A TRANSIENT HEAT CONDUCTION PROBLEM OF SEMI-INFINITE SOLID CIRCULAR CYLINDER AND ITS THERMAL DEFLECTION BY QUASI-STATIC APPROACH

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1 Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl RNSIEN HE CONDUCION PROBLEM O SEMI-ININIE SOLID CIRCULR CYLINDER ND IS HERML DELECION BY QUSI-SIC PPROCH * G.D. Kd d K.C. Dshmukh Dpm of Mhmics Kml Nhu Mhvidyly Ngpu Mhsh Idi Dpm of Mhmics RM Ngpu Uivsiy Ngpu Mhsh Idi *uho fo Cospodc BSRC his pp dls wih si h coducio poblm d dmiio of qusi-sic hml dflcio of smi-ifii solid cicul cylid subjcd o biy iiil h supply o h low sufc wih h cuvd sufc hvig o h flux. h umicl clculios hv b cid ou fo copp cylid d illusd gphiclly. Ky Wods: hml dflcio H Coducio Poblm Qusi-Sic d Smi-Ifii Cylid INRODUCION Hig of h vious ps of h mod mchis ks plc. Hig of hs ps cuss h dvlopm of h ssss i h body. Du o his body gs dfomd ud h hml ffcs. h pdicio of hs msus is possibl by solvig h coducio poblm by pdicio soluio mhod d sudyig hmolsic bhvio of h mllic bodis of y shp. Nowcki (957) hs dmid sdy-s hml ssss i cicul pl subjcd o xisymmic mpu disibuio o h upp fc wih o mpu o h low fc d h cicul dg. uh Roy Choudhui (97) hs succdd i dmiig h qusi-sic hml ssss i hi cicul pl subjcd o si mpu log h cicumfc of cicl ov h upp fc wih low fc o mpu d h fixd cicul dg hmlly isuld. Wkhd (98) dmid hml ssss i hi cicul pl subjcd o biy iiil mpu o h upp fc wih low fc o mpu d fixd cicul sufc hmlly isuld. Roy Choudhui (973) discussd hml dflcio of hi clmpd cicul pl du o mp-yp hig of cocic cicul gio of h upp fc wh low fc of h pl ws kp o mpu whil h cicul dg is hmlly isuld. Rcly Dshmukh l. (9) dmid qusi-sic hml dflcio of hi clmpd cicul pl du o h gio wihi i. Vy cly Dshmukh l. () solvd ivs h coducio poblm i smi-ifii cicul pl d is hml dflcio by qusi-sic ppoch. Kd l. () dmid hml ssss i smi-ifii solid cicul cylid subjcd o biy iiil h supply o h low sufc wih h cuvd sufc isuld. I his ps pp o modifis h poblm of Kd l. () d dls wih h dmiio of qusi-sic hml dflcio wh h ou dg of h cylid is fixd d clmpd (buil-i dg). h soluio of h coducio quio is obid i h sis fom i ms of Bssl s fucios. Mhmicl modl hs b cosucd wih h hlp of umicl illusio. his poblm is pplicbl i h fild of mchicl giig fo h hig of cylidicl ods i mchis. No o hs sudid such yp of poblm pviously d i is w coibuio o h fild of hmolsiciy. omulio of h Poblm Cosid smi-ifii solid cicul cylid of dius d. L h low sufc b subjcd o biy iiil mpu d cuvd boudy sufc is o h flux. Ud hs mo lisic pscibd codiios h qusi-sic hml dflcio i h cylid quid o b dmid.

2 Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl h mpu of h cylid im sisfis h quio () wih boudy codiios fo () fo (3) fo () Wh is h hml diffusiviy of h mil of h cylid. ollowig h pocdu Roy Choudhui (973) h diffil quio sisfyig h dflcio W sd s fucio W M D Wh D is h flxul igidiy d M cylid. h hml mom d flxul igidiy dfid s (5) is h hml mom of h smi-ifii M E d (6) 3 Eh D (7) Wh E d Youg s modulus Poisso s io d li coffici of hml xpsio of h mil. o buil-i dg h dflcio W d is fis diviv wih spc o h dius o h boudy sufc mus b o. W W (8) Iiilly W (9) Soluio o ssums h o obi h xpssio fo mpu f () Wh... h posiiv oos of h scdl quio d x Bssl s fucio of fis kid d of od d h fucio c b dmid. Equios () d () giv f () is h Wh is cos which c b foud fom h u of h mpu h low sufc of h cylid. hus h xpssio of h mpu bcoms

