Drying Steps under Superheated Steam: A Review and Modeling

Transcription

1 Eney and Envionment Reeach; Vol. 3, No. ; 013 ISSN E-ISSN Publihed by anadian ente of Science and Education Dy Ste unde Sueheated Steam: A Revie and odel Ihan Hamaand 1 1 National ente fo Enee Aicultue (NEA), Univeity of Southen Queenland, oooomba 4350 QLD, Autalia oeondence: Ihan Hamaand, National ente fo Enee Aicultue (NEA), Univeity of Southen Queenland, Queenland, Autalia. el: Ihan.hamaand@uq.edu.au Received: Setembe 6, 013 Acceted: Octobe 18, 013 Onle Publihed: Novembe 15, 013 doi: /ee.v3n107 URL: htt://dx.doi.o/ /ee.v3n107 Abtact Sueheated team dy ha been a ubject of eeach fo many decade. any eeache have claimed that ueheated team dy i av eney and oduce bette oduct quality comaed to ai dy. Sueheated team can be dituihed fom ai dy by the diffuion te the dy oce. Steam dy doe not clude moitue diffuion fom the teio of the aticle to it uface. Hoeve, ai dy, diffuion i the ma and the limit te. hi ae i eent a evie to the model have been ued to decibe dy unde ueheated team. Alo, modell a caied out to all the te that take lace the dy oce. hee te ae: itial condenation on the uface of the aticle, diffuion of the itially condened vaou to the teio of the aticle, evaoation of the itially condened vaou and fally dy of the hole aticle due to eced coe model. Undetand thee te i vey imotant fo contoll the quality of the died oduct and event difficultie uch a tick. hee te ee modelled u ALAB oftae. Numeical olution ith fite diffeence Eule method ee ued to olve the equation decibe the dy te. he theoetical eult ee then fomulated fiue to ho the behaviou of the hole dy oce. omaion of the theoetical eult fom thi tudy ith exeimental data a left fo the ucom aticle. Keyod: mathematical model, ueheated team, dy, itial condenation, eced coe model 1. Intoduction Dy can be defed a emov a ecific amount of ate fom the mateial due to evaoation by aly of heat unde contolled condition. he ma aim of the oce i to ceae the toae life of the mateial and deceae it tanotation cot. he eduction the amount of ate content of the mateial educe the ate activity. hi ill hibit micobial oth at the eiod of to. Goal of eeach imov cuent dy technoloie ae to imove the economic of oeation uch a educe eney conumtion, ceae caacity, educe ize of equiment, ceae eae of contol and envionmental conideation (mimize eney conumtion, educe emiion, ceae afety). In addition, imove the oduct quality ead to: unifom dy, mimize chemical, hyical and nutitional deadation (Ponyk et al., 004). hee ae to dy method eect of the dy medium, dy by hot ae like ai and the othe method i dy by hot olvent vaou like ate team. Hoeve hot ai ha been ued fo decade a a chea dy medium, team emeed a a dy a that uitable fo exloive mateial like coal. 1.1 Steam Dy and Ai Dy Reeach team and ueheated team dy ha evealed eat advantae of team dy ove ai dy. Envionmental ollution o odou emiion to the atmohee can be elimated ce dy occu cloed chambe ithout ai (Soononnait et al., 006). It ha been eoted that hihe quality oduct can be achieved ith ueheated team dy ecially fo tach-baed oduct. Fo examle, hihe head ice yield comae ith hot ai dy due to fate develoment of tach elatization, eult tenthen of temolecula bd foce amon tach anule (Soononnait et al., 006). Abence of oxyen event oxidative eaction hich i omoted by native enzyme lead to coloued comound hich undeme the oduct quality (Elutondo et al., 001). Sueheated team dy of bioma ive the oibility of often the ood tiue befoe alletiation. Futhemoe, ead to anaeobic envionment, the oxidation i avoided (Pakoiki et al., 007). Haubuand 1908 diued the concet of dy by ueheated team and the ability of ecycl the team 107

