Transient Heat Transfer Model for Car Body Primer Curing

Transcription

1 F F Vol:, No:9, 1 Transent Heat Transfer Model for Car Body rmer Curng D. Zabala, N. Sánchez and J. nto Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/17 Abstract A transent heat transfer mathematcal model for the predcton of temperature dstrbuton n the car body durng prmer bakng has been developed by consderng the thermal radaton and convecton n the furnace chamber and transent heat conducton governng equatons n the car framework. The car cockpt s consdered lke a structure wth sx flat plates, four vertcal plates representng the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transent heat conducton n each flat plate s modeled by the lumped capactance method. Comparson wth the expermental data shows that the heat transfer model works well for the predcton of thermal behavor of the car body n the curng furnace, wth devatons below 5%. Keywords Transent heat transfer, car body, lumped capactance, prmer bakng. H I. INTRODUCTION EAT transfer modelng n furnaces s a matter of nterest n dfferent materal scence applcatons [1]-[9] and n automotve ndustry. In ths one, corroson protecton s a major concern durng the car body assembly. In some process, heatng of the car body s needed after the electro-deposton prmer applcaton because t s necessary to acheve a prescrbed temperature/tme range for proper prmer curng or bakng. Below that range, the polymerzaton of the resn s ncomplete, and the prmer wll separate from the car surface and above t, the prmer wll be burned, affectng the fnal car pantng, producng changes n pgmentaton and damagng the resn of the prmer, resultng n poor adheson of followng pant layers. Due to the temperature n the furnace chamber, radaton and convecton are the modes of heat transfer from the furnace to the car structure. In order to desgn a new furnace or to mprove the performance of exstng ones, the modelng of the heat transfer process has to be done accurately. D. Zabala s professor at the Unversdad de Carabobo (CIMEC), Carabobo, Venzuela (correspondng author phone: ext 51; e-mal: dzabala@ uc.edu.ve). N. Sánchez, was student at Unversdad de Carabobo, Carabobo, Venezuela. Recently he worked for Mosenca (e-mal: nelsondavd@ hotmal.com). J. nto was student at Unversdad de Carabobo, Carabobo, Venezuela. He s now Busness Development Engneer at Kraft Foods Venezuela (emal: jesus-pnto@ hotmal.com). II. MATHEMATICA MODE A. Energy Balance n car body The car cockpt s consdered lke a structure wth sx flat plates, four vertcal plates representng the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transent heat conducton n each flat plate s modeled by the lumped capactance method. Fg.1 shows the energy balance done n each panel of the car body. Radaton s consdered to be added to the panel from the furnace walls (QBrsB), the other surroundng panels (QBropB) and from the gases nsde (QBrB) and outsde (QBreB) the car body. Also, emtted radaton (QBrEB) from the panel s consdered. Convecton s consdered from the gases nsde (QBcB) and outsde (QBceB) the car body. Control surface Ts Furnace wall Qce Qc Qre Qrs Tge Qr Qrop Tg QrE Fg. 1. Energy balance n left sde panel From the Fg. 1, the energy balance for each flat plate s shown n X(1)X: de Q re Q r Q rs Q rop Q ce Q c Q re dt = (1) Equaton X(1)X s transformed to X()X, n terms of temperature f the lumped capactance method s vald. Ths condton s verfed by calculaton of the Bot number for the car body, as n X()X. Ts Car body Moton drecton Internatonal Scholarly and Scentfc Research & Innovaton (9) 1 79 scholar.waset.org/17-89/17

