNN (((MMMRRReexxppi,,ii1---MMMRRRpprree,,ii)))222 winaflsu ernecpionrgt edd rytoin gb e rathtee bmyo stm aimnyp orrteasneta rcfahcetrosr.
χχ22  ii11 exp,i pre,i (4) Using higher drying temp((44e))r atures increases drying
χ2  i1 NN--nn rate significantly (Temp(4l4e) & van Boxtel 1999;
N-n11
PPP111NN000000∑∑∑MMMRRReeeMMxxxppp,,,iii1RR---MMMRRRppprrreee,,,iii (5) Pdteoamnwcpnhe artaroit yu1are0 es%t o afwl 42e00t ,0 b52a0)s., e D6d(((5550r )))y m ainnogdis ot7uf0r ae°r Ctcio clhnaotsetkenedt leaaatb voaeuisrt
N MReexxpp,,ii
TThheebbeetttteerr ggooooddnneessss ooff tthhee ffiitt mmeeaannss ettxhhpaa,itt tthhee vvaalluuee ooff RR22sshhoouulldd bbee hhiigghheerr wwhhiilleetthhee vvaalluuee ooff RRMMSSEE,,
22aannTddh ePPb essthhteooruu llgddo obbdeen lleooswws eeorrf.. tSSheeell eefccittt iioomnne aoonff stt hhtheea bbt eetsshtte ssvuuaiittlaaubbell eeo fdd rrRyy2iisnnhggo ummldoo ddbeeell hwwiaagssh eddroo wnneeh iuulesstiihnnegg vtthhaiilssu ecc rroiittfee rrRiiaaM..TTShhEee,
2and P should be lower. Selection of the best suitable drying model was done using this criteria.The
Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426 419
44
4
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
1.0 1.0
0.9 40C 0.6 mm/ ss-1 0.9 50C 0.6 mm /ss-1
0.8 40⁰C 0.9 mm/ ss-1 0.8 50⁰C 0.9 mm /ss-1
Moisture Ratio (MR)00000.....34567 40⁰⁰C 1.2 mm/ ss-1 Moisture Ratio (MR)00000.....34567 50⁰⁰C 1.2 mm /ss-1
0.2 0.2
0.1 0.1
0.0 0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Drying Time (h) Drying Time (h)
1.0 1.0
0.9 60C 0.6 mm /ss-1 0.9 70C 0.6 mm /ss-1
0.8 60⁰C 0.9 mm /ss-1 0.8 70⁰C 0.9 mm /ss-1
R)0.7 60⁰C 1.2 mm /ss-1 R)0.7 70⁰C 1.2 mm /ss-1
Ratio (M00..56 ⁰ Ratio (M00..56 ⁰
Moisture 00..34 Moisture 00..34
0.2 0.2
0.1 0.1
0.0 0.0
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
Drying Time (h) Drying Time (h)
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
40C 0.6 mm/ ss-1 50C 0.6 mm /ss-1
⋅-1mh)20.0 4400⁰⁰CC 01..92 mmmm// ssss--11 ⋅-1mh)20.0 5500⁰⁰CC 01..92 mmmm //ssss--11
⋅-1waterkgd15.0 ⁰ ⋅-1waterkgd15.0 ⁰
Δt (kg 10.0 Δt (kg 10.0
M/ M/
Δ 5.0 Δ 5.0
0.0 0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Drying Time (h) Drying Time (h)
25.0 25.0
60C 0.6 mm /ss-1 70C 0.6 mm /ss-1
⋅-1mh)20.0 6600⁰⁰CC 01..92 mmmm //ssss--11 ⋅-1mh)20.0 7700⁰⁰CC 01..92 mmmm //ssss--11
⋅-1waterkgd15.0 ⁰ ⋅-1waterkgd15.0 ⁰
Δt (kg 10.0 Δt (kg 10.0
M/ M/
Δ 5.0 Δ 5.0
0.0 0.0
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
Drying Time (h) Drying Time (h)
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 Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
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 th3a.5n, 01..05044, 85 dfoart aR. MTShEe , Mloiwdeilrl iv ealtu aels mthoand e0l. 0h0a0s2 t5h efo fr oll2o.awnidn glo wer values than 7.202 for P.Therefore,
1.04 and 0.71 h respectively. From thesteh efi Mndiidnigllsi et afl omrmod ealn wd acsa pnr erefevreraedl sbaetcisafuascet oorfy i tsr ebseutlttesr ifnit toor dderyr ing data. The Midilli et al model has the
it could be stated that drying time for artichoke
following formto panredd iccatn t hree veexapl esriamtisefnatcatlo vrya lureessu oltfs thine omrodiesrt utore predict the experimental values of the
leaves at 70 °C was 4.9 times shorter thmano itshtuart eo rfa tio rvaatiloue vsa floure asr ftiocrh aorkteic lheoakvees l.e aves.
