Advances in Environmental Biology

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1 Advances in Envirnental Bilgy, 8() Special 04, Pages: AENSI Jurnals Advances in Envirnental Bilgy ISSN EISSN Jurnal he page: The Mdeling f Mass and Heat Transfer f Dryers during the Drying Prcess Mhaad Taghavi, Mahd Hsseini neia, 3 Seiaa Danesiar, 4 Ali Pasandideh Flahdana, 5 Hata Hsseini neia, 6 Sadrlah Masdi, 7 Taleb Zarei, 8 ahan Jahanbazi,,3,4,5,6 Islaic Azad University Of Siran Branch, Departent Of Cheical Engineering, Siran, Iran 7 Hrzgan University, Bandarabas Branch, Mechanic Engineering, Badarabas, Iran 8 Islaic Azad University Of Shahreza Branch, Plyer Engineering, Shahreza, Iran A T I C L E I N FO Article histry: eceived 5 April 04 eceived in revised fr May 04 Accepted 5 May 04 Available nline 5 June 04 A B S T A C T In this research has been studied the deling f ass and heat transfer in dryers. Initially the attend t study f accplished things n the varius geetry f aterials that ust have been dry ;then is prpsed an deling fr a spherical shell that is the dinant fr in drying fruits.prvided del due t the heat and ass prfiles,can predict the isture cntent during the drying prcess. In the end prvided a nuerical ethd fr slving the dryer equatin. Keywrds: dryer, atheatical deling, unusual geetry, ass and heat transfer. 04 AENSI Publisher All rights reserved. T Cite This Article: Mhaad Taghavi, Mahd Hsseini neia, Seiaa Danesiar, Ali Pasandideh Flahdana, Hata Hsseini neia, Sadrlah Masdi, Taleb Zarei, ahan Jahanbazi., The Mdeling f Mass and Heat Transfer f Dryers during the Drying Prcess. Adv. Envirn. Bil., 8(), , 04 INTODUCTION Drying is ne f st iprtant peratin units in the industry such as fd prductin, pharacy, sewage filtratin,etc []. this peratin is invlve several echaniss f ass and heat transfer.hwever, the water transfer in the under survey prduct generally t be cnsider as a cntrller factr; and usually this transfer based n diffusin echanis and study accrding t the secnd law f fic [-6].In additin heat transfer within slids generally tae place by cnductin echanis [7-8]. Mass and heat transfer equatin at unsteady state fr isture diffusin and energy cnductin within hgeny and cnvergent aterial (being shwn by V ) is prvided by uiz Lpez etal [8]. ( d ).[ D ( d )] t ( CT p ).[ ( T )] t in V () in V () In additin, ass and heat transfer at prduct level ( A ) is expressed by bundary cnditin. Here the echanis is cnsidered fr ass and heat transfer fr prduct level t air ass [8]. hd ( i ) n. D ( d i ) n A (3) hc ( T i T ) n. ( T i ) n. Q. D ( d i ) n A (4) In additin, the isture cntent f the air and teperature at level between air and slid can be represented by the fllwing equilibriu relatins [8]. i f ( i, T i) n A (5) Ti Ti n A (6) Several researcher use fr equatin -6 fr the prductin behavir study fr flat surface, parallel tubular, circular cylinder r sphere frs, that by these equatin they can exaine the drying echanis during the prcess [, 9-]. Hwever, in se cases these geetries f siple, ay nt reflect the exactly the result shape. The iprtance f taing int accunt the actual shape f slids that ust t be dry, is expressed in se f the references. Thugh a inadequate assuptin r siplifier in the shape ay lead t the excess r less Crrespnding Authr: Mhaad Taghavi, Islaic Azad University Of Siran Branch, Departent Of Cheical Engineering, Siran, Iran E-ail: ehaad@yah.c

