OUTCOME 1 - TUTORIAL 1

Transcription

1 Un 42: Hea Transfer and Cmbusn Un cde: K/601/1443 QCF level: 5 Cred value: 15 OUTCOME 1 - TUTOIAL 1 1 Hea ransfer raes Inerfaces: cnducn (Furer s law, hermal cnducvy, hermal ressance, emperaure graden, cmpse plane walls and hck cylnders); cnvecn (descrpn f frced and naural cnvecn, cnvecve hea ransfer ceffcen, flm and verall ceffcen) adan: naure f radan; Sefan-Blzman law; black and grey bdy radan; emssvy; absrpvy; crrecn fr verall hea ransfer ceffcen Laggng: maeral ypes; cnducvy; energy css; ecnmc laggng Yu shuld judge yur prgress by cmpleng he self assessmen exercses. On cmplen f hs ural he suden shuld be able d he fllwng. Explan seady and nn-seady hea ransfer. Explan Furer s equan fr cnducn. Explan he analgy wh elecrcal ressance. Calculae he hermal ressance fr fla, cylndrcal and sphercal layers. Calculae he hermal ressance fr cmpund layers. Slve hea ransfer prblems fr he abve. D.J.Dunn 1 1

2 CONDUCTION INTODUCTION Hea exchangers are used n s many felds f engneerng frm cenral heang sysems large ndusral blers, frm sugar refnng l dsllan, frm refrgerars ar cndners and s n. The ls s endless. The desgn f suable uns s based n hery and emprcal daa and hs cvers a vas range f wrk. The purpse f hese urals s prvde he basc level f undersandng and sme advanced hery fr anyne sudyng he pc frm begnner s level. The ural nly cvers seady sae hea ransfer. Mre advanced sudes f cnducn wll enable yu sudy he fllwng pcs. NON STEADY HEAT TANSFE Ths ccurs when he emperaure n a maeral s changng wh me. Calculang he emperaure a any pn s beynd he scpe f hs ural. THEE DIMENSIONAL HEAT TANSFE When a blck f maeral s mananed a cnsan bu dfferen emperaures n all s faces, a seady flw f hea may be prduced a each face bu he emperaure a any gven pn n he blck s dffcul fnd and s als beynd he scpe f hs ural. CONDUCTION THEOY Hea ransfer ccurs frm ne bdy anher by hree mehds, cnducn, cnvecn and radan. Ms hea exchangers wll use elemens f all hree. A ne amun f hea s always ransferred frm he her bdy he clder bdy. Ths ural cvers cnducn, he prcess by whch hea s passed n hrugh slds, lquds and gasses frm ne mlecule anher. Hea r mre crrecly, nernal energy s bascally he knec energy f he mlecules vbrang r mvng arund n he maeral. The knec acvy ncreases as he emperaure s rased. If he maeral s all a ne unfrm emperaure, he knec mn s unfrm. When a h maeral cmes n cnac wh a clder maeral, he knec acvy s passed n hrugh cnac and he ransfer f mmenum beween he faser mvng mlecules and he slwer mvng mlecules s he clder maeral becmes her. Ths s he bass f cnducn. D.J.Dunn 2

3 FOUIE S CONDUCTION LAW Cnsder a fla sld maeral f hckness and surface area A. The surface emperaure n he h sde s h n he cld sde c. Hea wll flw frm ne sde he her a a rae f Was. The hea ransfer s drecly prprnal he emperaure dfference Δ and he area A. I s nversely prprnal he hckness snce he hcker s, he less he hea ransfer. I als depends n he maeral. Clearly cpper cnducs hea much beer han cncree s we need a prpery called he Thermal Cnducvy and hs s usually gven he symbl k. I fllws ha k A Δ k A c h k A h c The uns f k are Was/m K Here are sme ypcal values f k fr cmmn maeral a amben cndns. Maeral Alumnum Cpper Seel Cncree Glass Wd Waer Ar k W/m K WOKED EXAMPLE N. 1 Calculae he hea ransfer hrugh a fla cpper plae 200 mm all by 300 mm wde and 25 mm hck when he surface emperaures are 150 C and 55 C. k A 385 x 0.2 x h c W D.J.Dunn 3

4 ELECTICAL ANALOGY AND SIGN CONVENTION If we make he analgy ha s equvalen elecrc curren I and Δ s equvalen vlage ΔV, we may make an analgy wh Ohm s law ΔV Δ Elecrcal essance Thermal essance I k A We shuld ne ha Δ and ΔV are bh srcly negave quanes because Δ means he las fgure mnus he frs fgure s Δ = ( c h ). If we sck hs, we mus pu a mnus sgn n frn f he prevus equans. If we smply le Δ represen he emperaure dfference Δ = ( h c ) and remember ha hea flws frm h cld, we wll have n dffculy slvng basc prblems. CALCULUS FOM In realy, he emperaure drps n he drecn f hea flw s f we measure he dsance frm he h sde as x, he hea flw hrugh a very hn layer hckness dx wll be:- d k A dx Ths s mpran when analysng nn-seady flw cnducn and n he fllwng wrk. CONDUCTION THOUGH A TUBE Cnsder hea flwng frm he nsde f a ube he usde a a seady. Ths s he same a all rad. The hea flwng hrugh an elemenary layer f radus r and k A d k 2 π L r d lengh L s dx dr dr 2 π kl d earrange ge r Nw negrae beween lms. dr r 2π kl 2π kl d 2π kl r 2 π k L 2 π k L WOKED EXAMPLE N. 2 Calculae he hea ransfer hrugh a cpper ube 5 m lng wh nner dameer 80 mm and uer dameer 100 mm. The nsde emperaure s 200 C and he usde emperaure s 70 C. 2 π k L D.J.Dunn π x 385 x W

