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R E SE A R C HTOMATO INFRARED DRYING: MODELING AND SOME COEFFICIENOF THE DEHYDRATION PROCESSPaulo Cesar Corr ea' , Gabriel Henrique Horta de Oliveira^*, Fernanda Machado Baptestini^M ayra D arliane M artins Silva Diniz', and Aline Almeida d a Paixo'

Infrared dehydration is more advantageous than the convective system under similar conditions, and studying this procis impoiiant to further d evelop equipm ent and proce dures. Th us, the aim of this work was to study the dehydration proceof tomato (Solanum lycopersicum L.) slices obtained by infrared drying at three different maturity stages throughout twdifferent procedures: Firstly, the drying model was determined by applying the mass and energy balances under wet butemperature for the constant drying rate period and secondly, the mass effective diffusion coefficient was determinthroughout the experimental data and the theory of diffusion of the liquid phase for the decreasing drying rate periTomato fmits cv. Santa Cruz were used. Three maturity stages were selected: green (stage 1), orange (stage 2), and r(stage 3). Mathem atical m odels frequently used to represent drying of agricultural produ cts were fitted to the expe rimendata of tomato drying. The effective diffusion coefficient was obtained by adjusting the liquid diffusion mathematical modto the experimental data of the descending period of dehydration. The two-term model was the best one to represent ttomato dehydration process. The critical moisture content for tomato dehydration was 2.97 kgw kgdm'. There is an initdehydration period in which the drying rate reaches its maximum (approximately 1.05 kg, kgdm"', about 3 m in). Thdifferent method s we re used to obtain values of the effective diffusion coefficient, including the finite element m ethwhich had the lowest values for the least square sum of deviation 1.00 x 10 '' m- s''. The g lobal coefficient of heat transwas 12.45 W m'-K"', and the global coefficient of mass transfer was 0.0105 m s'.Key words: Critical moisture content, diffusion, finite element method, heat and mass transfer, mathematical modeliSolanum lycopersicum.

T omato (Solanum lycopersicum L.) is one of thevegetables m ost consum ed in the world. I t is a sourceof vitatnins A and C and mineral salts, such as K andMg. Tomato is a climacteric fruit with a short maturationand color change period, f irmness, aroma, and flavorthroughout shelf-life (Oliveira, 2010).

Dehydration has recently been used to increase shelf-life of several fruits and vegetables (Vasques et al., 2006) .Conservation through dehydration is based on the factthat microorganisms, enzymes, and the entire metabolicsystem of biological materials require water for theiractivit ies. A reduced amount of water decreases wateractivity and chemical reactions within the product, as wellas the development of microorganisms (Christensen andKaufm ann, 1974). Therefore, the main objective of dryingis reducing moisture content and water activity (D oym az,2005a; Correa et al., 2010a; Oliveira et al., 2010) sincethese param eters control produc t respiration rate and'Universidade Federal de Viosa. Agricultural EngineeringDeparttnent, Campus UFV, Av. PH Rolfs, i^n, 36570-000, Viosa,Minas Gerais, Brazil.

incidence of microorganisms and insects (Correa et2010b; Gonel i era/ . , 2010a; 2010b) .

Infrared dehydration is more advantageous thanconvective system under similar conditions (Sharmal., 200 5). Wh en infrared is used to warm up or d ehydwet materials, radiation encounters the exposed prodpenetrates it, and radiation energy is converted heat. The penetration depth of radiation depends onmaterial 's properties and the radiation wavelength. Wthe product is exposed to radiation, it is intensively heand the temperature g radient within the produc t is redin a short period of time.

Depending on the material to be dried, water move through its interior by different mechaniIn hygroscopic capillary-porous products, suchmost agricultural products, the possible mechanof moisture movement are liquid diffusion, capildiffusion, surface diffusion, hydrodynamic flow, vdiffusion, and thermal diffusion (Brooker et al., 19The effective diffusion coefficient has been studieddifferent researchers in different products (Campos e2009; Correa et al., 2010c); this parameter illustrates


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the behavior of each product duringis an important parameter to develop andet al., 2006;et al., 2010c) , as well as selecting mathematicalof food and other

aterials is a significant link betweenof these m aterials and product quality andet al, 2005) .Given the importance of studies on drying , the objectivewas to model the dehydration process ofat three different maturity stages, and alsothe effective diffusion coefficient and global valuesand mass transfer.

