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1.2. Basic Heat Exchanger Equations1.2.1. The Overall Heat Transfer CoefficientConsider the situation in Fig. (1.18). Heat is being transferred from the fluid inside (at a local bulk or average temperature of T i ), through a dirt or fouling film, through the tube wall, through another fouling film to the outside fluid at a local bulk temperature of T o . A i and A o are respectively inside and outside surface areas for heat transfer for a given length of tube. For a plain or bare cylindrical tube,i o i o i o r r L r L r A A ==ππ22 (1.13)The heat transfer rate between the fluid inside the tubeand the surface of the inside fouling film is given by anequation of the form Q/A = h(T f - T s ) where the area isA i and similarly for the outside convective processwhere the area is A o . The values of h i and h o have to becalculated from appropriate correlations.On most real heat exchanger surfaces in actual service, afilm or deposit of sediment, scale, organic growth, etc.,will sooner or later develop. A few fluids such as air orliquefied natural gas are usually clean enough that thefouling is absent or small enough to be neglected. Heattransfer across these films is predominantly by conduc-tion, but the designer seldom knows enough about eitherthe thickness or the thermal conductivity of the film to treat the heat transfer resistance as a conductionproblem. Rather, the designer estimates from a table of standard values or from experience a fouling factor R f .R f is defined in terms of the heat flux Q/A and thetemperature difference across the fouling ΔT f by theequation:A Q T R ff /Δ= (1.14)From Eq.1.14, it is clear that R f is equivalent to a reciprocal heat transfer coefficient for the fouling, h f :f f f T A Q R h Δ==1 (1.15)and in many books, the fouling is accounted for by a "fouling heat transfer coefficient," which is still an estimated quantity. The effect of including this additional resistance is to provide an exchanger somewhat larger than required when it is clean, so that the exchanger will still provide the desired service after it has been on stream for some time and some fouling has accumulated.The rate of heat flow per unit length of tube must be the same across the inside fluid film, the inside dirt film, the wall, the outside dirt film, and the outside fluid film. If we require that the temperature differences across each of these resistances to heat transfer add up to the overall temperature difference, (T i - T o ), we obtain for the case shown in Fig.1.18 the equation()o o o fo w i o i fi i i o i A h A R Lk r r A R A h T T Q 12/ln 1++++−=π (1.16)In writing Eq. (1.16), the fouling is assumed to have negligible thickness, so that the values of r i , r o , A i and A o are those of the clean tube and are independent of the buildup of fouling. Not only is this convenient – we don't know enough about the fouling to do anything else.Now we define an overall heat transfer coefficient U * based on any convenient reference area A *:(o i T T A U Q −≡∗∗) (1.17)Comparing the last two equations gives:()o o o fo w i o i fi i i A h A A A R Lk r r A A A R A h A U ******2/ln 1++++=π (1.18)Frequently, but not always , A * is chosen to be equal to A o , in which case U * = U o , and Eq. (1.18) becomes:()o fo w i o o i o fi i i o o h R Lk r r A A A R A h A U 12/ln 1++++=π (1.19)If the reference area A * is chosen to be A i , the corresponding overall heat transfer coefficient U i is given by:()o o i o i fo w i o i fi i i A h A A A R Lk r r A R h U ++++=π2/ln 11 (1.20)The equation as written applies only at the particular point where (T i - T o ) is the driving force. The question of applying the equation to an exchanger in which T i and T o vary from point to point is considered in the next section.The wall resistance is ordinarily relatively small, and to a sufficient degree of precision for bare tubes, we may usually write()()()()w i o i w i o i w i o o w i o o k r r X r Lk r r n A k r r X r Lk r r n A +Δ≅+Δ≅212/;212/ππl l (1.21)Inspection of the magnitudes of the terms in the denominator of Eqs. 1. 19 or 1.20 for any particular design case quickly reveals which term or terms (and therefore which heat transfer resistance) predominates. This term (or terms) controls the size of the heat exchanger and is the one upon which the designer should concentrate his attention. Perhaps the overall heat transfer coefficient can be significantly improved by a change in the design or operating conditions of the heat exchanger. In any case, the designer must give particular attention to calculating or estimating the value of the largest resistance, because any error or uncertainty in the data, the correlation, or the calculation of this term has a disproportionately large effect upon the size of the exchanger and/or the confidence that can be placed in its ability to do the job.1.2.2. The Design IntegralIn the previous section, we obtained an equationthat related the rate of heat transfer to the localtemperature difference (T-t) and the heat transferarea A, through the use of an overall heat transfercoefficient U. In most exchanger applications,however, one or both of the stream temperatureschange from point to point through the flow pathsof the respective streams. The change intemperature of each stream is calculated from theheat (enthalpy) balance on that stream and is aproblem in thermodynamics.Our next concern is to develop a method applyingthe equations already obtained to the case in whichthe temperature difference between the two streamsis not constant. We first write Eq. (1. 17) indifferential form()t T U dQ dA −=** (1.22)and then formally integrate this equation over the entire heat duty of the exchanger, Q t :∫−=t Q o t T U dQ A ** (1.23)This is the basic heat exchanger design equation, or the design integral.U * and A * may be on any convenient consistent basis, but generally we will use U o and A o . U * may be, and in practice sometimes is, a function of the amount of heat exchanged. If 1/U *(T-t) may be calculated as a function of Q , then the area required may be calculated either numerically or graphically, as shown in Fig. (1.19).The above procedure involving the evaluation of Eq. (1.23) is, within the stated assumptions, exact, and may always be used. It is also very tedious and time consuming. We may ask whether there is not a shorter and still acceptably accurate procedure that we could use. As it happens, if we make certain assumptions, Eq. (1.23) can be analytically integrated to the form of Eq. (1.24)()MTD U Q A t**= (1.24)where U * is the value (assumed constant) of the overall heat transfer coefficient and MTD is the "Mean Temperature Difference," which is discussed in detail in the following section.。