2 396 Mhaad Taghavi, et al., 04 Advances in Envirnental Bilgy, 8() Special 04, Pages: estiatin in ass transfer. Therefre, any researchers fcus n the geetries f that are nt such as traditinal geetries. Fr exaple, Dlya and nebra exained the drying prcess f lie-circular slids that were generally lie-banana [6]. Di Matte et al presented an analytical slutin fr ass transfer equatin in drying fruits that have shapes f lie curve spherical [7]. Analysis n a siilar geetry as well as was studied by Diane flash and salty t study f ass and heat transfer during the drying prcess f prus rcs fr cpressed air energy strage[5]. Dar and Dlya predicted the lentil dried behavir using a syste that is fit with it shape [6]. Mst f the references that entined, were based n traditinal shapes and did nt fcus n incplete shapes, infratin is very lw abut incplete shapes. Ang f the abve tass, ben et al presented a seianalytical slutin fr ass transfer equatin with a heispherical shape that predicted the isture behavir in fungu, aprict leaf, cffee grain and sei-cantalupe[3]. In additin, in recent wrs, researchers exained the sae geetry shape fr ass transfer in aprict leaf were lst water the tae place nly fr heisphere uter prtin recently, Hernandez Diaz et al using spherical drawn geetry the prpsed a del f ass and heat transfer fr cffee green bean drying. In additin, he using the geetry and siulated behavir with an average dried inetic and diffusin length due t the flat shape f the prduct, prpsed a siple expressin fr dried tie predictin f prduct []. Shape that selected in this research fr study is a heisphere that part f it in fruits is epty due t cre existence. The geetry is an cplex geetry and give a re accurate apprxiatin f ass and heat transfer in dryers, because it is nt based n traditinal geetries that behave a siplificatin and affect the results. In ttal, this shape is very clser t existence reality. -Mdeling thery: Equatin -4 can be rewritten again diensinless. Equatin as well as rewritten in spherical crdinate and gradient and divergence as well as are pen the crrespnding results fr a prduct with a heispherical geetry as figure is btained by the fllwing relatin[]. H H H (7) sin sin sin in,,0 H i fr n. e, (8) in i H i n. e fr (9) i, H i fr n. e 0 0 (0) sin Obtained in the fllwing, grups and diensinless variable e T T D t r () 0 e T0 T H H () d C e p T (3) d D D C p Lu 0 Bi e in 0 KLu in Bi K h eq d d r ( D / L ) T 0 T (4) (5) Q d (6) Q hc Bi / L r Lr (7) D Lu Q ( ) (8) / Cp 0 e K Cp ( T T 0) In these equatin is cnsidered the equilibriu distributin cicient f K eq t relate the aunt f water between slid and gas phases f Y i K eq and i e e As cnstant that are equal with [3]. In is iprtant that nte the nubers f Bi and Bi are nt based n the uter diaeter f but is accrding t the characteristic length fr diffusin that is defined as half the thicness spherical shell (External length as the characteristic length fr diffusin is nt with a physical

3 397 Mhaad Taghavi, et al., 04 Advances in Envirnental Bilgy, 8() Special 04, Pages: eaning, there fr is nt valid fr incplete geetry). Hwever, heispherical shell with the sae uter diaeter f that share the sae characteristic length fr diffusin (as well as in Bayt nuber ), fr any aunt is physically unstable. A fr f syetrical, therefre is heat transfer in spherical crdinate and in in the directin f, and cannt be f related expressin in deling (This assuptin is clser t reality). Fig. : ut f spherical shell in use fr deling. 3- Mdeling slutin: The gverning equatin can slve with different ethd and achieve it utces. A highly icient and cn ethd fr this actin is line ethd. The perfrance f this ethd is s that unchanged reain the tie dependent part and the ther parts be placeent as central derivative, then btained equatin that are in fr a series f first rder equatin, slutin using cn ethd such as runge ata, vlyr Etc. Outline f prble geetry tw-diensinal is shwn in figure with respect t the diensins f diensinless. After applying the line ethd, the fllwing equatin that tie is as the independent variable, can be btained. p, q, ( p / ) p, q, p, q, ( p / ) p, q, p, q. (9) ( ) ( ) p, q, ( ) ( q / ) p, q, p, q, ( q / ) p, q, p, q, ( ) ( ) p, q, ( sin ) ( p, q, ( sin ) ) ( ) q/ p ( ),, p,, q p,, p,, ( / ) ( p / ) p /, q, p, q, p, q, ( ) ( ) ( ) (0) ( q / ) p, q /, p, q, p, q. (sin ) (sin ) (sin ) () ( / ) p, q, / p, q, p, q. (sin ) (sin ) (sin ) (),,,, p q p q p, q, p, q, p, q, (3) ( ) fr p, n ;,,; (4),,,, p q p q p, q, p, q, p, q p, q, ( ) Fr q n ;,,; (6(,,,, p q p q p, q, p, q, p, q p, q, ( ) (7) n ;,, ; (8) fr q,, (9) p, q p, q After the abve changes, shuld be classified these first rder differential equatin f ccurred this figure in the directin f, radius and. Finally, fr each slve a first rder equatin in the directin f tie. As a result, with cnvergence f these equatin is btained after a certain tie, teperature distributin and stable cncentratin fr each these parts. (5)