MATERIALS AND METHODS

was conducted in the Laboratory ofand Quality Evaluation of Ag riculturalat the National Grain Storage Training Centerof Viosa, Viosa,Tomato fruits cv. Santa Cruz were acquired at the local

et . Three maturity stages were selected: green (stage, orange (stage 2), and red (stage 3). Each maturity stagemm thick and weighed on a digital scale with 0.001 gThe study used a dryer with an infrared radiationIV 2500, Gehaka, Sao Paulo, Brazil) fora scale with 0.001and an automatic data acquisit ion system.is located at a fixed distance of 15the product with an infrared power of 300 W.was carried out at 60 C. The moisture ratiohe tomato d uring drying was obtained by Equation [1]:

M/? = | J ^ [1]MR is the moisture ratio of the product,

[/,* is the moisture content of the producta certain drying t ime, decimal d.b.; Ui* is the initialof the product , decimal d.b.; and Ue* isof the product, decimalThe mathematical models frequently applied toof agricultural products were fitted toof tomato drying. These models arein Table 1.The goodness of fit of the mathematical models wasand the Gauss

8.0 (StatSoft, Tulsa,USA). The fitness degree of each model was

Table 1. Mathematical models used to represent the drying ph enomenoof tomato.Model name Model EquationDiffusion approximation MR = a exp (-kf) + (1 - a) exp (-kbt) [2](Yaldiz and Ertekin. 2001)Two-term (Henderson. 1974) MR = a exp (-kt) + b exp (-gt) [3]

MR = a exp (~kt) [4]enderson and Pabis(Henderson and Pabis, 1961)Midim(Midim era/.. 2002)Logarithmie(Yageiogluerai.. 1999)

Affi = exp (-kf) + bt [S \MR = a exp (-kt) + b [6]

Verma (Verma et al, 1985) AR = a exp (-kt) + (\-a) exp (-gt) [7]Page (Diamente and MR = exp (-kf) [8]Munro, 1993)MR: moisture ratio, dimensionless; a. b. g. n: model param eters, dimensionless; k: dryinrate, s''; t: drying time. s.

P = 100 V, \Y-Y\

DF

[2

[3where P is the mean relative percent deviation (%); SE ithe standard error, decimal d.b.; Y is the observed valuedimensionless; Y is the value estimated by the modedimensionless; n is the number of observed data; anD F is the degrees of freedom of the model (number oobserved data minus the number of model parameters).

The theories that govern the constant rate perioof dehydration of agricultural products, according tBrooker etal.{\992), can be approximated to the heat anmass transfer balance studies for wet bulb temperatureThus , the constant rate of dehydration can be representeby Equation [4]:

dM hcA ,rr ^ \ hdt L ' ""' R

where h^ is the global coefficient^Pvln. [4of heat transfer (W

m"^ K''); h,n is the global coefficient of mass transfer (s"'); i- is the latent heat of vaporization (J kg ') ; Rv is thuniversal constant of water vapor (461.91 J kg ' K') ; A ithe superficial area of tomato slices (m^); P,,;,,, is the vapopressure for th e wet bulb tem perature (Pa); P,, is the vapopressure for dehydration temperature (Pa); T/,,, is the webulb temperature (K); r is the dehydration temperatur(K); and dMIdt is the constant rate of dehydration (kg s"'

Coefficients were calculated with the followinparameters: plate geometric shape type, isothermaprocess, and neglecting volumetric shrinkage of thproduct .

The effective diffusion coefficient was obtaineby adjusting the liquid diffusion mathematical mode(Equation [5]) to the experimental data of the descendinperiod of dehydration. This equation is the analyticsolution of Fick's second law when considering th


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where L is the half thickness of the slab (m); De/ is theeffective diffusion coefficient (m^ s"'); and n is the num berof equation parameters.