2 s Vol:, No:9, 1 Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/17 dt ρ e C = σα T + T + T + h T T dt ( ) ( ) ( ) a a ge g s ex ge n g σα j σε j= 1, j + h T T + T T h B = C () k Where the characterstc length c s defned as the rato between the car body volume and surface area, k s the metal thermal conductvty and h s the convecton heat transfer coeffcent. For each flat plate, c s defned accordng the flat plate orentaton. Each flat plate s represented by X()X, and then the theoretcal car body temperature dstrbuton s obtaned by solvng the system of sx coupled ordnary dfferental equatons. These predcted temperatures are compared wth the expermental temperatures obtaned by the thermocouples attached to the car body. In fgure, there s an example of the expermental car body temperature measured n dfferent thermocouple locatons. The measurement system records the temperature values, so these values were used for comparson wth the predcted ones. Fg.. Car body temperature expermental curves B. Convecton heat transfer coeffcents The convecton heat transfer mode nsde the furnace s prmarly by the dffuson mechansm or natural convecton. Due to the selected structure for the car body parts, two dfferent convecton coeffcents must be calculated, for vertcal and horzontal flat plates. Because the temperature of gas nsde the car body s changng durng the tme, together wth the car body temperature, average convecton coeffcents must be calculated by dfferent average flm temperature (TBfB). In ths way, we obtan convecton coeffcents, hbexb and hbnb as temperature dependant functons. Vertcal flat plates: Churchll and Chu correlaton [1] can be used for calculaton of average Nusselt number X()X, vald over the entre range of the Raylegh number (RaBB) and dependng on the randtl number. Also, the Warner and Arpac correlaton () [11], shown n X(5)X, can be used for Nusselt number calculaton. Nu Nu.87 = r ( ) n ( ) 1 Ra () = C Ra (5) In X(5)X, the C and n constants depend on Raylegh number range. Ths dmensonless number s defned by X. C =.59, n = 1/ f 1 Ra 1 9 C =.1, n = 1/ f 1 Ra 1 Ra ( T ) 9 1 β g = () να Then, the convecton heat transfer coeffcent s calculated by X(7)X, where kbfb the flud thermal conductvty at TBfB. h Nu k f = (7) The characterstc length, used n X and X(7)X, s the plate heght for vertcal flat plates. Horzontal flat plates: The correlaton for the average Nusselt number s X(5)X and the C and n constants depend on the condton of the analyzed surface and the Raylegh number range, calculated by X. For upper surface of hot plate or lower surface of cold plate [1]. C =.5, n = 1/ f 1 Ra C =.15, n = 1/ f 1 Ra 1 For lower surface of hot plate or upper surface of cold plate [1]. 5 1 C =.7, n = 1/ f 1 Ra 1 The convecton heat transfer coeffcent s calculated by X(7)X. In X and X(7)X, the characterstc length s the relatonshp shown n X(8)X. Area of horzontal plate = (8) ermeter of horzontal plate Internatonal Scholarly and Scentfc Research & Innovaton (9) scholar.waset.org/17-89/17

3 R Vol:, No:9, 1 III. RESUTS External convecton heat transfer coeffcent, hbexb. The furnace gas temperature, Tge s constant but the car body temperature, T changes from the ntal value of 1 K to the equlbrum value near K. For that reason, the flm temperature Tf, needed for estmaton of gas thermo physcal propertes, s varable, so the Nusselt number and hbexb are varable along the furnace chamber. Gas propertes are consdered to be smlar to ar propertes (Table I). Results are shown n Tables II to IV. Temperature dependant functons for hbexb are shown n Fg. and these values were correlated n terms of the car body temperature (Table V), for beng used n X()X. Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/17 TABE I AIR THERMOHYSICA ROERTIES AT Tf, (Tge= 8K) T Tf β α T ν K r (1/K) (m /s) (K) (m /s) (W/mK) E E-5.7E E-5 15.E-5.8E E E-5.9E E-5 75.E-5.59E E E-5.7E E E-5.8E-.85 TABE II EXTERNA CONVECTION COEFF, VERTICA FAT ATES, *=.8m T Tf RaBB NuBB hbexb X() E E E E E E (W/m K) TABE III EXTERNA CONVECTION COEFFICIENT FOR FOOR, *=.m (8) T Tf RaBB NuBB hbexb X(5) (W/m K) E E E E E E TABE IV EXTERNA CONVECTION COEFFICIENT FOR ROOF, * =.m (8) T Tf RaBB NuBB hbexb X(5) (W/m K) E E E E E E *data provded by car manufacturer TABE V CORREATION FOR EXTERNA CONVECTIVE COEFF ICIENT Flat late hbexb (W/m K)=f (T(K)) Vertcal -8.E-5T +.9T E-T +.9T E-5T +.T hex (W/m K) 1 8 Vertcal (Chu) h ex flat plates T (K) Fg.. Flat plate hb exb vs car body temperature Internal convecton heat transfer coeffcent, hbnb. The nternal gas temperature, Tg s varable wth the tme and t s expermentally measured wth a thermocouple as t s shown n Fg.. After approxmately 9 mnutes, the nternal gas temperature reaches a stable value. Internatonal Scholarly and Scentfc Research & Innovaton (9) 1 79 scholar.waset.org/17-89/17