40 °C. The experimental data showed that there
is no constant drying rate period (Figure 3). The   (6) (6)
drying process of artichoke leaves during all of the 𝑛𝑛
tests took place in the falling rate period. ATsh see estna tisticalT 𝑀𝑀bha𝑅𝑅es e=dst ar 𝑎𝑎etiss𝑒𝑒ut𝑥𝑥ilct𝑝𝑝sa l(a sb 𝑘𝑘oa𝑡𝑡bstea)di+ ner𝑏𝑏eds 𝑡𝑡buyltMs iadsil lioebt taali nmedo debly w ere tabulated in Table 3. As seen from
from Figure 3, the drying rate increasest hweh italeb lteh,e the Mdriydiinllgi ecto nasl tamnot dkeiln cwreearese sta bounlcaet etdh ei nt eTmapbeler a3tu. rAe so f the drying air and velocity increases
time is shortened as the drying air tempewrahtuilree t ahne do thesr emeno dfreol mco tnhseta tnatbsl,e a, ,tnh aen ddr ybi nflgu cctounasttea.n t k increases
the velocity increases. The main factor t hat causes once the temperature of the drying air and velocity
this is the temperature of the drying air as followed increases while the other model consta nts, a, n and
by velocity. The effect of either 1.2 or 0.T9 amb lse− 12 -a iSrt atisbt iflcaulc atunaatley.sis of drying models at various drying air temperatures and velocities
Çizelge 2- Kurutmahavasınınfarklısıcaklıkvehızlarıiçinkurumamodellerininistatistikselanalizi
velocity in all of the drying tests was similar and
Some other re(Tgraebslsei o2n:E annsaolnydsaisn awlıenrıep baulrsaoy mayaedrlee ştrilecek)
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 con sidering 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,
statistical analyses are shown in Table 2. Some other regression analysis we re also made in order to consider the effect of the drying air
pteomwpeer,r aetuxrpeo naenndt ivael loacnidty A vrarrhieanbiluess otynp teh eu sdirnygi ntgh ec onstant k (h-1) of the Midilliet al model. The drying
The coefficient of multiple determination (R2) scoofntwstaanrets D(ka)t awfite r6e .0c o(rOrealaktdeadl et oE nthgei nde reyriinngg ).a iTr htee mperature and velocity by considering the different
indicating the goodness of the fit is over the values pcoowmebri nmatoiodnesl wofa s thaes suemqueadt ioton sb ea st hien atphper ofporriamte of simple linear, polynomial, logarithmic, power,
of 0.99395 in all drying conditions. Root mean mexopdoenle dnutiea lt oa nthde A erarshineneisus si nty upsee uesvineng tt hhoe usgohf tswoamree Datafit 6.0 (Oakdale Engineering). The power model
square error (RMSE) which gives the deviation hwigash ears sourdmeerd p otoly bneo mthiael afpupnrcotiporniast ep rmo doudceel dd bueet tteor the easiness in use even though some higher order
between the predicted and experimental values pproeldyincotimoniasl. functions produced better p redictions.