2 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 thouh the oce (Beeby, 1984). he eciculat dy of ue heated team and elimat ai thouh the dye ae eney av, the only eney leav the ytem i the exta vaou that have been evaoated fom the mateial unde dy. Sue heated team ae uitable fo combutible olid uch a coal hee it educe ik of exloion and fie hazad. Alo, et ae may be ued fo tat u and hut don the ytem to avoid combution o fie the cae of dy combutible olid. he contol on the quality of the oduct i eaie by monito the team temeatue, becaue the dy ate and fal moitue content ae function of the dy medium temeatue. Dut collection ueheated team dy i much imle by a the exce vaou thouh condene (ommelen & oby, 1969). Devente and Heijman (001) ave ome examle ead to team dy benefit and etiction of ueheated team dy. Ponyk et al. (004) illutated that the ue of ueheated team a a dy medium fo non-temeatue enitive oduct ha many otential benefit to the conume and the duty. Ue of ueheated team can lead to eney av a hih a 50 80% ove ue of hot ai o flue ae. hee av can be achieved due to hihe heat tanfe coefficient and the ceaed dy ate the contant and fall eiod if the team temeatue i above the veion temeatue. he dy at the contant ate eiod i lone ueheated team dy, thu ovid hih dy ate fo lone eiod of time. Some valuable volatile oanic comound eneated fom the dy mateial can be ecoveed and eaated by a condene (an & enkoki, 003; Wimmetedt & Hae, 1996). Some alication volv team dy ae: dy of fuel and biofuel ith hih moitue content io to combution a boile, attle feed exemlified by ua beet ul, lumbe, ae ul, ae and lude (Wimmetedt & Hae, 1996). Sueheated team cannot be ued fo temeatue enitive mateial a it i oeated at hih temeatue, hile oeation unde vacuum to educe boil ot ill add moe comlexity to the oce and equiment cot. o educe the temeatue of a do of ate fom 100 o to 86 o, thi ould equie oeat eithe at 0.6 atm o ith 40% ai eent (ommelen & oby, 1969). Alo bette and hihe ulation ae equied fo the dy uface to avoid condenation. It ha been ecommended that befoe u team fo dy, hot ai hould be ued fo om u the ytem until the temeatue the dy comatment eache the deied temeatue (Soononnait et al., 006). Behel and Rentom (00) built a dy ytem follo the equiement of duty. et ith adut caied out a fluidized bed and illo ood chi ee done a fixed bed. hey hoed that even ith vey mall team leak, thee i a ificant decle the eney efficiency of the dye. Alo, the mateial ut and outut to/fom the dye ae vey difficult to eal. Hoeve thee ae ome limitation fo u ueheated team a a dy medium, oof of cile fo team dy of ae and textile have been accomlihed (Devente & Heijman, 001). 1. Dy odel hee ae to diffeent mechanim eented liteatue ead to modell dy unde ueheated team. he fit i eced coe model hee evaoation occu only at a dy font, the font move fom the uface of the aticle to the coe a dy oee. And the econd i the th-laye model hich aume that the lo of moitue i at an exonential ate due to tenal ate diffuion to the a uface at hich the vaoization occu. hee to mechanim ae decib only the fall ate eiod. ot of eeache aumed, fo the contant ate eiod, a imle olynomial equation that take conideation to facto: temeatue and flo ate of the dy medium Reced oe odel A numbe of tudie ued the eced coe model to imulate dy unde ueheated team. he model eented by hen et al. (000) hich i a modification fo the model eented by Aaal et al. (1986), aume the emoval of moitue fom a oou aticle i due to fomation of dy-et teface and the eceion of thi teface ith time. Althouh, it take conideation the itial condenation henomena, thi model did not count fo the ceae the moitue content of the aticle du the heat eiod. Alo, it did not count fo the contant ate eiod a ell. In anothe tudy by Looi et al. (001), they ued the eced coe model tudied by both Shibata et al. (1988) and Khan et al. (1991). he model aume that evaoation occu only at a dy font, the font move fom the uface of the aticle to the coe a dy oee. Shibata et al. (1988) tudied the dy mechanim of teed hee of coae la bead at atmoheic eue and ueheated team a dy medium. hey found that the dy mechanim i contolled by uface evaoation at the contant ate eiod hee evaoation take lace only on the uface of the aticle. And, it i contolled by the eced font mechanim, hee the evaoation take lace the ne uface of the aticle, at the fall ate eiod. he tudy emhaied on the etimation of the citical moitue content ueheated team comaed to hot ai dy. he tudy alo found that du dy ueheated team, evaoation take lace not only on the uface of the aticle du the contant ate eiod but alo the th 108

3 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 laye belo the uface. Khan et al. (1991) tudied both le oou aticle and a backed bed dy unde ueheated team. he le aticle model a cooated to an oveall model fo dy a backed bed. Inteface eced theoy a ued to model the evaoation fom the le aticle. Hae et al. (1997 and 000) develoed a model fo ueheated team of a le oou heical ceamic mateial. In thei eeach, diffeent mechanim ee ued to eent ueheated team dy. a tanfe due to caillay foce i aumed to be domat itially then thi mechanim elaced by eue-diven aeou flo a the tenal eue ceae. hee to mechanim aumed to follo Dacy la. he oou mateial a aumed to have cyldical oe, and totuoity facto a the only adjutable aamete. hi model not only oe the itial condenation and the ceae the moitue content du the heat eiod but it i alo vey comlicated actice. Elutondo et al. (001 and 00) decibed the dy oce by divid it to fou eiod; (1) hot itial unteady am-u eiod, () contant ate eiod hee evaoation take lace at the extenal uface of the amle due to extenal heat tanfe, (3) the fall ate eiod tat hen diffuion i not fat enouh to comenate the evaoated ate fom the uface, thi ituation a dy laye tat to o cea the eitance to heat conduction and mak the ate to full, (4) fally hen the fee ate i totally emoved and the fal ate content aoach the hyocoic equilibium value, the temeatue of the amle ill tat to ie. hoe model dicued above did not eent the all te of the dy oce unde team becaue they did not count fo the itial condenation neithe fo the chane moitue content du the heat eiod. hee to nelected henomena ae vey imotant any dy ytem. Soononnait et al. (006) ued a model that count fo the itial condenation and the ceae the moitue content of the mateial. he model a fomulated fo dy a backed bed athe than le aticle. hi model did not ue the eced coe model. 1.. h-laye odel Anothe numbe of tudie caied out by Pachayaaakon et al. (00), Babali et al. (006), Soononnait et al. (006), hemkhi and Zaouba (005), Suvanakuta et al. (007), aaov and Baa (1975) and Ponyk et al. (004) have ued Fick unteady tate equation to decibe the dy ate of heical eomety. he effective diffuion coefficient a etimated fom the exeiment to ho the diffeence beteen the dy ueheated team and hot ai. ank 1975 eented an analytical olution of the Fick equation fo vaiou eometie. hi model a fomulated to decibe the dy hot ai athe than team. 1.3 Study Aim he aim of thi tudy i to combe all the thee majo te that take lace du dy unde ueheated team. Fit te i itial condenation hich haen at the ealy tae of dy. hi then lead to the econd te hich i diffuion of the condened ate to the teio of the aticle. hi te i eonible of cea the aticle itial moitue content. he lat te tat hen the aticle eache the atuation temeatue. hi te clude; evaoation of the itially condened ate and then evaoation of the mateial fee ate content at a contant ate. At the contant ate eiod evaoation only take lace at the uface o the fit laye of the mateial. he evaoated moitue fom the uface ill be elaced by miation fom teio. Fally fall ate eiod be, at thi te heat conduction thouh the aticle i aumed the limit te. In thi aticle, thee te ee modelled eaately u fite diffeence method and ALAB oftae. A thee i no tudy eent all thee te a le aticle, fo thi eaon thi aticle a emeed.. athematical odell athematical model hould enable ood oce de and mimize cot hile kee quality contat. A common modell aoach i to aume that one tanfe mechanim i a ate contoll amon the thee mechanim that contol dy unde ueheated team. hee thee mechanim ae: fitly, extenal heat tanfe hich i function of the heat tanfe ate by convection and adiation fom the dy medium to the uface of the mateial; econdly, tenal heat tanfe hich i function of the heat tanfe by conduction thouh the aticle, and fally, tenal ma tanfe hich i function of the emeability of the aticle. athematical model that ho the chane temeatue and moitue content a function of time fo a le oou heical aticle ee develoed fo dy unde ueheated team. he follo ae the te:.1 Initial ondenation, Heat Peiod he itial condenation of vaou on the uface of aticle at the ben of the contact beteen the cold olid feed and the team may lead thee aticle to tick to the hot uface of the dye. It ha been hon by Hamaand (011) that liquid bide hich connect the aticle to the uface of the dye at the ben may o thouh la tanition hae afte a eiod. hi i due to the hih temeatue of the ueheated team. Iyota et al. (001) focued thei model on henomena hich occu du the itial tae of dy, 109