RESULTS AND DISCUSSION

Infrared dehydration modelingTable 2 shows the values of P, SE, and R' for each modelconsidered in the present study (Table 1) for tomato fruitdrying.

Determ ining the coefficient (R-) for non-linear mo dels isnot a good decision-making tool. It is necessary to analyzedifferent statistical parameters. Thus, for model adequacyin describing a phenomenon, P values must be taken intoconsideration; the lowest values of P indicate a higherrepresentation of the model for the phenomenon understudy. Analyzing SE also helps to select models. LowerSE values indicate higher model reliability. Therefore, byanalyzing these three statistical parameters shown in Table2 , it was con cluded that the two-term model is the best oneto represent infrared drying of toma to fruit.

No significant difference was observed among tomatomaturity stages at a 5% probability level by the Tukeytest . As a result . Figure 1 represents the tomato dryingcurve. This f igure shows the drying values observed andestimated by the two-term model at maturity stage 1. Byanalyzing Eigure 1, the good adjustment of the two-termmodel to the experimental data can be observed, whichsatisfactorily represents tomato drying kinetics.Thus, it is possible to estimate the moisture content oftomato during infrared drying at 60 C by Equation [6]:

MR= 0.8952 exp(-0.1036,) + 0.1503exp(-0.0064,) [6]Eigure 1 show s that some linearity occurs at

appro xima tely 10 min after the moisture ratio is reducedfollowed by an exponential reduction. The crit icalTable 2. Mean relative percent deviation (P), standard error (SE), anddetermination coefficient (R^) for each mathematical model studied at 60"C at each maturity stage.

Observed valuesEstimated values

Maturitystage Model nameSE(decimald.b.)

Diffusion approxim ation 98.50 9..30 0.03Two-term 98.69 9.05 0.03Henderson and Pabis 96.36 19.23 0.05Logarithmic 98.68 9.31 0.03Midilli 98.59 9.79 0.03Page 97.40 13.79 0.04Verma 98.49 9.30 0.03nn d Diffusion approximationTwo-termHetiderson and PabisLogarithmicMidilliPage

VermaDiffusion approximationTwo-term

95.6695.8592.6195.8495.7194.1095.6697.2597.40

13.9313.8126.0013.8614.1719.6713.9311.0110.86

0.050.050.070.050.050.060.050.040.04

0 10 20 30 40 50 60 70Drying time (min)

Figure 1. Observed and estimated moisture ratio (MR) values by theterm model du ring drying of tom ato fruits at 60 C at maturity stage

moisture content is defined at this point. This paramdivides the drying curve into two parts: before point, it can be inferred that there is a constant falrate period in which the velocities of moisture remoat the periphery and moisture replacement from center to the periphery are considered to be equal; athis point of critical moisture content, a decrease inmoisture ratio with lower velocity is observed in whmoisture replacement previously observed cannot supthe removal of moisture by infrared drying at the svelocity.

By analyzing the linearity of experimental datacritical moisture content of 2.97 kgw kgdm"' was fofor tomato dehydration; this corroborates Brooker et( 1992), who stated that the critical mo isture conten t fordehydration of biological products presenting a high inmoisture content ranges from 2.33 to 3.00 kg kgdm'.

Eigure 2 reports drying rate vs. drying time of tomfruits dried at 60 "C. It can be observed in Eigure 2 there is an initial period in which the drying rate reacits maximum value (approximately 1.05 kgw kgdm', ab3 min). The product is being heated during this peof t ime. A decrease follows this increase. AccordingCelma et al. (2009), the initial evaporation occurs onsample surface. How ever, this fact become s less imporover t ime. Therefore, m oisture diffusion becom es


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for other agricultural products, such as okra(L.) Moench; Doymaz, 2005b)ve cake (Akgun and D oym az, 2005).