International Journal of Thermal Sciences46(2007)1311–1317/locate/ijtsPerformance analysis offinned tube and unbaffled shell-and-tubeheat exchangersJoydeep Barman,A.K.Ghoshal∗Department of Chemical Engineering,Indian Institute of Technology,Guwahati,North Guwahati781039,Assam,IndiaReceived15May2006;received in revised form26August2006;accepted6December2006Available online5February2007AbstractThis work considers an optimum design problem for the different constraints involved in the designing of a shell-and-tube heat exchanger consisting of longitudinallyfinned tubes.A Matlab simulation has been employed using the Kern’s method of design of extended surface heat exchanger to determine the behavior on varying the values of the constraints and studying the overall behavior of the heat exchanger with their variation for both cases of triangular and square pitch arrangements,along with the values of pressure drop.It was found out that an optimum fin height existed for particular values of shell and tube diameters when the heat transfer rate was the maximum.Moreover it was found out that the optimumfin height increased linearly with the increase in tube outer diameter.Further studies were also performed with the variation of other important heat exchanger design features and their effects were studied on the behavior of overall performance of the shell-and-tube heat exchanger.The results were thereby summarized which would proclaim to the best performance of the heat exchanger and therefore capable of giving a good idea to the designer about the dimensional characteristics to be used for designing of a particular shell and tube heat exchanger.©2007Elsevier Masson SAS.All rights reserved.Keywords:Fin height;Heat exchanger;Heat transfer rate;Longitudinalfins;Number of tube side passes;Pressure drop;Tube pitch layout1.IntroductionFins have long been recognized as effective means to aug-ment heat transfer.The literature on this subject is sizeable. Shell and tube heat exchanger with its tube eitherfinned or bare is extensively taught in the undergraduate level.Several text and reference books deal with the problems of longitudinalfinned tube in a shell and tube heat exchanger[1–4].It is well under-stood that with increase infin height of a longitudinalfin,heat transfer area increases to increase the heat transfer and at the same time the driving force decreases to decrease the heat trans-fer.However,one important design aspect,which probably is not discussed,is presented here.For a particular shell diameter, capacity of tube numbers is decided depending on tube size and pitch arrangement.In case offinned tube,height of thefin also plays an important role.Therefore,with increase infin height though surface area increases but number of tubes as well as *Corresponding author.E-mail addresses:joydeepb@iitg.ernet.in(J.Barman),aloke@iitg.ernet.in (A.K.Ghoshal).efficiency of thefin decreases.So,there might be an optimum condition of tube number andfin height for a particular tube arrangement and a particular shell diameter for which the heat transfer rate is the maximum[5].A Matlab coding has been de-signed to study the behavior of the overall performance of a heat exchanger on varying the important design features involved in it.The important constraints involved in the designing of a heat exchanger are studied here using the Matlab program.Several results and optimum conditions related to them are briefed out and tabulated in this literature to give a basic idea to the de-signer about the requirements and limitations to be included while designing afinned tube and unbaffled shell-and-tube heat exchanger.In the present article,Kern’s method of design[2]of ex-tended surface heat exchanger is applied for a shell-and-tube heat exchanger problem.Optimum conditions offin height and number of tubes in cases of triangular pitch and square pitch arrangements are found out along with the values of pressure drop.Other results concerning the various constraints of a heat exchanger like number of passes,tube outer diameter and tube pitch layout were also studied and compared in this literature.1290-0729/$–see front matter©2007Elsevier Masson SAS.All rights reserved. doi:10.1016/j.ijthermalsci.2006.12.0051312J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–1317 Nomenclaturea s,a tfluidflow area.............................m2 A o,A i tube surface area...........................m2c s,c t specific heat capacity...............J kg−1K−1d thickness of eachfin.........................m de equivalent diameter for heat transfercalculations................................m D,D1inner and outer diameter of tube..............m D2inner diameter of shell.......................m D b tube bundle diameter........................m De s equivalent diameter for pressure dropcalculations................................m f s,f t friction factor offluidh f heat transfer coefficient offins......W m−2K−1 h f i heat transfer coefficient of outside tube surface andfins with respect to the inner tubesurface............................W m−2K−1 h i heat transfer coefficient of inside tubesurface............................W m−2K−1 H f height of eachfin...........................m G s,G t mass velocity offluid...............kg m−2s−1 K s,K t thermal conductivity...............W m−1K−1 L length of each tube..........................m n number of tube side passes N f number offins per tubeN T total number of tubesP t tube pitch..................................m P w wetted perimeter............................m Pr s,Pr t Prandtl numberQ overall heat transfer rate per unit LMTD..W K−1 Re s,Re t Reynolds numbers s,s t specific gravity offluidU overall heat transfer coefficient......W m−2K−1 w tube sidefluid’s massflow rate...........kg s−1 W shell sidefluid’s massflow rate...........kg s−1 P s, P t pressure drop............................Pa Greek symbolsμs,μt,μw viscosity..............................Pa s ηffin efficiencySubscriptsffini inside of tubeo outside of tubes shell sidet tube sidew wall2.The mathematical program model of Kern’s method and solution procedure:determination of tube bundle diameter and maximum number of tubesA shell-and-tube heat exchanger with an internal shell diam-eter,D2,consisting offinned tubes of outer diameter,D1,inner diameter,D,length,L,withfins of height,H f,and thickness, d,is considered here.Total number offins per tube is N f and total number of tubes is N T.Tube bundle diameter is D b:D b=(D1+2H f)×(N T/K)(1/M)(1) The constants,K and M,are determined from Table1for dif-ferent tube passes and tube pitch layouts for a tube pitch,P t=1.25(D1+2H f)[1](2) Tube bundle diameter isfirst calculated by iterative process for bare tubes;henceforth maximum number offinned tubes,N T,is calculated from the derived tube bundle diameter from Eq.(1).3.Shell side calculationsTheflow area,a s,wetted perimeter,P w,equivalent diame-ter,d e,mass velocity,G s,Reynold’s number,Re s and Prandtl number,Pr s are calculated using Eqs.(3)–(8)as follows:a s=πD22/4−N TπD21/4+N f×d×H f(3) P w=N T(πD1−N f×d+2N f×H f)(4) d e=4a s/P w(5) G s=W/a s(6) Re s=d e×G s/μs(7) Pr s=c s×μs/K s(8) The heat transfer coefficient for the outside tube andfin surfaces can be calculated using Sieder–Tate correlation[4],Eqs.(9)and(10)as shown below:h f=1.86(K s/d e)×(Re s×Pr s×d e/L)1/3(9) for laminarflow;Table1Values of constants,K and M[1]Triangular pitch Square pitchNo.of passes1246812468K0.3190.2490.1750.07430.03650.2150.1560.1580.04020.0331 M 2.142 2.207 2.285 2.499 2.675 2.207 2.291 2.263 2.617 2.643J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–13171313h f =0.027(K s /d e )×Re 0.8s ×Pr 1/3s×(μs /μw )0.14(10)for turbulent flow.4.Tube side calculationsThe tube side flow area,a t ,mass velocity,G t ,Reynolds number,Re t and Prandtl number,Pr t ,for tube side fluid are calculated from Eqs.(11)–(14).With the values of viscosity,μt ,specific heat capacity,c t and thermal conductivity,K t ,for tube side fluid and using the Sieder–Tate correlation,the heat transfer coefficient of inside tube surface,h i ,can be calculated.a t =πN T ×D 2 /4n (11)G t =w/a t (12)Re t =DG t /μt (13)Pr t =c t ×μt /K t(14)5.Fin efficiency calculationsThe process is assumed as a steady state one and there isa continuous flow of fluid in the axial direction (both in the shell and tube side).Therefore,for a particular value of radial location,the temperature for any location in the axial direction would be almost same.Further,the angular directional variation of temperature is also neglected.Thus,the problem is reduced to a one-dimensional heat conduction problem.Hence,the fin efficiency is represented as ηf and calculated using Eqs.(15)and (16).ηf =tanh (mH f )/(mH f )(15)wherem =(2h f /K f d)1/2(16)6.Heat transfer calculationsHeat transfer coefficient of outside surface and fins with respect to the inner surface of tubes,h f i and heat transfer coef-ficient of inside surface,h i ,are given as below using Eqs.(17),(21)and (22):h f i =(H f ×P ×N f ×ηf ×N T +A o )h f /A i(17)A o and A i are the outside bare tube surface area and inside surface area of tubes respectively,where P is the perimeter of a fin,as given by Eqs.(18)–(20).A o =(πD 1−N f d)×N T L (18)A i =πDN T L (19)P =2(L +d)(20)The heat transfer coefficient for the inside tube surface can be calculated using Sieder–Tate correlation [4],Eqs.(21)and (22)as shown below:h i =1.86(K t /D)×(Re t ×Pr t ×D/L)1/3(21)for laminar flow;h i =0.027(K t /D)×Re 0.8t ×Pr 1/3t×(μt /μw )0.14(22)for turbulent flow.Thus the overall heat transfer coefficient,U ,with respect to the inside tube surface is given by Eq.(23):U =(h f i ×h i )/(h f i +h i )(23)Finally,the heat transfer rate with respect to the inside tube sur-face area,Q per degree LMTD is calculated using Eq.(24)as follows:Q =U ×A i(24)7.Pressure drop calculationsEquivalent diameter for pressure drop calculations in case of shell side fluid will be different from the diameter used for heat transfer calculations.This diameter is given by Eq.(25):De s =4a s /(P w +πD 2)(25)The pressure drops for shell side and tube side fluid, P s and P t respectively are calculated using Eqs.(26)–(29)as follows:P s = f s ×G 2s ×L / 5.22×1010×De s ×s s (26)f s =16/Re s(27)for laminar flow andf s =0.0035+0.24/Re 0.42s(28)for turbulent flow.Here,Re s =(De s ×G s )/μsP t = f t ×G 2t×L ×n / 5.22×1010×D ×s t (29)where f t is the tube side friction factor and can be calculated as shown above,Eqs.(27)and (28),using tube side Reynolds number,Re t .s s and s t are the specific gravities of shell side and tube side fluids respectively [2].8.Solution basisAn exemplary problem discussed below is used to study the objectives as discussed.Hot fluid (3.8kg s −1)in shell-side is to be cooled by a cold fluid (6.4kg s −1)in tube side.Inner di-ameter of the shell and length of the shell are kept constant as 0.5and 4.88m respectively.Inner and outer diameters of the tube are varied.Number of fins with thickness 9×10−4m per tube is 20and is kept constant for all the calculations.Ther-mal conductivity of the fin material is 45W m −1K −1.Hot and cold fluids are oxygen gas and water respectively.The values for thermal conductivity,viscosity and heat capacity of oxygen gas and water are calculated at an average temperature of 353and 305K respectively.9.Results and discussionsThe Kern’s method of designing of shell and tube heat ex-changers with extended surfaces was used for the designing of the heat exchanger concerned in this paper.The equations in-volved in this method are all simple and well established,and1314J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–1317were incorporated in a Matlab program specially coded for the purpose of this paper.This program is simply a step-wise cal-culation and does not involve any iteration or any optimization technique that may lead to some numerical errors.However,the program was thoroughly checked and thereafter run to arrive at the reasonable conclusions as reported in the manuscript.The results tabulated in Tables 2–5,and results shown graph-ically in Figs.1and 2were found out for a tube outer diameter of 0.0254m.Tables 2and 3present the maximum number of finned tubes of different fin heights for triangular pitch and square pitch arrangements respectively,which can be accom-modated in the shell of inner diameter 0.5m.They also reflect the obvious nature of variations of the shell-side and tube-side pressure drops with variation of fin height keeping one tube pass only.It is well understood that as the number of tubes decreases with the increase in fin height,the tube side fluid flow area is decreased thereby increasing the pressure drop.On the other hand,the shell side flow area increases leading to decrease in pressure drop,which is also shown through Figs.1and 2for tri-angular pitch and square pitch arrangements respectively.The variations of the heat transfer rates for both the pitches with variations