4 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 condenation of ueheated team on the mateial uface. hi henomenon eatly fluence the mateial quality afte dy. It i alo eonible fo quickly heat even the teio of the mateial. Futhemoe, it ceae the moitue content of the eion lihtly ad fom the uface. hey alo hoed that dy unde ueheated team i deendent of moitue diffuion coefficient (ma tanfe) and i moe domant by heat tanfe (conduction). Kozanolu et al. (006) did not eite itial condenation a a eult of additional heat ulied by the eitance talled on the all of the dye. hey hoed that thee a a deceae the amount of condenation the itial eiod of the oce by cea the dye all temeatue. In cae of educed oeat eue, a iven oeat temeatue coeond to a hihe deee of ueheat: o a t hi ill aticiate achiev a oce ithout itial condenation. he deceae the oeat eue oduce lihtly hihe fal moitue content. he imact of the vacuum condition i deceae the atuation temeatue and a a eult it ceae the deee of ueheat. Initially a a aticle ith a lo temeatue et to contact ith the dy medium, ue heated team (SHS) thi cae, thi natually lead to team condenation on it uface and ceae the aticle moitue content. hi eiod i called heat eiod hee the condenation contue and the aticle temeatue ceae until it eache the boil ot of the olvent. Aumtion ee made that the hole aticle i coveed by a laye of condened ate ditibuted unifomly ove the uface of the aticle. Alo aumed, thee i no temeatue adient thouh the aticle du the heat eiod. he temeatue of the aticle thi eiod eeent the hole aticle. Afte the temeatue of the aticle eache the boil ot of the olvent, hich i cae of ate 100 o, thi i tue unde atmoheic oeat eue. ondenation ill to and evaoation ill take ove hile diffuion of the moitue thouh the aticle contue du the entie eiod of both itial condenation and evaoation. he tantaneou location of the th laye of the condened ate i efeed to a, note R, hee R i the aticle adiu. Aum the temeatue of the aticle i eecially unifom at thi eiod. Heat tanfe by convection to a heical aticle, nelect the adiation (hen & Aaal, 000), can be eent by Equation (1). Equation (1) i a eult of eney balance ove iothemal heical aticle coveed by a laye of condened ate, ith adiu and temeatue ; d h ( ). va d.... ( 1 )... R dt R R dt (1) Whee; h ( ) heat tanfe coefficient beteen the SHS medium and the uface of the aticle; temeatue of the dy medium (SHS);,. temeatue of the aticle ( the hole aticle); denity and ecific heat of ate; denity and ecific heat of olid mateial;,. va latent heat of vaoization of ate; vaiation the aticle adiu due to condenation and evaoation; R itial adiu of the aticle; itial moitue content of the aticle; R dimenionle adiu. he fit tem eeent the chane temeatue of the aticle ith time conide the aticle mateial, moitue content and the itial laye of condened ate. he fit tem the RHS of the equation account fo the heat tanfe beteen the aticle and the heat medium. he econd tem eeent the latent heat of condenation of the ueheated team. In a teady tate condition, ueheated team temeatue vaie vey loly ith time o any chane can be nelected and adiabatic behaviou can be aumed (dy zone i 110

