Cork Institute of Technology. Spring 2005 DCE 3.5 Thermodynamics & Heat Transfer (Time: 3 Hours) Section A

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1 Ck Insttute f echnlgy Bachel f Engneeng (Hnus) n Chemcal and Pcess Engneeng Stage 3 Bachel f Engneeng n Chemcal and Pcess Engneeng Stage 3 (NFQ Level 8) Spng 005 DCE 3.5 hemdynamcs & Heat ansfe (me: 3 Hus) Answe FOUR questns; WO questns fm Sectn A and WO questns fm Sectn B. Use sepaate answe bks f each lectue. Sectn A Examnes: Pf. R. Ocne M. D. O Cnn M. G. Pete M. I. O Sullvan Q. A VLE study s t be undetaken n a methanl () methyl acetate () system at 45 C. Assume that the vapu phase mxtue behaves as an deal gas, but that the lqud mxtue behaves as a nn-deal slutn that s assume the VLE system beys mdfed Rault s Law. ake t that lqud phase nn-dealtes can be adequately mdelled by the celatn: g E x x R B (a) Statng wth the expessn that geneally defnes a patal mla ppety g n t deve ne the f the actvty ceffcent expessns gven belw: lnγ Bx ln γ Bx (0 maks) Gven the fllwng Antne vapu pessue celatns f each cmpnent and a value f the actvty ceffcent paamete B at 45ºC: P sat ln ( ~ K and sat P ~ kpa) P sat ln ( ~ K and sat P ~ kpa)

2 B.07 (-) (b) Gven that the dew-pnt lqud cmpstn s x 0.87, calculate the dew-pnt pessue f the mxtue at 45 C. he ntal supeheated vapu cmpstn s z 0.6. (8 maks) (c) Calculate the bubble-pnt pessue f the mxtue at 45ºC and the cmpstn f vapu phase, gven that the ntal subcled lqud cmpstn s z 0.5. (7 maks) Q. Vaus ppetes f butane as a satuated vapu and a satuated lqud ae needed at 360 K. F enthalpy calculatns use the fllwng efeence state: the deal gas state; tempeatue 5ºC; pessue.035 ba; and set the efeence enthalpy t ze when the gas s n ths hypthetcal state. Assume that the Val EOS accuately celates vapu ppetes. F satuated lqud ppetes use a calculatn ute that s cnsstent wth the Actvty Ceffcent Methd. (a) Calculate the cmpessblty fact, the mla vlume and the mla enthalpy f satuated butane vapu at 360 K. (0 maks) (b) Calculate the mla enthalpy f satuated butane lqud at 360 K. (5 maks) Butane has the fllwng ctcal and the ppetes: Ctcal Pessue Ctcal empeatue 37.9 ba 45.5 K Acentc Fact (-) Satuatn Pessue at 360 K Nmal blng Pnt ( n ) Unvesal Gas Cnstant (R).7 ba 7.65 K kj / kml K he deal gas heat capacty celatn f butane, as a functn f abslute tempeatue (), s gven belw: C g p R (36.95 x 0 3 ) (.40 x0 6 )

3 he fllwng expessn f the esdual enthalpy may be deved fm the tw-tem Val EOS: R h R c P B db d + ω B db d Ptze s genealsed celatn f BPc Rc s gven by: BP R c c B + ωb B B he latent heat f vapusatn (h fg ) may be estmated at the Nmal Blng Pnt ( n ) usng the Redel equatn: ( h fg ) R n n.09(ln P.03) c n Whee (h fg ) n s the mla latent heat at n (kj /kml). n s the Nmal Blng Pnt (K). P c s ctcal pessue (ba). s the educed tempeatue at n n (-). R s the unvesal gas cnstant (kj / kml K). Estmates f h fg at a tempeatue the n can be fund fm Watsn s equatn: ( h ( h fg fg ) )

4 Q3. Sulphu dxde and a ae fed nt an adabatc eact at ba and 98.5 K. ake as the bass f the calculatn kml f SO n the feed and 0% excess a (mla bass). he vapu phase xdatn f SO t SO 3 pceeds n accdance wth the stchmetc eactn gven belw: SO ( g) + O ( g) SO 3( g) (a) Gven the geneal cten f equlbum shwn by equatn (3.) and, assumng that the vapu mxtue behaves as an deal-gas, deve the smplfed cten f equlbum gven by equatn (3.): K Π ( ˆ ν a )..(3.) ν v P Π ( y ) K..(3.) (5 maks) P (b) Assume the fllwng: the eact s at a unfm tempeatue; the ext gases leavng the eact ae n equlbum; the eact tempeatue s K; the eact pessue s 00 kpa. Calculate the equlbum extent f eactn ( ε e ), the cmpstn f the ext gas mxtue leavng the eact and the factnal cnvesn f the lmtng eactant (see belw f all elevant data and equatns). (7 maks) (c) Demnstate hw a heat balance culd be set up t vefy that the eact des ndeed peate adabatcally d nt slve ths heat balance. (3 maks) he mla cmpstn f a s 79% ntgen and % xygen. ake the Standad State Pessue t be 00 kpa. In the equatns belw has unts f (K) and bth I and J ae cnstants f ntegatn: J b c d ln K + a ln I R 6 G R ln K 4