of fin height are reported in Tables 2and 3respec-Fig.1.Variation of heat transfer rate and shell-side pressure drop with increase in fin height for triangular pitch arrangement,one tube side pass and for tube outer diameter,0.0254m.tively.The nature of the variations is shown through Figs.1and 2for triangular pitch and square pitch arrangements respec-tively.It is observed from the figures that there exists an opti-mum fin height (0.4572×10−2m for triangular pitch and 0.4826×10−2m for square pitch arrangement),which gives the highest heat transfer rate.Corresponding to these optimum fin heights,optimum number of adjustable finned tubes is 78and 60respectively.Under these optimum conditions,heat transfer rates are 7798.4and 5843.0W K −1,tube side pressure drops are 0.2985and 0.4723kPa and shell side pressure drops are 1.3217and 0.8343kPa for triangular and square pitch arrange-ments respectively.Tables 4and 5show the corresponding values of optimum fin height,total number of tubes,heat transfer rate and pres-sure drop for different values of tube side passes.We notice from these tables (Tables 4and 5)that for a constant shell inner diameter,with increase in the number of tube-side pass the maximum heat transfer rate corresponding to the optimum value of fin height decreases.It is also noticed that as the total number of tubes decreases the tube side pressure drop values in-creases largely which is a major drawback from economicandFig.2.Variation of heat transfer rate and shell-side pressure drop with increase in fin height for square pitch arrangement,one tube side pass and for tube outer diameter,0.0254m.Table 2Capacity of finned tubes of 0.0254m outer diameter in the shell,pressure drops and heat transfer rate values for triangular pitch arrangement and for one tube side passHeight of fin,H f ×102,m 0.2540.3810.43180.45720.5080.55880.6350.762Total number of tubes,N T10286817873696355Shell side—pressure drop, P s ,kPa 1.4341 1.3692 1.3383 1.3217 1.2893 1.2569 1.2093 1.1335Tube side—pressure drop, P t ,kPa0.18820.2530.28270.29850.3330.36950.42950.546Heat transfer rate per unit LMTD,Q ,W K −17469.37767.17797.37798.47777.47730.57622.47371.2Table 3Capacity of finned tubes of 0.0254m outer diameter in the shell,pressure drops and heat transfer rate values for square pitch arrangement and for one tube side pass Height of fin,H f ×102,m 0.2540.3810.40640.43180.45720.48260.5080.5334Total number of tubes,N T8268666462605850Shell side—pressure drop, P s ,kPa 0.87630.86050.85430.8480.84110.83430.82740.8191Tube side—pressure drop, P t ,kPa0.27650.37570.39850.4220.44610.47230.49850.5268Heat transfer rate per unit LMTD,Q ,W K −15522.45797.55820.45835.15842.45843.05837.65826.8J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–13171315optimization point of views.As expected,the shell side pressure drop decreases with decrease in tube number but the decrease is much less in comparison to the increase for the tube side pressure drop.So,in this case,the tube side pressure drop val-ues bear more importance while selecting the number of passes.Hence,from the tabulated data obtained it can be said that one tube side pass is the best choice for the finest results of heat ex-changer performance unless a constraint related to the number of tubes is faced when higher values of tube side pass could be considered.Moreover,it was also noticed that for a particular fin height,the total number of adjustable tubes varies for the pitch arrangements.As the number of tubes that could be ad-justed in a square pitch arrangement were less in number than in triangular pitch arrangement so even the most optimum value of fin height in case of square pitch arrangement could not pro-duce the same heat transfer rate as compared to the other.But the shell side pressure drop is higher in magnitude in triangu-lar pitch than in square pitch arrangement,whereas the relation is just the opposite in case of tube side pressure drop values.So,in the absence of any pressure drop constraints,thetriangu-Fig.3.Variation of optimum fin height with outer diameter of tubes.lar pitch arrangement with the optimum value of fin height will prove to be the best choice.The other tables,i.e.,Tables 6–9give the values of different important parameters such as a s ,A i ,A o ,Re s ,Pr s ,h f ,ηf ,h f i ,h i and U used and determined during the calculations.Fig.3shows the variation of optimum fin height with the change of tube outer diameters for a fixed number of tube side passes and for triangular pitch arrangement.The relation between them is found to be linear and can be expressed by Eq.(30):H f =0.0852×D 1+0.0025(30)Thus by using this equation,an approximate value of optimum fin height for the highest heat transfer rate can be pre-calculated for a tube of particular diameter.Fig.4shows a comparison of the performance of the heat exchanger for one and two tube side passes for triangular pitch arrangement.It is found out that the performance of the heat exchanger based on the heat transfer rate values for two-tube side passes could never meet up with the results for one tube side pass.Also after inspecting thepres-parison of heat transfer rates with fin heights for one and two tubes side passes.Table 4Optimum fin height for maximum heat transfer rate,for different tube-side passes and corresponding values of total number of finned tubes and pressure drops for triangular pitch arrangement and for tube outer diameter as 0.0254m Number of tube side passes,n 12468Optimum fin height,H f ×102,m0.45720.45720.45720.43180.38Heat transfer rate per unit LMTD,Q ,W K −17798.47639.46523.84383.53166.4Total number of finned tubes,N T 7872624740Shell-side pressure drop, P s ,kPa 1.3217 1.12040.84170.50830.3567Tube-side pressure drop, P t ,kPa0.29852.29120.032298.8108297.322Table 5Optimum fin height for maximum heat transfer rate,for different tube-side passes and corresponding values of total number of finned tubes and pressure drops for square pitch arrangement and for tube outer diameter as 0.0254m Number of tube side passes,n 12468Optimum fin height,H f ×102,m0.48260.45720.48260.40640.4064Heat transfer rate per deg.LMTD,Q ,W K −158435476.75286.92911.72503.0Total number of finned tubes,N T 6056513632Shell-side pressure drop, P s ,kPa 0.8340.70310.63640.32520.2773Tube-side pressure drop, P t ,kPa0.47233.557827.9617160.236441.3241316J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–1317Table6Values of various parameters involved in determining the important variables of Table2Height offin,H f×102,m0.2540.3810.43180.45720.5080.55880.6350.762 Shell sideflow area,a s,m2 1.41 1.485 1.511 1.523 1.546 1.567 1.596 1.637 Inside tube surface area,A i,m231.326.3724.7123.9422.521.1819.4116.9 Outside tube surface area,A o,m231.10126.2124.5623.79322.3621.0519.2816.8 Shell side 3.988 3.612 3.521 3.483 3.423 3.377 3.33 3.294 Reynolds number,Re s×10−4Shell side0.7010.7010.7010.7000.7010.7010.7010.701 Prandtl number,Pr sFin heat transfer111.8108.26106.96106.34105.14104.01102.42100.05 coefficient,h f,W m−2K−1Fin efficiency,ηf0.98820.97460.9680.96450.95710.94920.93640.9133 Heat transfer coefficient of291.03365.342392.96406.34432.25457.06492.27545.82fins and outside tube surfacewith respect toinside tube surface,h f i,W m−2K−1Inside tube surface heat 1.325 1.52 1.601 1.642 1.726 1.811 1.943 2.17 transfer coefficient,h i×10−3,W m−2K−1Overall heat transfer coefficient238.63294.55315.52325.75345.68364.97392.74436.11 with respect toinside tube surface,U,W m−2K−1Table7Values of various parameters involved in determining the important variables of Table3Height offin,H f×102,m0.2540.3810.40640.43180.45720.48260.5080.5334 Shell sideflow area,a s,m2 1.532 1.595 1.606 1.6162 1.626 1.636 1.645 1.654 Inside tube surface area,A i,m225.0320.9820.28319.6218.9818.3817.8117.26 Outside tube surface area,A o,m224.8820.8520.15719.518.8718.2717.717.16 Shell side 4.987 4.54 4.484 4.434 4.392 4.355 4.323 4.296 Reynolds number,Re s×10−4Shell side0.7010.7010.7010.7010.7010.7010.7010.701 Prandtl number,P r sFin heat transfer98.3796.3295.9195.595.0994.794.393.92 coefficient,h f,W m−2K−1Fin efficiency,ηf0.98960.97730.97440.97130.96810.9650.96130.9577 Heat transfer coefficient of256.3325.67338.81351.72364.38376.81389.0400.96fins and outside tube surface withrespect to insidetube surface,h f i,W m−2K−1Inside tube surface heat 1.585 1.825 1.875 1.926 1.977 2.028 2.081 2.133 transfer coefficient,h i×10−3,W m−2K−1Overall heat transfer coefficient220.62276.36286.96297.4307.67317.78327.73337.52 with respect toinside tube surface,U,W m−2K−1sure drop values(Table4),it can be well concluded that the best option would be to select a heat exchanger with one tube side pass if there is no tube number constraint involved.Hence it can be well summarized by mentioning that a combination of triangular pitch arrangement,one tube side pass and a value of fin height calculated from Eq.(30),when incorporated in the designing of a shell-and-tube heat exchanger with no baffles would certainly proclaim to give the best performance until and unless some restriction is being levied on in terms of pressure drop or number of tubes.10.ConclusionsIn this work the variation of heat transfer rate withfin height for afinned tube shell-and-tube heat exchanger was studied for two different pitch arrangements.It was found out that for par-J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–13171317 Table8Values of various parameters involved in determining the optimumfin height and other important variables of Table4Number of tube side passes,n12468 Optimumfin height,H f×102,m0.45720.45720.45720.43180.38 Shell sideflow area,a s,m2 1.523 1.5619 1.6261 1.722 1.7725 Inside tube surface area,A i,m223.9422.0818.9914.512.238 Outside tube surface area,A o,m223.79321.9418.87514.4112.163 Shell side Reynolds number,Re s×10−4 3.483 3.778 4.391 6.0017.798 Fin heat transfer coefficient,h f,W m−2K−1106.34102.0495.184.3777.781 Fin efficiency,ηf0.96450.96590.96810.97460.9817 Heat transfer coefficient offins and outside406.34390.3364.4311.5263.33 tube surface with respect to inside tubesurface,h f i,W m−2K−1Inside tube surface heat transfer coefficient, 1.642 3.051 5.992 1.0285 1.4827 h i×10−3,W m−2K−1Overall heat transfer coefficient with respect325.75346.03343.51302.34258.74 to inside tube surface,U,W m−2K−1Table9Values of various parameters involved in determining the optimumfin height and other important variables of Table5Number of tube side passes,n12468 Optimumfin height,H f×102,m0.48260.45720.48260.40640.4064 Shell sideflow area,a s,m2 1.636 1.6644 1.692 1.795 1.8206 Inside tube surface area,A i,m218.3817.1515.7111.0379.788 Outside tube surface area,A o,m218.2717.0515.61310.979.728 Shell side Reynolds number,Re s×10−4 4.355 4.826 5.0978.249.291 Fin heat transfer coefficient,h f,W m−2K−194.791.0488.7275.9673.118 Fin efficiency,ηf0.9650.96940.9670.97960.9803 Heat transfer coefficient offins and outside376.81349.19353.61269.38259.44 tube surface with respect to inside tubesurface,h f i,W m−2K−1Inside tube surface heat transfer coefficient, 2.028 3.734 6.974 1.28 1.773 h i×10−3,W m−2K−1Overall heat transfer coefficient with respect317.78319.3336.54263.82255.69 to inside tube surface,U,W m−2K−1ticular shell and tube diameters an optimum value offin height exists,which gives the highest heat transfer rate.Moreover it was also found out that on increasing the number of tube side passes while keeping the shell diameter constant,though the number of tubes could be decreased but the performance on the basis of heat transfer rate kept on decreasing and tube side pressure drop values increased substantially.The optimumfin height also increased linearly with the increase of tube outer diameter.It is worth mentioning here that the Matlab coding designed for this problem and the results obtained on using it,might prove quite beneficial in choosing the most appropriatefin height,total number of tubes,tube dimensions,arrangements, number of tube side passes andfin dimensions for a known value of shell diameter as well as keeping the pressure drops in check.In this problem the physical properties of thefluids were assumed constant,tube andfin dimensions were assumed uniform,throughout the entire system.It can be further stated that no experimental verification could be possible due to lack of such experimental data.How-ever,it would be highly appreciated to carry experimental work in this regard.References[1]J.R.Backhurst,J.M.Coulson,J.H.Harkar,J.F.Richardson,Coulson&Richardson’s Chemical Engineering,Butterworth–Heinemann,Oxford, 2004.[2]D.Q.Kern,Process Heat Transfer,McGraw-Hill,New York,2000.[3]P.Harriott,W.L.McCabe,J.C.Smith,Unit Operations of Chemical Engi-neering,McGraw-Hill,New York,2001.[4]S.P.Dusan,R.K.Shah,Fundamentals of Heat Exchanger Design,John Wi-ley and Sons,New York,2003.[5]J.Barman,A.K.Ghoshal,in:Proceedings of Chemcon’05,58th AnnualChemical Engineering Congress,India,2005.。

