INFLUENCE OF MODELING OF TURBULENCE IN THE FLOW PARAMETERS WITHIN A FOOD OVEN USING THE OPENFOAM

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1 ênca/scence INFLUENE OF MODELING OF TURBULENE IN THE FLOW PARAMETERS WITHIN A FOOD OVEN USING THE OPENFOAM S. A. Verdéro Júnor a, V. L. Scalon b, and A. Padlha c Unversdade Esadual Paulsa Júlo de Mesqua Flho Deparameno de Engenhara Mecânca Faculdade de Engenhara de Bauru Barro Vargem Lmpa Bauru, São Paulo, Brasl EP a slvover_r@yahoo.com.br b scalon@feb.unesp.br c padlha@feb.unesp.br Receved: Ocober 29, 2015 Revsed: November 24, 2015 Acceped: December 04, 2015 ABSTRAT Because of he beer flexbly n warmng and hgh producon, he connuous furnace unnel s he beer opon o he processng of ndusralzed food producs. Ths sudy presens a numercal nvesgaon of he effecs of RANS urbulence modelng on he man parameers of he ar flow nsde a connuous oven wh ndrec heang - veloces, emperaures, sreamlnes and hea flows by convecon and radaon. The geomery and operang condons used for consrucng he model, seng he mesh and nal and boundary condons were obaned based on values of operang ovens. Modelng consder he hypohess of ar as an deal gas, ncompressble and Newonan; he equaons of connuy, momenum balance and energy n urbulen regme; closng model of wo equaons κ- and radaon model vewfacor. Ulzed he free open source sofware OpenFOAM for devce modelng. The Raylegh Number of he cavy was used o evaluae he reamen ndcaed o urbulence. onsderng he resuls obaned, he ncluson of model κ- sablzed he velocy felds and emperaures around he average value. In relaon o he hea exchanges nvolved, hea flow by convecon on he ma showed neglgble compared o he effecs of radaon. Due o he dscrepancy beween he orders of magnude of convecon and radaon, 's dffcul he precse evaluaon of he frs, because small flucuaons n emperaure and velocy affec consderably and nduce oscllaons n her behavor. However, he radaon model aaned good approxmaon he mos relevan exchanges, showng a good chance her applcaon n praccal cases. Keywords: hermal smulaon, numercal analyss, radaon model, urbulence modelng, OpenFOAM NOMENLATURE p υ specfc hea a consan pressure, J/kg.K specfc hea a consan volume, J/kg.K 1 = =1.92 = 0.09 emprcal consan of model k- ( ) 1 emprcal consan of model k- ( ) 2 emprcal consan of model k- ( ) E emssve power of black body, W/m² b F g G 0 vew facor vecor acceleraon of gravy, m/s² exernal radaon ha reaches he surface analyss, W/m² = 1,2,3,... couner or ndex of summaon ( ) couner or ndex of summaon ( =1,2,3,... ) q oal hea flow by radaon, W/m² rad ( υ ) q vscous hea flux, W/m² ( ) q urbulen hea flux, W/m² p sac pressure, N/m² P componen average of pressure n he RANS R Ra Ra Re R T T u U U ~ U x y z model, N/m² gas consan, J/kg.K Raylegh Number Turbulen Raylegh Number Reynolds Number Rchardson Number me, s emperaure, K average emperaure, K floang componens of velocy n he RANS model, m/s veloces feld, m/s average componens of velocy n he model RANS, m/s nernal energy, J/kg coordnae x, m coordnae y, m coordnae z, m Greek symbols α urbulen hermal dffusvy, m²/s Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

2 ênca/scence Verdéro Júnor, e al. Influence of Modelng of β δ coeffcen of volumerc hermal expanson, K -1 Kronecker dela funcon vscous dsspaon rae of urbulen knec energy, J/kg.s emssvy κ urbulen knec energy, J/kg dynamc or absolue vscosy, kg/m.s dynamc or absolue vscosy urbulen, kg/m.s ν knemac vscosy, m²/s ν urbulen knemac vscosy, m²/s ρ densy or specfc mass, kg/m³ ρ densy or specfc mass evaluaed n T for use n he Boussnesq model σ =1.3 σ =1 σ emprcal consan of model k- ( ) σ emprcal consan of model k- ( ) κ ( ) υ Φ hermal dsspaon funcon of he urbulen knec energy, s -2 ( υ ) Φ υ vscous dsspaon funcon, s -2 INTRODUTION The ncreasng world populaon, he decrease n food supply and he larges food secor coss show he need for beer undersandng and opmzaon of food processng processes. Besdes, changes n consumer profle lookng for agreeable food, of longer lfe and a he same me healher, wh fewer calores