Integral Transform Methods for Inverse Problem of Heat Conduction with Known Boundary of Semi- Infinite Hollow Cylinder and Its Stresses

Transcription

1 Iiol Joul of Ls chology i Egiig Mg & Alid cic IJLEMA Volu VI Issu IV Ail 7 IN Igl sfo Mhods fo Ivs Pol of H oducio wih Kow Boudy of i- Ifii Hollow ylid d Is sss.. igu N.. Khogd hi Dysh Mhvidyly Nwgo D of Mhics MJP Educiol us RM Ngu ivsiy Ngu Idi. Asc: h disiol ivs si holsic ol of si-ifii hollow cylid is cosidd wihi h cox of h hoy of glid holsiciy. h low sufc u sufc d i sufc of h siifii hollow cylid occuyig h sc 3 D { x y R : x y / } ow oudy codiios. ii Mchi-Zglich sfo d oui si sfo chius usd o di h uow u gdi u disiuio dislc d hl ssss o ou cuvd sufc of cylid. h disiuio of h cosidd hysicl vils oid d sd ghiclly. Kywods: holsic ol si-ifii hollow cylid hl sss ivs ol Mchi-Zglich sfo d oui si sfo. K I. INRODION hogd l. [ 5-] hv ivsigd u disiuio dislc fucio d ssss of hi s wll s hic hollow cylid d Khogd l. [] hv slishd dislc fucio u disiuio d ssss of si-ifii cylid. Yoo Hw hoi. l. [6] discussd h u disiuios of h hd l ivsigd wih h codiio h h li hig ocss ws uoic. h u viios w lso ivsigd wih h chgs of hos h vils. h uicl suls showd h h u dcsd s h ovig vlociy of h hig souc icsd. I lso vld h h us chgd lily wih h chgs of h hig souc. Xijig Li Hog u Jigwi Zhou d Qu H [5] sudid o-disiol li ivs h ol. his ill-osd ol is lcd y h ud ol wih o loclid oudy codiio. Af h divio of is closd-fo lyicl soluio h clculio o c did y h coiso w h uicl d xc soluios. Michl J. ilowsi d Adj ącowi [] sd lysis of soluio of Llc uio wih h us of EM hoic sic fucios. h ssc of h ol is id sig oxi soluio sd o ossily lg fii l. Ioducio of hoic fucios llows ducig h od of uicl igio s cod o clssicl ii El Mhod. Nuicl clculios cofi good fficicy of h us of sic hoic fucios fo solvig dic d ivs ols of sioy h coducio. o-li Liu [4] sudid h ivs h coducio ol wih f oudy d sfod io o wih colly ow oudy which is uch sil o hdl. As y-oduc h clssicl Kichhoff s sfoio fo ccouig fo vil coduciviy is divd d ivic oy of h ivs ol soluio wih sc o vil coduciviy is idicd. h i of coly xu icils is slishd o h ig l ovidig soud hoicl foudio fo h Ri s hod d fii l hod EM. A xl solvd y EM is lso giv. Michl J. ilowsi [3] sd h licio of h olyoils fo solvig ivs ol. h h olyoils fo h ff Mhod fo o-sioy h coducio ol. hy hv usd s s fucios i ii El Mhod. Alicio of h olyoils is o duc h od of uicl igio s cod o h clssicl ii El Mhod wih foulio of h ix of sys of uios. o-li Liu d Do- g Zhg [3] discussd wo hods of soluio glid Ri hod d vil-doi EM oh cl of hdlig ols wih uow oudis suggsd. h h sl uicl xls hv sd. h couiol ocss is ui sl d h suls cougig. his viiol och c xdd sighfowdly o 3-D ivs ols s wll s o oh ols i hicl hysics. I h s ol is d o sudy h h disiol ivs si holsic ols o di h uow u u disiuio dislc fucio d hl ssss o u l sufc of hi cgul ojc occuyig h Pg 5

