Impact of material parameters on temperature field within clothing laminates

49 IMPACT OF MATERIAL PARAMETERS ON TEMPERATURE FIELD WITHIN CLOTHING LAMINATES Rysza d Ko ycki1; Halina Sza anska2 1Lodz Uni e si y o Technology, Facul y o Ma e ial Technologies and Tex ile Design, Depa men o Technical Mechanics and Compu e Science, Lodz, Poland; 2Uni e si y o Technology and Humani ies, Facul y o Ma e ial Science, Technology and Design, Depa men o Shoes and Clo hing Technology, Radom, Poland e-mail: 1 ysza d.ko y[email p o ec ed] Abs ac Inlaye s secu e bo h aes he ic quali ies and s i ness agains c easing o clo hing lamina es. Lamina e is c ea ed by he moplas ic glue be ween inlaye and clo hing ma e ial which is so ened by hea . S a e a iable is empe a u e. Tempe a u e dis ibu ions wi hin lamina e can be de e mined by nume ical simula ion o di e en empe a u es o hea ing pla es. Impac o di e en ma e ial pa ame e s on empe a u e dis ibu ion is analysed. In oduc ion Inlaye s secu e aes he ic quali ies and ma e ial s i ness agains c easing o clo hing lamina es [1, 2, 3, 4]. Some pa em e s o inlaye s a e discussed by di e en au ho s [3, 4]. The subs an ial p oblem is a choice o echnology, i.e. hea ing sys em applied o so en he polyme du ing lamina ion c . S oka, Koenen [5]. The e a e some impo an echnological pa ame e s o clo hing lamina es: empe a u e, hea ing ime, p essu e applied a e hea ing, ex e nal ma e ial cha ac e is ics, kind o polyme glue, cha ac e is ics o a hea e sys em. Le us i s de e mine he physical model. S a e a iable is he empe a u e wi hin lamina e s uc u e which consis s o inlaye , ex e nal ma e ial and polyme glue poin s. I should e ec i ely desc ibe he echnological p ocess. The s uc u al shape is de ined by ec o o c ucial poin coo dina es. The mos impo an in o ma ion is he empe a u e dis ibu ion wi hin lamina e du ing he hea ing phase. The only hea sou ce a e hea e s in a hea ing de ice. Hea is anspo ed h ough inlaye , polyme glue laye and ex ile ma e ial. The e a e di e en hea loss mechanisms by adia ion, con ec ion and conduc ion on app op ia e ma e ial su aces. The nex s ep is o desc ibe he ma hema ical model. Hea ans e is desc ibed by hea anspo equa ion and se o bounda y and ini ial condi ions, c . Li [6]; Dems, Ko ycki [7]. Hea ans e equa ion is he second-o de di e en ial co ela ion wi h espec o ec o o coo dina es. The p oblem can be sol ed by using di e en me hods. The mos popula is he nume ical in eg a ion wi hin s uc u e [8, 9]. The o he me hod is o in oduce i s a ia ional o m and ind i s solu ion. The main goal is o analyze he sensi i i y o empe a u e ield o polyme glue laye wi h espec o di e en ma e ial and echnological pa ame e s. Va ious desc ip ions o polyme glue dis ibu ion can be in oduced. I can be modeled as a sepa a e laye o by means o egula o i egula dis ibu ed poin s. Addi ionally, di e en hea -insula ing p o ec ions can be in oduced o imp o e hea ans e , c . side housings. Gene ally speaking, he analyzed p oblem has a 3D space cha ac e . To simpli y he solu ion, some cases can be educed o an op ional c oss-sec ion o s uc u e. The e o e, space 3D p oblem can be educed o i s plane 2D c oss-sec ion. The impo an ac o desc ibing he s uc u e can be he mean empe a u e in he glue laye which is assumed as a compa a i e elemen o es ima e he sensi i i y. 50 1 Desc ip ion o hea anspo Clo hing ma e ials and inlaye made o ex iles ha e pe iodically epe eable s uc u e which should be i s