One of the most effective methods of increasing the rate of heat transfer in heat exchangersis using tubes with lengthwise corrugations (Fig. i). Among the different methodsknown here and abroadfor making such tubes (longitudinal and rotary rolling, welding, drawing,forging), cold drawing occupies an important position. This is because of the highproductivity of this method, the accuracy of the tube dimensions, the good surface finish,and the fact that the tool is relatively simple to fabricate. A technology has been developedand introduced at several nonferrous metallurgical plants for drawing copper-alloy tubeswith lengthwise corrugations.The Pervouralsk New Tube Plant is developing a technology for drawing such tubes madeof carbon steel. Trial lots of tubes with a corrugated outer surface have been made andstudies are being conducted to determine the optimum geometry of the die.There are certain distinctive features of drawing stainless steel tubes that owe to theproperties of the material. The cold working of alloy steels -- thus, stainless steels -- ischaracterized by a high susceptibility to work hardening, low thermal conductivity, and thepresence of a hard and strong film on the surface which is passive to lubricants. The presenceof the film leads to seizing of the tube in the die. Existing lubricants and prelubricantcoatings do not provide a plasticized layer that will prevent the metal from adheringto the die and ensure a uniform strain distribution over the tube wall thickness.The Ural Polytechnic Institute and the Institute of Electrochemistry of the Ural ScienceCenter under the Academy of Science of the USSR have developed a technology for applying acopper coating to the surface of tubes made of corrosion-resistant steels. The coating isapplied in the form of a melt containing copper salts at 400-500~ and allowed to stand fori0 min. The layer of copper 10-40 ~m thick formed on the surface by this operation is stronglybound to the base metal. The copper coating makes it possible to draw tubes of stainlesssteel on a mandrel.The sector metallurgical-equipment laboratory at the UralPolytechnic Institute studiedthe process of drawing stainless steel tubes using the copper coating on short(stationary)and long (movable) mandrels. The study showed that the metal does not adhere to the die, thecoating is strongly bound to the base metal, and large reductions can be made in one pass.These results suggested that stainless-steel tubes with lengthwise corrugations could beproduced by cold drawing. Thus, the laboratory prepared trial lots of corrugated steel12KhI8NIOT tubes.其中一个最有效的办法来增加率换热器的传热利用管corrugations与纵向(Fig.我)。

