Heat exchanger. Heat exchanger

Transcription

1 s are deves n w eat s transferred between tw fluds at dfferent teperatures wtut any xng f fluds. type. Dret eat transfer type 2. Strage type 3. Dret ntat type ttps:// Dret eat transfer type A dret transfer type f eat exanger s ne n w te ld and t fluds flw sultaneusly trug te deve and eat s transferred trug a wall separatng te fluds t flud t flud ld flud ld flud nentr tube eat exangers. (a) Parallel flw. (b) unter flw.

2 2. Strage type eat exanger A dret transfer type f eat exanger s ne n w te eat transfer fr te t flud and te ld flud ur tug a uplng edu n te fr f prus sld atrx. e t and ld fluds alternatvely trug te atrx. e t flud strng eat n t and te ld flud extratng eat fr t. 3. Dret ntat type eat exanger A dret transfer type f eat exanger s ne n w te tw fluds are nt separated. If eat s t be transferred between a gas and a flud, te gas s eter bubbled trug te lqud r te lqud s sprayed n te fr f drplets n te gas.

3 Dret type eat exanger. ubular 2. Plate 3. Extended surfae ubular eat exanger. nentr tube 2. Sell and tube nentr tube Sell and tube e eat transfer area avalable per unt vlue / 3

4 Plate eat exanger Seres f large retangular tn etal plates w are laped tgeter t fr narrw parallel-plate annel. e eat transfer area avalable per unt vlue / 3 Extended surfae eat exanger Fns attaed n te prary eat transfer surfae wt te bjet f nreasng te eat transfer area. e eat transfer area avalable per unt vlue / 3

5 lassfatn by flw arrangeent e tree bas flw arrangeents: Parallel flw unter flw rss flw Parallel flw unter flw

6 rss flw Bt fluds unxed One flud xed and te ter unxed Overall eat transfer effent (U) and fulng fatr In a eat exanger, te eat s transferred by bt nvetn and ndutn. q = UA ( a b ) a U s verall eat transfer effent 2 b

7 Plate eat exanger q nv. ) a 2 b a A q nd. ka x nv. 2 q A 2 b 2) 3) q a U A b 4) Addng abve tree equatns (, 2, 3) Fr (4) q q x q a A ka A q UA a b b Arss a plan wall q q q x q UA A ka A x U k U b k 2

8 ubular eat exanger r 2 R R a R b r a R = R nv + R nd + R nv2 R nv A R nd x ka R nv2 A Based n nner area U A A A = 2πr L (r r ) ka A l U (r r )r kr l r r โดย r l (r r ) ln(r / r ) Based n utter area (r r ) U A A ka l A U r r (r r )r kr l

9 Wen te wall tkness f te tube s sall and te teral ndutvty f te tube ateral s g, s as usually te ase, te teral resstane f te tube s neglgble. U beause A A Fulng e perfrane f eat exangers usually deterrate wt te as a result f auulatn f depsts n eat transfer surfaes, representng addtnal resstane, alled fulng.

10 (Lg) Mean eperature Dfferene t da ld dq U da Were: tal eat transfer rate n eat exanger q U da If U s assued t be a nstant q U da Defne ean teperature dfferene us: A da area q UA s s te bas perfrane equatn fr a dret transfer type eat exanger

11 Parallel Flw Assuptn. U s a nstant 2. s adequately nsulated.e. n eat lss t surrundng nsder n eleentary area da (B.dx) dq U B dx p p d d d ( ) d d dq p dq p U B dx p p

12 L 0 p p dx UB ) d ( Were:,,,, UA ln p p UA q,,,, ln UA q s s te perfrane equatn fr a parallel-flw eat exanger UA q parng wt: ln Were:

13 Fr unter flw Assuptn. U s a nstant 2. s adequately nsulated.e. n eat lss t surrundng nsder an eleentary area da (B.dx) dq U ( p p ) B d d dx d ( ) d d dq p dq p U B dx p p

14 L 0 p p dx UB ) d ( UA ln p p UA q ln,,,, Were:,,,, ln UA q,,,, UA q parng wt: ln Were:

15 Speal ase f unter flw p p en:,,,, Or,,,, Substtutng nt te expressn fr, we get an ndeternate quantty Defne en: p l p Apply L Hptal s rule l p (p ) ln p () p

16 rss flw ase : bt fluds unxed Ht flud,,, ld flud B y x, L rss flw ase 2: ne flud xed, te ter unxed Ht flud,,, ld flud B y x L, = f (x,y) = f (x)

17 rss flw ase -: Bt flud xed Ht flud,,, ld flud B y x L, = f (y) = f (x) Bt and are funtns f x and y nsderng an eleentary area da (= dx dy) dq U ( ) dx dy q 0 B 0 L U ( )dx dy parng wt q UA B L ( BL 0 0 )dx dy Mre plated tan befre but t as been dne.