homogenized. The e a e a ew e ec i e homogeniza ion me hods [7, 10]. The mos applied is he ule o mix u e de ined in he ollowing o m. . VV V ξ ; VV V ξ ; ξ λ ξ λλ m m m m mmz     (1) whe e Vm is olume o ib es in m3, V is olume o in e ibe spaces illed by ai o he glue in m3, λm; λ desc ibe hea conduc i i y coe icien s o ma e ial (m) and illing ( ) in W/(m K), ξm; ξ a e olume coe icien s o ib es o olume Vm and he in e ibe spaces o olume V . Hea is anspo ed h ough polyme poin s as well as ai be ween he glue. Bo h polyme glue and ai a e homogeneous. The polyme glue laye should secu e he co ec connec ion be ween he inlaye and ex ile ma e ial. The mos e ec i e me hod is o apply he poin -wise sp ead p ocedu e o polyme . We ob ain egula and i egula polyme poin dis ibu ion o di e en scales desc ibed as “mesh” pa ame e o “compu e poin ” pa ame e . Consequen ly, he mos simple and e ec i e me hod is o de ine polyme glue as he con inuous laye . Sou ce: Meye Fig. 1: Scheme o he con inuous au oma ic usion p ess KFH 600 o shi – and blouse usion wi h p essu e cooling s a ion a he ou pu Sou ce: Meye Fig. 2: Scheme o he In e al Con ac Cooling wi h he CoolVac Sys em 51 The des ip ion o hea anspo depends on echnology and hea ing p ess applied. The e a e di e en solu ions o a ious hea ing sys ems. Le us assume he con inuous au oma ic usion p ess KFH 600 o shi – and blouse usion wi h p essu e cooling s a ion a he ou pu , c . S oka and Koenen [5], Figu e 1, Figu e 2. P ess de ice has he addi ional con ac cooling o secu e he egula hea anspo and equalized empe a u e wi hin glue laye . Le us assume he s eady hea anspo desc ibed by ime-independen hea lux densi y o hea ing de ices. Nei he inlaye no ex ile s uc u es con ain hea sou ces. The only hea sou ce a e always hea e s wi hin hea ing p ess. I means ha hea can be only los du ing hea ing p ocess by lamina e. Hea can be accumula ed by ex ile ibe s and anspo ed o su oundings h ough ex e nal s uc u al bounda y. In oducing now hea balance which is he sum o hea losses, we o mula e he hea anspo equa ion. I is he second-o de di e en ial equa ion wi h espec o ec o o coo dina es. To sol e he abo e equa ion, i is necessa y o de e mine he se o bounda y condi ions. I depends on he pa icula solu ion o hea ing p ess, c . Figu e 3. 1 – hea ing elemen s, 2, 7 – hea ing de ices, 3 – inlaye , 4 – homogenized polyme laye , 5 – side he mal housing, 6 – ou e ex ile ma e ial Sou ce: Own Fig. 3: Scheme o ma e ial laye s in hea ing de ice The uppe pa o inlaye and he lowe pa o ex ile ma e ial a e exposed o cons an empe a u e T = T0. This bounda y po ion ΓT is subjec ed o he i s -kind condi ion. The side pa s o hea ed elemen s as well as ex e nal housing a e subjec ed o con ec i e and adia i e hea anspo . The e a e bounda y pa s ΓC and Γ loaded by con ec ional and adia ional hea lux densi ies i.e. he hi d-kind and adia ion condi ions. We assume on in e nal bounda ies Γi he same hea lux densi ies, i.e. he ou h-kind condi ions. Hea anspo equa ion o (i)- h laye supplemen ed by se o condi ions is shown in Figu e 4 and desc ibed by Eq. (2). Sou ce: Own Fig. 4: Bounda y condi ions o sys em inlaye – polyme glue – ex ile ma e ial 1 2 3 4 6 7 5 ΓC: qn=qn con Γ : qn=qn ΓT T=T0 Γi ΓT T=T0 ΓC: qn=qn con Γ : qn=qn Γi qn (i)=qn (i+1) 52           ; y x ; T 0di i *iii i              xx qAq q                                 . qq ; Tσq ; T-Thq ; TT i 1i n i n 4i n C i nC T 0i       xxx xxx xxxx xxx (2) whe e q is ec o o hea lux densi y, q* is ec o o ini ial hea lux densi y, qn=n·q deno es ec o o hea lux densi y no mal o su ace de ined by uni ec o n, A is ma ix o hea conduc ion coe icien s, T is empe a u e, is eal ime, T0 deno es p esc ibed empe a u e, h is su ace ilm conduc ance, T is su ounding empe a u e, σ is S e an-Bol zmann cons an . 