管壳式换热器强化传热研究摘要：从管程强化和壳程强化两方面论述了管壳式换热器强化传热技术的机理，指出了管壳式换热器今后发展中的主要方向;同时对换热器的防腐措施以及改进动向作了介绍。

关键词：强化传热;管壳式换热器;防腐Abstract: shell and tube heat exchanger was discussed from two aspects of the strengthening of the tube side and the strengthening of the shell to strengthen the mechanism of heat transfer technology, pointing out that the main direction of future development of the shell and tube heat exchanger; heat exchanger anti-corrosion measures well as improved trends were introduced. Keywords: heat transfer enhancement; shell and tube heat exchanger; anti-corrosion引言管壳式换热器是当今应用最广泛的换热设备，它具有高的可靠性和简单易用性。

特别是在较高参数的工况条件下，管壳式更显示了其独有的长处“目前在提高该类换热器性能所开展的研究主要是强化传热，适应高参数和各类有腐蚀介质的耐腐材料以及为大型化的发展所作的结构改进。

一、换热器的强化传热研究换热器的强化传热就是采用一定的措施增大换热设备的传热速率，力图用较少的传热面积或体积的设备来完成传热任务。

各种强化型换热器在石油、化工、制冷、航空、车辆、动力机械等工业部门己得到广泛应用。

强化传热已被学术界称为第二代传热技术。

Refrigeration System Performance using Liquid-Suction Heat ExchangersS. A. Klein, D. T. Reindl, and K. BroWnellCollege of EngineeringUniversity of Wisconsin - MadisonAbstractHeat transfer devices are provided in many refrigeration systems to exchange energy betWeen the cool gaseous refrigerant leaving the evaporator and Warm liquid refrigerant exiting the condenser. These liquid-suction or suction-line heat exchangers can, in some cases, yield improved system performance While in other cases they degrade system performance. Although previous researchers have investigated performance of liquid-suction heat exchangers, this study can be distinguished from the previous studies in three Ways. First, this paper identifies a neW dimensionless group to correlate performance impacts attributable to liquid-suction heat exchangers. Second, the paper extends previous analyses to include neW refrigerants. Third, the analysis includes the impact of pressure drops through the liquid-suction heat exchanger on system performance. It is shoWn that reliance on simplified analysis techniques can lead to inaccurate conclusions regarding the impact of liquid-suction heat exchangers on refrigeration system performance. From detailed analyses, it can be concluded that liquid-suction heat exchangers that have a minimal pressure loss on the loW pressure side are useful for systems using R507A, R134a, R12, R404A, R290, R407C, R600, and R410A. The liquid-suction heat exchanger is detrimental to system performance in systems using R22, R32, and R717.IntroductionLiquid-suction heat exchangers are commonly installed in refrigeration systems With the intent of ensuring proper system operation and increasing system performance.Specifically, ASHRAE(1998) states that liquid-suction heat exchangers are effective in:1) increasing the system performance2) subcooling liquid refrigerant to prevent flash gas formation at inlets to expansion devices3) fully evaporating any residual liquid that may remain in the liquid-suction prior to reaching the compressor(s)Figure 1 illustrates a simple direct-expansion vapor compression refrigeration system utilizing a liquid-suction heat exchanger. In this configuration, high temperature liquid leaving the heat rejection device (an evaporative condenser in this case) is subcooled prior to being throttled to the evaporator pressure by an expansion device such as a thermostatic expansion valve. The sink for subcooling the liquid is loW temperature refrigerant vapor leaving the evaporator. Thus, the liquid-suction heat exchanger is an indirect liquid-to-vapor heat transfer device. Thevapor-side of the heat exchanger (betWeen the evaporator outlet and the compressor suction) is often configured to serve as an accumulator thereby further minimizing the risk of liquid refrigerant carrying-over to the compressor suction. In cases Where the evaporator alloWs liquid carry-over, the accumulator portion of the heat exchanger Will trap and, over time, vaporize the liquid carryover by absorbing heat during the process of subcooling high-side liquid.BackgroundStoecker and Walukas (1981) focused on the influence of liquid-suction heat exchangers in both single temperature evaporator and dual temperature evaporator systems utilizing refrigerant mixtures. Their analysis indicated that liquid-suction heat exchangers yielded greater performance improvements When nonazeotropic mixtures Were used compared With systems utilizing single component refrigerants or azeoptropic mixtures. McLinden (1990) used the principle of corresponding states to evaluate the anticipated effects of neW refrigerants. He shoWed that the performance of a system using a liquid-suction heat exchanger increases as the ideal gas specific heat (related to the molecular complexity of the refrigerant) increases. Domanski and Didion (1993) evaluated the performance of nine alternatives to R22 including the impact of liquid-suction heat exchangers. Domanski et al. (1994) later extended the analysis by evaluating the influence of liquid-suction heat exchangers installed in vapor compression refrigeration systems considering 29 different refrigerants in a theoretical analysis. Bivens et al. (1994) evaluated a proposed mixture to substitute for R22 in air conditioners and heat pumps. Their analysis indicated a 6-7% improvement for the alternative refrigerant system When system modifications included a liquid-suction heat exchanger and counterfloW system heat exchangers (evaporator and condenser). Bittle et al. (1995a) conducted an experimental evaluation of a liquid-suction heat exchanger applied in a domestic refrigerator using R152a. The authors compared the system performance With that of a traditional R12-based system. Bittle et al. (1995b) also compared the ASHRAE method for predicting capillary tube performance (including the effects of liquid-suction heat exchangers) With experimental data. Predicted capillary tube mass floW rates Were Within 10% of predicted values and subcooling levels Were Within 1.7 C (3F) of actual measurements.This paper analyzes the liquid-suction heat exchanger to quantify its impact on system capacity and performance (expressed in terms of a system coefficient of performance, COP). The influence of liquid-suction heat exchanger size over a range of operating conditions (evaporating and condensing) is illustrated and quantified using a number of alternative refrigerants. Refrigerants included in the present analysis are R507A, R404A, R600, R290, R134a, R407C, R410A, R12, R22, R32, and R717. This paper extends the results presented in previous studies in that it considers neW refrigerants, it specifically considers the effects ofthe pressure drops,and it presents general relations for estimating the effect of liquid-suction heat exchangers for any refrigerant.Heat Exchanger EffectivenessThe ability of a liquid-suction heat exchanger to transfer energy from the Warm liquid to the cool vapor at steady-state conditions is dependent on the size and configuration of the heat transfer device. The liquid-suction heat exchanger performance, expressed in terms of an effectiveness, is a parameter in the analysis. The effectiveness of the liquid-suction heat exchanger is defined in equation (1):Where the numeric subscripted temperature (T) values correspond to locations depicted in Figure 1. The effectiveness is the ratio of the actual to maximum possible heat transfer rates. It is related to the surface area of the heat exchanger. A zero surface area represents a system Without a liquid-suction heat exchanger Whereas a system having an infinite heat exchanger area corresponds to an effectiveness of unity.The liquid-suction heat exchanger effects the performance of a refrigeration system by in fluencing both the high and loW pressure sides of a system. Figure 2 shoWs the key state points for a vapor compression cycle utilizing an idealized liquid-suction heat exchanger on a pressure-enthalpy diagram. The enthalpy of the refrigerant leaving the condenser (state 3) is decreased prior to entering the expansion device (state 4) by rejecting energy to the vapor refrigerant leaving the evaporator (state 1) prior to entering the compressor (state 2). Pressure losses are not shoWn. The cooling of the condensate that occurs on the high pressure side serves to increase the refrigeration capacity and reduce the likelihood of liquid refrigerant flashing prior to reaching the expansion device. On the loW pressure side, the liquid-suction heat exchanger increases the temperature of the vapor entering the compressor and reduces the refrigerant pressure, both of Which increase the specific volume of the refr igerant and thereby decrease the mass floW rate and capacity. A major benefit of the liquid-suction heat exchanger is that it reduces the possibility of liquid carry-over from the evaporator Which could harm the compressor. Liquid carryover can be readily caused by a number of factors that may include Wide fluctuations in evaporator load and poorly maintained expansion devices (especially problematic for thermostatic expansion valves used in ammonia service).（翻译）冷却系统利用流体吸热交换器克来因教授,布兰顿教授, , 布朗教授威斯康辛州的大学–麦迪逊摘录加热装置在许多冷却系统中被用到，用以制冷时遗留在蒸发器中的冷却气体和离开冷凝器发热流体之间的能量的热交换.这些流体吸收或吸收热交换器,在一些情形中，他们降低了系统性能, 然而系统的某些地方却得到了改善. 虽然以前研究员已经调查了流体吸热交换器的性能, 但是这项研究可能从早先研究的三种方式被加以区别. 首先，这份研究开辟了一个无限的崭新的与流体吸热交换器有关联的群体.其次，这份研究拓宽了早先的分析包括新型制冷剂。

武汉工程大学邮电与信息工程学院毕业设计(论文)外文资料翻译原文题目： Effectively Design Shell-and-Tube Heat Exchangers 原文来源： Chemical Engineering ProgressFebruary 1998文章译名：管壳式换热器的优化设计姓名： xxx学号： xx指导教师(职称)：王成刚（副教授）专业：过程装备与控制工程班级： 03班所在学院：机电学部管壳式换热器的优化设计为了充分利用换热器设计软件，我们需要了解管壳式换热器的分类、换热器组件、换热管布局、挡板、压降和平均温差。

管壳式换热器的热设计是通过复杂的计算机软件完成的。

然而，为了有效使用该软件，需要很好地了解换热器设计的基本原则。

本文介绍了传热设计的基础，涵盖的主题有：管壳式换热器组件、管壳式换热器的结构和使用范围、传热设计所需的数据、管程设计、壳程设计、换热管布局、挡板、壳程压降和平均温差。