18 e ntegratn f te tree ases f rss flw as been dne nuerally. e results are presented n te fr f a rretn fatr (F) F rss flw f f te tearrangeent arrengeentwas wasenunter-flw flw If te bulk ext teperatures n te t sde and ld sde are, and,, ten unter flw,,,, / ln,,,, Mean teperature dfferene n rss flw F rss flw f te arrengeent was unter flw Fr gven values f, ;, ;, ;, unter flw s te gest angst all flw arrangeents erefre: 0 F

19 q q rssflw rssflw UA UAF rssflw unter flw F s pltted as a funtn f tw paraeters, R and S R, 2,, 2, S 2,, 2, 2, Subsrpts and 2 rrespnd t te tw fluds Fr ase: (bt fluds unxed) and ase 3 (bt fluds xed) It s ateral w subsrpt rrespnds t te t sde and w t te ld sde. Fr ase: and ase 3 Subsrpts = 2 = r = 2 =

20 Hwever fr ase 2, are ust be taken t see tat te xed flud as subsrpt Wat s te paraeter R? e rat f ange f teperature f te tw fluds R 0 Wat s te paraeter S? e rat f ange n teperature f ne f te flud t te dfferene f nlet teperature f te tw fluds 0 S, 2, 2,, R, 2,, 2, Bt fluds unxed rss flw eat exanger S 2,, 2, 2,

21 , xed 2, unxed, 2, R, 2,, 2, One fluds xed and te ter unxed S 2,, 2, 2,

22

23

24

25

26

27

28 e effetveness - NU etd Generally, we enunter tw type f prbles: ype Gven: w fluds U Fnd A?,,,,,, ype 2 Gven: w fluds A eat exanger A,, Fnd, ;,?

29 ype ype 2 q UA A? q q U UA? We wll need a tral and errr appra t slve ts type f prble.e. assung, ral and errr an be avded f we adpt te alternatve etd alled te effetveness -NU Effetveness f a eat exanger = Rate f eat transfer n eat exanger Maxu pssble eat transfer rate q q ax,,,, Lengt f eat exanger,, ( ( p p p p ) ) ( s ( s, (, (,,,, ) ) ) ),,

30 Hene f p, ten p p p s,,,, Hene f p, ten p p p s,,,, Nte ) e defntn are equvalent wen p p 2) By defntn 0 Effetveness parallel flw Assue p ( p ) s,,,, p p p p q p, (, (, p p,,, ) ),,,,,,,, p p

31 Effetveness parallel flw p p,,,, UA exp p p,,,, Derved earler (slde 23) UA ln p p p p p p p UA exp Substtutng

32 If we ad assued ntally s p p ) ( p p p p p UA exp, ten We bne te tw expressns fr b p s p s p b p s p UA exp Defne tw new paraeters apaty rat () ax n b p s p r ) ( ) ( Nuber f transfer unt (NU) n s p UA r ) ( UA NU Nte: ) Bt are densnless 2) 3) NU 0 0

33 Effetveness parallel flw exp NU Effetveness unter flw exp exp NU NU Speal ases apaty rate (. p) s nfnte eter n te t sde r te ld sde 0 Fr ts slutn, we btan te relatn exp NU

34

35

36 Exaple Stuatn: Lgt lubratng l ( p =2090 J/kg-K) s led wt water n a sall eat exanger. Ol flw = 0.5 kg/s, nlet = 375 K Water flw = 0.2 kg/s, nlet = 280 K Part : If desred utlet teperature f te l s 350 K, and yu knw te estated verall eat transfer effent, U = 250 W/²-K, fr anufaturer s data fr ts type f eat exanger Fnd: Requred eat transfer area fr a parallel flw eat exanger and pare t te area needed fr a unter flw eat exanger.

37 LMD Slutn, Part : l, n 350 K p, q 4,8, J / Kg.K, l, n 375 K water, n 280 K water, ut? and,, q / 0.5 2,090 ( ) 26,25 W ,25 /(0.2 4,8) 3 K Fr parallel flw, ln / ln( 95 / 39), PF Fr unter flw, ln / ln( 64 / 70), F

38 Fr parallel flw, A PF q /(U,PF ).66 2 Fr unter flw, A F q /(U,F ).56 2 Part 2: Use -NU etd t deterne te requred NU and eat transfer area fr parallel and unter flw Slutn p, 4,8 J / Kg.K deterne te nu eat apaty rate, p W / K p 0.2 4, W / K ( p ) s

39 en q ax n (,, ) q ( ) 79,440 26,25 W, e effetveness s, W q / q ax 26,25 / 79, Wt ( ( p p ) ) s b 836.2, Parallel flw unter flw A A PF F n n NU NU F PF / U.84 / U

40

41

42

43 Oter nsderatn n desgnng eat exangers. Pressure drp n eter sdes 2. Sze restrtn 3. Stress nsderatn 4. Servng requreents 5. Materals f nstrutn 6. Syste peratn 7. st