5 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 efectly iolated) (Elutondo et al., 00). he follo itial condition ee aumed to tat the modell: R itial aticle adiu; (j) ( 0 ) itial aticle temeatue ( t 0 ); t time teval; i, j eeent oition and time, eectively. he temeatue of the aticle afte a time teval of t deend on the numbe of ate laye condene ove it uface. U numeical method, fite defeence Eule method, Equation (1) can be olved fo the aticle temeatue a hon Equation (): (i 1 ).h ( ) va (i 1 ). 1. (j) t.. (j)... R R R R R t (j 1 ) R. R () (j 1) In ode to olve equation () fo the aticle temeatue a function of time teval, it need to conide the adiu of the aticle, actually the adiu of the aticle add to it the thickne of the ( i1) condened ate, the actual aticle adiu a aumed contant, at each laye of ate condened on it uface. When fee ate i contact ith ue vaou, the equilibium ate of molecule tanfe fom vaou to the liquid hae and fom the liquid to the vaou hae i iven by the ketic theoy of ae. When the ytem i not at equilibium, the net ate of evaoation o condenation e unit dolet (aticle coveed comletely by ate laye) uface aea i ovened by modified Hetz-Kunden equation (hen & Aaal, 000). hi equation a fit ooed by Alty 1931 (aa, 1967). aa (1967) tudied the evaoation ate of diffeent olvent clud ate. he tudy ho that thee i little o no eitance to molecule co the vaou-liquid teface. hi mean that the evaoation coefficient i unity. Equation (3) ho the evaoation-condenation ate of ate a eented by aa (1967): P d at( ) P.. atm dt..r (3) Whee, P atm oeation Peue of the dy medium; P atuation vaou eue of condened ate at aticle uface temeatue; at ( ) R molecula eiht of ate; univeal a contant. he atuation vaou eue of ate at diffeent aticle uface temeatue, actually the ate hell aound the aticle, can be iven by Equation (4) (Antoe equation); LnP at( ) / ( ) (4) U numeical method, fite defeence Eule method, Equation (3) and (4) can be eitten a follo; P at( ( j ) t ) P atm (i 1 )...R ( j ) (5) 111

6 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 (j) LnP (j) / ( ) at( ) (6) Equation (5) and (6) can be ued to edict the condenation-evaoation time teval and the amount of ate condened ove the aticle. he evaoation ill tat hen the temeatue of the aticle eache aoximately 100 o. At thi temeatue the thickne of the condened ate on the uface of the aticle i knon fom Equation (5) and (6). he evaoation ill occu at contant aticle temeatue. he evaoation ill be domated by heat tanfe beteen the condened ate and the dy medium. At thi eiod an aumtion a made that the hole aticle i a dolet of ate at 100 o until the entie condened ate evaoate. Eney balance ove a dolet of ate can be eent by Equation (7);..R d d. h.( ) 3 dt ( ) va dt (7) d Fo contant aticle temeatue at 100 o, 0 dt d h ( ).( ) dt (8) va Whee 100 o he adiu of the condened ate deend on the ate of evaoation fom the dolet uface, by u numeical method, fite defeence Eule method, Equation (8) can be eitten a belo; h ( ) (i 1 ) dt..( ) va (9) Fom the above Equation (, 5, 6 and 9) fal temeatue of the aticle can be found at the end of the heat eiod. he condenation evaoation eiod (heat eiod) i vey imotant fo the calculation of the amount of moitue abobed. Alo, the thickne of the condened ate ith time can be tacked. ommelen and oby (1969) demontated the ue of coelation of heat tanfe coefficient hich i alicable fo evaoation of mall ue ate do ai i alo valid fo evaoation ueheated team. Foced convective heat tanfe can be aumed to take lace beteen the bulk ueheated team and the aticle uface eithe coveed ith ate laye o not, ooed by Hae et al. (1997), Equation (10); h ( ).d Re.P k (10) h( ) Aveae convective heat tanfe coefficient, J/m.k.; k hemal conductivity of team, J/m.k.. Re.u.d.. P k 11

7 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 u denity of the ueheated team; ueficial velocity of the ueheated team; vicoity of the ueheated team;. heat caacity of the ueheated team.. Wate Diffuion fom the Suface houh the Paticle he moitue content of the aticle ill ceae du the heat eiod due to diffuion of the condened ate at the uface to the teio of the aticle. hi henomenon i imotant dye uch a otay dum dye hee the aticle have much time fo et (contact ith the uface) (Hamaand & Yuaf, 013). Unlike fluidized bed dye the ate condened on the aticle uface evaoate a hote time due to contuou contact beteen the aticle and the dy medium. he fit laye of the aticle uface ill be atuated ith moitue du the heat eiod. hi can be decibed by the diffuion equation fo a heical aticle (Soononnait et al., 006; hemkhi & Zaouba, 005), a hon Equation (11); D eff R t (11) moitue content k ate / k dy bai; D eff effective diffuivity coefficient m /. he effective diffuivity coefficient can be detemed fom the dy exeiment itelf a hon by hemkhi and Zaouba (005) and Soononnait et al. (006). hemkhi and Zaouba (005), vetiated the moitue diffuivity thouh a oou clay mateial ai dy at diffeent humidity. he moitue diffuivity can be etimated by: analyi of the dy data, otion ketic and emeability meauement. hey etimated the effective diffuivity fom the dy data, fom the loe of the dy cuve and/o fom comaion of the exeimental data ith that edicted by Fick econd la. Alo, the equilibium moitue content a etimated fom the otion iothem of the aticle. he effective diffuivity can be edicted by Equation (1); Whee; E a activation eney; D o equation contant; R Univeal a contant (J/mol.K); aticle temeatue (K); D effective diffuivity coefficient m /. eff D eff. t ode to have the numeical olution table. E D D ex a eff o R. (1) Initial and bounday condition at thi eiod ae a follo (Soononnait et al., 006); (,t) t 0 (R,t) eq t 0, R 0 t 0 0 Whee eq coeond to the maximum moitue content fo hich the aticle can hold, thi can be edicted by oak the aticle ate ove niht (Soononnait et al., 006). he bounday condition ooe contant moitue content at the cente and maximum at the uface. he uface of the aticle ill be equilibium ith the condened ate. U numeical method, fite defeence Eule method, Equation (11) 113