关于换热器管程和壳程的热传导和压力降的基本方程已众所周知。

在这里，我们将专注于换热器优化设计中的相关应用。

后续文章是关于管壳式换热器设计的前沿课题，例如管程和壳程流体的分配、多壳程的使用、重复设计以及浪费等预计将在下一期介绍。

管壳式换热器组件至关重要的是，设计者对管壳式换热器功能有良好的工作特性的认知，以及它们如何影响换热设计。

管壳式换热器的主要组成部分有：壳体封头换热管管箱管箱盖管板折流板接管其他组成部分包括拉杆和定距管、隔板、防冲挡板、纵向挡板、密封圈、支座和地基等。

管式换热器制造商协会标准详细介绍了这些不同的组成部分。

管壳式换热器可分为三个部分：前端封头、壳体和后端封头。

图1举例了各种结构可能的命名。

换热器用字母编码描述三个部分，例如， BFL 型换热器有一个阀盖，双通的有纵向挡板的壳程和固定的管程后端封头。

根据结构固定管板式换热器：固定管板式换热器（图2）内装有直的换热管，这些管束两端固定在管板上，管板则被焊接在壳体上。

毕业设计（论文）外文文献翻译文献、资料中文题目：U形管换热器文献、资料英文题目：文献、资料来源：文献、资料发表（出版）日期：院（部）：专业：过程装备与控制工程专业班级：姓名：学号：指导教师：翻译日期： 2017.02.14毕业设计（论文）外文翻译毕业设计（论文）题目： U形管式换热器设计外文题目： U-tube heat exchangers译文题目：指导教师评阅意见U-tube heat exchangersM. Spiga and G. Spiga, Bologna1 Summary:Some analytical solutions are provided to predict the steady temperature distributions of both fluids in U-tube heat exchangers. The energy equations are solved assuming that the fluids remain unmixed and single-phased. The analytical predictions are compared with the design data and the numerical results concerning the heat exchanger of a spent nuclear fuel pool plant, assuming distinctly full mixing and no mixing conditions for the secondary fluid (shell side). The investigation is carried out by studying the influence of all the usual dimensionless parameters (flow capacitance ratio, heat transfer resistance ratio and number of transfer units), to get an immediate and significant insight into the thermal behaviour of the heat Exchanger.More detailed and accurate studies about the knowledge of the fluid temperature distribution inside heat exchangers are greatly required nowadays. This is needed to provide correct evaluation of thermal and structural performances, mainly in the industrial fields (such as nuclear engineering) where larger, more efficient and reliable units are sought, and where a good thermal design can not leave integrity and safety requirements out of consideration [1--3]. In this view, the huge amount of scientific and technical informations available in several texts [4, 5], mainly concerning charts and maps useful for exit temperatures and effectiveness considerations, are not quite satisfactory for a more rigorous and local analysis. In fact the investigation of the thermomechanieal behaviour (thermal stresses, plasticity, creep, fracture mechanics) of tubes, plates, fins and structural components in the heat exchanger insists on the temperature distribution. So it should be very useful to equip the stress analysis codes for heat exchangers withsimple analytical expressions for the temperature map (without resorting to time consuming numerical solutions for the thermal problem), allowing a sensible saving in computer costs. Analytical predictions provide the thermal map of a heat exchanger, aiding in the designoptimization.Moreover they greatly reduce the need of scale model testing (generally prohibitively expensive in nuclear engineering), and furnish an accurate benchmark for the validation of more refined numerical solutions obtained by computer codes. The purpose of this paper is to present the local bulk-wall and fluid temperature distributions forU-tube heat exchangers, solving analytically the energy balance equations.122 General assumptionsLet m, c, h, and A denote mass flow rate (kg/s), specific heat (J/kg -1 K-l), heat transfer coefficient(Wm -2 K-l), and heat transfer surface (m2) for each leg, respectively. The theoretical analysis is based on classical assumptions [6] :-- steady state working conditions,-- equal flow distribution (same mass flow rate for every tube of the bundle),-- single phase fluid flow,-- constant physical properties of exchanger core and fluids,-- adiabatic exchanger shell or shroud,-- no heat conduction in the axial direction,-- constant thermal conductances hA comprehending wall resistance and fouling.According to this last assumption, the wall temperature is the same for the primary and secondary flow. However the heat transfer balance between the fluids is quite respected, since the fluid-wall conductances are appropriately reduced to account for the wall thermal resistance and thefouling factor [6]. The dimensionless parameters typical of the heat transfer phenomena between the fluids arethe flow capacitance and the heat transfer resistance ratiosand the number of transfer units, commonly labaled NTU in the literature,where (mc)min stands for the smaller of the two values (mc)sand (mc)p.In (1) the subscripts s and p refer to secondary and primary fluid, respectively. Only three of the previous five numbers are independent, in fact :The boundary conditions are the inlet temperatures of both fluids3 Parallel and counter flow solutionsThe well known monodimensional solutions for single-pass parallel and counterflow heat exchanger,which will be useful later for the analysis of U-tube heat exchangers, are presented below. If t, T,νare wall, primary fluid, and secondary fluid bulk temperatures (K), and ξ and L represent the longitudinal space coordinate and the heat exchanger length (m), the energy balance equations in dimensionless coordinate x = ξ/L, for parallel and counterflow respectivelyread asM. Spiga and G. Spiga: Temperature profiles in U-tube heat exchangersAfter some algebra, a second order differential equation is deduced for the temperature of the primary (or secondary) fluid, leading to the solutionwhere the integration constants follow from the boundary conditions T(0)=T i , ν(0)≒νifor parallel T(1) = Ti ,ν(0) = νifor counter flow. They are given-- for parallel flow by - for counterflow byWishing to give prominence to the number of transfer units, it can be noticed thatFor counterflow heat exchangers, when E = 1, the solutions (5), (6) degenerate and the fluidtemperatures are given byIt can be realized that (5) -(9) actually depend only on the two parametersE, NTU. However a formalism involving the numbers E, Ns. R has been chosen here in order to avoid the double formalism (E ≤1 and E > 1) connected to NTU.4 U-tube heat exchangerIn the primary side of the U-tube heat exchanger, whose schematic drawing is shown in Fig. 1, the hot fluid enters the inlet plenum flowing inside the tubes, and exits from the outlet plenum. In the secondary side the fluid flows in the tube bundle (shell side). This arrangement suggests that the heat exchanger can be considered as formed by the coupling of a parallel and a counter-flow heat exchanger, each with a heigth equal to the half length of the mean U-tube. However it is necessary to take into account the interactions in the secondary fluid between the hot and the cold leg, considering that the two flows are not physically separated. Two extreme opposite conditions can be investigated: no mixing and full mixing in the two streams of the secondary fluid. The actual heat transfer phenomena are certainly characterized by only a partial mixing ofthe shell side fluid between the legs, hence the analysis of these two extreme theoretical conditions will provide an upper and a lower limit for the actual temperature distribution.4.1 No mixing conditionsIn this hypothesis the U-tube heat exchanger can be modelled by two independent heat exchangers, a cocurrent heat exchanger for the hot leg and a eountercurrent heat exchanger for the cold leg. The only coupling condition is that, for the primary fluid, the inlet temperature in the cold side must be the exit temperature of the hot side. The numbers R, E, N, NTU can have different values for the two legs, because of thedifferent values of the heat transfer coefficients and physical properties. The energy balance equations are the same given in (2)--(4), where now the numbers E and Ns must be changed in E/2 and 2Ns in both legs, if we want to use in their definition the total secondary mass flow rate, since it is reduced in every leg to half the inlet mass flow rate ms. Of course it is understood that the area A to be used here is half of the total exchange area of the unit, as it occurs for the length L too. Recalling (5)--(9) and resorting to the subscripts c and h to label the cold and hot leg, respectively, the temperature profile is given bywhere the integration constants are:M. Spiga and G. Spiga: Temperature profiles in U-tube heat exchangersIf E, = 2 the solutions (13), (14) for the cold leg degenerate into4.2 Full mixing conditionsA different approach can be proposed to predict the temperature distributions in the core wall and fluids of the U-tube heat exchanger. The assumption of full mixing implies that the temperaturesof the secondary fluid in the two legs, at the same longitudinal section, are exactly coinciding. In this situation the steady state energy balance equations constitute the following differential set :The bulk wall temperature in both sides is thenand (18)--(22) are simplified to a set of three equations, whose summation gives a differential equation for the secondary fluid temperature, withgeneral solutionwhere # is an integration constant to be specified. Consequently a second order differential equation is deduced for the primary fluid temperature in the hot leg :where the numbers B, C and D are defined asThe solution to (24) allows to determine the temperaturesand the number G is defined asThe boundary conditions for the fluids i.e. provide the integration constantsAgain the fluid temperatures depend only on the numbers E and NTU.5 ResultsThe analytical solutions allow to deduce useful informations about temperature profiles and effectiveness. Concerning the U-tube heat exchanger, the solutions (10)--(15) and (25)--(27) have been used as a benchmark for the numerical predictions of a computer code [7], already validated, obtaining a very satisfactory agreement.M. Spiga and G. Spiga: Temperature profiles in U-tube heat exchangers 163 Moreover a testing has been performed considering a Shutte & Koerting Co. U-tube heat exchanger, designed for the cooling system of a spent nuclear fuel storage pool. The demineralized water of the fuel pit flows inside the tubes, the raw water in the shell side. The correct determination of the thermal resistances is very important to get a reliable prediction ; for every leg the heat transfer coefficients have been evaluated by the Bittus-Boelter correlation in the tube side [8], by the Weisman correlation in the shell side [9] ; the wall material isstainless steel AISI 304.and the circles indicate the experimental data supplied by the manufacturer. The numbers E, NTU, R for the hot and the cold leg are respectively 1.010, 0.389, 0.502 and 1.011, 0.38~, 0.520. The difference between the experimental datum and the analytical prediction of the exit temperature is 0.7％ for the primary fluid, 0.9% for the secondary fluid. The average exit temperature of the secondary fluid in the no mixing model differs from the full mixing result only by 0.6%. It is worth pointing out the relatively small differences between the profiles obtained through the two different hypotheses (full and no mixing conditions), mainly for the primary fluid; the actual temperature distribution is certainly bounded between these upper and lower limits,hence it is very well specified. Figures 3-5 report the longitudinal temperaturedistribution in the core wall, τw = (t -- νi)/(Ti -- νi), emphasizing theeffects of the parameters E, NTU, R.As above discussed this profile can be very useful for detailed stress analysis, for instance as anM. Spiga and G. Spiga: Temperature profiles in U-tube heat exchangersinput for related computer codes. In particular the thermal conditions at the U-bend transitions are responsible of a relative movement between the hot and the cold leg, producing hoop stresses with possible occurrence of tube cracking . It is evident that the cold leg is more constrained than the hot leg; the axial thermal gradient is higher in the inlet region and increases with increasing values of E, NTU, R. The heat exchanger effectiveness e, defined as the ratio of the actual heat transfer rate(mc)p (Ti-- Tout), Tout=Tc(O), to the maximum hypothetical rateunder the same conditions (mc)min (Ti- νi), is shown in Figs. 6, 7respectively versus the number of transfer units and the flow capacitance ratio. As known, the balanced heat exchangers E = 1) present the worst behaviour ; the effectiveness does not depend on R and is the same for reciprocal values of the flow capacitance ratio.U形管换热器m . Spiga和g . Spiga,博洛尼亚摘要:分析解决方案提供一些两相流体在u形管换热器中的分布情况。

