OUTCOME 3 - TUTORIAL 1

Transcription

1 Unit 42: Heat Transfer and Cmbustin Unit cde: K/60/443 QCF level: 5 Credit value: 5 OUTCOME 3 - TUTORIL 3 Heat transfer equipment Recuperatrs: cncentric tube (parallel and cunter flw, crss flw, shell and tube, plate, extended surface) Heat transfer perfrmance: steady state perfrmance; verall heat transfer cefficient; LMTD; effectiveness; pressure drp; fulin factrs Fluids: water; il; air; refrierants; steam pplicatins: specificatin f suitable recuperatr and fluids fr iven applicatins such as il clin and heat recvery; calculatin f heat transfer rates iven fluid and recuperatr data Yu shuld jude yur prress by cmpletin the self assessment exercises. On cmpletin f this tutrial the student shuld be able t d the fllwin. This is the third tutrial in the series n heat transfer and cvers sme f the advanced thery f cnvectin. The tutrials are desined t brin the student t a level where he r she can slve prblems invlvin practical heat exchaners. On cmpletin f this tutrial the student shuld be able t d the fllwin. Explain the larithmic mean temperature difference. Describe the basic desins f heat exchaners. Parallel, Cunter and Crss Flw Heat Exchaners. Explain the factrs invlved in heat transfer. Slve heat transfer prblems fr heat exchaners. Nte a recuperatr is anther name fr a heat exchaner in which heat is transferred frm ne fluid t anther thruh a barrier that separates the fluids. In this tutrial the 'term heat exchaner' is preferred. It is assumed that the student is familiar with fluid prperties and the use f steam and ther fluid tables. If nt, this shuld be studied first and this may be fund in ther tutrials n thermdynamics. D.J.Dunn

2 INTRODUCTION Mst heat exchanes make use f frced cnvectin. Heat exchaners use a variety f surfaces a typical ne bein a tube with fins. The effectiveness f the heat exchaner depends n many thins such as the fllwin. The shape f the surface. The texture f the surface. The rientatin t the directin f flw. The prperties f the fluids. In utcme 2 yu studied heat transfer cefficients fr a variety f circumstances. This can be applied t heat exchaners. Many heat exchaners take the frm f tubes with a fluid n bth sides. The frmulae used in previus tutrials needs mdifyin t take accunt f the temperature chane as the fluids travel thruh the heat exchaners. HET TRNSFER THROUGH LONG TUE Cnsider a ht fluid () flwin thruh a ln tube exchanin heat with a cler fluid () flwin in a parallel directin n the utside f the tube. s the fluids flw frm inlet t utlet, fluid () cls and fluid () is heated. The net heat exchane is Φ. The temperature f the tw fluids varies with the surface area r path lenth as shwn. Cnsider a shrt lenth with surface area d. The temperature difference at any pint is:- = T T. The heat exchane is dφ ver this small area. The heat lst r ained by a fluid ver the small lenth is iven by dφ = mc p dt m is the mass flw rate and c p the specific heat capacity and this is assumed t be cnstant in this wrk. dt is the chane in temperature ver the path lenth. D.J.Dunn 2

3 Heat lst by fluid dφ = m c p dt dφ dt m c dφ Heat ained by fluid dφ = m c p dt dt dφ dφ d dt dt d dφ mcp mc p p...(i) Interate between the utlet and inlet and Φ m c p i m c p...(ii) Nw cnsider the chane in the temperature difference ver the shrt path lenth. In terms f the verall heat transfer cefficient dφ = U d...(iii) Equate (i) and (iii) d d d U d U d m c m c p p mcp Interatin ver the whle path U mcp i m i c p m c p...(iv) U Substitute (iv) int (ii) Fr the whle system we may use U i Φ i Φ = U m where m is a mean temperature difference. Cmparin it is apparent that m i i This is called the larithmic mean temperature difference. If we did the same analysis fr the fluids flwin in ppsite directins, we wuld et the same result. Next let s discuss the basic types f heat exchaners. D.J.Dunn 3

