Mathematical Modelling of Thin Layer Mangoes (Mangifera indica L.) Drying Process

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1 Reserch Article Interntionl Journl of Current Engineering nd Technology E-ISSN , P-ISSN INPRESSCO, All Rights Reserved Avilble t Mthemticl Modelling of Thin Lyer Mngoes (Mngifer indic L.) Drying Process EDOUN Mrcel Ȧ*, MATUAM Blbine Ȧ nd KUITCHE Alexis Ȧ Ȧ Lbortory of Energetic nd Applied Therml Process, Deprtment of Automtic, Energetic nd Electricl Engineering, ENSAI, P.O BOX 455 University of Ngoundere Cmeroon Accepted 5 Oct 14, Avilble online 3 Oct 14, Vol.4, No.5 (Oct 14) Abstrct This study ws conducted to investigte the ect drying process on hot-ir drying kinetics of mngoes (Mngifer indic L.) slices nd to evlute the best model predicting the drying kinetics. The experimentl study ws crried out in n electric dryer t 4 C, 5 C nd 6 C,.6 m/s with two configurtions (verticl irflow btch drying nd verticl countercurrent irflow drying). To estimte nd select the pproprite drying model, seven different models were pplied to the experimentl dt nd compred. The performnces of these models were compred using the coicient (R²), reduced chi squre (χ²) nd root men squre error (RMSE) between the observed nd predicted moisture rtios. The nlysis of results showed tht the verticl countercurrent irflow drying permits us to obtin best qulity of products in terms of moisture rtion. Among the models used, the Midilli et l., model ws found to best explin thin lyer drying of mngoes slices s compred to the other models over the experimentl temperture rnge. By incresing the drying ir temperture, the ective moisture diffusivity vlues incresed from 5.18 x 1-1 to x 1-1 m /s for verticl irflow btch drying nd from x 1-1 to 7.66 x 1-1 m /s for verticl countercurrent irflow drying. The ctivtion energy ws clculted using n exponentil expression bsed on Arrhenius eqution nd E = kj/mol nd D o = 3.8 x 1-7 m /s for verticl irflow btch drying nd E = kj/mo nd D o = 6.55 x 1-5 countercurrent irflow drying. Keywords: ctivtion energy, ective diffusivity, drying process, models. m /s for verticl Introduction 1 Mngo fruit (Mngifer indic L.) is one of the most importnt sesonl fruits of Cmeroon nd subtropicl countries. It contins high mounts of sugrs nd considerble mounts of vitmin C nd provitmin A. Mngo fruit is highly perishble nd must be consumed within few dys fter hrvesting. Becuse of indequte methods of preservtion, substntil quntity of hrvests is lost ech seson. Drying cn constitute n icient solution of preservtion (Diss et l., 8). This process improves the food stbility, since it reduces considerbly the wter nd microbiologicl ctivity of the mteril nd minimizes physicl nd chemicl chnges during its storge. Generlly to improve the iciency of the drying process, products re sliced before drying. Thin-lyer drying equtions s function of drying conditions re used to estimte drying time of severl products nd lso to generlize drying curves. Mny mthemticl models hve been developed nd used to describe the drying process of food products in different drying conditions (Doymz, 4; Velic et l., 4; Krim nd Hwlder, 5; Siml et l., 5; Kuitche et l., 7; Kshninejd et l., 7; Meismi-sl et l., *Corresponding uthor: EDOUN Mrcel: Lecturer in Energetic nd Therml Process; ENSAI of Ngoundere 9; Ghtrehsmni et l., 1; Ryguru nd Routry, 1). Studies focusing on the mngoes behvior during the drying process hve been reported by severl reserchers in the literture. Among others, Nieto et l., (1) studied the influence of pre-tretments by blnching nd/or osmotic dehydrtion with glucose syrups on ir drying kinetics of mngo during the flling rte period. An exponentil correltion which llowed determining mngo diffusivity s function of thickness nd drying temperture re developed in cse of btch