Module 7: Solved Problems
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1 Mdule 7: Slved Prblems 1 Denzed water flws trug te nner tube f 30-mm dameter n a tn-walled nentr tube eat exanger f 019-m lengt Ht press water at 95 flws n te annulus frmed wt te uter tube f 60-mm dameter e denzed water s t be eated frm 40 t 60 at a flw rate f 5 kg/s e term pysal prpertes f te fluds are: kg/m3 p (J/kgK k(w/mk Ns/m pr DEIONIZED WAER PROESS WAER (a nsderng a parallel-flw nfguratn f te eat exanger determne te mnmum flw rate requred fr te t press water (b Determne te verall eat transfer effent requred fr te ndtns f part a ( nsderng a unter flw nfguratn determne te mnmum flw rate requred fr te t press water Wat s te effetveness f te exanger fr ts stuatn?
2 Semat: =95 Press water =40 Δ 1 m =5kg/s 0 Denzed water 0 =60 x nentr tube PFL=019m D=30mm Assumptns: (1 Neglgble eat lss t surrundngs ( Neglgble knet and ptental energy anges Analyss: (a frm verall energy balanes q ( m ( ( m ( Fr a fxed term (m wll be a mnmum wen s a mnmum Wt te parallel flw nfguratn ts requres tat = =60 Hene m mn ( m ( ( 5kg / s 4181J / kg K( J / kg K( kg / s (bfrm te rate equatn and te lg mean temperature relatn q UA lm PF lm PF 1 - ln 1
3 And sne Δ =0 Δ lm =0 s tat UA= Sne A=DL s fnte U must be extremely large Hene te eatng annt be amplsed wt ts arrangement ( Wt te F arrangements ṁ wll be a mnmum wen s a mnmum s requres tat s a mnmum s requres tat s a mnmum s requres tat = =40 Hene frm te verall energy balane 5kg / s 4181J / kg K(60 40 K m 181kg / s 4197J / kg K(95 40 K Fr ts ndtn mn = w s led frm t ene =1 mments: Fr te unter flw arrangement te eat exanger must be nfntely lng
4 Water wt a flw rate f 005kg/s enters an autmble radatr at 400K and leaves at 330 K e water s led by ar n rss flw w enters at 075kg/s and leaves at 300K If te verall eat transfer effent s 00W/m K wat s te requred eat transfer surfae area? Semat: Water =400K m =005kg/s Ar =300K m =075kg/s =330K Assumptns: (1 Neglgble eat lss t surrundngs and knet and ptental energy anges ( nstant prpertes Analyss: e requred eat transfer rate s q ( m ( 005kg / s(409j / kg K 70K 14 73W Usng te -NU metd
5 mn 1045W / K 7555W / K ene mn / ( 1045W / K(100K 1045W and q / q 1473W / 1045W 0700 Frm fgure NU15 ene A NU( m mn / U W / K(00W / m K 1 58 mments: (1 te ar utlet temperature s q / 300K (1473W / 7555W / K 319 5K ( Usng te LMD appra Δ lm =51 K R=079 and P=07 Hene frm fg F095 and A q / FUlm (1473W /[095(00W / m K 51K ] 151m
6 3 Saturated steam leaves a steam turbne at a flw rate f 15kg/s and a pressure f 051 bars e vapr s t be mpletely ndensed t saturated lqud n a sell-and tube eat exanger w uses water as te lant e water enters te tn-walled tubes at 17 and leaves at 57 If te verall eat transfer effent f 00W/m K determne te requred eat exanger surfae area and te water flw rate After extended peratn fulng auses te verall eat transfer effent t derease t 100W/m K Fr te same water nlet temperature and flw rate wat s te new vapr flw rate requred fr mplete ndensatn? Semat: Assumptns: (1 Neglgble eat lss t surrundngs ( Neglgble wall ndutn resstane Prpertes: able fr satwater: ( 310K : p 4178J / kg K;(p 051 bars : sa 355K 304kJ/kg t fg Analyss: (a e requred eat transfer rate s q m fg 6 15kg / s(30410 J / kg W And te rrespndng eat apaty rate fr te water s