8 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 can be eitten a Equation (13); (j) (j) (j) (j) (j) (j ) (j) (i ) (i ) (i 1) t.d eff (13) ( 0 ) ( 0) ( 0) t 0 (,t) ( 0 )... ( 1) ( ) ( 0 ) ( 1) ( ) R (R,t) eq ( 0 )... t 0, ( 0) ( 0) (j) 0 (n) (n 1 ) t 0 Whee i and j eeent oition and time, eectively. Equation (13) can be ued to fd the moitue content each laye of the aticle alon the entie heat eiod hee the diffuion occu. Du the heat eiod the aticle abob ate thouh it uface. hi abobed ate ill ditibute thouh the aticle adially. he aveae moitue content at the end of heat eiod cab be etimated u Equation (14) (Soononnait et al., 006); 4 0 R (t). (,t) d V (14) U numeical teation, Simon ule; 4 4 (t). R.. 3 ( R,t ) 1. ( 1,t ). V (,t ) (15) Whee V i the aticle volume (m 3 ). he amount of ate abobed by the aticle afte an teval of t t ; heateiod diffuion m abobed( t ) m. (t ) (16) m abobed the amount of ate abobed du the heat eiod (k); m olid eiht of the dy aticle (k); At the end of the heat eiod the aveae temeatue and moitue content of the aticle ill be 100 o, and (t ) eectively..3 ontant Dy Rate Peiod At the itial tae of dy, the dy ate i contant due to the vaoization of ate at aticle a uface. hi eiod i dicated by a le eent moitue content veu dy time. he aumtion i made that evaoation ill tat hen the temeatue of the mateial eache aoximately 100 o. he evaoation ill be domated by the heat tanfe beteen the aticle uface and the dy medium. he amount of ate evaoate fom the aticle uface ill be elaced by liquid diffuion fom the ne eion. At thi eiod, anothe aumtion a made that the hole aticle i at 100 o until the entie fee ate evaoate. Evaoation fom a aticle uface can be eeent by Equation (17);..R d d. h.( ) 3 dt ( ) va dt (17) 114

9 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 d Fo contant aticle temeatue at 100 o, 0 dt d h ( ).( ) dt (18) va Whee 100 o. At thi eiod, the evaoation ill occu at the uface of the aticle, o thee i no chane the et zone adiu. Equation (18) can be eitten fom of moitue content a hon Equation (19); he amount of moitue can be calculated by Equation (0); d h ( ).A.( ) dt (19) va A h. (t) (o) ( ).( ).dt va (0) Whee i the itial amount of moitue the amle (k ate), and (o) h( i the heat tanfe ) coefficient at the bounday of the amle a hon Fiue (1). By divid Equation (0) by the itial eiht of the amle, moitue content of the aticle can be etimated. he itial eiht of the amle can be fomulated a Equation (1); SamleWeiht..( 1 ).V (1) hen, Equation (0) can be eitten a moitue content on et bai a Equation (); 3.( ).dt (t) (o) h ( ). eva.[. ( 1 )]. () Whee; and (t) i the time deendent and itial moitue content on et bai (k ate/ k amle), (o) i the denity of the olid, i the denity of ate, i the faction of olid the amle and ( 1 ) i the faction of ate the amle, A i the co ectional uface aea, and i the adiu of the amle. Died th laye Heat tanfe coefficient h (-) Dy medium Samle Sub-laye Fiue 1. A chematic diaam fo the heat tanfe bounday 115

10 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; Fall Rate Peiod he temeatue ditibution a heical dy aticle can be eented by the diffeential equation belo. he heat tanfe fom the dy medium to the aticle uface by convection and then thouh the aticle by conduction;. R t (3) U numeical method, fite defeence Eule method, ith an exlicit fomulation, Equation (3) can be eitten a; (j) (j) (j) (j) (j) (j ) (j) (i ) (i ) (i 1) ( i ) ( i ) t.. (4) Whee,, and. k.. t ode to have the numeical olution table; Whee; k themal eitance of the aticle mateial, it i beteen dy denity of the aticle, it i beteen and ; et. dy. ecific heat caacity, it i beteen. and dy.. et he itial and bounday condition at thi eiod ae; ( 0 ) 100 t 0. k. and k. ; et h ( ) R k 0 0 Equation (4) can be ued to edict the chane temeatue of each laye d ith time diectly afte the eceion of it moitue. he Aumtion a made that the temeatue of each laye i contant du the eceion of it moitue and ket at 100 o. Afte thi eiod, the temeatue of the aticle laye ent thouh eceion ill tat to ie due to equation (4). In ode to olve equation (4) fo temeatue adient thouh the aticle, the time teval fo eceion of moitue fom each laye need to be edicted. Eney balance ove the fit laye can be eent by Equation (5); d h ( ) ( ) va ( c ).. dt (5) Equation (5) can be eitten numeical fomula a; d 1 (j) dt.h ( ) ( ) va ( c ). ( 0 ) ( 1 ) 373K (6) Solve fo the temeatue of the fit laye, thi can be done by equat the heat tanfeed to the fit laye by convection to the heat tanfeed by conduction thouh the aticle. he temeatue of the fit laye can be edicted via Equation (7); 116

