Shape Design of the Pan in Bread Baking Oven

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1 Advn Journl of Food Sin nd Thnology 5(8): , 13 ISSN: ; -ISSN: Mwll Sintifi Orgniztion, 13 Submittd: Aril, 13 Atd: My 3, 13 Publihd: Augut 5, 13 Sh Dign of th Pn in Brd Bking Ovn 1 Luhng Xi, Xinlu H, Hng Liu nd Chunzhi Yng 1 Drtmnt of Lif Sin, Drtmnt of Mthmtil nd Comuttionl Sin, Huinn Norml Univrity, Huinn, 338, Chin Abtrt: In thi tudy, w nlyz digrm of ht ditribution round th bking n outr dg. By uing Fourir' lw, th modl of ht ditribution i dvlod. Modl of intntnou ht flu dnity on th n r ontrutd for n of diffrnt h-from rtngulr to irulr nd othr h in btwn. Thn, w utiliz two r to ubtitut th two rlll lin of th rtngl, rting trk-hd n nd diovrd tht in thi dign, thr i good rformn in th bking ro nd ht i ditributd vnly ovr th ntir outr dg of th n. Finlly, imultion rult r rntd to how th fftivn of th rood mthod. Kyword: Bking ovn, ht trnfr, h of th bking n dign INTRODUCTION A on kind of th oldt nd mot oulr food roing thniqu, bking ovn h bn undr invtigtion by mny rrhr to imrov th nrgy ffiiny of th ro nd th food rodut qulity (Svoy t l., 199; Sblni t l., 1998; Loti t l., ; Skin t l., 7, b, 9). In bking ovn, th hot ir flow ovr th bking ovn by nturl onvtion, th rdition from th ovn hting urf, th onvtion from th ir nd th ondution ht trnfr ro ontt r btwn rodut nd th ovn urf. Th moitur in th food imultnouly diffu towrd th h urf, thn, it trnfr from th urf nd th rodut lo moitur with ontinuou movmnt of th ovn ir. Th r th imultnou momntum, ht nd moitur trnfr mhnim within bking rodut (Tong nd Lund, 199; Ozilgn nd Hil, 1994) nd btwn th rodut nd it nvironmnt (Broyrt nd Trytrm, ), whih, thortilly, hv bn wll known. Th tudy of th bking ovn rquir th following nly: ht utiliztion nd ht trnfr. During tndrd ooking rodur, lrg roortion of th nrgy uly to th ovn i borbd by th trutur nd lot in th round nvironmnt (Plotu t l., 1). In th ontt of nrgy ffiiny, w hould rdu onumtion by djuting th thrml ity of th ovn nd th ir tmrtur lvl nd otimiz rdition whilt mintining th qulity of th rodut. Whn bking in rtngulr n ht i onntrtd in th four ornr nd th rodut gt ovrookd t th ornr (nd to lr tnt t th dg). In round n th ht i ditributd vnly ovr th ntir outr dg nd th rodut i not ovrookd t th dg. Howvr, in mot ovn r rtngulr in h uing round n i not ffiint with rt to uing th in n ovn. To th bt of th uthor knowldg, thr r littl work onrning h dign roblm of th n in bking ovn. In thi tudy, w will dvlo modl to how th ditribution of ht ro th outr dg of n for n of diffrnt h - rtngulr to irulr nd othr h in btwn. MODEL OF HEAT DISTRIBUTION IN THE BAKING OVEN Ht ditribution modl: In thi tion, w will dvlo modl to how th ditribution of ht ro th outr dg of n for n of diffrnt h nd thu roviding n lntion to why rtngulr n tnd to b ovrookd t th ornr nd dg whil in round n ht i vnly ditributd ovr th ntir outr dg nd th rodut i not ovrookd t ll. Th h of th ovn n b n in Fig. 1. Through ronbly uming tht th roblm i undr n idl ondition tht th ovn i homothrml, th mttr of ht hng btwn th ovn nd th n n b imlifid. W know tht in ordr to bk browni th ovn mut b rhtd to rtin tmrtur nd thrfor, w uo tht, on th n i inid th ovn, th boundry ondition for vry urf t th to urf of th n r tly th m ftr om tim T (mning tht Corronding Author: Hng Liu, Drtmnt of Mthmtil nd Comuttionl Sin, Huinn Norml Univrity, Huinn 338, Chin, Tl.: ; F:

2 Adv. J. Food Si. Thnol., 5(8): , 13 Lt u dfin T (, τ) = t (, τ) t, thn () n b rwrittn : t t α = τ T(, τ) = = f( τ) lim T(, τ ) = T(, τ ) τ = = (3) By uing th Ll trnformtion (Broyrt nd Trytrm, ) with rt to timτ, w hv: dt (, ) T (, ) = d T (, ) = = f( ) lim T (, ) = (4) Fig. 1: Th h of bking ovn boundry tmrtur hv ll rhd th rhtd tmrtur t th to urf). Ht trnfr modl: Th roblm n thn b intrrtd roblm of ht hng mong objt with qul initil tmrtur undr th firt boundry ondition. Aording to Fourir' Lw in rfrn (Broyrt nd Trytrm, ), mthmtil modl for thi roblm n b dribd follow: t t t t α( + + ) =, α = y z τ ρc whr, α = Th thrml diffuivity = Ht trnfr offiint ρ, C = Th dnity nd th ifi ht ity t = Th tmrtur t t α = τ t (, τ) = = f( τ) lim t (, τ ) = t t (, τ ) τ = = t () 19 (1) Th bov thr-dimnionl ht ondution modl i bd on th ondution of lmntry r in. But in thi tudy, w um vry urf t th to urf n b htd uniformly. Thn th ondution of h urf n b trtd ondimnionl ht ondution modl. Th modl n b imlifid : And Eq. (4) n b olvd : 1 T(, ) = C + C (5) From Eq. (4) w know tht C = ndc 1 = f ( ). Subtituting C = into Eq. (5), w n obtin: T(, ) = C (6) Sin C = f ( ), w hv: 1 1 T(, ) = f( ) (7) From bov diuion, w n gt th ht trnfr modl : ' τ f( τ ) T(, τ) = ' 3/ 4π ( τ τ ) ' 4 ατ ( τ ) ' dτ (8) whr, f( τ ) = T = t t, with t i boundry tmrtur. Modl of Intntnou ht flu dnity: Aording to Fourir' lw, w n know tht th intntnou ht flu dnity through th tngnt ln with th ditnt d rt for th urf: q d d T = = d (9)

3 Adv. J. Food Si. Thnol., 5(8): , 13 y z ( y) = + ( y+ ) ( bz) + + T + ( z+ b) (1) Th intntnou ht ditribution on irl n i hown in Fig. 3. Similrly vilbl, w hv th following qution: Fig. : Ht ondution on th n in rtngulr h y z m = + T + ( rm) (11) Thr r mny robbl h btwn rtngulr nd irulr h. In thi tudy, w ontrut th following h dribd in Fig. 4. W u two r to tk th l of two rlll lin in th rtngl. From bov diuion, w n obtin th following qution: Fig. 3: Ht ondution on th n in irl h y z ( dz) = + ( z+ d) n + + T + ( rn) SIMULATION STUDIES (1) Fig. 4: Ht ondution on th n in h btwn irl nd rtngl Thn w will furthr diu th ditribution of ht on th browni n by th thr ml, nmly rtngulr, irl nd rtngulr to irulr nd othr h in btwn. Th intntnou ht ditribution on rtngulr n n b n in Fig.. From Eq. (9) nd Fig. 1, w n obtin th following qution: 193 Whn n full of rodut with room tmrtur i ut in th ovn, in ft th n' urf n no b htd to th tmrtur of th ovn immditly. In thi tudy w n think tht ftr mll ontnt T, th urf t th to urf will b htd to th nvironmntl tmrtur inid th ovn. In th imultion tudi, w bgin omut t tim T nd th othr rt of th n r umd to hv th room tmrtur. Th nvironmntl tmrtur nd tmrtur in th ovn r umd to b nd 19, rtivly. Firtly w tudy th tht th n h rtngulr h. A th ttmnt in Svoy t l. (199), Sblni t l. (1998) nd Skin t l. (9),