< 0.6), the diffusionied by a one-term series (Senadeera2003). Therefore, assuming that Def is independent[5] can be rewritten as

lnA_i^j?s/ [7]The effective diffusion coefficient can thus be

Theeffective diffusion coefficient is determinedvs . drying time, in which the angular

According to Karathanos et al. (1990), theof biological materials

of intrinsic mass in the formion, gaseous diffusion, hydrod ynam ic flow, andecha nism s. Values of De/for tom ato fruits dried by

Figure 3 shows the plotting of In MRvs. dryingof tomato fruits at maturity stage 1. Although the

aination coefficient (R^ = 97.9 9% ), it can beinFigure 3 that there is a nonlinear tendency

etl. (2009 ) repor ted that the effective diffusion coefficient

on moisture content when this nonlinearity isa relationship betweenmoisture content represented by Equ ations [8] and

Fo=-0.0851 - 0.4052 \n MR [8][9 ]

X 60C

Values were found by this method for the effectivdiffusion coefficient of3.75, 3.42, and 3.80 x lO'' m^ s'at maturity stages 1,2, and 3, respectively. The valueof these two methods were different and the ANSYS 5.3(ANSYS, Canonsburg, Pennsylvania, USA) softwarsystem was used to detect which method showed thelowest error using the finite element method.The finite elemen t method (F EM ), with its optimiza tionroutines, has been recently applied because it iseasy touse forcomplex models and geometries (Gastn et a2002). This methodology was used to determine theeffective diffusion coefficient of wheat with spherical andellipsoidal geometries (Gastn et ai, 2002); to determinDef values ofdifferent apple tissues (Veraverbeke et al.2003); and to obtain Def values during the soaking ofrice by considering the expansion feature (Bakalis et al2009). Therefore, Def values were found by using the twabovementioned methods and a geometry representinthe shape of tomato samples.Moisture transfer within tomato fruit was close to theliquid diffusion theory without gen erating w ater inside thcontrol volume and is represented by Equation [10]. Thinitial condition is stated by Equation [11] by consideringthat water distribution at the beginning of the process ishomogeneous. The boundary condition is representedby Equation [12] by considering the water vapor masequilibrium between the product and the drying air:

[10[11[12

/; ( = 0) = m In Qwhere Q is thecontrol volume andF is the contousurface.The equilibrium moisture content was calculated bythe two-term equation. The geometry of the product waapproximated to a sphere with an equivalent diameter o70.55 mm. This diameter was calculated based on thmean of characteristic dimensions obtained with a 0.0mm precision digital caliper. The analysis was carriedout with a 45 angle semi-circle because of geometrisymmetry.A mesh with quadrangular elements and axis symmetryat the surface control was created. Geometry, mesgeneration, and model implementation were carried ouwith the ANSYS 5.3 software system. Simulation resultwere compared with experimental data in each effectivdiffusion coefficient. The Def values were selected witthe least square sum of deviations (Equ ation [13]) betw eenexperimental and simulated data.

RSD=pYj-Yj) [13where RSD is the least squ'e sum of deviations; Y, is th


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Table 3. Values for effective diffusion coefficients (Da) and least squaresum of deviations (RSD) at each maturity stage of tomatoes obtained withdifferent methods.Matu r i tys t ag e123

D ef(x l O ' m - s ' )3.333.752.783.423.053.80

RSD (decimal d.b.)0.01380.01520.01620.01970.01360.0129

RSD obt a i ne d l o r e a ch me t hod . The RSD va l ue s r a nge dfrom 0.0129 to 0.0197 mois ture content d .b. Despi te theselow va lues none of the methods were able to e ffect ive lypredict the drying curve (Figure 4) . There fore , anopt im iza t ion procedure of A. / va lues wa s s imu la ted wi ththe ANS YS 5.3 sof tware sy s tem . The A-/va lu e was 1.00X 1 0 ' m2 s ' (RSD = 0.0009 d.b. ) .