process drying (Jy nd Ds, 3). Touré nd Kibngu-Nkembo (4) studied the free convection sun-drying of cssv, bnn nd mngo nd estblished n expression linking slices initil moisture content to the mximl temperture difference between drying ir nd ech product. Goyl et l., (6) studied the thin-lyer drying kinetics of rw mngo slices t 55, 6 nd 65 C ir temperture. Mercer (1) presented comprtive study of the kinetics of mngo drying in open-ir, solr, nd forced-ir dryers. Omym nd Khled (1) presented the chrcteristics of dried mngo slices s ffected by pre-tretments nd drying type. Aremu et l., (13) studied the ect of slice thickness nd temperture on the drying kinetics of mngo (mngifer indic L.) in btch dryer. Tkmte et l., (13) conducted numericl simultion of thin-lyer mngoes drying t 4, 5 nd 6 C by control externl 367 Interntionl Journl of Current Engineering nd Technology, Vol.4, No.5 (Oct 14)

2 EDOUN Mrcel et l Mthemticl Modelling of Thin Lyer Mngoes (Mngifer indic L.) Drying Process Tble 1: Thin lyer mthemticl models Models Expressions References Newton Lewis (191) Pge Pge (1949) Henderson et Pbis Henderson et Pbis (1961) Logrithmique Ygcioglu et l. (1999) Two term Henderson, (1974) Diffusion pproximtive 1-)exp(-kbt) Ksem (1998) Midilliet l., Midilliet l., () conditions. Most of the bove mentioned studies pplied for the sme drying process (horizontl or verticl irflow btch) t different level ir velocity nd drying temperture. The present study ws therefore undertken to investigte the thin lyer drying chrcteristics of mngoes slices in convective dryer t verticl irflow btch nd verticl countercurrent irflow drying. Also the experimentl dt were fit to propose the best mthemticl model to estimte the constnt prmeters for clculting the ective diffusivity nd ctivtion energy for drying mngoes (Mngifer indic L.). Mterils nd methods Fully-ripened mngoes (Mngifer indic L.) were collected to the locl mrket, wshed, mnully peeled nd trnsversely cut into 3 mm slices using stinless steel knife. Drying experiments were conducted t 4, 5 nd 6 C (± C). The ir velocity of dryer ws fixed t.6 m/s. Two configurtions (verticl irflow btch drying nd verticl countercurrent irflow drying) were used to study ect of drying process. Ech experiment ws terminted when the weights of the smples were stbilized up to deciml points. The initil moisture content of fresh slices nd the finl moisture content of dried smples were determined by hot ir oven method t 15ºC for 4 h. Ech experimentl run ws conducted in triplicte nd the verge of the results ws nlyzed. Drying nlysis nd evlution of thin lyer drying models Bsed on the initil moisture content from oven drying, the weight loss ws used to clculte the moisture content. The drying chrcteristic curves were plotted fter nlyzing the experimentl dt. The moisture content ws converted to moisture rtio (MR) using the following eqution (1) where MR is moisture rtio, X the verge moisture content of the product, X the initil moisture content, Xeq the equilibrium moisture content. Empiricl models In order to estimte nd select the pproprite drying model mong different semi-theoreticl nd/ or empiricl models, mthemticl modeling ws crried out to describe the drying curve eqution of stone pple slices nd to determine the prmeters of the thin lyer drying models by fitting experimentl dt to the model eqution. The thin lyer drying equtions mentioned in Tble 1 were tested to select the best model. The non-liner regression nlysis ws performed using the TbleCurve V5.1. of CIRAD of Montpellier Frnce. Although the coicient of determintion (R²) ws one of the primry criterions for selecting the best model to describe thin-lyer drying curves of slices, the sttisticl test methods such s the reduced chi- squre (χ²), root men squre error (RMSE) s described by Eqution () nd (3) were lso