4 R Vol:, No:9, 1 Here, Tf s also varable, so the Nusselt number and hbnb are varable along the furnace chamber. The ar thermophyscal propertes are shown n Table VI. Results are shown n Tables VII to IX. Temperature dependant functons for hbnb are shown n Fg. 5 and these values were correlated n terms of the car body temperature (Table X), for beng used n X()X. Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/17 Fg.. Internal gas temperature (Tg) vs tme TABE VI AIR THERMOHYSICA ROERTIES AT Tf, (Tg VARIABE) T Tf β α T ν K r (1/K) (m /s) (K) (m /s) (W/mK) E E-5.7E E-5.1.9E-5.E E-5..5E-5.5E E-5..8E-5.9E E E-5.8E E-5 1.E-5.7E-.858 TABE VII INTERNA CONVECTION COEFF, VERTICA FAT ATES, =.8m T Tf RaBB NuBB hbnb X() 1.E E E E E E (W/m K) TABE VIII INTERNA CONVECTION COEFFICIENT FOR FOOR, =.m (8) T Tf RaBB NuBB hbnb X(5) (W/m K) 1.95E E E E E E TABE IX INTERNA CONVECTION COEFFICIENT FOR ROOF, =.m (8) T Tf RaBB NuBB hbnb X(5) (W/m K) 1.95E E E E E E+..9 Flat late Vertcal hn (W/m K) TABE X CORREATION FOR IXTERNA CONVECTIVE COEFF ICIENT hbnb (W/m K)=f (T(K)) 5 1 Bot numbers -1.81E-T +.95T E-T +.117T E-5T +.T Vertcal (Chu) h n flat plates T (K) Fg. 5. Flat plate hb nb vs car body temperature The maxmum Bot number was calculated for each flat plate, usng the hghest value of the estmated convectve coeffcent. Bot values n Table XI are consderably lower than.1, so the lumped capactance method s vald [1]. Internatonal Scholarly and Scentfc Research & Innovaton (9) scholar.waset.org/17-89/17

5 order Vol:, No:9, 1 TABE XI MAXIMUM BIOT NUMBER (k= 8. W/mK) Flat late h (W/m K) B Vertcal Car body temperature The mathematcal model shown n X()X was solved usng the th Runge- Kutta method and the temperature for each flat plate s compared wth the expermental values (Fgures to 11) Front panel T (C ) model 1 Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/ eft sde T1(C ) model 1 Fg.. eft sde, car body temperature vs tme Rght sde T (C) model 1 Fg.7. Rght sde, car body temperature vs tme In general, the model results are n good agreement wth the trend n all the expermental curves. The hghest devaton (,7%) was found for the rear panel (Fg. 9) and the mnmum devaton (1,%) was for the floor (Fg. 11), calculated as n X(9)X. These results valdate the model and t can be used for evaluatng furnace modfcatons. Fg.8. Front sde, car body temperature vs tme Rear panel T (C ) model 1 Fg. 9. Rear sde, car body temperature vs tme T5 (C ) model 1 Fg.1., car body temperature vs tme Internatonal Scholarly and Scentfc Research & Innovaton (9) scholar.waset.org/17-89/17