11 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 h ( ) ( i 1 ) d.. k ( i ) h R ( ) 1d k (7) By aum the value of dt Equation (6), the location of the teface afte moitue eceion fom the fit laye can be edicted, du thi eiod the temeatue of each laye i aumed contant at 100 o. Afte elaed time of dt, the fit laye become dy. At the next time teval dt, the fit laye ill tat to heat u ove 100 o, it temeatue can be calculated u Equation (7). Fo the econd and the follo laye, Equation (8) belo can be ued to etimate the thickne (o location) of each laye oe unde eceion; Equation (8) can be itten numeically a; d d k va ( c ).. d dt (8) k 1 dt ( i ) ( i ) (i 1 ) ( )... c va (9) Whee i the citical moitue content of the aticle. c he moitue content can be calculated a function of time by conduct mateial balance ove each laye, a hon Equation (30); /.( ). V t (30) he equation above ive the accumulated moitue content a function of location. 3. ateial Poetie A oou aticle i conit of the olid tuctue of the aticle and the moitue fill the vacancie. he oetie of the aticle ill chane afte evaoation of the entie ate content. When the ate be to evaoate fom the aticle oe, the aticle ill be conit of the olid tuctue and vaou the oe. Fo thi eaon the oetie of the aticle uch a; denity, ecific heat, and themal conductivity [,,, k ] mot be edicted at diffeent eiod and oition, the effect of temeatue can be nelected (Iyota et al., 001). Shibata et al. (1988) eented a imlified quantitative eence of each comonent to the elationhi. At the et zone, the aticle i comoed of olid tuctue ith ate fill the oe; theefoe the denity of the aticle at thi zone i; ).. et (1 )(1 A the ate the oe evaoate due to conductive heat tanfe, the ate the oe ill elaced by the team. hen the denity of the aticle at the dy zone i;. dy (1 v)(1 c). vv he ame teatment fo the denity ill be ued fo edict the ecific heat and the themal conductivity, the ecific heat caacity the et zone become; he ecific heat caacity at the dy zone i; ( 1 )(... et. 117 )

12 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 he themal conductivity at the et zone ill be; v. dy ( 1 v)(.. c). v.. v. d. d k. et k (1 ) k he themal conductivity at the dy zone can be eeented a; k 1 v. dy k ( k k). ( kv (. c) 1 Whee ubcit,, v eeent the liquid, olid, and vaou comonent, vaou and ate the aticle. A the vaou ill elace the ate du the eceion, then the ma faction of the olid can be eeented by; ( 1 ) k ) v v, ae the ma faction of and Iyota et al. (001) aumed that the hyical oetie ae contant ead to temeatue, and the aaent hyical value of comound can be diven fom the ecific olid and ate value ith ead to moitue content. an and enkoki, (000, 003), ave a fomula fo the denity of ue heated team a; fo team chane beteen 100 to 00 o a 04 to 1975 J/k. ecific heat of moitue, 4193 beteen 0 to 100 o, and 4313 beteen 100 to 00 o. 4. odell Reult 4.1 Initial ondenation hi te etimate both the temeatue of the aticle hich i calculated u Equation (5) and the amount of liquid condened ove the uface of the aticle a an dication of the aticle adiu u both Equation (6) and (7). Equation (5) i an eney balance, it ho that the temeatue of the aticle ceae a team condened ove it uface. he condenation of team ill to heneve the temeatue of the hole aticle each ate boil ot. A hon Fiue (), the temeatue of the aticle aie haly tat fom itial aticle temeatue. hi temeatue then flatten at 100 o, the boil ot temeatue of dy olvent ( thi cae ate). At thi temeatue team condenation ill to and the evaoation of the condened team ill be. he adiu of the aticle (the condened laye of ate) tat to deceae fom thi ot foad. Fiue () ho a ha ie temeatue of the aticle fom it itial temeatue to aoximately 100 o, thi i due to the hih ecific heat of the condened ate, the eed of thi ie temeatue i alo function of the aticle ize. v 118

13 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; Paticle emeatue (K) time(h) x 10-4 Fiue. Paticle temeatue du itial condenation 4. Initial Evaoation hi te etimate the evaoation ate of the itial liquid condened du the heat eiod. Equation (8) etimate thi by conide the adiu of the aticle a dication of the amount of the evaoated ate. By divid the chane the adiu of the aticle ove the time teval, the ate of evaoation can be edicted. In the fit at of Fiue (3), the i at of the cuve eent the data edicted fom both Equation (6) and (7). hee to equation etimate the amount of condened vaou u the adiu of the aticle a dication. Wheneve the temeatue of the condened vaou i belo ate boil temeatue o it atial eue i belo the atuation, the condenation ill contue. In the econd at of Fiue (3), the decled le i eent the evaoation eiod. A the fiue ho, the evaoation haen at a contant ate (contant loe), thi i becaue the evaoation i haen fom a uface coveed ith fee ate. Althouh, the uface aea of evaoation i chan becaue of the eduction the adiu of the condened laye; it a nelected due to it mall thickne x Paticle Radiu (m) time(h) x 10-4 Fiue 3. Paticle adiu du itial condenation and late evaoation 119

14 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; Diffuion of oitue fom the Suface to the Inteio of the Paticle hi te etimate the moitue ditibution thouh the teio of the aticle du the heat eiod u Equation (13). Alo, it etimate the chane the amount of the aticle moitue content (aveae moitue content) u Equation (14). A hon Fiue (4), the aveae moitue content of the aticle a aied fom 0.15 (itial moitue content) to du the heat eiod. he cuve Fiue (4) ho the ditibution of moitue the aticle tat fom the uface to the cente. he fit laye of the aticle i at atuation becaue the uface i coveed totally by a laye of condened ate. he moitue diffue fom the uface to the teio a decle equence due to the eitance to diffuion. he hae of the cuve Fiue (4) deend on the time teval of thi eiod (heat eiod). A the teval of the heat eiod ceae, the aveae moitue content of the aticle ceae a ell. 0.3 moitue content (K ate/ K dy olid) Paticle Radiu (m) x 10-3 Fiue 4. Ditibution of moitue thouh the aticle du heat eiod, the Aveae oitue content of the aticle oe fom 0.15 to Dy hi eiod a divided to to te; the contant ate eiod and the fall ate eiod ontant Rate Peiod hi te etimate the moitue content of the aticle a function of heat tanfe coefficient. hi eiod aume that the evaoation of the moitue haen only at the uface of the aticle becaue miation of moitue fom the teio of the aticle to the uface i hihe than the evaoation ate at the uface. Equation () etimate the amount of moitue loe a function of time a hon Fiue (5). Fiue (5) ho a lea decle the moitue content becaue at the contant ate eiod it a aumed that evaoation i haen fom a laye of fee ate at the uface. In thi eiod the uface of the aticle ill be coveed by a laye of miated moitue until no moe moitue can be uoted by diffuion fom ide of the aticle. 10

