Chapter 4.4: Heat Exchangers

Transcription

1 Sort type Questons Capter 4.4: Heat Excangers 1. Defne effectveness of eat excanger? o Effectveness ( T t ) Were, t t t o Cold flud outlet temperature t Cold flud nlet temperature T Hot flud nlet temperature Cold flud temp.range Inlet temp. dff. of 2. Wat do you mean by eat duty of a eat excanger? ot & cold flud Heat duty of a eat excanger s defned as te eat tat s transferred from ot flud to cold flud per unt tme. 3. Menton 2 basc parameters tat ave to be measured at ste to evaluate te performance of a eat excanger? 1. Hot and cold flud n let and outlet temperatures 2. Mass flow rate of cold and ot fluds 4. Wat do you mean by capacty rato n a eat excanger? R Were, T t o T t o Temp. range of ot flud Temp. range of Cold flud t o Cold flud outlet temperature t Cold flud nlet temperature T Hot flud nlet temperature T o Hot flud outlet temperature 5. Fnd te Overall eat transfer coeffcent for a sell and tube counter flow eat excanger were te eat excanged s GJ/our wt te eat transfer area of 96 m 2. Assume te LMTD as 76 o C. Heat Transfer Co-effcent Overall HTC, U Q/ (A x LMTD) x 10 6 / (3600 x 96 x 76) 0.43 kw/m 2. K 6. Gve te equaton to calculate te Overall eat transfer coeffcent. Heat excanger performance s normally evaluated by te overall eat transfer coeffcent U tat s defned by te equaton UQ/ (A x LMTD) Were Q Heat transferred n kcal/r A Heat transfer surface area n m 2 LMTD Log Mean Temperature Dfference n 0 C U Overall eat transfer Coeffcent kcal/r/m 2 / 0 C Heat excangers (table format) 22

2 7. Gve te equaton to Calculate LMTD for a counter flow eat excanger LMTD Counter current Flow ((T-to) (-t)) / ((T-to)/(-t)) Were, T- Hot flud nlet temperature, t- Cold flud nlet temperature - Hot flud outlet temperature, to- Cold flud outlet temperature 8. Gve te equaton to Calculate LMTD for a parallel flow eat excanger LMTD Parallel Flow ((T-t) (-to)) / ((T-t)/(-to)) Were, T- Hot flud nlet temperature, t- Cold flud nlet temperature - Hot flud outlet temperature, to- Cold flud outlet temperature 9. Wrte te equaton to calculate eat duty for a eat excanger. Heat Duty, Q Wx Cp x (T-)..Eqn-1 Heat Duty, Qc Wx Cpc x ( t-to) 10. Wat do you mean by overall eat transfer coeffcent?...eqn-2 Te rato of eat flux per unt dfference n approac across eat excange equpment consderng te ndvdual coeffcent and eat excanger metal surface conductvty. Te magntude ndcates te ablty of eat transfer for a gven surface. Hger te coeffcent lesser wll be te eat transfer surface requrement Long type questons 1. Explan te followng a) Over all eat transfer coeffcent b) Log mean temp dfference c) Co-current and counter current flow d) Heat duty of eat excanger a) Over all eat transfer coeffcent: Heat excanger performance s normally evaluated by te overall eat transfer coeffcent U tat s defned by te equaton QU x A x LMTD Were Q Heat transferred n kcal/r A Heat transfer surface area n m 2 LMTD Log Mean Temperature Dfference n 0 C U Overall eat transfer Coeffcent kcal/r/m 2 / 0 C Wen te ot and cold stream flows and nlet temperatures are constant, te eat transfer coeffcent may be evaluated usng te above formula. It may be observed tat te eat pck up by te cold flud starts reducng wt tme. b) Log mean temp dfference Heat excangers (table format) 23

3 a) Counter current Flow b) Co-current flow T T to t t to LMTD Counter current Flow ((T-to) (-t)) / ((T-to)/(-t)) LMTD Co current Flow ((T-t) (-to)) / ((T-t)/(-to)) c) co current and counter current flow If te flow of ot and cold fluds s n te same drecton ten te flow s descrbed as co current flow. If te flow s n opposte drecton ten t s called as counter current flow. d) Heat duty of eat excanger Te capacty of te eat excanger equpment expressed n terms of eat transfer rate, vz. magntude of energy or eat transferred per tme. It means te excanger s capable of performng at ts capacty n te gven system. 2. Explan wt equatons te procedure for calculatng te overall eat transfer co-effcent for eat excangers 1. Heat Duty, Q qs + ql qs s te sensble eat and ql s te latent eat qs Wx Cp x(t- )/1000/3600 (or) qs w x Cpc x (to-t)/1000/3600 ql W x λ, n kw λ Latent eat of Condensaton of a ot condensng vapour (or) w x λ c, λ c - Latent eat of Vaporzaton 2. Hot Flud Pressure Drop, P P Po 3. Cold flud pressure drop, Pc p- po 4. Temperature range ot flud, T T- 5. Temperature range cold flud, t to t 6. Capacty rato, R W x CP / w Cpc (or) (T- ) / (to- t) 7. Effectveness, S (to- t) / (T t) 8. LMTD a) Counter current Flow b) Co-current flow T T to t t to Heat excangers (table format) 24