5 H b J + R ( a) + c d Each f the a, b, c, d efe t the elevant a, b, c, d heat capacty cnstants, multpled by the apppate speces stchmetc ceffcent (v ), then summed ve the eactn. he deal-gas heat capacty elatn s gven belw: C R P a + b + c + d Whee s tempeatue (K), R s the unvesal gas cnstant (8.344 kj /kml K). he heat f fmatn (98.5 K), the Gbb s fee enegy f fmatn (98.5 K) and the deal-gas heat capacty cnstants, f each speces, ae all gven n able 3. belw: Cmpnent H f 98 (kj/kml) G f 98 (kj/kml) a b x03 c x06 d x0-5 (SO ) g -96, , (O) g (SO 3 ) g -395,70-37, (N ) g able 3. 5

6 Sectn B Q4. A duble ppe heat exchange s emplyed t heat 5 kg/s f Dwthem A fm 5 C t 65 C usng waste ht wate whch s n tun cled fm 95 C t 75 C. he ht wate flws n the nne tube n cunteflw t the Dwthem, whch flws n the annulus. ncease the effectveness f the heat exchange 3 lngtudnal cabn steel fns ae utlsed. Detemne the length f heat exchange equed t cay ut the equed duty gven the fllwng nfmatn. Inne damete f tube (d ) Oute damete f tube (d ) Inne damete f shell (d S ) Fn heght (H) Fn thckness (W) Wdth f the fn t (W ) mm 48.3 mm 75.0 mm.7 mm 0.89 mm 4.0 mm Dwthem A Wate CabnSteel ρ (kg/m 3 ) C p (J/kgK) λ (W/mK) η (Ns/m ) ν (m /s) κ (m /s) P f { α λ } { α/wλh} tanh / W H η Nu 0.03Re P

7 Q5. A shell and tube heat exchange has the fllwng gemety: Shell ntenal damete Ds m Numbe f tubes N 58 ube O.D. D.54 cm ube I.D. D.0574 cm ube ptch (squae) P 3.75 cm Baffle spacng L B.70 cm Shell Length L S m ube t baffle dametal cleaance tb 0.8 mm Shell t baffle dametal cleaance sb 5.0 mm Bundle t shell dametal cleaance b 35.0 mm Numbe f sealng stps pe css flw w N ss / NC /5 hckness f baffles t b 5 mm Numbe f tubesde passes n 4 Use the Ken methd t calculate the shell sde heat tansfe ceffcent and pessue dp f the flw f a lght hydcabn wth the fllwng specfcatn (at bulk tempeatue). Use the Bell-Delawae methd (wth the ad f Fgue Q5) t calculate the shell sde heat tansfe ceffcent. tal mass flw ate kg/s Densty 730 kg/m 3 hemal cnductvty 0.34 W/mK Specfc heat capacty.470 kj/kgk Vscsty 40 µns/m 7

8 Useful Equatns S L D D D + D P D ( ) OL O m B S OL O P Nu 0.36 Re P Nu 0.Re P ( ) D L D L D L FC π+ sn cs cs π DOL DOL DOL s C S C S C D L Ssb π cs DS S sb C S tb ( + F ) πdo tb N C JC FC Ds SS C'L P B 8

9 Q6. A feeze dyng chambe cnssts f a lng ectangula duct 0.3m n wdth. he mateal beng feeze ded s at a tempeatue f 0ºC and makes up the fl f the duct (suface ). he f f the duct (suface ) s a ht metal plate that s 0.5 m abve the fl, paallel t the fl and at a tempeatue f 350ºC. Heat s beng tansfeed by adatn fm the ht plate t the cld mateal that s beng ded. he walls f the chambe (suface R) ae themally nsulated and can be taken t have a unfm tempeatue. he chambe s lng enugh t gne end effects and any aea calculatns can be dne n a (m / m) bass. An end-elevatn f the chambe s shwn n Fgue 4. belw. Data: ε 0.88 ε 0.0 ε R σ W/ m K 4 (a) Calculate the adant heat tansfe (kw) fm the ht plate t the fzen mateal. (5 maks) (b) Calculate the unfm tempeatue f the sde walls. (0 maks) he vew fact fm the ht plate, wdth w t fzen mateal, sepaatn d s: d F + w d w 9

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