4 PRLLEL FLOW HET EXCHNGERS The fluid bein heated and the fluid bein cled flw in the same parallel directin as shwn. The heat is cnvected t the wall f the tube, then cnducted t the ther side and then cnvected t the ther fluid. If the tube wall is thin, the heat transfer rate is i Φ U i is the surface are f the tubes. The diaram shws typically hw the temperature f the tw fluids varies with the path lenth. Fluid ets htter and fluid ets cler s the temperature difference is reatest at inlet. COUNTER FLOW The fluids flw in ppsite but parallel directins as shwn. The temperature f the fluid bein heated can be raised t near the inlet temperature f the fluid bein cled. This is imprtant fr exchaners that heat up air fr cmbustin such as the exhaust as heat exchaners n as turbines. Fr a iven heat transfer the surface area is less. The heat transfer frmula is the same. CROSS FLOW The fluids flw at riht anles t each ther as shwn. This desin is ften the result f the plant layut and is cmmn in industrial bilers where the ht asses flw in a path nrmal t the water and steam. (superheaters, recuperatrs and ecnmisers). The tubes are ften finned t imprve the efficiency. Sty depsits n the utside are mre likely t be dislded in this cnfiuratin. Lare steam cndensers als use this style. D.J.Dunn 4

5 CONDENSING ND EVPORTING If ne f the fluids is evapratin r cndensin durin the prcess the temperature is cnstant s ln as it des nt cmpletely evaprate r cndense. WORKED EXMPLE N. heat exchaner transfers heat frm ht carbn dixide t superheated steam. The steam flws inside tubes and the as flws ver the utside in a parallel directin. The steam is at 200 bar pressure and is heated frm 375 C t 500 C respectively. The carbn dixide is cled frm 750 C t 600 C and flws at 0.35 k/s. The tubes are thin walled and 40 mm diameter. The ttal lenth is 250 m. Determine the fllwin. (i) (ii) (iii) The flw rate f the steam. The larithmic mean temperature. The effective heat transfer cefficient fr the unit. SOLUTION The mean temperature f the as is ( )/2 = 675 C Frm the fluids tables the specific heat is. kj/k K Heat Transfer rate frm as = m c p = 0.35 x. ( ) = kw Frm the steam tables The enthalpy f the steam at 200 bar and 500 C is 3239 kj/k = hs 2 The enthalpy f the steam at 200 bar and 375 C is 2605 kj/k = hs Heat Transfer rate t steam = m s (hs 2 - hs ) = m s k/s i = = 375 = = 00 i m 208 C i = πdl = π x 0.04 x 250 = 3.46 m 2 U Φ T m x W/m 2 K D.J.Dunn 5

6 WORKED EXMPLE N. 2 n exhaust pipe is 75 mm diameter and it is cled by surrundin it with a water jacket. The exhaust as enters at 350 C and the water enters at 0 C. The surface heat transfer cefficients fr the as and water are 300 and 500 W/m 2 K respectively. The wall is thin s the temperature drp due t cnductin is neliible. The asses have a mean specific heat capacity c p f 30 J/k K and they must be cled t 00 C. The specific heat capacity f the water is 490 J/k K. The flw rate f the as and water is 200 and 400 k/h respectively. Calculate the required lenth f pipe fr (a) parallel flw and (b) cntra flw. SOLUTION Overall Heat Transfer Cefficient is U where The wall is very thin s inre cnductin 4 U = 0.25 U h h PRLLEL FLOW Heat lst by the as is Φ = mc p = 200 x.3 (350 00) Φ = kj/h Heat Gained by water Φ = = mc p = 400 x 4.9 x (θ 0) θ = 9.63 C i i = 340 K = K Φ U kw 3600 i = m 2 = πdl L = 0.349/(π x 0.075) =.48 m CONTR FLOW i = K = 90 K i Φ U i = 0.34 m = πdl L = 0.34/(π x 0.075) =.44 m U h h w w x k D.J.Dunn 6

7 FOULING FCTOR Many heat exchaner surfaces becme fuled due t depsits frmin n them such as lime scale with hard water and sty scale with burned asses. This prduces a resistance t the cnductin path and the temperature chane thruh the wall f the tube is n lner neliible. T cmpensate fr this a heat transfer cefficient U f used where U f is equivalent t k/x. This is called the fulin factr. This will vary with the type f depsit and the time taken t build up. Cleanin the tubes is hihly desirable. This especially applies t fssil fuel bilers in the water walls, superheaters and feed water heaters. The feed water heaters in particular are subject t build up f st n the clin fins and this is cleaned by mechanical scrapers and blastin with steam. If the flw rates and inlet temperatures are unchaned, the heat transfer rate will be reduced and the temperatures f bth fluids chane at exit. WORKED EXMPLE N. 3 Repeat wrked example N.2 but this time there is a fulin factr U f f 20 W/m 2 K SOLUTION Overall Heat Transfer Cefficient is U where The wall is very thin s inre cnductin U h h U = 8.08 kw/m 2 K D.J.Dunn 7 U PRLLEL FLOW Heat lst by the as is Φ = mc p = 200 x.3 (350 00) Φ = kj/h Heat Gained by water Φ = = mc p = 400 x 4.9 x (θ 0) θ = 9.63 C i i = 340 K = K Φ U kw 3600 i =.075 m 2 = πdl L =.075/(π x 0.075) = 4.56 m CONTR FLOW i = K = 90 K i Φ U i =.047 m 2 = πdl L =.047/(π x 0.075) = 4.44 m h w h w U f