5 CONDUCTION THOUGH A HOLLOW SPHEE The dervan s smlar ha fr a ube. The surface area f a sphere s 4πr 2 2 k A d 4 π r k d dx dr dr 4 π k d earrange ge 2 r Nw negrae beween lms. dr 1 4 π k r 2 4 k d r π k 4 π k -1-1 WOKED EXAMPLE N. 3 A sphercal seel reacn vessel has an uer radus f 1.5 m and s cvered n laggng 200 mm hck. The hermal cnducvy f he laggng s 0.1 W/m K. The emperaure a he surface f he seel s 340 C and he surface emperaure f he laggng s 45 C. Calculae he hea lss. 4 π x kw SELF ASSESSMENT EXECISE N Calculae he hea lss hrugh fla shee f glass 2 m x 1 m and 5 mm hck when he surface emperaures are 20 C and 5 C. (Answer 6 kw) 2. A seam ppe has an exernal dameer f 75 mm and s cvered wh laggng 25 mm hck wh a hermal cnducvy f 0.09 W/m K. The surface emperaure f he laggng s 300 C n he nsde and 80 C n he usde. Calculae he hea lss per mere lengh. (Answer W/m) 3. A seel ppe has an nner dameer f 50 mm and uer dameer f 100 mm. The usde emperaure s 400 C and he nsde emperaure s 120 C. The hermal cnducvy 60 W/m K. Calculae he hea flw frm he usde he nsde fr 1 m lengh. (Answer kw/m) 4. A sphercal vessel 2 m dameer s lagged a deph f 300 mm. The hermal cnducvy f he laggng s 0.1 W/m K. The emperaure f he nsde and usde f he laggng s 180 C and 40 C respecvely. Calculae he hea lss. (Answer W) D.J.Dunn 5

6 COMPOUND LAYES If hea s cnduced hrugh a cmpund layer, he prblem s analgus elecrcy flwng hrugh a seres f ressrs. Cnsder a fla wall made up f hree layers f dfferen maerals A, B and C as shwn. The hea ransfer rae s he same hrugh each layer. Usng he hermal ressance we have: a A h 2 A 2 h A ka A b B 2 3 B 3 2B h A B k b A c C 3 c A k c A c 3 C h A B C c h A B C h c h c A B C All we need d s calculae he ressance f each par and add hem up. Δ Cylndrcal layers -1-1 Δ Sphercal layers 2 π k L 4 π k OVEALL HEAT TANSFE COEFFICIENT When we have cmpund layers (hs may als nclude cnvecn), s cnvenen use he equan = - U A Δ where U s he verall hea ransfer ceffcen and Δ s he emperaure change acrss he enre layer. Ths wll be cvered and used n he fllwng urals. WOKED EXAMPLE N. 4 A wall wh an area f 25 m 2 s made up f fur layers. On he nsde s plaser 15 mm hck, hen here s brck 100 mm hck, hen nsulan 60 mm hck and fnally brck 100 mm hck. The hermal cnducvy f plaser s 0.1 W/m K. The hermal cnducvy brck s 0.6 W/m K The hermal cnducvy he nsulan s s 0.08 W/m K The nner surface emperaure f he wall s 18 C and he uer s -2 C. Calculae he hea lss and he emperaure a he nerface beween he plaser and he brck Plaser x 10 K/W k1 A 0.1x Brck x 10 K/W k 2 A 0.6 x Insulan 3 30 x 10 K/W k3 A 0.08 x 25 Tal essance = = 49 x 10-3 K/W h c 18 - (-2) W (Answer calculaed wh all memry reaned) x x 10 Temperaure drp ver plaser = 1 = 405 x 6 x 10-3 = 2.43 K Hence he emperaure a he nerface s = C D.J.Dunn 6

7 WOKED EXAMPLE N. 5 A seel ppe 120 mm nsde dameer has a wall 10 mm hck. I s cvered wh nsulan 20 mm hck. The hermal cnducvy f seel s 60 W/m K and fr he nsulan s 0.09 W/m K. The ppe carres seam a 150 C and he uer surface emperaure f he nsulan s 0 C. Calculae he hea lss per mere lengh. Calculae he emperaure a he ppe s uer surface Ppe x 10 K/W 2 π k L 2 π x 60 x Insulan K/W 2 π k L 2 π x 0.09 x 1 Tal ressance =0.445 K/W = Δ/ = (150 0)/0.445 = W Temperaure drp ver ppe wall = = x 10-4 x = K The surface emperaure f he ppe s C Ths llusraes ha a well nsulaed ppe warms up he same emperaure as he flud nsde and s que nrmal neglec he emperaure drp hrugh he meal wall. SELF ASSESSMENT EXECISE N The nsde dmensns f a refrgeraed bx s 2m x 1 m x 1.2 m. I s cvered wh nsulan 50 mm hck and hen a lner 5 mm hck. I s requred exrac 150 W frm he bx. Smplfyng he prblem a plan fla surface calculae he nsde emperaure when he uer surface s mananed a 20 C. The hermal cnducvy f he nsulan s W/m K and 0.2 W/m K fr he lner. (Answer 4.09 C) 2. A nyln ppe has a bre f 50 mm and a wall hckness f 5 mm. I s cvered wh nsulan 10 mm hck. The hermal cnducvy f he nyln s 0.25 W/m K and fr he nsulan s 0.1 W/m K. The nsde f he ppe carres h waer a 50 C and he uer surface f he ppe s a 10 C. Calculae he hea lss per mere lengh and he emperaure beween he w maerals. (Answer 70 W and 41.9 C) D.J.Dunn 7