is in the range of 0.001413 and 0.021848 in the
all drying conditions. The reduced chi-square (χ2)   (7) (7)
is in the range of 0.000002 and 0.001032 in all 𝐵𝐵 𝐶𝐶
drying conditions. The mean relative deviation II𝑘𝑘nn =mmo o𝐴𝐴ddee𝑇𝑇ll,, TT𝑉𝑉 isis t etemmppeeraratuturere ( °(CC),) ,V V i si sth teh ed rdyriynign g air velocity (ms-1), A, B and C are constants. The
modulus (P) values were found in the range of afiitrt ivnegl otoc itthye ( mab osv-1e), wAr,i tBte na nmdo Cde al,r eth ceo c nosetaffnitcsi.e nTths,e A, B and C was found to be 0.0002048, 2.408351 and
1.495 and 39.388 in the all drying conditions. fi0t.5ti6n3g2 t6o8 ,t hree sapbeocvtiev ewlyri twteinth m ao cdoeel,f ftihceie cnot eofffi cdieetnetrsm, ination of 97.829%. The experimental and predicted
The statistical analysis results of experiments Adr, yBin gan cdo nCs twanats ( kfo) uonf dt hteo Mbeid 0il.l0ie0t0 a2l0 m4 8o,d 2e.l4 b0y8 3u5s1e of the developed model is compared and the findings
generally indicate high correlation coefficients afrnodm 0 t.h5e6 c3o2m68p,a rriessopne acrtiev deleyp icwteitdh ina Fcigo uefrfie4c.i ent of
for the all drying models. The highest values of d etermination of 97.829%. The exper imental and
R2 and the lowest values of RMSE, χ2 and P can predicted drying constant (k)7 .0of the M idilli 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

"
k
Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426d "4.0 421
cte
edi3.0
Pr

2.0

1.0

0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Experimental "k"

Figure 4- Comparison of the experimental and predicted drying constant (k) of the Midilli et al model.
Şekil 4-Midillivdmodelindekikurumakatsayısının (k) deneyselvetahminlenendeğerlerilekarşılaştırılması.

  (R2=0.97829) (8)
2.408351 0.563268
𝑘𝑘 =T h0e.0 d0r0y2in0g4 8co𝑇𝑇nstant, k w𝑉𝑉as employed in model developed by Midilliet aland predictio7n s were made.
For this purpose, regression analysis were made and the predicted results were correlated with the
experimental data in order to obtain a higher R2 while reducing the RMSE and 2and the values of a, n and
b were found to be 0.983970, 1.039708 and 0.0074083 respectively.
The Midilli et al model as a function of the temperature of drying air and velocity in order to use for
artichoke drying has the following form:

      (R2=0.992995)(9)
2.408351 0.563268 1.039708
𝑀𝑀𝑅𝑅T=he 0g.9en8e3r9al7is0edex dpr[yi(n0g. 0m0o0d2e0l 4i8s v𝑇𝑇alid unde𝑉𝑉r the foll)o𝑡𝑡wing con]d+iti 0on.0s0 o7f4 a0i8r 3te𝑡𝑡mperature (T) and air
velocity (V).

40°C T 70°C 0.6 ms-1 V 1.2 ms-1

The dimensionless moisture ratio values found from experimental data and predicted models are
depicted in Figure 5. As seen from this figure, the predicted values generally accumulate around the
9
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
4 2 8 9 8 5 9 8 5 6 2 2 6 9 0 5 7 4 4 8 2
3 3 1 0 2 1 0 2 1 7 3 1 6 2 1 0 1 0 0 1 0
χ2 001 000 000 000 000 000 000 000 000 000 000 002 000 000 000 000 000 000 000 000 000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
2 2 2 7 3 0 7 3 0 5 0 6 9 3 7 2 8 7 6 8 3