DESIGN OF HEAT EXCHANGER FOR HEAT RECOVERY IN CHP SYSTEMSABSTRACTThe objective of this research is to review issues related to the design of heat recovery unit in Combined Heat and Power (CHP) systems. To meet specific needs of CHP systems, configurations can be altered to affect different factors of the design. Before the design process can begin, product specifications, such as steam or water pressures and temperatures, and equipment, such as absorption chillers and heat exchangers, need to be identified and defined. The Energy Engineering Laboratory of the Mechanical Engineering Department of the University of Louisiana at Lafayette and the Louisiana Industrial Assessment Center has been donated an 800kW diesel turbine and a 100 ton absorption chiller from industries. This equipment needs to be integrated with a heat exchanger to work as a Combined Heat and Power system for the University which will supplement the chilled water supply and electricity. The design constraints of the heat recovery unit are the specifications of the turbine and the chiller which cannot be altered.INTRODUCTIONCombined Heat and Power (CHP), also known as cogeneration, is a way to generate power and heat simultaneously and use the heat generated in the process for various purposes. While the cogenerated power in mechanical or electrical energy can be either totally consumed in an industrial plant or exported to a utility grid, the recovered heat obtained from the thermal energy in exhaust streams of power generating equipment is used to operate equipment such as absorption chillers, desiccant dehumidifiers, or heat recovery equipment for producing steam or hot water or for space and/or process cooling, heating, or controlling humidity. Based on the equipment used, CHP is also known by other acronyms such as CHPB (Cooling Heating and Power for Buildings), CCHP (Combined Cooling Heating and Power), BCHP (Building Cooling Heating and Power) and IES (Integrated Energy Systems). CHP systems are much more efficient than producing electric and thermal power separately. According to the Commercial Buildings Energy Consumption Survey, 1995 [14], there were 4.6 million commercial buildings in the United States. These buildings consumed 5.3 quads of energy, about half of which was in the form of electricity. Analysis of survey data shows that CHP meets only 3.8% of the total energy needs of the commercial sector. Despite the growing energy needs, the average efficiency of power generation has remained 33% since 1960 and the average overall efficiency of generating heat and electricity using conventional methods is around 47%. And with the increase in prices in both electricity and natural gas, the need for setting up more CHP plants remains a pressing issue. CHP is known to reduce fuel costs by about 27% [15] CO released into the atmosphere. The objective of this research is to review issues related to the design of heat recovery unit in Combined Heat and Power (CHP) systems. To meet specific needs of CHP systems, configurations can be altered to affect differentfactors of the design. Before the design process can begin, product specifications, such as steam or water pressures and temperatures, and equipment, such as absorption chillers and heat exchangers, need to be identified and defined.The Mechanical Engineering Department and the Industrial Assessment Center at the University of Louisiana Lafayette has been donated an 800kW diesel turbine and a 100 ton absorption chiller from industries. This equipment needs to be integrated to work as a Combined Heat and Power system for the University which will supplement the chilled water supply and electricity. The design constraints of the heat recovery unit are the specifications of the turbine and the chiller which cannot be altered.Integrating equipment to form a CHP system generally does not always present the best solution. In our case study, the absorption chiller is not able to utilize all of the waste heat from the turbine exhaust. This is because the capacity of the chiller is too small as compared to the turbine capacity. However, the need for extra space conditioning in the buildings considered remains an issue which can be resolved through the use of this CHP system. BACKGROUND LITERATUREThe decision of setting up a CHP system involves a huge investment. Before plunging into one, any industry, commercial building or facility owner weighs it against the option of conventional generation. A dynamic stochastic model has been developed that compares the decision of an irreversible investment in a cogeneration system with that of investing in a conventional heat generation system such as steam boiler combined with the option of purchasing all the electricity from the grid [21]. This model is applied theoretically based on exempts. Keeping in mind factors such as rising emissions, and the availability and security of electricity supply, the benefits of a combined heat and power system are many.CHP systems demand that the performance of the system be well tested. The effects of various parameters such as the ambient temperature, inlet turbine temperature, compressor pressure ratio and gas turbine combustion efficiency are investigated on the performance of the CHP system and determines of each of these parameters [1]. Five major areas where CHP systems can be optimized in order to maximize profits have been identified as optimization of heat to power ratio, equipment selection, economic dispatch, intelligent performance monitoring and maintenance optimization [6].Many commercial buildings such as universities and hospitals have installed CHP systems for meeting their growing energy needs. Before the University of Dundee installed a 3 MW CHP system, first the objectives for setting up a cogeneration system in the university were laid and then accordingly the equipment was selected. Considerations for compatibility of the new CHP setup with the existing district heating plant were taken care by some alterations in pipe work so that neither system could impose any operational constraints on the other [5]. Louisiana State University installed a CHP system by contracting it to Sempra EnergyServices to meet the increase in chilled water and steam demands. The new cogeneration system was linked with the existing central power plant to supplement chilled water and steam supply. This project saves the university $ 4.7 million each year in energy costs alone and 2,200 emissions are equivalent to 530 annual vehicular emissions.Another example of a commercial CHP set-up is the Mississippi Baptist Medical Center. First the energy requirement of the hospital was assessed and the potential savings that a CHP system would generate [10]. CHP applications are not limited to the industrial and commercial sector alone. CHP systems on a micro-scale have been studied for use in residential applications. The cost of UK residential energy demand is calculated and a study is performed that compares the operating cost for the following three micro CHP technologies: Sterling engine, gas engine, and solid oxide fuel cell (SOFC) for use in homes [9].The search for different types of fuel cells in residential homes finds that a dominant cost effective design of fuel cell use in micro – CHP exists that is quickly emerging [3]. However fuel cells face competition from alternate energy products that are already in the market. Use of alternate energy such as biomass combined with natural gas has been tested for CHP applications where biomass is used as an external combustor by providing heat to partially reform the natural gas feed [16]. A similar study was preformed where solid municipal waste is integrated with natural gas fired combustion cycle for use in a waste-to-energy system which is coupled with a heat recovery steam generator that drives a steam turbine [4]. SYSTEM DESIGN CONSIDERATIONSIntegration of a CHP system is generally at two levels: the system level and the component level. Certain trade-offs between the component level metrics and system level metrics are required to achieve optimal integrated cooling, heating and power performance [18]. All CHP systems comprise mainly of three components, a power generating equipment or a turbine, a heat recovery unit and a cooling device such as an absorption chiller.There are various parameters that need to be considered at the design stage of a CHP project. For instance, the chiller efficiency together with the plant size and the electric consumption of cooling towers and condenser water pumps are analyzed to achieve the overall system design [20]. Absorption chillers work great with micro turbines. A good example is the Rolex Reality building in New York, where a 150 kW unit is hooked up with an absorption chiller that provides chilled water. An advantage of absorption chillers is that they don’t require any permits or emission treatment [2]Exhaust gas at 800°F comes out of the turbine at a flow rate of 48,880 lbs/h [7]. One important constraint during the design of the CHP system was to control the final temperature of this exhaust gas. This meant utilizing as much heat as required from the exhaust gas and subsequently bringing down the exit temperature. After running different iterations on temperature calculations, it was decided to divert 35% of the exhaust air to the heat exchanger whilethe remaining 65% is directed to go up the stack. This is achieved by using a diverter damper. In addition, diverting 35% of the gas relieves the problem of back pressure build-up at the end of the turbine.A diverter valve can also used at the inlet side of the heat exchanger which would direct the exhaust gas either to the heat exchanger or out of the bypass stack. This takes care of variable loads requirement. Inside the heat exchanger, exhaust gas enter the shell side and heats up water running in the tubes which then goes to the absorption chiller. These chillers run on either steam or hot water.The absorption chiller donated to the University runs on hot water and supplies chilled water. A continuous water circuit is made to run through the chiller to take away heat from the heat input source and also from the chilled water. The chilled water from the absorption chiller is then transferred to the existing University chilling system unit or for another use.Thermally Activated DevicesThermally activated technologies (TATs) are devices that transform heat energy for useful purposed such as heating, cooling, humidity control etc. The commonly used TATs in CHP systems are absorption chillers and desiccant dehumidifiers. Absorption chiller is a highly efficient technology that uses less energy than conventional chilling equipment, and also cools buildings without the use of ozone-depleting chlorofluorocarbons (CFCs). These chillers can be powered by natural gas, steam, or waste heat.Desiccant dehumidifiers are used in space conditioning by removing humidity. By dehumidifying the air, the chilling load on the AC equipment is reduced and the atmosphere becomes much more comfortable. Hot air coming from an air-to-air heat exchanger removes water from the desiccant wheel thereby regenerating it for further dehumidification. This makes them useful in CHP systems as they utilize the waste heat.An absorption chiller is mechanical equipment that provides cooling to buildings through chilled water. The main underlying principle behind the working of an absorption chiller is that it uses heat energy as input, instead of mechanical energy.Though the idea of using heat energy to obtain chilled water seems to be highly paradoxical, the absorption chiller is a highly efficient technology and cost effective in facilities which have significant heating loads. Moreover, unlike electrical chillers, absorption chillers cool buildings without using ozone-depleting chlorofluorocarbons (CFCs). These