and reduced conen of sugar, sodum, gluen, rans fas, ec. are ncreasngly evden. Thus, he sudy, modelng and opmzaon of processes and food ovens seek o mee hese demands wh he lowes possble power consumpon (Assocação Braslera das Indúsras de Almenação ABIA, Avalable n hp:// coneudo.aspx?d=29 and accessed on 03/08/2015). The oven s a very mporan devce n an ndusral nsallaon. I requres a sgnfcan nal nvesmen, a complex manenance and adusmen and delcae operaon. The ovens are usually classfed accordng o he heang sysem, he fuel ype, he hea ransfer sysem and he ype of feed used. The onnuous ovens are used for large-scale producon. In hs ype of devce, he producs ha are auomacally loaded, are processed and, n he end, are dscharged. They have usually lengh of 25 m or more and are dvded no zones, wh condons of emperaure, humdy and velocy conrolled accordng o he ype of produc beng processed. They have sll movng surfaces, whch are srucured n seel bels or maeral ceramc or conveyor mas (Fellows, 2006 and Maz, 1992). In ndrec heang ovens, he combuson gases do no come no conac wh he produc. The κ amosphere of he ovens s heaed by a sysem hea exchangers, where each regon has a burner. They may use fuel ol, gas, sold fuel or elecrcy. Is man feaure s o provde greaer heang sysem desgn flexbly, beng possble faclae radaon mechansm by placng more ubes or heang ressors and he mechansm of forced convecon hrough he warm ar crculaon whn he chamber (Fellows, 2006 and Maz, 1992). The man obecve of hs work s he numercal nvesgaon of he effecs of urbulence modelng, usng RANS mehod wh he model of wo equaons k-, on he man parameers of he flow (velocy and emperaure felds, hea fluxes, sreamlnes and velocy profles) of a connuous oven wh ndrec heang. Dfferenly from a seres of sudes made by Anshaparvn e. al. (2010), hhanwal e. al. (2010), Tank e. al. (2014) and Mondal and Daa (2010), he presen sudy ams o evaluae he parameers and physcal condon of he ar flow nsde he oven whou consderng s effecs drecly on he hea ransfer on a parcular produc beng processed. For he boundary condons were esablshed emperaures as from measured values n a real oven. For he elaboraon of numercal model was used and free sofware and opensource OpenFOAM for performng he numercal smulaon of flow and profles he velocy and emperaure. PHYSIAL MODEL Oven Geomery The geomery of he oven suded has cross secon of 1.5 m wde, 0.5 m n hegh and longudnal lengh of 23.6 m. The dmensons and operaonal condons used n buldng he model are smlar o he real oven o pre-bakng pzzas, used n a food company. The physcal model was dvded no dfferen regons for fxng nal and boundary condons, as can be seen n Fgures 1 and 2. In hs scheme can be hghlghed some mos mporan regons o he sudy: OPEN INLET (z = 0) and OPEN OUTLET (z = 23.6) no resrcons o arflow from nsde he oven and represenng large energy losses. LOSED INLET (z = 0) and LOSED OUTLET (z = 23.6) meal plaes o obsrucon of he arflow from nsde he oven. BURNERS (y = 0.5) se of varous burners ubes presen n he upper regon of he oven, passng hroughou he all exen longudnal, and represened by a sngle surface wh unform emperaure and equal o 300º. SIDES walls sdes of he oven and MAT (y = 0) conveyor. These regons are characerzed by smlar boundary condons and defned n he smulaon as 70 Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

3 ênca/scence Verdéro Júnor, e al. Influence of Modelng of paches. Fgure 1. Fron vew of he physcal model. ρ ν κ + ν + σ κ + p DT D 2 ( U ) = 1 uu κ U 2 ν + ν + κ σ x ( υ ) ( ) ( υ ) ( ) ( ( q + q ) + ( Φυ + Φυ ) (7) =. (8) N = 1 δ 1 1 F. q rad N [ δ F ]. Eb G 0 = 1 = (9) Fgure 2. Isomerc vew of he physcal model. Governng Equaons In he selecon of he governng equaons and defnon of he mahemacal model o be solved, several smplfyng assumpons and physcal models were adoped. Based on he physcs of he problem and ypcal condons esablshed n Brd e. al. (2004), Verseeg and Malalasekera (2007) and Modes (2003), were used he followng condons and equaons for he soluon: U ρ + ρu p = ρrt (1) ~ U = T U U υ = 0 3 P + κ 2 = U U ( ) g ( ( T T ) ρ 1 + β x x κ + (2) (3) (4) 2 κ = (5) ρ ν = ( U κ ) = u u U (6) Where: Equaon of sae for deal gas o he ar nsde he oven, as equaons (1) and (2); The oher physcal properes were assumed consan and evaluaed n he average emperaure of he 450 K, as shown n Table 1; Hypohess of flow ncompressble and Newonan; Ulzaon he algorhm SIMPLE for he couplng pressure-velocy; Transen smulaon unl he convergence of he soluon for he seady sae; Ulzaon of he equaon of connuy n urbulen regme equaon (3); Ulzaon of he balance equaon of momenum n urbulen regme and model of Boussnesq o ncluson of feld srenghs equaon (4); Modelng of he urbulence hrough he RANS mehod wh he model of wo equaons (k-), accordance wh he equaons (5) and (7) and consans shown n Table 2; ulzaon of energy conservaon equaon n urbulen regme equaon (8); Radaon model vewfacor for hea exchanges beween surfaces wh non-parcpang meda equaon (9). Table 1. Physcal properes used. T ν α 450 K m 2 s kg m. s m 2 s Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

4 ênca/scence Verdéro Júnor, e al. Influence of Modelng of g = kg ρ m 3 p J 1021 kg.k β Pr Pr 0.7 ( g g g ) x y z K m s ( ) 2 Table 2. Emprcal condons usually ulzed n he urbulence model k-. σ 1 2 σ κ Expermenal Daa Survey A smlar oven of a food ndusry was ulzed o collec he expermenal daa he process of prebakng of pzzas. These nformaons were used n he oven geomery, mesh consrucon and defnon of some nal and boundary condons. The emperaures used were colleced by an nfrared hermomeer conacless, brand Raynger, model MX4, wh laser sghng and adusable emssvy. Boundary ondons The nal and boundary condons used are defned accordng o he real condons n each pach. The Table 3 llusraes he boundary condons ulzed o dfferen paches defned. Those ables show how o mplemen he physcal condons hrough ypcal commands of OpenFOAM, accordng wh The Open Source FD Toolbox User Gude (2014, avalable n hp://foam.sourceforge. ne/docs/gudesa4/usergude.pdf and accessed on 25/10/2015) and The Open Source FD Toolbox Programmer's Gude (2014, avalable n hp://foam.sourceforge.ne/docs/gudesa4/programm ersgude.pdf and accessed on: 25/10/2015). The equvalence o physcal condons and boundary s dealed hroughou he res of hs secon. Table 3. Inal and boundary condons. p U T Open Inle ( ) K Open Oule nleoule T = 0 losed Inle K losed Oule Sdes Burners calculaed ( 0 0 0) Ma ( ) T = K K Table 3. (con.) Inal and boundary condons. alpha p_rgh G IDefaul Open Oule 10 5 Pa Open Inle losed Inle losed Oule Sdes Burners Ma compressble:: alphawallfuncon fxedfluxpressu re MarshakRadaon greydffusve Radaon Table 3. (con.) Inal and boundary condons. Q r Epslon k mu Open Inle Open Oule losed Inle losed Oule Sdes Burners Ma greydffusve RadaonVewFacor compressble epslonwallfuncon compressble kqrwallfuncon mukwallfuncon The sac pressure (p) s calculaed from he oal pressure, excludng he feld effec (p_rgh). The condon fxedfluxpressure defnes he pressure graden from he mass flow a he boundares. Ths erm and vod f no mpermeable walls. The velocy condon (U) for he regon of open oule, nleoule, s a condon oupu mxed. In he case of posve flow apples o condon zerograden ( U = 0) and n he case of negave flow apples o unform velocy condon s equal o (0 0 0), as specfed n he varable nlevalue. The emperaure of he ma was esmaed as he smple arhmec average of he ar nle emperaure (T = K) and he oule emperaure of fnal produc of ma (T = K), expermenally measured. Alpha s he urbulen hermal dffusvy ( ) α. alculaed usng he froner condon compressble::alphawallfuncon, whch provdes a condon of urbulen dffusvy, used o capure he effecs near he wall for urbulen flow wh low Reynolds Number ( ) Re. The boundary condons for radaon are defned by parameers G, IDefaul and Q r, The greaness G s he ncden radaon, calculaed from he emperaures feld of prevous me sep, hrough he sandard boundary condon MarshakRadaon. IDefaul s he nensy of radaon and he boundary condon greydffusveradaon esablshes he behavor of gray and dffuse body. Q r s he flow of hea by radaon, calculaed usng he condon greydffusveradaonvewfacor. Ths procedure provdes a boundary condon of gray and dffuse body for use n radaon model vewfacor. The urbulen condons are defned by he varables of some addonal greanesses urbulen. Epslon ( ) s he vscous dsspaon of urbulen 72 Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