used to evlute the goodness of fit of the models. The lower chi- squre (χ²) nd SE vlues nd the higher R² vlues, were chosen s the bsis for goodness of fit (Akpinr et l., 3; Midilli nd Kucuk, 3). i ( exp,i- pre,i) χ -z 3673 Interntionl Journl of Current Engineering nd Technology, Vol.4, No.5 (Oct 14) () SE ( pre,i- exp,i) i (3) Effective wter diffusivity determintion The wter diffusivity of mngoes is evluted by using the simplified mthemticl Fick s second lw. Assuming one-dimensionl moisture trnsfer, homogenous nd prllelepipedic shpe for the mngoes smples, uniform initil moisture distribution, nd the nlyticl solution of Fick s eqution (4) is (Crnk, 1975): n cr ( n ) D.t exp [-( n )² ] (4) 4 Where X cr is the criticl wter content, l the hlf thickness of the slice, t is the drying time (s), D the wter diffusivity, n the Fourier s series number nd the shpe fctor equl 8 to for prllelepiped. In convective drying of solids, this solution is vlid only for the flling rte period when the drying process is controlled by internl moisture diffusion for slice moisture content below the criticl vlue. Therefore, the diffusivity must be identified from Eq. (5) by setting the initil moisture content to the criticl vlue X nd by setting the drying time to zero when the men moisture content of the smple reches tht criticl moisture content. For long diffusion time, the crnk eqution for slb which involved series of exponents cn be simplified to Eqution 6 using the first term. l

3 Moisture rtion EDOUN Mrcel et l Mthemticl Modelling of Thin Lyer Mngoes (Mngifer indic L.) Drying Process Tble : Sttisticl results of different thin lyer models for verticl irflow btch drying Models T ( C) x 1 - b x 1 - k x 1-3 n x 1 - c x 1 - k 1x 1-3 R RMSE x x 1-3 Newton x x x 1-4 Pge x x x 1-3 Henderson nd x 1-3 Pbis x x 1-5 Logrithmic x x x 1-5 Two term x x 1-4 Diffusion pproximtive Midilli et l x x x x x x 1-4 Tble : Sttisticl results of different thin lyer models for verticl countercurrent irflow drying Modèles T ( C) x 1 - b x 1 - k x 1-3 n x 1 - c x 1 - k 1x 1-3 R RMSE x x 1-3 Newton x x x 1-4 Pge x x x 1-3 Henderson nd x 1-3 Pbis x x 1-6 Logrithmic x x x 1-5 Two term x x x 1-6 Diffusion x 1-5 pproximtive x x 1-6 Midilli et l x x 1-6 MR X x 8 D exp 4l eq x X cr eq. t where, MR is the moisture rtio, D (m²/s) is the ective moisture diffusivity, ln 8 D MR ln. t 4l cn be put in the generl form K. t b nd K is the ln MR f ( t grdient of ) D where : K r Activtion energy ws thus identified from diffusivity ccording to Arrhenius dependence s: D (5) (6) E D exp (7) RT Where D o is the diffusivity coicient t infinite tempertures nd E the ctivtion energy of the (kj/mol), R the gz constnt, T temperture in K. Results nd discussion Figure 1 present the evolution of the moisture rtion of mngo slices in two study configurtions Drying time (min) VABD t 4 C VABD t 5 C VABD t 6 C VCAD t 4 C VCAD t 5 C VCAD t 6 C Figure 1: Effect of drying principle on mngoes slices drying time t 4 C, 5 C nd 6 C In the experimentl temperture rnge, the higher hot ir temperture led to the fster drying rte nd the shorter 3674 Interntionl Journl of Current Engineering nd Technology, Vol.4, No.5 (Oct 14)

4 Ln(D) EDOUN Mrcel et l Mthemticl Modelling of Thin Lyer Mngoes (Mngifer indic L.) Drying Process Tble3: Effective diffusivities of mngoes slices t different tempertures nd drying process Drying process Temperture ( C) Diffusivity (m ²/s) x 1-1 Verticl irflow btch drying x x x 1-1 Verticl countercurrent irflow drying x x 1-1 drying time. As the drying ir temperture rises, the trnsfer rte of moisture from the internl of the drying mngoes to its surfce nd the vporiztion potentil of moisture t the surfce incresed, resulting in the higher drying rte. Moreover, we observed tht the drying time vries with the drying principle. The