8 THERML RTIO ND EFFECTIVENESS These are terms ften used with exhaust as heat exchaners n as turbines. Cnsider the heat exchaner in the diaram. Ideally the T = T and T C = T and the maximum pssible heat transfer wuld be btained. The effectiveness is defined as the rati f the heat transfer t the air and frm the ht as. This is nt efficiency but simply a way t calculate the temperatures. The rati may be iven a symbl E. macpa TD TC E m c T T p If the specific heats and mass flw are the same (ften assumed in a as turbine prblem) this TD TC simplifies t E T T TD T It is als ften taken that T = T C s it further reduces t E and this is usually called the T T thermal rati. The same principles may be applied t recuperatrs that preheat the incmin air fr cmbustin n a biler burnin fssil fuel. WORKED EXMPLE N.4 as turbine exhausts as at 950 K and this is passed thruh an exhaust as heat exchaner t the air bein supplied t the cmbustin prcess. The air enters at 503 K. The effectiveness f the exchaner is The mass flw f bth are the same but the specific heat f the air is.005 kj/k K and the specific heat f the exhaust as is.5 kj/k K. Calculate the temperature f the air enterin the cmbustin chamber. SOLUTION Nte that wrkin in abslute temperatures is nrmal fr as turbines but wrkin in C ives the same answers. c 0.88 c pa p T T D T T TD K In C θ = = 62.4 C.005 TD D.J.Dunn 8

9 SELF SSESSMENT EXERCISE N.. n il cler cnsists f a ciled tube inside a shell thruh which clin water is circulated. The il flws at 0.7 k/s. The inlet and exit temperatures are 80 C and 30 C respectively. The clin water enters at 2 C and is required t be heated t 8 C. Calculate the flw rate f water required. The specific heat f water is 4.2 kj/k K and 2.2 kj/k K fr il. (0.742 k/s) 2. pwer statin burns fssil fuel and the air fr cmbustin is preheated by a recuperatr. The air enters at 5 C and is heated by ht flue ases enterin at 80 c and exitin at 20 C. The effectiveness is Calculate the temperature f the preheated air. Take the specific heats fr the air and burned as as.005 and.05 kj/k K respectively. The mass flw f bth is the same. (nswer 54.5 C) 3. cntra flw heat exchaner transfers heat frm refrierant 34a t water. The refrierant passes thruh tubes surrunded by a water jacket. The refrierant enters at 20 C as dry saturated vapur and leaves as wet vapur with dryness fractin 0.6. The water flws at 0.2 k/s. It enters at 0 C and leaves at 6 C. The specific heat f water is 490 J/k K. The tubes are thin walled and 5 mm diameter. The ttal lenth is 5 m. (i) The heat transfer rate. (5028 W) (ii) The flw rate f the refrierant. (0.068 k/s) (iii) The larithmic mean temperature. (6.548 C) (iv) The effective heat transfer cefficient fr the unit. (3.259 kw/m 2 K) 4. recuperatr cnsists f a shell with parallel pipes 25 mm diameter. Ht as enters the pipes at 420 C and it is cled by water flwin thruh the shell n the utside f the pipes. The water temperature is 5 C at inlet. The surface heat transfer cefficients fr the as and water are 250 and 700 W/m 2 K respectively. The wall is thin s the temperature drp due t cnductin is neliible. The ases have a mean specific heat capacity c p f 020 J/k K and they must be cled t 50 C. The specific heat capacity f the water is 4200 J/k K. The flw rate f the as and water is k/s and 0.4 k/s respectively. Calculate the heat transfer rate, the water exit temperature and the required lenth f pipe fr bth parallel and cntra flw cnfiuratin. (nswers 5.47 kw, 24 C, 3.7 m and 3.65 m) 5. The parallel flw recuperatr described in questin 4 becmes fuled ver a perid f time resultin in the as temperature risin at utlet t 200 C. If the water flw rate is unchaned, calculate the new heat transfer rate, the exit temperature f the water and the fulin factr. (2.34 kw, C and W/m 2 K) D.J.Dunn 9