6 data data K Vol:, No:9, 1 Internatonal Scence Index, Mechancal and Mechatroncs Engneerng Vol:, No:9, 1 waset.org/ublcaton/ T (C ) model Fg.11., car body temperature vs tme AENDIX TABE XII GENERA DATA Absortvty, α.11 Emssvty, ε a.88 Ca (J/kg K) b 7 ρa (kg/m ) b 787 σ (W/m ) a provded by prmer manufacturer b provded by car manufacturer TABE XIII ARTICUAR DATA late 1 left rght front rear 5 roof floor Thckness (mm) Intal T (K) % dev = n = 1 ( ( ) exp ( ) ) T K T K calc x 1 T ( K) exp n a -8 ACKNOWEDGMENT The authors thank to the engneers Romer Gutérrez and Rafael Scovno for ther help. (9) [] M. Cum, H. Chen,. Xu and B. Wu. Total heat exchange factor based on Non-Gray radaton ropertes of Gas n reheatng furnace, Journal of Iron and Steel Research, Internatonal, vol. 1 (), 9, pp.7-1. [] W.F. Wu, Y.H. Feng and X.X. Zhang. Heat transfer analyss durng rollng of thn slab n CS, Acta Metallurgca Snca (Englsh letters), vol. 19 (),, pp.-5. [5] A. Jaklc, F.Vode and T. Kolenko. Onlne smulaton model of the slab-reheatng process n a pusher-type furnace, Appled Thermal Engneerng, vol. 7 (5-), 7, pp [] S. J. Barnett, M.N. Soutsos S.G. Mllard and J.H. Bungey. Strength development of mortars contanng ground granulated blast-furnace slag: Effect of curng temperature and determnaton of apparent actvaton energes, Cement and Concrete Research, vol. (),, pp.-. [7]. Zashkova. Mathematcal modellng of the heat behavour n the ceramc chamber furnaces at dfferent temperature bakng curves, Smulaton Modellng ractce and Theory, vol. 1 (1), 8, pp [8] M.Y. Km. A heat transfer model for the analyss of transent heatng of the slab n a drect-fred walkng beam type reheatng furnace. Internatonal Journal of Heat and Mass Transfer, Volume 5, ( 19-), 7, pp [9] M.E. Masoum, S.M. Sadramel, J. Towfgh and A. Nae. Smulaton optmzaton and control of a thermal crackng furnace. Energy, Volume 1, (),, pp [1] S. W. Churchll and H.H.S. Chu, Correlatng equatons for lamnar and turbulent free convecton from a vertcal plate, Int. J. Heat Mass Transfer, vol. 18, 1975, pp [11] C.Y.Warner and V.S. Arpac, An expermental nvestgaton of turbulent natural convecton n ar at low pressure along a vertcal heated flat plate, Int. J. Heat Mass Transfer, vol. 11, 198, pp.97-. [1] F. Incropera and D.. DeWtt. Fundamentos de Transferenca de Calor. Méxco: rentce Hall, 1999, chapter 9. [1] J. nto and N. Sánchez. Redseño de un horno para el curado de carrocería en una empresa ensambladora de vehículos. Thess, Mech. Eng. School, Unversdad de Carabobo, Venezuela, may 9. REFERENCES [1] S. H. Han, S.W. Baek, S.H. Kang and C.Y. Km. Numercal analyss of heatng characterstcs of a slab n a bench scale reheatng furnace, Int. J. Heat Mass Transfer, vol. 5 (9-1), 7, pp.19-. [] S.H. Han, S.W. Baek and M.Y. Km. Transent radatve heatng characterstcs of slabs n a walkng beam type reheatng furnace, Int. J. Heat Mass Transfer, vol. 5 (-), 9, pp Internatonal Scholarly and Scentfc Research & Innovaton (9) scholar.waset.org/17-89/17