similr results re presented by (Meismi-sl et l., 9; Tkmte et l., 14; Edoun, 14). The moisture rtio clculted from the drying dt t different tempertures ws fitted to the thin lyer models given in Tble 1. The sttisticl results from models re summrized in Tbles nd 3. The best model describing the thin-lyer drying chrcteristics of mngoes ws chosen s the one with the highest R² vlues nd the lowest nd RMSE vlues. The R² for Logrithmic, Two terms, Diffusion pproximtive nd Midilli models were bove.99 but for Newton, Pge, Henderson nd Pbis model tht vlue ws bove.9. During the verticl irflow btch drying, Two term model gives the highest vlue of ² nd the lowest vlues of χ² nd SE nd during the verticl countercurrent irflow drying the Midilli model gives the best sttisticl results t different temperture. In the cse of verticl irflow btch drying, the ect of temperture on the drying constnts of the Two term model ws tken into ccount by developing the reltion between these constnts nd the drying temperture. The regression equtions relting the constnts of the selected model nd the drying temperture re the following:.exp(-kt) b.exp (-k t) (8) where : Effective moisture diffusivity Effective diffusivities (D ) of mngoes t three different tempertures ws evluted by plotting ln(mr) vs time nd the dt ws presented in Tble 3. Vlues of D ws clculted for the two drying principle nd the icient diffusivity of mngoes slices rnged form 5.18 x 1-1 to x 1-1 m /s for verticl irflow btch drying nd from x 1-1 to 7.66 x 1-1 m /s for verticl countercurrent irflow drying. These vlues re within the generl rnge 1-9 to 1-11 m²/s for drying of food mterils (Mskn et l., ). The ective moisture diffusivity incresed s drying ir temperture ws incresed. The similr results re presented in the literture (Kuitche et l., 7; Kdm et l., 1; Aremu et l., 13). Activtion energy Activtion energy is the minimum energy required to initite moisture diffusion from product. Figure presents ln( D ) f (1/ T) respectively for verticl irflow btch drying nd verticl countercurrent irflow drying. From the slop of the stright lines described by the Arrhenius eqution, E = kj/mol nd D = 3.8 x 1-7 m /s for verticl irflow btch drying nd E = kj/mol nd D = 6.55 x 1-5 m /s for verticl countercurrent irflow drying. We observe tht the ctivtion energy of mngoes slices ws lower t verticl irflow btch drying s compred to tht t verticl countercurrent irflow drying.... b k... 4 k... 4 The sme developing re done for verticl concurrent irflow drying nd the regression equtions relting the constnts of midilli model nd the drying temperture re the following:.exp(-kt n ) b.t (9) where : b. -.. k n /T ( K-1) ''VABD'' ''VCAD'' Figure : Evolution of ln(d ) with 1/T for the different tempertures 3675 Interntionl Journl of Current Engineering nd Technology, Vol.4, No.5 (Oct 14)

5 EDOUN Mrcel et l Mthemticl Modelling of Thin Lyer Mngoes (Mngifer indic L.) Drying Process Conclusion Drying of mngoes slices study ws crried to determine the ect of drying process (verticl irflow btch drying nd verticl countercurrent irflow drying) nd drying ir temperture on drying kinetics. The results show tht the increse in drying ir temperture decresed the drying time in both the drying process. Midilli et l. thin lyer drying eqution represented the thin lyer drying behviour of mngoes slices in the two cses. Efficient moisture diffusivity of mngoes slices rnged form 5,18 x 1-1 to 7,395 x 1-1 m /s for verticl irflow btch drying nd from 3,698 x 1-1 to 7,66 x 1-1 m /s for verticl countercurrent irflow drying.. Activtion energy ws 16,86 kj/mol nd 31,51 kj/mol respectively for verticl irflow btch nd verticl countercurrent irflow drying. References Akpinr, E.K., Midilli, A. nd Bicer, Y. 3. Single lyer drying behviour of potto slices in convective cyclone dryer nd mthemticl