0°C RMSE 0.01147 0.00561 0.00421 0.00290 0.00518 0.00386 0.00290 0.00518 0.00386 0.00856 0.00557 0.01431 0.00792 0.00529 0.00315 0.00214 0.00403 0.00184 0.00204 0.00410 0.00141
7
5 2 4 0 3 7 0 3 7 6 5 7 0 9 1 7 1 7 8 9 2
1 9 4 8 2 6 8 2 6 0 9 3 2 9 6 8 4 8 8 3 9
2R 98 98 99 99 99 99 99 99 99 98 98 95 98 98 99 99 99 99 99 99 99
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 n
90. 30. 30. 90. 90. 40. 90. 90. 40. 10. 20. 50. 40. 80. 20. 10. 50. 00. 40. 30. 0.9 atio
P 8.20 10.52 9.88 6.36 11.46 10.92 6.36 11.46 10.92 5.40 10.54 9.72 12.32 5.83 2.24 1.99 1.70 3.17 1.88 1.57 1.93 e devi
χ2 0.000057 0.000037 0.000046 0.000013 0.000017 0.000045 0.000013 0.000017 0.000045 0.000043 0.000034 0.000046 0.000041 0.000033 0.000030 0.000007 0.000014 0.000015 0.000008 0.000014 0.000016 uare of th
60°C RMSE 0.007478 0.006048 0.006692 0.003518 0.004047 0.006563 0.003518 0.004047 0.006563 0.006462 0.005758 0.006677 0.006238 0.005598 0.005356 0.002501 0.003563 0.003747 0.002668 0.003669 0.003839 d mean sq
2R 9897 9902 9890 9972 9953 9912 9972 9953 9912 9893 9900 9894 9897 9902 9910 9983 9961 9956 9981 9958 9954 duce
ng air temperature χ2P 000365.5990.9 000216.5960.9 0003114.4310.9 000316.0370.9 000166.6780.9 0001814.9890.9 000316.0370.9 000166.6780.9 0001814.9890.9 000305.2850.9 000176.4100.9 0002214.4760.9 000277.4360.9 000139.0150.9 000155.2070.9 000251.4950.9 000122.5240.9 000132.9550.9 000272.1400.9 000133.5780.9 000141.6930.9 2quare error; χ, re
Dryi 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 an s
50°C RMSE 0.005927 0.004546 0.005548 0.005479 0.003992 0.004143 0.005479 0.003992 0.004143 0.005371 0.004024 0.004607 0.005052 0.003493 0.003762 0.004850 0.003291 0.003443 0.004995 0.003480 0.003669 E, root me
45 69 62 38 63 58 38 63 58 41 64 54 45 69 62 49 73 69 46 69 64 MS
2R 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 R
0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 on;
57 20 52 25 94 35 25 94 35 48 08 89 65 06 89 16 22 02 55 99 59 ati
P 2 8 9 7 2 0 7 2 0 0 6 5 0 2 2 9 3 9 5 9 0 n
6. 6. 9. 5. 6. 9. 5. 6. 9. 6. 6. 9. 4. 4. 5. 2. 3. 4. 3. 3. 6. mi
χ2 000381 000574 001032 000008 000012 000012 000008 000012 000012 000173 000291 000460 000079 000129 000296 000006 000006 000011 000007 000006 000011 of deter
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. nt
40°C RMSE 80.019353 80.023750 00.031848 80.002864 40.003422 20.003367 80.002864 40.003422 20.003367 10.012933 10.016758 50.021064 00.008657 10.011074 70.016748 10.002459 20.002272 20.003266 00.002561 10.002426 30.003197 2R, coefficie
2R 0.9988 0.9980 0.9953 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9981 0.9968 0.9939 0.9989 0.9981 0.9953 0.9999 0.9999 0.9998 0.9999 0.9999 0.9998 error;
P 25.177 33.291 39.388 5.638 7.629 6.548 5.638 7.628 6.548 18.473 25.533 27.499 7.220 10.664 18.099 4.141 4.351 7.202 4.496 4.899 7.237 percent
yt1i-cso mleV 0.6 0.9 1.2 0.6 0.9 1.2 0.6 0.9 1.2 0.6 0.9 1.2 0.6 0.9 1.2 0.6 0.9 1.2 0.6 0.9 1.2 ative
el
Model name Levis Page Modified Page Hender-son and Pabis Logarith-mic Midilli et al Demir et al P, mean r
422 Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
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