Table 4 shows a wide var ia t ion among productsand among cui t iva rs of the same product . This t rend i sprobably due to di f fe rences in the chemica l composi t ion,phys ica l s t ructure , and geometry of the products ; theseva lues can vary wi th boundary condi t ions , dryingmethods, and predict ion methods of Def va l ue s (Ca mposetal., 2009; Gonel i etal., 2009; Correa etal., 2010c) .Mass transfer coefficientsThe globa l coefficient of heat t ransfer (Ac) was 12.45W m"^ K"' and the global coefficient of ma ss transfer{hm) 0.0105 m s ' . The va l ue s o f h,,, in the present workcorrobora te the va lues reported by Tour and Kibangu-Nkem bo (2004), who found 0.00974 m s ' for na tura ldehydra t ion of mango fru i t s wi th sola r energy, 0 .00475

Expetimental da u3 . 3 3 x l O ' m ' s - '3.75 I 10' m' s 'L O O x l O ' t n ^ s '

50 100 150 200 250Drying time (min)Figure 4. Moisture content variation of tomato frtiits dried at 60 C atmaturity stage 1 as a function of different values of effective diffusioncoefficient.

Table 4. Effective diffusionproducts. coefficients (Dct) of different agriculturalProduct ReferenceCoffee (cv. Catuat' Vermelho) 2.145 to 2.702 X 1 0 " Campos et al. (2009)

m s ' for cassava roots , and 0.00876 and 0.00943 mfor two banana cui t iva rs , re spect ive ly . Fur thermore , va lues of he were expected s ince , according to Bi rd e(2004), the values of the global coefficient of heat t ranfor free convection is between 3 and 20 W m"^ K ' .

C O N C L U S I O N SDehydra t ion kine t ics by infra red drying of tomato s lcan be s imi la r to the theore t ica l s tudies on hea t and mtransfe r m echa nism s. The va lues found for the g lcoefficient of heat and ma ss transfer wer e 12.45 W K 'a n d 0.0105 m s ' , re spect ive ly . An e ffect ive di ffucoefficient of 1.00 x 10"' m^ s ' was found throu ghopt imiza t ion procedure us ing the f ini te e lement methThe t wo- t e rm m ode l wa s t he be s t to r e pre se n t t he t omdehydra t ion process , and the cr i t ica l mois ture contenttom ato dehydra t ion was 2.97 kgw kgdm ' . The dry ing reached i ts maximum value (1.05 kg kgdtn"' ) a t 3 minde hydra t i on .

A C K N O W L E D G E M E N T SThe authors thank FAPE M IG and CNPq for fundwhich was indispensable to ca rry out thi s work.

Secado de tomate por infrarrojo: modelacin algunos coeficientes del proceso de deshidrataciLa deshidratacin por infrarrojo es ms ventajosa quesistema convectivo, en condiciones sim ilares, y e l estudde este proceso es im portante para e l desarrollo de equipy procedimientos. Por tanto, el presente trabajo tucomo objetivo el estudio del proceso de deshidratacien tres diferentes estados de maduracin de rebanadde tomate {Solanum lycopersicum L.) por medio dsecado por infranojo, usando dos mtodos: aproximacidel perodo constante de deshidratacin a la teora detransferencia de calor y masa para e l term m etro de bulhmedo; y al perodo decreciente de la deshidratacia la teora de difusin de lquidos. Se utilizaron frude tomate cv. Santa Cruz. Tres estados de maduracifueron obte nidos: verde (estado 1), naranja (estado y rojo (estado 3). M odelos matem ticos u sualm enuti l izados para representar e l secado de productagrcolas fueron ajustados a los datos experimentales dsecado de tomate. El coeficiente de difusin efectivo fobtenido por medio del ajuste del modelo matemtico difusin lquida a los datos experimentales del perodecreciente de deshidratacin. El rnodelo Dos Trminrepresent mejor e l proceso del secado de rebanadas tomate. La humedad cr t ica para la deshidratacin tomate fue 2.97 kgw kgjm'' . Existe un perodo inicial


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mtodo de elementos finitos, en que present los menoresvalores de la suma de desviaciones m nimas al cuadrado,1.00 X 10'^ m- s"'. El coeficiente global de transferenciade calor fue 12.45 W m"^K"', y el coeficiente global detransferencia de masa fue 0.0105 m s ' .Palabras clave: humedad crtica, difusin, mtodode elementos finitos, transferencia de calor y masa,modelacin matemtica, Solanum lycopersicum.

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