2 Impac o ma e ial pa ame e s on empe a u e ield The e a e some basic pa ame e s which can in luence he clo hing lamina e. The mos impo an a e he ollowing:  Type o lamina e. Inlaye can be made o di e en ex iles: ab ics, kni ed ab ics and non-wo ens which depends on p edic ed applica ions. Thus, su ace mass and in e nal po osi y a e also impo an and limi ed o he speci ic lamina e.  Type o ibe s wi hin inlaye ; he mos popula a e: polyes e , polyamide, co on, iscose, Lyc a- ibe s and bamboo ibe s.  Place and a ea o applica ion which de e mines s i o he mo e lexible connec ion.  Finishing p ocedu e which secu es s abili y and aes he ic quali ies o ex ile lamina e.  Lamina ion echnology de ined by hea sou ce pa ame e s, loca ion o hea ing de ices, ime o hea ing and ime o p essu e, o ce wi hin he p essu e olle e c. Le us analyze he sensi i i y i.e. he impac o he abo e men ioned pa ame e s on empe a u e dis ibu ion wi hin polyme glue laye . To de e mine empe a u e ields in ex ile lamina e, i is con enien o assume he same hea lux densi y o he hea e . The homogenized polyme laye has he same geome y and hea anspo condi ions wi hin he hea ing de ice. The hea desc ip ion is consequen ly simpli ied o he 2D plane p oblem. 2.1 Impac o ma e ial po osi y on empe a u e ield We assume he ou e ex ile made o wo en ab ic and he co on inlaye , bo h o iso opic hea ans e p ope ies. Ma e ial pa ame e s can be de ined acco ding o [6,11,12]. Iso opic ma e ial has he single-componen ma ix o hea ans e coe icien s de ined o i- h laye     λλ ii A ; i=1,2,3; ( o inlaye , polyme laye , ou e ex ile ma e ial). Hea ans e coe icien o co on ib e be o e homogeniza ion is cons an λ=0,072W/(mK) whe eas o polyme glue empe a u e-dependen : λ=0,08W/(mK) o T<115°C, λ=0,10W/(mK) o 116°C<T<125°C; λ=0,11W/(mK) o 126°C<T<135°C; λ=0,12W/(mK) o 136°C<T<145°C. The hea ans e capaci y o co on is c=1320J/(kgK); polyme c=1200J/(kgK). The po osi y o co on ab ic is assumed as cons an ε=0,350. The ai con en wi hin he laye o polyme is also de ined as cons an ε=0,450. F ee spaces a e illed by ai o he cons an hea ans e coe icien λ=0,028W/(mK) and cons an hea ans e capaci y c=1005J/(kgK). The su ounding empe a u e wi hin he housing is assumed T∞=25°C. The su ace ilm conduc ance has he cons an alue h=0,1 W/(m2 K). The p oblem was sol ed be means o ADINA-so wa e. The s uc u e is app oxima ed by 3D space Fini e Elemen Ne made o 4-nodal elemen s because con ec ion and adia ion a e de ined by ADINA-p og am as he spa ial unc ion, Figu e 5a. Hea ans e equa ion is 53 in eg a ed using he Gauss me hod [9]. The ob ained empe a u e dis ibu ion is shown in Figu e 5b. The side su aces ha e complica ed shapes subjec ed o hea con ec ion and hea adia ion. Consequen ly, he cen al polyme laye has unequal empe a u e dis ibu ion which can in luence he s abili y o lamina e c ea ed. Tempe a u e maps a e always symme ic ela i e o e ical plane o symme y which con i ms he co ec calcula ions. F ee spaces wi hin polyme laye illed by ai a e hea isola o s and p e en he hea ans e . Tempe a u e maps enable o c ea e he mean empe a u e wi hin he polyme glue laye s. empe a u e o he pla e wi