4 LMTD Counter current Flow ((T-to) (-t)) / ((T-to)/(-t)) LMTD Co current Flow ((T-t) (-to)) / ((T-t)/(-to)) b) Correcton factor for LMTD to account for Cross flow 1 / 2 1 SR (R + 1) x 1 S F 1 / 2 2 S(R +! (R + 1) (1 R) x 1 / 2 { 2 S(R + 1) + R + 1 } ( ) 9. Corrected LMTD F x LMTD 10. Heat Transfer Co-effcent U Q / (A x Corrected LMTD) Numercal type questons 1. In a double ppe eat excanger ot flud s enterng at 220 C and leavng at 115 C. Cold flud enters at 10 deg c and leaves at 75 C. Mass flow rate of ot flud 100 kg/r, cp of ot flud 1.1 kcal/kg C. Cp of cold flud 0.95kcal/kg C. Calculate LMTD ) If te flow s parallel ) If te flow s counter current. ) Fnd te mass flow rate of cold flud f te eat loss durng te excange s 5%.. LMTD Parallel flow t2 LMTD t2 210 C t2 40 C LMTD C LMTD Counter current flow 145 C t2 105 C Heat excangers (table format) 25

5 LMTD t2 t C. Mass flow rate of cold flud Data: m. Mass flow rate of ot flud 100 kg/r cp. 1.1 kcal/kg C CPC 0.95 kcal/kg C Cold flud nlet temperature 10 C Cold flud outlet temperature 75 C Hot flud nlet temperature 220 C Hot flud outlet temperature 115 C Q m. xcp X t x 0.95 m c x CPC x t c Mass flow rate of cold flud m c m cp cp T x x t c x 1.1 x( )x x (75 10) kg/r 2. Wen a eat excanger was desgned ts overall eat transfer co-effcent was 600 kcal/r mt² C. Te eat transfer area provded 10mt². Over a perod of tme, ts overall eat transfer coeffcent as fallen to 450 kcal/r mt² C due to foug. Data: Specfc eat of ot flud 1 kcal/kg C Hot flud enterng temperature 80 C Hot flud leavng temperature 60 C Cold flud enterng temperature 25 C Cold flud leavng temperature 40 C Calculate: How muc addtonal area s to be added to mantan te same rate of eat transfer? Assumpton: Flow s assumed n counter current drecton Q A U T LM t2 T LM t C Heat excangers (table format) 26

6 T 1 40 C T 2 35 C Q 10 X 600 X kcal/r After foug area requred A 13.3 mt 450 X Addtonal eat transfer area to be provded s 3.3 m2 3. An after cooler of sell and tube type wt sngle pass s used for coog compressed ar from 85 o C to 35 o C. Te compressed ar generated s 1350 m 3 / at mean ar temperature. Calculate: 1) Te amount of coog water to be crculated at a temperature of 30 o C. Assume te coog water outlet temperature as 35 o C. 2) Te LMTD and no of tubes f te da of te tube s 25.4 mm and 2500 mm lengt. Assume overall eat transfer coeffcent for ar to water s 150 W/m 2.K. 3) Te p of te pump requred f te pressure requred s 3.5 kg/cm 2.g. Indcate all assumptons clearly. Ans: 1) Inlet compressed ar temperature 85 o C Ext compressed ar temperature 35 o C Coog water temperature 30 o C Coog water outlet temperature 35 o C Densty of ar at 60 o C 1.06 kg/m 3 Mass of compressed ar 1350 x kg/r Specfc eat of water at 30 o C kj/kg o K Heat duty: Hot flud: m Cp deta.t 1431 x x ( 85-35)/ kw Mass of water to be crculated /(4.178 x (35-30) 3442 kg/r (Ans) 2) LMTD ( 85 35) (35 30) In (50/5) o C ( Ans) Heat transfer area /( 0.15 x 19.54) 6.81 m 2 No of tubes 6.81/ ( 3.14 x x 2.5 ) 35 tubes ( Ans) 3) Teoretcal power requred for te pump 3442 x 9.81 x 35 / ( 3600 x 1000 ) 0.33 kw Assumng pump effcency of 70% and motor effcency of 85%, te requred pump Motor power 0.33/ (0.7 x 0.85) kw Heat excangers (table format) 27

7 Motor requred 1 p (Ans) 4. Hot ar s to be generated at te rate of 30,000 m 3 / at C from 35 o C for pocket ventlaton purpose n a g speed paper macne. Steam s used n ndrect eat excanger steam cols to produce ot ar at 120 o C. Steam s avalable at a pressure of 5.0 bar at te user sde eader. Fnd out te quantty of steam requred. Calculate LMTD. Data: tal entalpy of steam at 5 bar 2757 kj of kg Latent eat of steam at 5 bar 2086 kj/kg Note: Assume tat condensate s leavng at a temperature of 100 C. Inlet ar temperature 35 o C Outlet ar temperature 120 o C Steam pressure 5.0 bar tal eat of steam at 5 bar 2757 kj/kg Latent eat of steam at 5 bar 2086 kj/kg Saturaton temperature of steam 159 o C Mass of ot ar requred 30,000 x kg/r Specfc eat of ar at 120 o C kj/kg o K Heat duty: Cold flud: m Cp delta.t x x (120-35)/ kw Mass of steam to be crculated x 3600/ kg/r (Ans) LMTD ( ) ( ) In (124/39) o C Heat excangers (table format) 28