mperature°C Velocity-1m s eplication k a n b P R2 RMSE χ2
Te R
1 1.112265 0.994631 0.883051 0.000700 4.628 0.999894 0.002674 7.653E-06
0.6 2 1.148662 0.996646 0.875175 0.001010 4.671 0.999890 0.002711 7.865E-06
3 1.094725 0.996981 0.899273 0.000900 3.304 0.999919 0.002364 5.980E-06
1 1.249831 0.998437 0.862140 0.001325 4.916 0.999901 0.002557 7.020E-06
40 0.9 2 1.329317 1.002016 0.851355 0.001509 4.321 0.999920 0.002272 5.545E-06
3 1.273962 1.001094 0.849801 0.001481 3.909 0.999923 0.002226 5.324E-06
1 1.356235 0.998106 0.788721 -0.000587 7.491 0.999824 0.003269 1.150E-05
1.2 2 1.413097 1.001369 0.786712 -0.000040 6.728 0.999854 0.002949 9.353E-06
3 1.320560 0.998131 0.796229 -0.000756 7.436 0.999665 0.004546 2.223E-05
1 1.834230 0.985748 1.010571 0.002182 3.613 0.999396 0.005310 3.018E-05
0.6 2 1.913430 0.987839 1.019477 0.003203 3.159 0.999450 0.005069 2.749E-05
3 1.854856 0.989230 1.007723 0.003885 2.213 0.999577 0.004427 2.097E-05
1 2.512386 0.992101 1.005202 0.003502 3.044 0.999823 0.002656 7.547E-06
50 0.9 2 2.529225 0.988270 1.002063 0.002949 4.240 0.999275 0.005345 3.057E-05
3 2.465516 0.992277 1.004665 0.003752 2.828 0.999833 0.002581 7.127E-06
1 2.851674 0.992316 0.984463 0.002619 5.036 0.999742 0.003127 1.046E-05
1.2 2 2.859636 0.989110 0.981150 0.003525 5.682 0.999515 0.004261 1.943E-05
3 2.747172 0.992062 0.989060 0.003475 4.119 0.999760 0.003035 9.858E-06
1 2.881234 0.990799 1.108364 0.003324 2.150 0.999805 0.002744 8.058E-06
0.6 2 3.324264 0.990232 1.125468 0.005456 1.556 0.999780 0.002872 8.829E-06
3 2.854406 0.992319 1.083662 0.004832 1.268 0.999844 0.002423 6.283E-06
1 3.808960 0.989667 1.086432 0.003214 2.710 0.999644 0.003418 1.250E-05
60 0.9 2 4.264571 0.990612 1.080361 0.005065 1.895 0.999582 0.003628 1.408E-05
3 3.994963 0.988930 1.082727 0.002063 3.747 0.999506 0.003998 1.710E-05
1 4.171691 0.994334 1.065097 0.009271 3.001 0.999719 0.003044 9.915E-06
1.2 2 4.833548 0.991000 1.070963 0.008885 3.099 0.999403 0.004313 1.991E-05
3 4.123418 0.991314 1.037263 0.008903 2.693 0.999487 0.004050 1.755E-05
1 4.042290 1.007230 1.137207 0.000496 2.847 0.999823 0.002496 6.667E-06
0.6 2 4.367799 1.004047 1.163435 0.002166 4.797 0.999929 0.001577 2.660E-06
3 3.685662 1.008259 1.125381 0.007454 1.552 0.999812 0.002564 7.033E-06
1 5.579094 0.993387 1.061496 0.006544 1.717 0.999348 0.004244 1.928E-05
70 0.9 2 5.659406 0.992359 1.081631 0.007641 1.920 0.999284 0.004473 2.141E-05
3 5.200341 0.994378 1.032644 0.007303 1.472 0.999568 0.003447 1.272E-05
1 6.017516 1.000903 1.046930 0.007840 3.222 0.999891 0.001678 3.013E-06
1.2 2 6.342867 1.001279 1.052964 0.010255 2.994 0.999821 0.002136 4.881E-06
3 6.137372 1.001025 1.035744 0.008883 3.571 0.999861 0.001877 3.769E-06
Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426 423
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.

  (7)
𝐵𝐵 𝐶𝐶
I𝑘𝑘n =m o𝐴𝐴de𝑇𝑇l, T𝑉𝑉 is temperature (C), V is the drying air velocity (ms-1), A, B and C are constants. The
fittiSnogm teo tohthee ar broegvree swsirointt eann amlyosidse lw, etrhee aclosoe fmficaideen tisn, oAr,d eBr aton dc oCn swidaesr ftohue nedf fteoc tb oef 0t.h0e0 0d2ry0i4ng8 , a2ir. 408351 and