hin hea ing de ice. The mean alue o he empe a u e in he homogenized laye made o polyme and ai is de e mined in 27 poin s loca ed symme ically wi hin his laye . In enginee ing p ac ice, alues o po osi y o co on ab ic can change signi ican ly and i is now assumed a bi a y om he ange 0,250≤ε≤0,450. These wo alues can help o de e mine he mean empe a u e o he polyme laye by means o empe a u e maps by means o he abo e desc ibed p ocedu e. Di e en po osi ies de e mine a ious hea ans e coe icien s and hea ans e condi ions. The ob ained mean empe a u es a e shown in Figu e 6. a) Fini e Elemen Ne o homogenized laye o polyme , b) homogenized laye o polyme , empe a u e o uppe and lowe su aces T = 110 °C; empe a u e in housing T∞ = 25 °C Sou ce: [13] Fig. 5: Fini e Elemen Ne and example o empe a u e dis ibu ion 54 Sou ce: Own Fig. 6: Mean empe a u e o polyme laye o di e en co on po osi ies The ob ained dis ibu ions o mean empe a u es s. empe a u e o pla e in hea ing de ice a e simila . The cou ses can be app oxima ed linea ly. I is e iden ha he highe he po osi y, he be e isola ion o polyme glue laye . Thus, he change o po osi y can in luence he mean empe a u e o he polyme laye . 2.2 Impac o su ace masses on empe a u e ield Change in mass in ac de e mines a ious hea ans e coe icien s. Calcula ions a e de e mined simila ly o p e ious case o he po osi y o he co on ab ic ε=0,350. We can de e mine a e homogeniza ion ha he hea ans e coe icien s can now change wi hin he ange 0,048W/(mK)≤ε≤0,055W/(mK). The ob ained empe a u e maps ha e analogical dis ibu ion o he shown in Figu e 5b. Mean empe a u es a e conside ably close as shown in Figu e 6 o he po osi y ε=0,350. The di e ences a e no g ea e han 2%. Thus, he pa ame e is de e mined now in Figu e 6. Consequen ly we can conclude ha he mean empe a u e is no sensi i e o change o su ace mass o he inlaye ma e ial. 2.3 Impac o ype o ibe s wi hin inlaye on empe a u e ield The nex p oblem is o de e mine he sensi i i y o lamina e wi h espec o di e en ibe s applied. The mos popula a e: polyes e , polyamide, co on, iscose, Lyc a- ibe s, bamboo ibe s ec . The choice o ibe s de e mines hea ans e coe icien o he inlaye ma e ial. Simila ly o subclause 2.1, iso opic ma e ial has he single-componen ma ix o hea ans e coe icien s     λλ ii A ; i=1,2,3. Hea ans e coe icien be o e homogeniza ion is cons an and equal o polyes e (PES) λ=0,200W/(mK); polyamide (PA) λ=0,210W/(mK); co on λ=0,072W/(mK); iscose λ=0,063W/(mK) and Lyc a λ=0,025W/(mK). Fo simplici y, ab ic po osi y is assumed as cons an ε=0,350. All pa ame e s ch ac e izing polyme glue, ai and su ounding a e de ined in subclause 2.1. Thhe p oblem was sol ed by means o ADINA- so wa e. The s ucu e is de ined by 3D space Fini e Elemen Ne made o 4-nodal elemen s. Hea ans e equa ion is in eg a ed using he Gauss me hod [9]. The ob ained empe a u e dis ibu ion has always he same cha ac e as shown in Figu e 5b bu he alues a e now di e en . Tempe a u es on side su aces a e conside ably lowe han in he cen e o he inlaye because he shapes a e complica ed as well as subjec ed o bo h con ec ion and adia ion. The empe a u e maps a e symme ic ela i e o e ical plane which con i m he co ec calcula ions. 20 30 40 50 60 70 80 90 100 20 40 60 80 100 120 140 Mean empe a u e o polyme laye [°C] Tempe a u e o pla e in hea ing de ice [°C] 0,45 0,35 0,25 55 The empe a u e maps help us o c ea e he mean empe a u e dis ibu ion in polyme laye s. empe a u e o pla e wi hin he