5 ênca/scence Verdéro Júnor, e al. Influence of Modelng of knec energy calculaed by he froner condon compressble epslonwallfuncon, whch s ndcaed for urbulen flows wh hgh Reynolds Number. The urbulen knec energy ( κ ) s calculaed usng he froner condon compressble kqrwallfuncon, whch mposes a condon of zero graden. The urbulen vscosy, mu ( ), s calculaed by he condon mukwallfuncon and whch provdes a wall funcon based on he urbulen knec energy. pons oalng egh ess. The emperaures feld n he lef sde wall n he cenral regon of he oven afer 3600 s smulaon, for each es and s used as a parameer for analyzng and comparng dfferen mesh szes and, s llusraed n Fgure 3. Numercal Model The free and opensource sofware OpenFOAM, verson 2.4.0, s used n he numercal smulaon. The consrucon of he geomery s defned usng keypons, where he defnon of mesh parameers s made n he preprocessor blockmesh. The resoluon of algebrac lnear equaons obaned hrough he dscrezaon of he ranspor equaons by Fne Volume Mehod (FVM) was performed by a own solver for modelng, presen n OpenFOAM. The pos-processng s made hrough he oher opensource sofware he paravew. The solver used s he buoyansmplefoam, whch s characersc for compressble flow, lamnar or urbulen and ncorporaed no he algorhm of he couplng pressure-velocy he ranspor equaons, SIMPLE. Has pre-mplaned no he source code he mechansms of he hea exchange by radaon and compressbly models. Mesh Varous sofwares, commercal and free, are shown as opons for he consrucon of he geomery and mesh defnon, hghlghng he GAMBIT and SALOME. However, n hs sudy we oped for he applcaon of he blockmesh, presen n OpenFOAM. Alhough consrucon process s more complex, because nvolves several geomerc calculaons, s capable of generang srucured meshes and adequae for execued smulaon, reducng he compung power demanded. However, he use of hs code for geomeres of grea complexy and wh many deals s dffcul o become vable. The applcaon blockmesh decomposes he geomery of he physcal doman suded n a se of one or more of hexahedral hreedmensonal blocks. RESULTS AND DISUSSION Inally, for he defnon of sze of he elemen was performed a es of ndependence and conssency of he mesh. Where used were elemens of 0.20 m and 4284 pons; m and 5440 pons; 0.15 m and 6952 pons; m and pons; 0.10 m and pons; m and pons; 0.06 m and pons and 0.05 m and Fgure 3. omparson beween he emperaures felds n he lef sde wall cenral n 3600 s of smulaon for egh dfferen mesh szes. I s observed n hese resuls ha he meshes wh elemens of 0.06 m and pons and 0.05 m and pons hey showed o be more approprae o do he smulaons, wh a maxmum devaon compared o more refned mesh of he order of 1.31%. Thus, by quesons of smaller demandng of compung power, we oped for he use of mesh wh elemens of 0.05 m and pons. The Fgure 4 llusraes he mesh wh he chosen elemen. Fgure 4. Fron vew of compuaonal mesh wh he use of cubc conrol volumes and homogeneous wh 0.05 m edges. The Fgures 5 a 7 show he effecs of he ncluson of urbulence model n he flow equaons. In Fgures 5 and 6 have, respecvely, he curves of veloces and emperaures for he cenral regon, n oal lengh of he oven and n hegh y = In Fgure 7 are shown he emperaure curves for he walls n he cener, z = 11.8, hroughou he oven hegh. Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