Some other regression analysis were also m0tae.d5me6p 3ein2ra 6tou8rr,de e rrae nstpdo e vcceotlinovsceiidltyyer vwtahirteiha b ealfef sec coote nof ftfih cetih eden rytd ironygfi n dcgoe ntaesirrt amnit nka t(iho-1n) ooff t9h7e. 8M2i9d%illi.e Tt ahle m eoxdpeel.r iTmhee ndtrayli nagn d predicted
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
temperature and velocity variables on the dryingdc rocyoninsntsagtna ntcsto (nkk s)(t haw-n1)et ro(ekf )ct ohorefr eMtlhaitede idMl liteiodt iatlhll ieme tdo radylei nlm.g To adhieer ld tbermyyi pnuegsr eat uorfe thaned d evveleolcoiptye db ym coodnesli diesr icnogm tphea rdeidf faernedn tt he findings
constants (k) were correlated to the drying air fctreoommmpbe itrnhaaettui ocreon sma npodaf rviteshloeo nc eiatqyru eab tdyioe npcsoi cntaseisdd e iirnni n Fgth iegth uefr oedr4imf. f eroefn ts imple linear, polynomial, logarithmic, power,
combinations of the equations as in the form e xpoof nesinmtipall ea nldin Aearrr,h epnoiulysn toympeia ul,s inlogg athreit hsmofitcw, apreo wDeart,a fit 6.0d e(Opaicktdeadle inE nFgiingeuerrein 5g.) . ATsh es epeonw efrr ommod tehl is figure, the
exponential and Arrhenius type using the softwarwe aDs aa7ta.s0fsiut m6e.0d (tOoa bked atlhee E anpgpinroeperriinatge) . mTohdee pl odwueer tmo otdheel easiness in use even though some higher order
was assumed to be the appropriate model due tpoo ltyhneo emaisainl efussn citnio unsse p reovdeunc ethdo bue7gt.th0e rs pormede ichtiigohnesr. order predicted values generally accumulate around the
polynomial functions produced better predictions. 6.0 straight line. This indicates how the developed
  6.0 model fi ts to th e data o btained (i7n) the laboratory for
  5.0 𝐵𝐵 𝐶𝐶 (7) the drying of artichoke leaves.
I𝑘𝑘n =m o𝐴𝐴de𝑇𝑇l𝐵𝐵, T𝑉𝑉 𝐶𝐶is temperature (C), V is the dryfiinttgd "k"iI𝑘𝑘n nag4 =i. 0rmt o vo 𝐴𝐴tedhle𝑇𝑇oel c,a ibTt𝑉𝑉yo iv(sem twes-m1r)ipt,t eeArna, tmBur oead ne(dl5, C. C0t)h, eaV rce oi sec fotfhnicesit eadnnrttyssi,.n ATg, h aBei ra vnedl oCc iwtya1 s.(0 mfosu-1n)d, Ato, bBe a0n.0d0 C02 0ar4e8 ,c 2on.4s0ta8n3t5s1. Tanhde
fd0frir.to5ytim6inn3 ggt2 h t6ceo8o c,tn hosremeta sapnpbate orc(ivktsie)ov noew lfayr rit thewt eedi ntMeh pm iiadco itdcleloedilee ,itf n tfahi cFle ii megcnuootred eofe4ffli. c bdiyeen tuetrssf d0m,err. o 5AyioPredictemn6i,fn a3 B23gttt2..hih 00o6caeen8on cd ,dn ooes rfvmCet aes9 pnplw7oate .arpc(8isekts2 id)ofv9 o noe%mu lfayn o.rt dhdeTw eetdhi lotMe eh ipbs ii eeadccx ito0Predicted "k"cpleml.odei0ee34r p0iitf..nma00 0fair 2Fcele 0indimeg4t naa8uotlnr,d edoa2e4 nfl.t. 4 d hbd0 eyep8 tfr3ueie5rnsdme1di icioanntfnega ddtsthi oen d oefv e9l7o.p800..e892d9 %mo. dTehl eis ecxopmerpimareendt aaln da ntdh ep frienddiicntegds
7.0 0.7
7.0 01..00 6.0 12..00 O değerleri0.6
6.0 N
Predicted "k"345...000 FFpmriioggeduuderricleet e404.d-0 - C dCormy1o.im0pnagpr aic2rso.oi0snnos Enotxa f3pPredicted "k" no.te0thrf2345i m....e0000( tekehn0)x4t.e a0.p0l o 0"efek.r 0"xitpmh5e.ee0r n1iMmt.0aiel6d n.a0itlnla2idl . 0 ep7at.r 0nEeadxdl3p i.ec 0rtimeden Tahminlenen Ad4ta.0000r0l....2345 y"kin"g5 c.0onsta6.n0t (k)7 o.0f th e Midilli et al model.