7 mn q /( W / 40 K 86400W / K ene q /( mn [ 6 ] W / 86400W / K(65K 06 sne mn / 0 NU -ln(1 - ln( And A NU( mn / U 097(86400W / K / 000W / m K 419m m / 86400W / K / 4178J / kg K 07kg / s p (b usng te fnal verall eat transfer effent fnd Sne / 0 mn 1 exp( NU 1 exp( ene q mn ( 0384(886400W / K 65K 16106W m q / fg W 6 / J / kg 0936kg / s mments: e sgnfant redutn (38% n ṁ represents a sgnfant lss n turbne pwer Perd leanng f ndenser surfaes suld be emplyed t mnmze te adverse effets f fulng
8 4 Water at 5 kg/ s t be eated frm 35 t 95 by means f a nentr tube eat exanger Ol at 5kg/ and 10 wt a spef eat f 095 J/kgK s t be used as te t flud If te verall eat transfer effent based n te uter dameter f te nner tube f 550W/m K determne te lengt f te exanger f te uter dameter s 100mm Semat: Assumptns: (1 Neglgble eat lss t surrundngs ( Neglgble knet and ptental energy anges (3 nstant prpertes Prpertes: able fr Water: _ ( (35 95 / 338K : p 4188J / kg K Analyss: Frm rate equatn wt A =D L L=q/U D Δ m e eat rate q an be evaluated frm an energy balane n te ld flud 5kg / q m ( 4188J / kg K(95 35 K 15 W 3600s / In rder t evaluate Δ m we need t knw weter te exanger s peratng n F r PF Frm an energy balane n te t flud fnd q / m 10 5kg / J 15705W / s / kg K 901
9 Sne < t fllws tat HXer peratn must be F Frm eq fr lg mean temperature dfferene 1 (10 95 ( m F 81 5 n / n(115 / 551 ( 1 Substtutng numeral values te HXer lengt s L 15705W / 550W / m K (010m 814K 1 1m mments: e NU metd uld als be used It wuld be neessary t perfrm te t flud energy balane t determnng F peratn exsted e apaty rate s mn / =050 Frm eq fr effetveness and frm wt q evaluated frm an energy balane n te t flud =10 Δ1 =901 Δ =95 =35 1 x Frm fg fnd NU15 gvng L NU W W / U D (010m 1 14m K m K mn Nte te gd agreement by bt metds
10 5 nsder a very lng nentr tube eat exanger avng t and ld water nlet temperatures f 85 and 15 e flw rate f te t water s twe tat f te ld water Assumng equvalent t and ld water spefes eats; determne te t water utlet temperature fr te fllwng mdes f peratn (a unter flw (b Parallel flw Semat: =15 =85 = Assumptns: (1 equvalent t and ld water spef eats ( Neglgble Knet and ptental energy anges (3 N eat lss t surrundngs Analyss: te eat rate fr a nentr tube Heat exanger wt very large surfae area Operatng n te unter flw mde s q q mn ( mbnng te abve relatn and rearrangng fnd mn ( ( Substtutng numeral values
11 (85 1 Fr parallel flw peratn te t and ld utlet temperatures wll be equal; tat s = Hene ( ( Settng = and rearrangng / / mments: Nte tat wle =1 fr F peratn fr PF peratn fnd = q/q =067
12 6 A nentr tube eat exanger uses water w s avalable at 15 t l etylene glyl frm 100 t 60 e water and glyl flw rates are ea 05 kg/s Determne te mum pssble eat transfer rate and effetveness f te exanger Determne w s preferred a parallel flw r unter flw mde f peratn? Knwn: Inlet temperatures and flw rate fr a nentr tube eat exanger Fnd: (a Maxmum pssble eat transfer rate and effetveness (b Prffered mde f peratn Semat: UA Etylene glyl =100 =60 m =05kg/s Water =15 m =05kg/s Assumptns: (1 Steady-state peratn ( Neglgble KE and PE anges (3 Neglgble eat lss t surrundngs (4 Fxed verall eat transfer and effent Prpertes: able: Etylene glyl ( n 80; p=650j/kgk; Water( _ 30 : 4178J / kg K m p Analyss: (a Usng te -NU metd fnd _ mn m p (05kg / s(650j / kg K 135W / K q ma x mn ( (135W / K ( W
13 5 q m p ( 05kg / s(650j / kg K ( W q / q (b / q kg / s 4178J / kg K m p Sne < a parallel flw mde f peratn s pssble Hwever wt ( mn / = ( / m =063 m p Frm fg (NU PF 095 (NU F 075 Hene (A F /A PF = (NU F/ (NU PF (075/095=079 Beause f te redued sze requrement ene aptal nvestment te unter flw mde f peratn s preferred p
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