6 ênca/scence Verdéro Júnor, e al. Influence of Modelng of Fgure 5. Veloces curves for he cenral regon of he oven. Number (Ra ) does no change sgnfcanly. Therefore, he reamen of urbulence by he mehod RANS and wh he model of wo equaons (k-) was mplemened n he proposed soluon. The RANS urbulence modelng elmnaes he observed oscllang behavor, sablzng he felds of emperaures and veloces. From he above, o he cener of he oven, observe n Fgure 6 ha he oscllang behavor of emperaures n he model whou reamen of he urbulence s approxmaed by a unform ncrease curve. For velocy curve, as shown n Fgure 5, has s approxmaon n a curve almos consan and equal o 5 cm/s, excep for he nal and fnal regons of he oven. For he walls n he cener of he oven, shown n Fgure 7, observed he approxmaon wh a behavor more sable, and wh lower emperaures gradens ha he model whou reamen of urbulence. Agan, he excepons are he nal and fnal pars of he oven. The Fgures 8 and 9 show he resuls of sreamlnes for he model whou reamen and wh reamen of RANS urbulence, respecvely. Fgure 6. Temperaure curves for he cenral regon of he oven. Fgure 8. Isomerc vew of sreamlnes, based on he veloces and o he enre lengh of he oven, whou reamen of urbulence. Fgure 7. Temperaure curves for walls n he cenral regon of he oven. Analyzng he resuls, for he model whou urbulence of he reamen shown n Fgures 5 and 6, are vsble oscllaons n emperaures and veloces n he cener of he oven, feaurng a flow around a mean value. The presence of ypcal perurbaons hs regme of flow, as vorces and sagnaon regons, no allowed he sablzaon of he emperaure and velocy felds. Furhermore, he value of Raylegh Number (Ra) o he dsplayed flow s Ra = Accordng Incropera e. al. (2006), emprcal resuls for caves wh heang n he upper regon show ha changng of he flow regme o urbulen, happens when Ra > Alhough he geomeres are no dencal, s expeced ha he order of magnude of he Turbulen Raylegh Fgure 9. Isomerc vew of sreamlnes, based on he veloces and o he enre lengh of he oven, wh he RANS urbulence modelng. In Fgure 8, n whou reamen model of urbulence, observed an rregular flow, characerzed by he presence of recrculaons, vorces and zones of sagnaon hroughou he enre neror of he 74 Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

7 ênca/scence Verdéro Júnor, e al. Influence of Modelng of oven. I s observed sll ha he ar has more velocy near of he ma, and has less velocy n he regons of he burner, beng characerzed varous subregons of sagnaon. Noeworhy s also he formng a larger hermal plume, comprehended n he upper regon of he oven n he range z = 9 and z = 14. As a resul s formed n hs regon a sagnaon zone wh hgh emperaures and near-zero veloces. The Fgure 9, urn, shows he resulng average behavor of flow wh modelng urbulence. Noe also, n hs case, he presence of a hermal plume of hgh dmenson, bu locaed n he upper regon of he oven from z = 16. The Fgures 10 and 11 show he velocy profles for he cross secon z = 11.8, exacly n he cener of he oven for he model whou reamen and wh reamen of RANS urbulence, respecvely. n poson y = 0.34 m has he reversal of moon. For he regon where y > 0.34 m and when approachng he burner, here s a reverse moon, wh velocy profle lnear medum, wh maxmus n he order of 8 cm/s. Fnally, was evaluaed he nfluence of ncluson of urbulence model n hea ransfer raes by radaon, convecon and lqud n ma, as llusraed n Fgures 12, 13 and 14, respecvely. Table 4 shows he negraed resuls for he enre ma surface. Fgure 12. Hea ransfer by radaon on ma. Fgure 10. Veloces profles for cross secon z = 11.8 for he model whou reamen of urbulence. Fgure 13. Hea ransfer by convecon on ma. Fgure 11. Veloces profles for cross secon z = 11.8 for he model wh RANS reamen urbulence. For he model whou reamen of urbulence, shown n Fgure 10, s observed ha near of he ma, has a regular profle and maxmum veloces of he order of 23 cm/s. Besdes, when approachng he burner, he velocy profle becomes que rregular, characerzng several regons of he recrculaon n flow. By analyss of Fgure 11, wh modelng of urbulence, s observed ha, near he ma wh y < 0.34 m, here s a progressve movemen, wh maxmum veloces of he order of 16.9 cm/s. Then, Fgure 14. Ne hea ransfer on ma. Table 4. Hea ransfer by radaon and convecon negraed no he ma. Q rad [W] Q conv [W] Q ne [W] Whou Model of Turbulence Turbulence model k Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p