15 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; moitue content time(h) Fiue 5. oitue content du contant ate eiod 4.4. Fall Rate Peiod, Receion of oitue ontent ontolled by Heat onduction hi te etimate the temeatue ditibution alon the adiu of the aticle u Equation (4). Alo, Equation (7) a ued to edict the temeatue of the fit laye of the aticle. o etimate the eceion of moitue fom each laye of the aticle tat fom the uface, Equation (9) a ued to locate the died laye movement thouh the aticle. he eult fom thi equation then can be ued to calculate the moitue content of the aticle via Equation (30) hen the eomety of the aticle i knon. Fiue (6) ho the temeatue at to ot the aticle, the uface and the cente of the aticle. he cuve at the to i eeent the aticle uface temeatue. he temeatue of the fit laye at the uface of the aticle ie to ate boil temeatue a vey hot eiod. Recall Fiue (3), it take le than one econd fo the temeatue at the uface of the aticle to ie to 100 o (deend on the aticle ize). hi temeatue then ema contant at 100 o until the aticle moitue content eache a citical. Afte thi ot the cuve ie haly becaue the uface of the aticle i dy and it i no moe been cooled via evaoation. Simila eult i hon Fiue (6) fo the aticle cente temeatue. he loe cuve ho that the temeatue at the cente ema at it itial temeatue, afte i to 100 o, fo the hole heat eiod. hi i becaue the heat tanfeed fom the dy medium i conumed by the evaoation at the uface. Fo thi eaon it temeatue ill only tat to ie hen the uface i dy and the heat tude the teio of the aticle emeatue () time(h) Fiue 6. emeatue at the uface and the cente of the aticle 11

16 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 he moitue content of the aticle du thi eiod deceae moothly fom the citical moitue content to the equilibium moitue content. In thi eiod, the heat ill tanfe thouh the teio of the aticle via conduction and eceion of moitue ill take lace each laye tat fom the uface. A hon Fiue (7), thi eiod take lone time by many manitude comaed to the contant ate eiod. hi i due to hih eitance to heat conduction and the difficultie aociated ith the eced moitue fom a citical value to equilibium moitue content. itical moitue content eeent the moitue that i available the cell of the mateial. A the eceion o deee thouh the aticle, the eitance to the heat conduction ceae. hi exla the emi-flatten cuve afte lon time of dy. he model alo ho the oition of the moitue a eced thouh the aticle. Fiue (8) illutate the time equied fo each laye of the aticle to dy to thei equilibium moitue content. he leaity thi elation i due to eula ceae the time of eceion of each laye. When all the laye of the aticle each the equilibium moitue content, the le flatten becaue thee i no moe moitue i available, excet that chemically bonded oitue content (K/K) time(h) Fiue 7. oitue content du the fall ate eiod 6 x Receion ediu (m) time(h) Fiue 8. Receion of moitue thouh the aticle 1

17 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; oncluion he model have been alied thi eeach ae eult of liteatue evie conducted the field of dy unde ueheated team. Alo, eney balance a conducted ome othe occaion. hi ae i comb diffeent model eented by many eeache thi filed to come u ith a comlete modell et fo the entie dy te unde ueheated team. Fite diffeence ith the aid of ALAB oftae a ued ode to aly the model. he theoetical eult edicted fom the model illutate the dy behaviou unde ueheated team. Hoeve, exeiment ee not conducted, the tend of the eult ae aee ith the actual behaviou of dy unde ueheated team. hi aticle uccefully eented a liteatue evie focued on the modell of dy unde ueheated team. Alo, full detail ead to modell the all te that take lace unde ueheated team dy ee demontated. Nomenclatue Symbol Decition Unit Value aumed h( ) heat tanfe coefficient beteen the SHS medium and the uface of the aticle. J /m.k temeatue of the SHS K (0) itial temeatue of the aticle K 98 denity of ate K/ m ecific heat of ate KJ/ K.K 4.7 denity of aticle mateial (ceamic) K/ m ecific heat of aticle mateial KJ/ K.K 0.64 v denity of the team K/ m v ecific heat of the team KJ/ K.K.007 va latent heat of vaoization of ate KJ / K 598 R c t adiu of the aticle m 5 E-3 itial moitue content of the aticle citical moitue content of the aticle time teval K ate/ K dy olid K ate/ K dy olid E-8 P atm vaou eue of the ue heated team KN/ m 100 molecula eiht of ate K / mol 18 R univeal a contant J / mol.k k themal conductivity of team J / m.k..48e-0 u ueficial velocity of the team m/.7 vicoity of the team Pa E-05 D eff effective diffuivity coefficient m / m / 13