3 Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl 3 () Usig codiio (6) i quio () o obis (3) Usig h ohogol popy of Bssl s fucios o gs d () Hc h mpu disibuio i h cylid is obid s d (5) Usig mpu disibuio fom quio (5) i quio (6) h xpssio fo hml mom c b obid s d M (6) Hc d M (7) ccodig o h boudy codiios s miod i quio (8) o c ssum h C W (8) C W (9) Hc kig h xpssio fo hml mom i cosidio (6) o obis hml dflcio usig lio (5) s d W () Wh 3 h () NUMERICL CLCULIONS h umicl clculios hv b cid ou fo copp cylid wih h followig mil popis. Mil popis hml diffusiviy 6.3 s m Poisso io 35. Coffici of li hml xpsio K Lmé cos Rdius of h cylid m

4 Dflcio W() Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl High of cylid Roos of scdl quio h m h fis oos of scdl quio d o cosuc h mhmicl hmolsic bhvio of smi-ifii cicul cylid w s h fucio h mximum dflcio is obsvd h c of h cylid d i gos o dcsig owds ou sufc d bcoms gligibl f dius. 8 m s show i igu. lso h mximum cl dflcio is obsvd fo h im d i is obsvd h h dflcio moooiclly dcss wih spc o im s show i igu Rdius (m) igu : Dflcio log dius s.

5 Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl igu shows h mpu disibuio cicul lvl fo wih spc o im. h mpu is high h c d moooiclly dcss log dil dicio owds ou sufc of h cylid s show i igu 3. Sic h upp sufc is miid o mpu h h flux c b obsvd blow h lvl of oly d h f i mis s such fl o. CONCLUSION Wkhd (98) dmid mpu disibuio i hi cicul pl subjcd o biy iiil h supply o h upp fc wih low fc o mpu d fixd cicul sufc hmlly isuld. I his pp w xdd h wok of Wkhd (98) fo smi-ifii cicul cylid subjcd o biy iiil h supply i h fom of o h low sufc d dmid h hml dflcio d obsvd h i icss pidly o high h c d gdully dcss owds ou sufc of h cylid s i is buil-i dg. W cosid biy iiil h supply jus 5

6 Iiol oul of Physics d Mhmicl Scics ISSN: 77- (Oli) Oli Iiol oul vilbl hp:// Vol. () Ocob-Dcmb pp.-6/kd d Dshmukh Rsch icl lik bu low sufc of solid which is mo lisic du o which cl dflcio is high d gdully i go o dcsig wih im. Du o biy iiil h supply mpu gos dow wih spc o im bu is of coolig is slow d i is obsvd h dflcio dcss lily wih im. REERENCES Dshmukh KC Wbh SD Kd GD d Kulki VS (). Ivs H Coducio Poblm i Smi-Ifii Cicul Pl d is hml Dflcio by Qusi-Sic ppoch. pplicios d pplid Mhmics: Iiol oul (M) 5() -7. Dshmukh KC Wbh SD d Kulki VS (9). Qusi-sic hml dflcio of hi clmpd cicul pl du o h gio. oul of hml Ssss Kd GD Wbh SD Dshmukh KC d Kulki VS (). hml ssss i smi-ifii solid cicul cylid. Iiol oul of pplid Mhmics d Mchics 8() Oisik MN (968). Boudy vlu poblms of h coducio (Iiol xbook Compy Sco Psylvi) Roy Choudhui SK (97). o o h qusi-sic sss i hi cicul pl du o si mpu pplid log h cicumfc of cicl ov h upp fc. Bull. cd. Polo. Sci. S. Sci. ch... Roy Choudhuy SK (973). o o h qusi-sic hml dflcio of hi clmpd cicul pl du o mp-yp hig of cocic cicul gio of h upp fc. oul of kli Isiu 96(3) 3-9. Wkhd PC (98). O h qusi-sic hml ssss i cicul pl. Idi oul of Pu pplid Mhmics 3() Nowcki W (957). h s of ssss i hick cicul pl du o mpu fild. Bull. cd. Polo. Sci. S. Sci. ch