2.0 ŞŞeekkiill 44-- MMiiddiilllliiv vddm modoedleinlidnedkeikkiu kruumruamkaa tksaatysıasıynısının (ıkn) (dke) neyselv0e.1tahminlenendeğerlerilekarşılaştırılması.
deneysel ve tahminlenen değ1e.0rler ile karşılaştırılması 0.0
1.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.0 Deneysel ANO değerleri
  0.0 1. 0 (R2=20.0.97 823.90) (8)4.0 5.0 6.0 7.0 (R2=0.97829) (8)
0.0
0.0 1.0 2.0 3.0 4.0 5.0 62.0.408375.10 0.563268 Experimental "k"Figure 5- Comparison of the experimental and
E𝑘𝑘xp=erTTim hh0eeen.0 t add0l rr"0kyy"2iinn0gg4 8ccoo𝑇𝑇nnssttaanntt,, kk w𝑉𝑉waass eemmppllooyyeedd iinn mmo oddeell devperloedpiecdt ebdy m Moiisdtiull riee tr aaltaion dfo prr tehdei cdtieovneslo wpeedre m moaddeel.
Fdeovr etlhoipse dp ubrpyo sMe,i driellgi reests iaol n aannda lpyrseisd icwtieorne s mwaedree and the predicted results were correlated with the
Fig ure 4- Comparison of the experimental and predicted dryinŞge kcioln s5ta- nDt (ekn) eoyf stehle Mvei dgilelil ieştt airl imleond eml. odel yardımıyla
Figure 4- Comparison of the experimental and premŞexdeakpicdielte er4.id- mM Fdeirodnyriitl nalitglvh ddcimsoa notpads tueialnrinpn todo (erskdke)ie ,ko ruf rr tetuohgm eora eMbkstasiatdisioianlnly iaı se ıahtn niaıgnal hlm(ykeo)sr di dsRee ln2.w e wyeshreeilvl eet arehtdamhuinmclieinnngelen tndheeeğn eR rnlMeemrSil Eeok raaarnnşdııl adşet2ığareınlrmdl eatrshıie.n ivna kluaerşsı loafş taı,r ınlm aansdı
Şekil 4-Midillivdmodelindekikurumakatsayısının (k) bmd ewandeeyers eea lnfvoedtu atnhhdme itpnolr eebndeein c0dt.ee9ğd8e r3rle9ers7iul0el,kt sa1 r.wş0ı3elar9şe7tı r0cıo8lmr araenslıda. t0e.d0 0w7i4th0 83 respectively.
t he Texhpee Mrimideilnltia el td aalt am iond oerl daesr ato f uonbctatiionn a o hf itghhee rt eRm2 perature of drying air and velocity in order to use for
awrhtiiclhe orkede udcriynign gth hea Rs MthSe Efo alnlodw χi2n agn fdo trhme : v alues of a, 4. Con clusion(Rs2=0.97829) (8)
 2.408351 0.563268 n𝑘𝑘 a= nT dh0 e.b0 d0 rw0y2ie n0rge4 8cfoo𝑇𝑇nu2sn.t4a d0n8 t3t,5o 1k bw𝑉𝑉e0a (.s50R 6.e239=m2860p83.9l9o77y8e02d,9 )i1 n . 0 m(38o9)d 7e0l 8d eavnedlo pedI nby  tMhiisd ilsliteutd ayla, ndth per eddircytiionngs  wb(Reerh2e=a mv0i.ao9dr9e 2. o9f9 5a)r(t9i)c hoke
𝑘𝑘=T h0e.0 d0r0y2in0g4 8co𝑇𝑇nstant, k w𝑉𝑉as employed in mod0eFl.o 0dr0 e7tvhe4ils0o 8pp3eud rr pebosysp eMe, cirtdeiigvlrleieelsyts .iaolann da nparleydsiics tiwonesre w meraed me aadned. the plreeadvicetse dw raess ulitns vwesetrieg actoerdre. laDterdy iwngit h atrhtiec hoke leaves