2 Iiol Joul of Ls chology i Egiig Mg & Alid cic IJLEMA Volu VI Issu IV Ail 7 IN gio D: x ; y ; h wih ow oudy codiios. H Mchi-sulo sfos d Llc sfo chius hv usd o fid h soluio of h ol. I h s is d o sudy h hoicl soluio fo holsic ol o di h u disiuio dislc d sss fucios of hollow cylid wih oudy codiios occuyig h sc 3 / D { x y R : x y h} wh x y. A sfo dfid y Zglich l. [] is usd fo ivsigio which is gliio of Hl s doul diio fii sfo d usd o h ol wih diio y oudis codiios. II.PROBLEM ORMLAION osid hollow cylid s show i h figu. h il of h cylid is isooic hoogous d ll ois ssud o cos. ssu h h cylid is of sll hicss d is oudy sufcs i cio f. h iiil u of h cylid is h s s h u of h suoudig diu which is cos. h dislc fucio sisfyig h diffil uio s Khogd [9] is wih d wh d Poisso io d li coffici of hl xsio of h il of h cylid scivly d is h hig u of h cylid i sisfyig h diffil uio s Khogd [9] is g wh κ K / ρc is h hl diffusiviy of h il of h cylid K is h coduciviy of h diu c is is scific h d is is cloific cciy which is ssud o cos scivly sujc o h iiil d oudy codiios M fo ll 4 M f fo ll 5 M f fo ll 6 3 M H uow 7 M fo ll 8 M fo ll 9 ig: M f s f f s wh h i ^ dos diffiio wih sc o diio coss d o h cuvd sufcs of h l scivly. h dil d xil dislc d sisfy h ucould holsic uio s Khogd [9] wh ˆ 3 4 h sss fucios giv y 5 i o 6 wh i d o h sufc ssu ssud o uifo ov h oudis of h cylid. h sss fucios xssd i s of h dislc coos y h followig lios s Khogd [9] igu : oy of h ol Pg 6

3 Iiol Joul of Ls chology i Egiig Mg & Alid cic IJLEMA Volu VI Issu IV Ail 7 IN Pg wh / is h L s cos is h sh odulus d h dislc coos. Euios - cosiu h hicl foulio of h ol ud cosidio III. OLION O HE O HE PROBLEM Alyig sfo dfid i [9] o h uios 3 4 d 6 ov h vil hvig wih sods o h oudy codiios of y 5 d ig oui cosi sfo o ois d * wh coss ivolvd * s oid y usig oudy codiios 6. illy lyig h ivsio hos of sfo dfid i [9] d ivs Llc sfo y s of colx coou igio d h sidu ho o ois h xssios of h u disiuio d uow u gdi H fo hig ocsss scivly s si d si H d 3 h h oos of h scdl uio u is h sfoio s dfid i dix is h oui si sfo. IV. DIPLAEMEN AND RE NION usiuig h vlu of u disiuio fo i uio o ois h holsic dislc fucio s si d 4 sig 4 i h uios d o ois si si d 5 cos d 6 usiuio h vlu of 6 7 i 7 o o ois h sss fucios s si d si si

4 Iiol Joul of Ls chology i Egiig Mg & Alid cic IJLEMA Volu VI Issu IV Ail 7 IN Pg 8 d 7 si d si si d 8 si d si si d 9 cos d 3 V. PEIAL AE 3 Alyig fii Mchi-Zglich sfo dfid i [9] o h uio 3 o ois 3 usiuig h vlu of 3 i h uios o 3 o ois si d 33 si H d 34 VI. NMERIAL REL DIION AND REMARK o i h uicl couio w cosid il ois of low co sl AII 9 which c usd fo diu duy shfs suds is disiuo cs c shfs d uivsl jois hvig chicl d hl ois ] / 3.97[ s.9 ] /.9 [ 5 K d /.7 4. ig h hysicl wih 5. 3 d 5 h sc. VII. ONLION I his w odify h cocul id oosd y Khogd l. [9] fo hollow cylid d h u disiuios dislc d sss fucios o h cuvd sufc occuyig h gio of h cylid hv oid wih h ow oudy codiios. dvlo h lysis fo h u fild y ioducig h sfoio dfid y Zglich l fii oui cosi sfo chius wih oudy codiios of diios y. h sis soluios covg ovidd w suffici u of s i h sis. ic h hicss of cylid is vy