modeling. Energy Conversion nd Mngement 44 (1): AremuAdemolKbiru, AdedokunAdetyo Joshu &AbdulgniyOlyinkRji (13): ect of slice thickness nd temperture on the drying kinetics of mngo (MngiferIndic); IJRRAS 15 (1) Diss A.O., Desmorieux H., Bthiebo J., Kouliditi J. 8. Convective drying chrcteristics of Amelie mngo (MngiferIndic L. cv. Amelie ) with correction for shrinkge. Journl of Food Engineering 88, Doymz, I. 4b. Convective ir drying chrcteristic of thin lyer crrots. Journl of Food Engineering 61(3): Ghtrehsmni S.H., Ddshzdeh M. nd Zomorodin A. (1), kinetics of pricot thin lyer drying in mixed nd indirect mode solr dryer, Interntionl Journl of Agriculture Sciences 4 (6), Goyl, R.K., Kingsly, A.R.P., Mnikntn, M.R., Ilys, S.M., 6. Thin-lyer drying kinetics of rw mngo slices. Biosystems Engineering 95 (1), Henderson SM, Pbis S (1961).Grin drying theory I. Temperture ect on drying coicient. J. Agric. Eng. Res., 6(3): Henderson, S.M., Progress in developing the thin lyer drying eqution. Trn. ASAC, 17: Jy, S., Ds, H., 3.A vccum drying model of mngo pulp. Drying Technology 1 (7), Kdm D. M., Goyl R. K. nd Gupt M. K. (11), Mthemticl modeling of convective thin lyer drying of bsil leves, Journl of Medicinl Plnts Reserch 5(19), Krim M.nd Hwlder M.N.A., 5: Drying chrcteristics of bnn: theoreticl modelling nd experimentl vlidtion, Journl of Food Engineering 7, Kshninejd M., Mortzvi A., Sfekordi A., Tbil L.G. (7): Thin-lyer drying chrcteristics nd modeling of pistchio nuts. Journl of Food Engineering 78, KuitcheA., Edoun M., Tkmte G. (7), Influence of Pretretment on Drying on the Drying Kinetic of A Locl Okro (Hibiscus ersculentus) Vriety, World Journl of Diry & Food Sciences (), Mskn A, Ky S, Mskn M (). Hot ir nd sun drying of grpe lether (pestil). Journl of Food Engineering 54, Meismi-sl E., Rfiee S., Keyhni A. nd Tbtbeefr A. 9.Mthemticl Modeling of Moisture Content of Apple Slices (Vr. Golb) During Drying,Pkistn Journl of Nutrition 8 (6): Meismi-slElhm, RfieeShhin, KeyhniAlirez nd Tbtbeefr Ahmd (9), Mthemticl Modeling of Moisture Content of Apple Slices (Vr. Golb) During Drying, Pkistn Journl of Nutrition 8 (6): 84-89, Mercer Donld (1): comprison of the kinetics of mngo drying in open-ir, solr, nd forced-ir dryers; Africn journl of food, griculture, nutrition nd development, 1 (7), Midilli, A. nd Kucuk, H. 3. Mthemticl modeling of thin lyer drying of pistchio by using solr energy. Energy Conversion nd Mngement 44(7): Nieto, A., Cstro, M.A., Alzmor, S.M., 1. Kinetics of moisture trnsfer during ir drying of blnched nd/or osmoticlly dehydrted mngo. Journl of Food Engineering 5, Omym M. Ismil nd Khled S.A. Ngy (1): Chrcteristics of Dried Mngo Slices s Affected by Pre- Tretments nd Drying Type; Austrlin Journl of Bsic nd Applied Sciences, 6(5): 3-35 Pge, G.E., 1949.Fctors influencing the mximum rtes of ir drying shelled corn in thin lyers.m.s. Thesis, Deprtment of Mechnicl Engineering, Purdue University, purdue, USA. Ryguru, K. nd Routry, W. (1): Mthemticl modeling of thin lyer drying kinetics of stone pple slices. Interntionl Food Reserch Journl 19(4): Siml, S., Femeni, A., Gru, M.C. nd Rosselló, C. 5. Use of exponentil, Pge s nd diffusionl models to simulte the drying kinetics of kiwi fruit. Journl of Food Engineering 66(3): Tkmte G., Edoun M., Monkm L., Kuitche A., Kmg R. (13). Numericl Simultion of convective Drying of Mngoes (mngiferindic L.) Under Vrible Therml Conditions,Interntionl Journl of Therml Technologies, 3 (), 48-5 Touré, S., Kibngu-Nkembo, S., 4.Comprtive study of nturl solr drying of cssv, bnn nd mngo. Renewble Energy 9, Velic, D., Plninic, M., Toms, S. nd Bilic, M. 4. Influence of ir flow velocity on kinetics of convection pple drying. Journl of Food Engineering 64(1): Interntionl Journl of Current Engineering nd Technology, Vol.4, No.5 (Oct 14)