8 ênca/scence Verdéro Júnor, e al. Influence of Modelng of To evaluae whch regme of convecon prevals convecon naural, forced or mxed has he calculaon of Rchardson Number (R). For he flow suded, has R = 0.128, whch he characerzes as a flow wh forced convecon, because R << 1, accordng Incropera e. al. (2006). The Fgure 13 and Table 4 show ha modelng of he urbulence affeced sgnfcanly he convecon ransfer raes; ncreasng he n 2.77 mes. I s noeworhy ha he ma connues losng hea; however, observed a more regular profle, whch ends o sablze n -115 W/m². I s noeworhy ha, n boh models, he order of magnude of convecon s much lower han radaon. Thus, small varaons of emperaures and veloces affec sgnfcanly he behavor of hea ransfer n hs regon and cause sgnfcan flucuaons n her behavor. In relaon o ransfers by radaon, as shown n Fgures 12 and Table 4, wh modelng of urbulence s observed a very smlar profle bu slghly lower; wh a dfference of 2.38% n relaon o he negraed. Were no really expeced changes n hs case, once when usng a radaon model of ype vewfacor, hese depend only on he geomery of he problem. Thus, he small oscllaons observed may be he resul of her own esmae based on sascal pons and used for deermnng he vew facors. Fnally he analyss of he ne raes of hea ransfer, as shown n Fgure 14 and Table 4, demonsraes he agreemen of resuls n boh models; wh an order error 4% relave o he oal negraed. I s also observed ha he curve of Fgure 14 has praccally he same forma as ha n Fgure 12, whch s due o he small nfluence of hea ransfer by convecon. Thus, s concluded ha modelng from urbulence had lle nfluence on hea exchanges by radaon and ne. ONLUSIONS In he sudy of ovens presened, was observed ha exchange of hea by convecon s of order of magnude lower he radaon. Thus, seems mpossble he modelng of ovens wh conssen physcal resuls, whou he use of an approprae model for he evaluaon of radaon. By he dscrepancy beween he nenses of hea exchange by radaon and convecon, becomes dffcul he correc evaluaon of he laer. Ths s due he fac ha small varaons of emperaures and veloces affec sgnfcanly he behavor of hea ransfer by convecon, and nduce sgnfcan varaons n her behavor. The resuls llusrae he necessy of urbulence modelng for he soluon of he flow. The ncluson of model of wo equaons (k-) n he urbulence modelng presened he small nfluence on ne hea exchanges over he ma, because predomnaes he hea exchange by radaon. Despe hs, was observed a sablzaon effecve of he resuls, elmnang ransen flucuaons ha were occurrng n lamnar ransen model. AKNOWLEDGEMENTS The auhors acknowledge wh graude he fnancal suppor graned by APES. REFERENES Anshaparvn A., hhanwal N., Indran D., Raghavarao K. S., and Anandharamakrshnan., 2010, An Invesgaon of Bread-Bakng Process n a Plo-Scale Elecrcal Heang Oven Usng ompuaonal Flud Dynamcs, Journal of Food Scence, Vol. 75, No. 9, pp Brd, R. B., Sewar, W. E., and Lghfoo E. N., 2004, Transpor Phenomena, 2nd, John Wley & Sons. hhanwal, N., Anshaparvn, A., Indran, D., Raghavarao, K., and Anandharamakrshnan,., 2010, ompuaonal Flud Dynamcs (FD) Modelng of an Elecrcal Heang Oven for Bread- Bakng Process, Journal of Food Engneerng, Vol. 100, No. 3, p Fellows, P. J., 2006, Tecnologa do Processameno de Almenos: Prncípo e Práca, 2ª edção, Armed. (n Poruguese) Incropera, F. P., Dew, D. P., Bergman T. L., and Lavne, A. S., 2008, Fundamenos da Transferênca de alor e de Massa, 6ª Edção, LT. (n Poruguese) Maz, S. A., 1992, Bakery Technology and Engneerng, 3rd edon, Pan-Tech Inernaonal. Modes, M. F., 2003, Radave Hea Transfer, 2nd edon, Academc Press. Mondal, A., and Daa, A. K., 2010, Two- Dmensonal FD Modelng and Smulaon of rusless Bread Bakng Process, Journal of Food Engneerng, Vol. 99, No. 2, pp Tank, A., hhanwal, N., Indran, D., and Anandharamakrshnan,.., 2014, ompuaonal Flud Dynamcs Modelng of Bun Bakng Process Under Dfferen Oven Load ondons, Journal of Food Scence and Technology Mysore, Vol. 51, No. 9, pp Verseeg, H. K., and Malalasekera, W., 2007, An Inroducon o ompuaonal Flud Dynamcs The Fne Volume Mehod, 2nd Edon, Longman Scenfc and Techncal. 76 Engenhara Térmca (Thermal Engneerng), Vol. 14 No. 2 December 2015 p