5 Iiol Joul of Ls chology i Egiig Mg & Alid cic IJLEMA Volu VI Issu IV Ail 7 IN sll h sis soluio giv h will dfiily covg. Assigig suil vlus o h s d fucios i h sis xssios c div y icul cs. h u dislc d hl ssss h oid c lid o h dsig of usful sucus o chis i giig licios. APPENDIX ii Mchi-Zglich Igl sfo: h fii Mchi-Zglich igl sfo of f is dfid s f f d A wh d h coss ivolvd i h oudy codiios f f d f f fo h diffil uio f f / f f is h sfo of f wih sc o l d wigh fucio h ivsio of uio A is giv y f f [ ] wh l fucio c dfid s J [ Y Y ] d Y [ J J ] d J d Y Bssl fucio of fis d scod id scivly. OPERAIONAL PROPERY: f / f / f d f f f f f / AKNOLEDEMEN h uhos hful o ivsiy oissio Nw Dlhi fo ovidig il ficil ssisc ud Mio Rsch Pojc ch. REERENE [] Dg K; Khogd N d Dug M H : hl sss of fii lgh hollow cylid du o h gio I. J. of Pu d Al. Mhs [] h d Khogd N : si holsic Pol of A i-ifii ylid wih H oucs Joul of isics d Mhics Vol. 3 Issu BIO INO Pulicio. [3] o-li Liu d Do-g Zhg.: Nuicl hods fo ivs ol of h coducio wih uow oudy sd o viiol icils wih vil doi Joul of hl cic Volu Nu [4] o-li Liu: A ovl viiol foulio of ivs ol of h coducio wih f oudy o ig l Joul of hl cic Volu 5 Nu [5] Khogd N 3: hl ssss of hollow cylid wih diio y codiios I. J. of Egg. Ad Ioviv chology vol. 3 Issu [6] Khogd N 3: holsic lysis of solid cicul cylid I. J. of Egg. Ad Ioviv chology vol. 3 Issu [7] Khogd N 3: holsic lysis of hic hollow cylid wih diio codiios I. J. of Egg. Ad Ioviv chology vol. 3 Issu [8] Khogd N d Pil V: o Ascs of holsic Pols o Diff olids LAP LAMBER Acdic Pulishig y IBN: [9] Khogd N : o holsic Pols o ylid LAP LAMBER Acdic Pulishig y IBN: [] Khogd N : holsic Pols o icul Pl d Aul Disc LAP LAMBER Acdic Pulishig y IBN: [] L N K d Khogd N : Igl sfo hods fo ivs ol of h coducio wih ow oudy of hi cgul ojc d is ssss ocsss Joul of hl cic Volu Nu [] Michl J ilowsi d Adj ącowi.: oluio of h sioy D ivs h coducio ol y ff hod Joul of hl cic Volu Nu [3] Michl J ilowsi.: Nw y of sic fucios of EM i licio o soluio of ivs h coducio ol Joul of hl cic Volu Nu [4] Nod N; Hsi R B d igw Y: hl sss scod diio ylo & cis Nw Yo 3 6. [5] Xijig Li Hog u Jigwi Zhou d Qu H.: lculio o of uicl soluio fo oudy-vlu ivs h coducio ol Joul of hl cic Volu 5 No [6] Yoo Hw hoi; Yo o L; Kwg hoi; Dog H Doh d Kyoug Joo Ki: u disiuio d hl ssss i vious codiios of ovig hig souc duig li hig ocss Joul of hl cic Volu Nu Pg 9