INVERSE HEAT CONDUCTION PROBLEM IN A THIN CIRCULAR PLATE AND ITS THERMAL DEFLECTION

Transcription

1 INVERSE HEA CONDUCION PROBLEM IN A HIN CIRCULAR PLAE AND IS HERMAL DEFLECION G G G G A ik C DsukG ABSRAC A ivs obl of si coducio i i fii cicul l wi giv u disibuio o iio sufc of i cicul l big fucio of bo i d osiio s b solvd wi l of igl sfo ciqu d lso di l dflcio o ou cuvd sufc of i cicul l dfid s suls obid i sis fo i s of Bssl s fucios illusd uiclly INRODUCIONG A ivs olsic obl cosiss of diio of u of ig diu flux o boudy sufcs of solid w codiios of dislc d ssss kow so ois of solid ud cosidio Gys d Cilkowski [] Gys d olowski [] ivsigd o disiol si olsic obls d divd ig u d flux o sufc of isooic ifii slb Nod N [] sudid ivs obl of could l sss filds i ick l Asid F l [] sudid ivs obl of wo-disiol Pioolsiciy i oooic l xibiig cysl clss Nod N l [5] d ivs olsic obl i isooic l ssocid wi Piolcic cic l dic Pobls of ol dflcio of xisyiclly d cicul l i cs of fixd d sily suod dgs v b cosidd by Boly d Wi [6] Fu Roy Coudui [7] s succdd i diig ol dflcio of i cld cicul l du o -y ig of cocic cicul gio of u fc I is w cosuc obl sudid by Roy Coudui [7] d dls wi ivs olsic obl of i cld cicul l u disibuio ukow u gdi d l dflcio o ou cuvd sufc of i cicul l of ickss dfid s D : discuss No o s d is obl so f suls obid i sis fo ivolvig Bssl s fucios illusd uiclly SAEMEN OF HE INVERSE HEA CONDUCION PROBLEM Cosid i cicul l of ickss occuyig sc D : l is iiilly o u wi u disibuio o iio sufc of i cicul l d fcs of i cicul l k o u GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG y Wods : Qusi-sic si obl l dflcio Ivs obl AMS No : 5-XX -XX 8-XX HE OREAN SOCIEY FOR INDUSRIAL AND APPLIED MAHEMAICS 5

2 diffil quio govig u fucio is s subjc o iiil codiio boudy codiios d iio codiio scivly s g ukow 5 d f ; < < < < kow 6 w is l diffusiviy of il of cicul l quios o 6 cosiu icl foulio of ivs coducio obl SOLUION OF HE INVERSE HEA CONDUCION PROBLEM Diio of u Fucio d Ukow u Gdi g O lyig fii Foui si sfo d Llc sfo o quios o 6 d lyig i ivsios o sul quios o obis xssios fo u disibuio d ukow u gdi scivly s si 7 d si g 8 w d osiiv igs d is osiiv oo of scdl quio 9 d s d f } x{ Diio Of Qusi-Sic l Dflcio Diffil quio sisfid by dflcio ω s i [7] is / ω ν M D w M is l o of l ν is Poisso s io of l il d D is flxul igidiy of l ν E D

3 d Sic dg of cicul l is fixd d cld w ω Assu soluio of sisfyig codiios s { } ] [ C w w C slcd i suc wy ω sisfis quio l o M is dfid s d E M α 5 w E d α coffici of li l xsio d Youg s odulus scivly O subsiuig vlu of u 7 i 5 o obis M cos E α 6 Usig 6 d wll kow sul 7 i quio o obis cos C s cos v D E C α 8 Filly subsiuig quio 8 i quio o obis xssio fo qusi-sic l dflcio ω s ] } { [ cos v D E w α 9 Scil Cs S f A w > > A coss O lyig fii Foui si sfo o obis A s f if is odd Subsiu i o obis A A O usig i 7 8 d 9 o obis xssios fo u disibuio ukow u gdi d l dflcio scivly s