4 398 Mhaad Taghavi, et al., 04 Advances in Envirnental Bilgy, 8() Special 04, Pages: Fig. : landscape f geetry shape in tw diensins, in diensinless scale fr slving the gverning equatin. Discussin and cnclusin: The results btained fr this geetry in tw diensinal de that prvided by ze Lpez and their clleagues shwed that deling used cpared with in vitr cnditin with gd accuracy[4]. But they did nt cnsider changes in the directin f in spherical crdinate. If we cnsider these change, certainly will iprve the results, because respect t drier cnditins and it teperature asyetry, the aunt f ass and heat transfer is related t. Hwever, ay be sall this dependence but is ipressive and it cnsidering cause deling iprve. Cnclusin: In this research, is prvided a deling f ass and heat transfer in tree-diensinal fr an spherical shell that is cn geetry in drying industrial, then prpsed a nuerical ethd fr slve f gverning equatin it See t be due t nn-traditinal geetry and cnsider f re diensinal in deling, with re accuracy and therefre re practical. EFEENCES [] Lulu, T., B. Adhiari, D. Lecte, 006. Estiatin f cncentratin dependent diffusin cicient in drying prcess fr the space-averaged cncentratin versus tie with experiental data. Cheical Engineering Science, 6: [] Arrieche, L.S.,.G. Crrea, D.J.M. Sartri, 009. Drying stresses and strains in a spherical fd del. Cputers and Cheical Engineering, di:0.06/.cpcheeng [3] Bn, J., C. ssell, A. Feenia, V. Ei, S. Sial, 007. Matheatical deling f drying inetics fr apricts: Influence f the external resistance t ass transfer. Drying Technlgy, 5: [4] Bn, J., S. Sial, C. sell, A. Mulet, 997. Drying characteristics f heispherical slids. Jurnal f Fd Engineering, 34: 09-. [5] Dayan, A., J. Flesh, C. Saltiel, 004. Drying f a prus spherical rc fr cpressed air energy strage. Internatinal Jurnal f Heat and Mass Transfer, 47: [6] de Lia, A.G.B., M.. Queirz, S.A. Nebra, 00. Siultaneus isture transprt and shrinage during drying f slids with ellipsidal cnfiguratin. Cheical Engineering Jurnal, 86: [7] Di Matte, M., L. Cinquanta, G. Galier, S. Crescitelli, 003. A atheatical del f ass transfer in spherical geetry: Plu (Prunus destica) drying. Jurnal f Fd Engineering, 58: [8] uiz-lpez, I.I., A.V. Crdva, G.C. driguez-jienes, M.A. Garcia-Alvarad, 004. Misture and teperature evlutin during fd drying: Effect f variable prperties. Jurnal f Fd Engineering, 63: 7-4. [9] Gastn, A.L.,.M. Abalne, S.A. Giner, 00. Wheat drying inetics. Diffusivities fr sphere and ellipsid by finite eleents. Jurnal f Fd Engineering, 5: [0] Gastn, A.L.,.M. Abalne, S.A. Giner, D.M. Bruce, 004. Effect f delling assuptins n the ective water diffusivity in wheat. Bisystes Engineering, 88:

5 399 Mhaad Taghavi, et al., 04 Advances in Envirnental Bilgy, 8() Special 04, Pages: [] Hernandez-Diaz, W.N., I.I. uiz-lpez, M.A. Salgad-Cervantes, G.C. driguez-jienes, M.A. Garcia- Alvarad, 008. Mdeling heat and ass transfer during drying f green cffee beans using prlate spheridal geetry. Jurnal f Fd Engineering, 86: -9. [] Spiegel, M.., 968. Schau s utline f atheatical handb f frulas and tables. USA: McGraw- Hill. [3] Pavn-Melendez, G., J. A. Hernandez, M.A. Salgad, M.A. Garcia, 00. Diensinless analysis f the siultaneus heat and ass transfer in fd drying. Jurnal f Fd Engineering, 5: [4] uiz-lópez, I.I., H. uiz-espinsa, M.L. Luna-Guevara, M.A. García-Alvarad, 0. Mdeling and siulatin f heat and ass transfer during drying f slids with heispherical shell geetry. Cputers & cheical engineering, 35(): 9-99.