chillers can be powered by natural gas, steam or waste heat.Absorption chiller systems are classified in the following two ways:1. By the number of generators.i) Single effect chiller –this type of chiller, as the name suggests, uses one generator and the heat released during the absorption of the refrigerant back into the solution is rejected to the environment.ii) Double effect chiller –this chiller uses two generators paired with a single condenser, evaporator and absorber. Some of the heat released during the absorption process is used to generate more refrigerant vapor thereby increasing the chiller’s efficiency as more vapor is generated per unit heat or fuel input. A double effect chiller requires a higher temperature heat input to operate and therefore its use in CHP systems is limited by the type of electrical generation equipment it can be used with.iii) Triple effect chiller –this has three generators and even higher efficiency than a double effect chiller. As they require even higher heat input temperatures, the material choice and the absorbent/refrigerant combination is limited.2. By type of input:i) Indirect-fired absorption chillers –they use steam, hot water, or hot gases from a boiler, turbine, engine generator or fuel cell as a primary power input. Indirect-fired absorption chillers fit well into the CHP schemes where they increase the efficiency by utilizing the otherwise waste heat and producing chilled water from it.ii) Direct-fired absorption chillers –they contain burners which use fuel such as natural gas. Heat rejected from these chillers is used to provide hot water or dehumidify air by regenerating the desiccant wheel.An absorption cycle is a process which uses two fluids and some heat input to produce the refrigeration effect as compared to electrical input in a vapor compression cycle in the more familiar electrical chiller. Although both the absorption cycle and the vapor compression cycle accomplish heat removal by the evaporation of a refrigerant at a low pressure and the rejection of heat by the condensation of refrigerant at a higher pressure, the method of creating the pressure difference and circulating the refrigerant remains the primary difference between the two. The vapor compression cycle uses a mechanical compressor that creates the pressure difference necessary to circulate the refrigerant, while the same is achieved by using a secondary fluid or an absorbent in the absorption cycle [11].The primary working fluids ammonia and water in the vapor compression cycle with ammonia acting as the refrigerant and water as the absorbent are replaced by lithium bromide (LiBr) as the absorbent and water (H2O) as the refrigerant in the absorption cycle. The process occurs in two shells - the upper shell consisting of the generator and the condenser and the lower shell consisting of the evaporator and the absorber.Heat is supplied to the LiBr/H2O solution through the generator causing the refrigerant (water) to be boiled out of the solution, as in a distillation process. The resulting water vapor passes into the condenser where it is condensed back into the liquid state using a condensing medium. The water then enters the evaporator where actual cooling takes place as water is passes over tubes containing the fluid to be cooled.Heat ExchangerA very low pressure is maintained in the absorber-evaporator shell, causing the water to boil at a very low temperature. This results in water absorbing heat from the medium to be cooled and thereby lowering its temperature. The heated low pressure vapor then returns to the absorber where it mixes with the LiBr/H2O solution low in water content. Due to the solution’s low water content, vapor gets easily absorbed resulting in a weaker LiBr/H2O solution. This weak solution is pumped back to the generator where the process repeats itself.The heat recovery steam generator (HRSG) is primarily a boiler which generates steam from the waste heat of a turbine to drive a steam turbine. The heat recovery boiler design for cogeneration process applications covers many parameters. The boiler could be designed as a fire-tube, water tube or combination type. Further for each of these parameters, there is a variety of tube sizes and fin configurations. For a given boiler, a simplified method that determines the boiler performance has been developed [8].The shell and tube heat exchanger is the most common and widely used heat exchanger in different industrial applications [13]. It is compared to a classic instrument in a concert playing all the important nodes in different complex system set-ups and can be improved by using helical baffles. There are other ways to augment the heat transfer in a shell and tube exchanger such as through the use of wall-radiation [25].The design of a shell and tube heat exchanger fora combined heat and power system basically involves determining its size or geometry by predicting the overall heat transfer coefficient (U). The process of obtaining the heat transfer coefficient values is obtained from literature by correlating results from previous findings in the determination of heat exchanger designs.This involves listing assumptions at the beginning of the procedure, obtaining fluid properties, calculation of Reynolds number and the flow area to obtain the shell and tube sizes. Once U is calculated, the heat balances are calculated. This study also compares the theoretical U values with the actual experimental ones to prove the theoretical assumptions and to obtain the optimum design model [18].A mathematical simulation for the transient heat exchange of a shell and tube heat exchanger based on energy conservation and mass balance can be used to measure the performance. The design of the heat exchanger is optimized with the objective function being the total entropy generation rate considering the heat transfer and the flow resistance [20].Once a heat exchanger is designed, a total cost equation for the heat exchanger operation is deduced. Based on this, a program is developed for the optimal selection of shell-tube heat exchanger [24].The heat exchanger to be used in the CHP system in the end needs to be tested for its performance. A heat recovery module f orcogeneration is tested before use for CHP application through a microprocessor based control system to present the system design and performance data [19].The basis of a CHP system lies in efficiently capturing thermal energy and using it effectively. Generally in CHP systems, the exhaust gas from the prime mover is ducted to a heat exchanger to recover the thermal energy in the gas. The commonly used heat recovery systems are heat exchangers and Heat Recovery Steam Generators depending on whether hot water or steam is required.The heat exchanger is typically an air-to-water kind where the exhaust gas flows over some form of tube and fin heat exchange surface and the heat from the exhaust gas is transferred to make hot water. Sometimes, a diverter or a flapper damper is used to maintain a specific design temperature of the hot water or steam generation rate by regulating the exhaust flow through the heat exchanger.The HRSG is essentially a boiler that captures the heat from the exhaust of a prime mover such as a combustion turbine, gas or diesel engine to make steam. Water is pumped and circulated through the tubes which are heated by exhaust gases at temperatures ranging from 800°F to 1200°F. The water can then be held under high pressure to temperatures of 370°F or higher to produce high pressure steam [21].The Delaware method is a rating method regarded as the most suitable open-literature available for evaluating shell side performance and involves the calculation of the overall heat transfer coefficient and the pressure drops on both the shell and tube side for single-phase fluids [12]. This method can be used only when the flow rates, inlet and outlet temperatures, pressures and other physical properties of both the fluids and a minimum set of geometrical properties of the shell and tube are known. Emission ControlEmission control technologies are used in the CHP systems to remove SO2 (sulphur dioxide), SO3 (sulphur trioxide) NOx (nitrous oxide) and other particulate matter present in the exhaust of a prime mover. Some common emission control technologies are:1、Diesel Oxidation Catalyst (DOC) –They are know to reduce emissions of carbon monoxide by 70 percent, hydrocarbons by 60 percent, and particulate matter by 25 percent (Emissions Control : CHP Technologies Gulf Coast CHP 2007) when used with the ultra-low sulfur diesel (ULSD) fuel. Reductions are also significant with the use of regular diesel fuel.2、Diesel Particulate Filter (DPF) - DPF can reduce emissions of carbon monoxide, hydrocarbons, and particulate matter by approximately 90 to 95 percent (Emissions Control : CHP Technologies Gulf Coast CHP 2007). However, DPF are used only in conjunction with ultra-low sulfur diesel (ULSD) fuel.3、Exhaust Gas Recirculation (EGR) – They have a great potential for reducing NOx emissions.4、Selective Catalytic Reduction (SCR) –SCR cuts down high levels of NOx by reducing NOx to nitrogen (N2) and oxygen (O2).5、NOx absorbers –catalysts are used which adsorb NOx in the exhaust gas and dissociates it to nitrogen.CONCLUSIONSThe various components needed in a CHP system have been presented. Important parameters such as the mass flow rates of the exhaust gas and water can then be defined. The CHP system has been integrated by the use of a heat recovery unit, the design of which has been discussed. A shell and tube configuration is commonly selected based on literature survey. The pressure drops at both the shell and the tube side can be calculated after the exchanger has been sized.Integrating equipment to form a CHP system generally does not always present the best solution. In our case study, the absorption chiller is not able to utilize all of the waste heat from the turbine exhaust. Approximately 65% goes is left to go out the stack. This is because the capacity of the chiller is too small as compared to the turbine capacity. However, the need for extra space conditioning in the buildings considered remains an issue which can be resolved through the use of this CHP system.The heat exchanger designed can either be constructed following the TEMA standards or it can be built and purchased from an industrial facility. The design that is used is based on the methodology of the Bell-Delaware method and the approach is purely theoretical, so the sizing may be slightly different in industrial design. Also the manufacturing feasibility needs to be checked.After the heat exchanger is constructed, the CHP equipment can be hooked together. Again since the available equipment is integrated to work as a system, the efficiency of the CHP system needs to be calculated. Some kind of co ntrol module needs to be developed that can monitor the performance of the entire system. Finally, the cost of running the set-up needs to be determined along with the air-conditioning requirements.。

Heat exchanger is the equipment that transfer the heat from the heat fluid to the cold fluid. It is widely used in the chemical field, power field, food and other industrial field, so it plays an important role in the industry. In the chemical field, heat exchanger can be taken as the heater, cooler, condenser, evaporator and reboiler and so on. According to the working principle, it can be divided into three types: recuperative heat exchanger, mixing heat exchanger and regenerative heat exchanger. Among these three typies heat exchangers, recuperative heat exchanger is most widely used.换热器，是将热流体的部分热量传递给冷流体的设备，又称热交换器。

换热器是化工、石油、动力、食品及其它许多工业部门的通用设备，在生产中占有重要地位。

在化工生产中换热器可作为加热器、冷却器、冷凝器、蒸发器和再沸器等，应用更加广泛。

换热器种类很多，但根据冷、热流体热量交换的原理和方式基本上可分三大类即：间壁式、混合式和蓄热式。

在三类换热器中，间壁式换热器应用最多。

弓形折流板换热器螺旋折流板换热器板翅式换热器板式换热器混合式换热器（冷却塔）。