4 Tbl 1: Prmtr vlu in th omuttion of th modl Vribl Vlu Unit A. m.1 m b.5 m.6 m α m / 54 w/(m[] C) Adv. J. Food Si. Thnol., 5(8): , 13 Fig. 7: Intntnou ht flu dnity of th n in diffrnt h Fig. 5: Intntnou ht flu dnity of rtngulr n t diffrnt tim in thi tudy, th rmtr ud in th imultion r hon Tbl 1. Th imultion rult r hown in Fig. 5. Th q i rrnt th intntnou ht flu dnity. From th rult w n tht th ht in th ornr of th rtngulr browni n ri quikly nd to lr tnt t othr l. Sondly, with rt to th irulr browni n, th omuttion rult r rntd in Fig. 6. Thn w n ily gt th rdiu r = A/ π =.798m. From th Fig w n tht whn th rodut r bkd on th irulr n, th ht i ditributd vnly ovr th ntir outr dg. And 1 ond ltr, th whol n roimtly hiv th m intntnou ht flu dnity. Thn, w utiliz th n in h btwn irulr nd tringl to tt th modl. To imlify th omuttion, w lt th r b mi-irl. Th lngth nd width of th rtngl r hon.15 m,.1m, rtivly. Thn w n onlud tht th rdiu of th mi-irl i.5 / π. Th omuttion rult r hown in Fig. 7. Sin th n i ymmtril, w only drw th rt of y. Form th rult w n tht th h of th browni n w ontrutd btwn irl nd rtngl hv good rformn in th bking. And th ht i ditributd vnly ovr th ntir outr dg of th n. Fig. 6: Intntnou ht flu dnity of irulr n t diffrnt tim 194 CONCLUSION Normlly, w u rtngulr n in whih ht i onntrtd in th four ornr nd ditributd unvnly round th outr dg nd thu th browni gt ovrookd t th ornr nd lo th dird tt. Howvr, with round n thi n b voidd, though thn th numbr of n fit in th ovn won t b mimizd. With th roblm in mind nd through omutr imultion, w nlyzd digrm of ht

5 Adv. J. Food Si. Thnol., 5(8): , 13 ditribution round th n outr dg for h from rtngulr to irulr nd on in btwn, to find olution to bk mimum quntity of rft hommd browni in th hortt mount of tim. It i lr to tht th irulr n o wondrfully vn ditribution of ht round th outr dg nd thi i onfirmd through th ft tht w hv rn imultion to rov tht th ridity of tmrtur ri i dirtly rltd to th hrn of th ornr on th n, whih dtrmin whthr th browni i ovrookd or not. In ordr to void ovrooking th browni, w hngd th ointy ornr on th rtngulr n to th irulr dg on round n, rting wht w ll th trk-hd dign. Thi dign omri th dvntg of both rtngulr nd round n, mning tht not only do it ditribut ht vnly round th outr dg, but it n lo mimiz th numbr of n inid th ovn. ACKNOWLEDGMENT Projt i uortd by th Nturl Sin Foundtion of th Anhui Highr Edution Intitution of Chin (Grnt No. KJ11Z359) nd th Nturl Sin Foundtion of th Anhui Highr Edution Ellnt Young Tlnt of Chin (Grnt No. 1SQRL179). REFERENCES Broyrt, B. nd G. Trytrm,. Modlling ht nd m trnfr during th ontinuou bking of biuit. J. Food Eng., 51: Loti, M., R. Pzlki, J. Andriu nd M. Lurnt,. Study of ong k bttr bking ro. II. Modling nd rmtr timtion. J. Food Eng., 55(4): Ozilgn, M. nd J.R. Hil, Mthmtil modlling of trnint ht nd m trnort in bking ro. J. Food Pro. Prrv., 18: Plotu, J.P., V. Niol nd P. Glounn, 1. Numril nd rimntl hrtriztion of bth brd bking ovn. Al. Thrml Eng., 48: Sblni, S.S., M. Mrott, O.D. Bik nd F. Ctign, Modling of imultnou ht nd wtr trnort in th bking ro. Food Si. Thnol., 31: 1-9. (In Grmn) Skin, M., F. Kymk-Ertkin nd C. Ilili, 7. Modling th moitur trnfr during bking of whit k. J. Food Eng., 8: Skin, M., F. Kymk-Ertkin nd C. Ilili, 7b. Simultnou ht nd m trnfr imultion lid to onvtiv ovn uk bking. J. Food Eng., 83: Skin, M., F. Kymk-Ertkin nd C. Ilili, 9. Convtion nd rdition ombind urf ht trnfr offiint in bking ovn. J. Food Eng., 94: Svoy, I., G. Trytrm, A. Duqunoy, P. Brunt nd F. Mrhin, 199. Ht nd m trnfr dynmi modling of n indirt biuit bking tunnl-ovn. Prt I: Modlingrinil. J. Food Eng., 16: Tong, C.H. nd D.B. Lund, 199. Efftiv moitur diffuivity in orou mtril funtion of tmrtur nd moitur ontnt. Biothnol. Progr., 6:

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