4 si 6 A A si 6 A g A d ] } { [ 8 A v D E w A α 5 NUMERICAL RESULS AND DISCUSSIONS Fo couiol wok w k sl il SN5C s xl fo wic il coss s follows : 6 6 α [ ] 6 59 ] [ s ] [ 5 GP E 8 ν 5 A i scod l is i du o o fif ickss of lgs disio i wok of Nowiski [8] d fis fiv oos of scdl quio s i [9] Usig uicl vlus of bov il coss d oos of scdl quio u disibuio ukow ig u d l dflcio vlud viios sow i figus o 6 Figu sows u oscills fo diff is Figu sows flucuio i u fo diff dii Figu sows u icss uo ci lii d s dcli fo diff dii Figu sows ukow u disibuio is gos o icsig uo ci lii d ss dcli d cs o boudy fo diff is Figu 5 sows l dflcio gos o icsig s i icss fo dii of l Figu 6 sows iiilly l dflcio gos o icsig fo sll dii d w dii icss dflcio ss dcsig fo diff is

5 FIGURE : Viio of vsus 5 fo diff i FIGURE : Viio of vsus fo diff dii 5 FIGURE : Viio of vsus fo diff vlus of 5

6 FIGURE : Viio of g vsus fo diff vlus of FIGURE 5 : Viio of & vsus 5 fo diff vlus of 5 *859DULDWLRQRI&YHUVXVUU «IRU diff vlus of 5

7 5 CONCLUDING REMARS Roy Coudui [7] wo sudid dic obl d dls wi qusi-sic l dflcio of i cld cicul l du o -y of ig of cocic cicul gio of u fc wil w odify wok of Roy Coudui [7] d dls wi ivs coducio obl o ou cuvd sufc of i cld cicul l As scil cs icl odl is cosucd d did xssios fo u disibuio ukow ig u d l dflcio o ou cuvd sufc of i cicul l d illusd uiclly suls obid ily licbl i giig obls icully fo idusil cis subjcd o ig suc s i sf of l ubis d oll of ollig ill Ay icul cs of scil is c b divd by ssigig suibl vlus o s d fucios i xssios 7 8 d 9 ACNOWLEDGEMEN uos xss i sic ks o D P C Wkd Ex Pof d Hd D of Mics Ngu Uivsiy Ngu Idi d UGC Nw Dli Idi fo ficil suo ud jo sc ojc sc REFERENCES [] Gys W d Cilkowski M O Ci Ivs Pobl of u d l Sss Fild Ac Mcic Vol [] Gys W d olowski Z O Disiol Pobls of u d H Flux Diio Sufcs of olsic Slb P : Alyicl Soluios Nucl Egg Ds Vol 7 98 [] Nod N O Ci Ivs Pobl of Could l Sss Filds i ick l ZAMM Vol 68 No [] Asid F Nod N d uc R Ivs Pobl of wo-disiol Pioolsiciy i Oooic Pl Exibiig Cysl Clss SME Iiol oul Sis A Vol 7 No [5] Asid F Coi d Nod N A Ivs olsic Pobl i isooic l ssocid wi Piolic Cic l oul of l Ssss Vol 9 No [6] Boly B A d Wi H oy of l Ssss o Wily d Sos Ic Nw Yok 96 [7] Roycoudui S A No o Qusi-Sic l Dflcio of i Cld Cicul Pl du o R-y of Hig of Cocic Cicul Rgio of U Fc oul of Fkli Isiu Vol 96 No [8] Nowiski L oy of olsiciy wi licio P7 Sijof Noodoff Q Al A D Rij 978 [9] Öisik M N Boudy Vlu Pobl of H Coducio Iiol xbook Coy Sco Psylvi 968

8 A ikg D of Mics L Z S Scic Collg Bi - 5 lsw Dis Ngu Idi E-il : C DsukG D of Mics Pos Gdu D of Mics Ngu Uivsiy Ngu Idi E-il : kcdsuk@diffilco