bFex owpr eetrrhiemi sfoe nuptnuadrlp dtooas teba,e i nr0e .og9rr8de3es9sr7 ito0on, o 1ba.0nta3ail9ny7 sa0i sh8 i agwnheder re0 R.0m20 aw7d𝑀𝑀 vt4hbeeeex0i mlw𝑅𝑅lp8eaoTe3eT Tpnrcr=r hedehhrieimdee tr eefys ua t oeM0hp ctgnu(Muee.iVi9etnnc rdangtd8pei)liid .l e vr 3dtl teirohie oal9 dale fletybili7a tci R.e d s0t ai eeMner0ltdy de. moS9 ix arEn8rdodpel3g d reas[9 yeurnm7a lildt (tn0iooa sr0,g sd o1.2 wa0ebaa.mn0l nte0 afd3rdou0iea9 nnd t2sv7 hceca 00eeto laih 8l 4orv oii rn8aasgefc n lhuliouva𝑇𝑇detnfetya r e2sc0 t ldR .ht.i4oi0id en20of0 w 8 wtna7u3eoi,4 h5tn mrhn10ioddl p8efaeet𝑉𝑉e 3 nhrrrr td ee 0arhttd e .t5houesu6epr c3e ei2 nfco6ogt8faail vtptl)dheo prle𝑡𝑡cwyyr 1oiR.oin. n0nxMg3sgi 9tSma 7aEic0nra o8 tata n]enn1dld+dy. i 2t vi 1 2e0oa0mln.no0%dsc 0 i s tto7-h(y1wfe 4 i dna0ver iat8ory l br3uidtneaee𝑡𝑡sgsmr i o stpafo) ie armur, asnvoet u eaifslnrootedruc r(ietTy )c odanontdwe nnat i rta ot
The Midilli et al model as a function of the teuamrstpeice fhroaotrku ear erd toricyfi hndogrky hiena gsd rtahyieri nafgonl dlho vawesil nothgce ift yof roimnll :oo wrdienr gto f oursme f:or air temperature of 40, 50, 60 and 70 °C in the dryer
artichoke drying has the following form: 40°C T 70°C 0.6l amstse-1d  aVbo u1t. 23 .m50s,- 11 .54, 1.04 and 0.71 h respectively.
     It is evident from th(Re 2e=x0p.9e9r2im99e5n)(t9a)l data there is no
    The dimensionless moist(uRr2e= 02r.a.490t9i8o325 91v9a5l)0u(.95e6)s 3 2f6(o89u)nd1. 0f3cr9oo70nm8s teanxtp eraritme denrytainl gd aptear iaondd. predicted models are
2.408351 0d𝑀𝑀.5e6𝑅𝑅p3T2i=6ch8tee 0dg. 9e1i.n80ne33 9r9Fa70l7ii8gs0euderx edp r[5y.i (n0Ag. 0sm 0os0ed2ee0ln 4 i8sf rv𝑇𝑇oamlid tuhnisd e𝑉𝑉fri gthuer ef,o ltl)oh𝑡𝑡we inpgre cdoin]cdt+eitdi 0o n.v0sa0 lo7uf4e a0si 8rg 3tee𝑡𝑡nmeprearlaltyu rae c(cTu)m anudla ateir around the
𝑀𝑀𝑅𝑅T=he 0g.9en8e3r9al7is0edex dpr[yi(n0g. 0m0o0d2e0l 4i8s v𝑇𝑇alid unde𝑉𝑉r vtheelo Tfcoihtlly)eo 𝑡𝑡(wgVei)nn. ge rcaoln]isd+eitdi 0o dn.0rs0y o7inf4 ga0i 8rm 3toe𝑡𝑡mdeple riast uvrael i(dT )u nandde ra itrh e For describing the drying behavior of artichoke
velocity (V). leaves, seven models were applied to the drying
following conditions of air temperature (T) and air
40°C T 70°C 0.6 ms-1 pVro 1c.e2s sm. sT-1 he different mathematical drying models
velocity (V).
40°C T 70°C 0.6 ms-1 V 1.2 ms-1
considered in this study were evaluated according
T40h e° Cdi ≤m eTn ≤si o7n0l°eCss mois0tu.r6e mrast-i1o ≤ v Val u≤e s1 .f2o umnds -1from experimental data and predicted models are
The dimensionless moisture ratio values foduenpdi cftreodm i ne xFpigeruirme e5n.t aAl sd asteae na nfdr opmre dthiciste dfi gmuroed, etlhs ea rper edictetdo vthaleu eRs2 ,g RenMerSaElly, χa2c acnumd uPla ttoe easrotiumnda teth de rying curves.
depicted in Figure 5. As seen from this figure, the Tphreed idcitmede nvasliuoensl egsesn emraolliys tuacrecu rmautiloat ev aalruoeusn df othuen d The correlation coefficients of all of the mod9el s
from experimental data and predicted models are considered in this study was found to be close to
424 Tarım Bilimleri Dergisi – Journal of Agricultural Sciences 20 (2014) 415-426
9
9