18 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 E a D o activation eney equation contant J / mol m / eq moitue content fo hich the aticle can hold K ate/ K dy olid m olid eiht of the dy aticle K thickne of the element mm E-8 k themal conductivity of the olid J / m.k..5 k themal conductivity of the ate J / m.k K emeability m E-15 m ueheated team flux K / m. 0.15, 0.5, 0.35 v 1 ) ma faction of ate ma faction of vaou ( ma faction of olid Refeence Aaal, P. K., Genetti, W. E., & Lee, Y. Y. (1986). ouled dy and devolatilization of coal fluidized bed. hem. En. Science, 41(9), htt://dx.doi.o/ / (86) Babali, S. J., Paanicolaou, E., Kyiaki, N., & Beleiti, V. G. (006). Evaluation of th-laye model fo decib dy ketic of fi. Jounal of Food Enee, 75, htt://dx.doi.o/ /j.jfooden Beeby,. (1984). Dy Sueheated team-fluidized bed (PhD thei). Univeity of onah, hem. En. Det, Autalia. Behel, J., & Rentom, R. (00). Baic de citeia and coeond eult efomance of a ilot-cale fluidized ueheated atmoheic condition team dye. Bioma and Bioeney, 3, htt://dx.doi.o/ /s (0) hemkhi, S., & Zaouba, F. (005). Wate diffuion coefficient clay mateial fom dy data. Dealation, 185(1-3), htt://dx.doi.o/ /j.deal hen, Z., Wu, W., & Aaal, P. K. (000). Steam dy of coal at 1. odel the behavio of a le aticle. Fuel, 79(8), htt://dx.doi.o/ /s (99) Devente, H.., & Heijman R.. H. (001). Dy ith ueheated team. Dy echnoloy, 19(8), htt://dx.doi.o/ /dr Elutondo, D.., ujumda, A. S., & Ubica,. J. (00). Otimum oeat condition dy foodtuff ith ueheated team. Dy echnoloy, 0(), htt://dx.doi.o/ /dr Elutondo, D., Elutondo,. P., & Ubica,. J. (001). athematical modell of moitue evaoation fom foodtuff exoed to ubatmoheic eue ueheated team. Jounal of Food Enee, 49, htt://dx.doi.o/ /s (00) Hae, J., Hemanon,., & Wimmetedt, R. (1997). odell team dy of le oou ceamic hee: Exeiment and imulation. he. En. Science, 5(8), htt://dx.doi.o/ /s (96) Hae, J., Wimmetedt, R., & Whitake, S. (000). Steam dy a bed of oou hee: heoy and exeiment. he. En. Science, 55(9), htt://dx.doi.o/ /s (99)00398-x Hamaand, I. (011). Effect of olloidal Paticle aociated ith the Liquid Bide Stick du Dy 14

19 .ccenet.o/ee Eney and Envionment Reeach Vol. 3, No. ; 013 Sueheated Steam. Intenational Jounal of Enee, 4(), Hamaand, I., & Yuaf,. (013). Paticle otion a acad Rotay Dum Dye. anadian Jounal of hemical Enee. In Pe. htt://dx.doi.o/10.100/cjce.1845 Iyota, H., Nihimua, N., Yohida,., & Nomua. (001). Simulation of ueheated team dy conide itial team condenation. Dy echnoloy, 19(7), htt://dx.doi.o/ /dr Khan, J. A., Bealey, D. E., & Alata, B. (1991). Evaoation fom acked bed of oou aticle to ueheated vaou. Int. J. Heat a anfe, 34(1), htt://dx.doi.o/ / (91)90193-i Kozanolu, B., Vaquez, A., hane, J., & Pato, J. (006). Dy of eed ueheated team vacuum fluidized bed. Jounal of Food Enee, 75, htt://dx.doi.o/ /j.jfooden Looi, A. Y., Golonka, K., & Rhode,. (00). Dy ketic of le oou aticle ueheated team unde eue. hemical Enee Jounal, 87, htt://dx.doi.o/ /s (01) aa, J. (1967). Evaoation coefficient of liquid. Ind. En. hem. Fundam, 6(4), htt://dx.doi.o/10.101/i16004a005 Pakoiki, Z., Kuka, B., & Adamki, R. (007). Pediction of otion equilibium both ai and ueheated team dy of eneetic vaiety of illo alix vimali ide temeatue ane. Fuel, 86, htt://dx.doi.o/ /j.fuel Pachayaaakon, S., Soononnait, S., Wetchacama, S., & Jaiut, D. (00). Deotion iothem and dy chaacteitic of him ueheated team and hot ai. Dy echnoloy, 0(3), htt://dx.doi.o/ /dr Ponyk,., enkoki, S., & ui, W. E. (004). Dy foodtuff ith ueheated team. Dy echnoloy, (5), htt://dx.doi.o/ /dr Shibata, H., ada, J., & Shohaa, H. (1988). Dy mechanim of teed hee of la bead ueheated team. Indutial & enee chemity eeach, 7(1), htt://dx.doi.o/10.101/ie00084a00 Soononnait, S., Pachayaaakon, S., Rodat, W., Nathakaanakule, A., & ia, W. (006). A ueheated team fluidized bed dye fo Paboiled Rice: tet of ilot-cale and mathematical odel Develoment. Dy technoloy, 4(11), htt://dx.doi.o/ / Suvanakuta, P., Devahat, S., & ujumda, A. S. (007). A mathematical model fo lo eue ueheated team dy of biomateial. hemical Enee and Poce, 46(7), htt://dx.doi.o/ /j.ce an, Z., & enkoki, S. (000). Dehydation dynamic of otatoe ueheated team and hot ai. anadian Aicultual Enee, 4(1), an, Z., & enkoki, S. (003). odell the ueheated team dy of a fixed bed of Bee ent a. Bioytem Enee, 87(1), aaov, V.., & Baa, B. N. (1975). Ketic of dy of moit mateial ueheated team. anlated fom Inzheneno-Fizichekii Zhunal, 8(1), ommelen, A.., & oby, E. J. (1969). Evaoation and dy of do ueheated vaou. AIHE Jounal, 16(5), htt://dx.doi.o/10.100/aic Wimmetedt, R., & Hae, J. (1996). Steam dy modell and alication. Dy echnoloy, 14(5), htt://dx.doi.o/ / oyiht oyiht fo thi aticle i etaed by the autho(), ith fit ublication iht anted to the jounal. hi i an oen-acce aticle ditibuted unde the tem and condition of the eative ommon Attibution licene (htt://ceativecommon.o/licene/by/3.0/). 15