hea ing de ice o di e en ma e ials. The mean empe a u e wi hin he homogenized laye made o polyme and ai is de e mined in 27 poin s loca ed symme ically. The mean empe a u es a e illus a ed in Figu e 7. Sou ce: Own Fig. 7: Mean empe a u e o polyme laye o di e en inlaye ma e ials The mean empe a u es a e ela i ely close and he dis ibu ions can be app oxima ed by a s aigh line. The highe he hea ans e coe icien o inlaye ma e ial, he be e he hea anspo h ough he ex ile inlaye . Thus, he mean empe a u e wi hin polyme laye is now highe han he empe a u e o he mo e insula ing ma e ial o lowe hea ans e coe icien s. 2.4 Impac o o he ac o s on empe a u e ield The e a e some o he ac o s which can in luence he empe a u e dis ibu ion wi hin he polyme laye . Place and a ea o applica ion can c ea e a s i o mo e lexible connec ion. The main di icul y is ha he e is a p oblem o pa icula lamina e connec ion which should be analyzed indi idually. I is di icul o de e mine he gene al hea anspo model desc ibing all pa icula cases o lamina ion echnology. Finishing p ocedu e helps o secu e he s abili y and aes he ic quali ies o ex ile lamina e. The e a e di e en inishing echnologies o a ious pa ame e s. Thus, a he momen i is impossible o de ine he hea ans e coe icien p ecisely. Addi ionally, ma e ial cha ac e is ics a e inishing p ocedu e can change laye by laye wi hin ex ile ma e ial. These phenomena can be desc ibed s a is ically wi hin each laye . Lamina ion echnology is a complex p oblem de ined by hea sou ce pa ame e s, he loca ion o hea ing de ices, he ime o hea ing and he ime o p essu e, he o ce wi hin he p essu e olle e c. The exac desc ip ion wi hin subclause In oduc ion de e mines he speci ic case o lamina ion echnology. Any o he p oblems should be de ined and sol ed indi idually. Conclusion Tempe a u e maps can gi e some impo an in o ma ion conce ning maximal and minimal alues o s a e a iable wi hin ex ile lamina e. The mean empe a u e wi hin polyme laye can be u he de e mined in selec ed 27 poin s. This empe a u e is assumed as he pa ame e cha ac e izing polyme laye and consequen ly ex ile lamina e. The e a e some pa ame e s 20 30 40 50 60 70 80 90 100 20 40 60 80 100 120 140 Mean empe a u e o polyme laye [°C] Tempe a u e o pla e in hea ing de ice [°C] Lyc a iscose co on PES / PA 56 which can in luence he mean empe a u e. We can also desc ibe he sensi i i y o he mean empe a u e o hese pa ame e s. We ha e p o ed ha he ma e ial po osi y and ype o ib es wi hin inalye can in luence he empe a u e ield o polyme glue. Mo eo e , he su ace mass is no sensi i e in ela ion o he mean empe a u e. O cou se, a ew addi ional pa ame e s can be deeply analyzed, c . he place and he a ea o applica ion, inishing p ocedu e, lamina ion echnology e c. The pe o med analysis can be also applied o shape op imiza ion wi hin he inlaye ma e ial. We can in oduce he space 3D s uc u e wi h espec o di e en pa ame e s. The p oblem should be sol ed nume ically because only he basic cases can be calcula ed analy ically. The nex impo an p oblem is o in oduce he co ec physical and ma hema ical models o hea ans e wi hin ex ile lamina e. The simples solu ion is always he only homogenized polyme laye bu i can lead o some impo an and in e es ing conclusions. The mo e complica ed shape app oxima ion can in oduce he poin wise glue poin s as well as de ailed analysis o glue poin s / ee spaces be ween hese poin s. 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