John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 19
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We havealready noted that no F -correction is needed to adjust the LMTD in thiscase. The reason is that when only one fluid changes in temperature, theconfiguration of the exchanger becomes irrelevant. Any such exchangeris equivalent to a single fluid stream flowing through an isothermal pipe.3Since all heat exchangers are equivalent in this case, it follows thatthe equation for the effectiveness in any configuration must reduce tothe same common expression as Cmax approaches infinity.
The volumetric heat capacity rate might approach infinity because the flow rate orspecific heat is very large, or it might be infinite because the flow is absorbing or giving up latent heat (as in Fig. 3.9). The limiting effectivenessexpression can also be derived directly from energy-balance considerations (see Problem 3.11), but we obtain it here by letting Cmax → ∞ ineither eqn. (3.20) or eqn. (3.21). The result islim ε = 1 − e−NTUCmax →∞3(3.22)We make use of this notion in Section 7.4, when we analyze heat convection in pipesand tubes.Heat exchanger design126§3.4Eqn.
(3.22) defines the curve for Cmin /Cmax = 0 in all six of the effectiveness graphs in Fig. 3.16 and Fig. 3.17.3.4Heat exchanger designThe preceding sections provided means for designing heat exchangersthat generally work well in the design of smaller exchangers—typically,the kind of compact cross-flow exchanger used in transportation equipment. Larger shell-and-tube exchangers pose two kinds of difficulty inrelation to U . The first is the variation of U through the exchanger, whichwe have already discussed. The second difficulty is that convective heattransfer coefficients are very hard to predict for the complicated flowsthat move through a baffled shell.We shall achieve considerable success in using analysis to predict h’sfor various convective flows in Part III.
The determination of h in a baffledshell remains a problem that cannot be solved analytically. Instead, itis normally computed with the help of empirical correlations or withthe aid of large commercial computer programs that include relevantexperimental correlations. The problem of predicting h when the flow isboiling or condensing is even more complicated. A great deal of researchis at present aimed at perfecting such empirical predictions.Apart from predicting heat transfer, a host of additional considerations must be addressed in designing heat exchangers. The primary onesare the minimization of pumping power and the minimization of fixedcosts.The pumping power calculation, which we do not treat here in anydetail, is based on the principles discussed in a first course on fluid mechanics.
It generally takes the following form for each stream of fluidthrough the heat exchanger:kgpumping power = ṁs∆p N/m2ρ kg/m3ṁ∆p N·mρsṁ∆p(W)=ρ=(3.23)where ṁ is the mass flow rate of the stream, ∆p the pressure drop ofthe stream as it passes through the exchanger, and ρ the fluid density.Determining the pressure drop can be relatively straightforward in asingle-pass pipe-in-tube heat exchanger or extremely difficulty in, say, a§3.4Heat exchanger designshell-and-tube exchanger.
The pressure drop in a straight run of pipe,for example, is given byL ρu2av(3.24)∆p = fDh2where L is the length of pipe, Dh is the hydraulic diameter, uav is themean velocity of the flow in the pipe, and f is the Darcy-Weisbach frictionfactor (see Fig. 7.6).Optimizing the design of an exchanger is not just a matter of making∆p as small as possible. Often, heat exchange can be augmented by employing fins or roughening elements in an exchanger. (We discuss suchelements in Chapter 4; see, e.g., Fig.
4.6). Such augmentation will invariably increase the pressure drop, but it can also reduce the fixed cost ofan exchanger by increasing U and reducing the required area. Furthermore, it can reduce the required flow rate of, say, coolant, by increasingthe effectiveness and thus balance the increase of ∆p in eqn. (3.23).To better understand the course of the design process, faced withsuch an array of trade-offs of advantages and penalties, we follow Taborek’s [3.6] list of design considerations for a large shell-and-tube exchanger:• Decide which fluid should flow on the shell side and which shouldflow in the tubes.
Normally, this decision will be made to minimizethe pumping cost. If, for example, water is being used to cool oil,the more viscous oil would flow in the shell. Corrosion behavior,fouling, and the problems of cleaning fouled tubes also weigh heavily in this decision.• Early in the process, the designer should assess the cost of the calculation in comparison with:(a) The converging accuracy of computation.(b) The investment in the exchanger.(c) The cost of miscalculation.• Make a rough estimate of the size of the heat exchanger using, forexample, U values from Table 2.2 and/or anything else that mightbe known from experience.
This serves to circumscribe the subsequent trial-and-error calculations; it will help to size flow ratesand to anticipate temperature variations; and it will help to avoidsubsequent errors.127128Heat exchanger design§3.4• Evaluate the heat transfer, pressure drop, and cost of various exchanger configurations that appear reasonable for the application.This is usually done with large-scale computer programs that havebeen developed and are constantly being improved as new researchis included in them.The computer runs suggested by this procedure are normally very complicated and might typically involve 200 successive redesigns, even whenrelatively efficient procedures are used.However, most students of heat transfer will not have to deal withsuch designs.
Many, if not most, will be called upon at one time or another to design smaller exchangers in the range 0.1 to 10 m2 . The heattransfer calculation can usually be done effectively with the methods described in this chapter. Some useful sources of guidance in the pressuredrop calculation are the Heat Exchanger Design Handbook [3.7], the datain Idelchik’s collection [3.8], the TEMA design book [3.1], and some of theother references at the end of this chapter.In such a calculation, we start off with one fluid to heat and one tocool. Perhaps we know the flow heat capacity rates (Cc and Ch ), certaintemperatures, and/or the amount of heat that is to be transferred. Theproblem can be annoyingly wide open, and nothing can be done untilit is somehow delimited.
The normal starting point is the specificationof an exchanger configuration, and to make this choice one needs experience. The descriptions in this chapter provide a kind of first levelof experience. References [3.5, 3.7, 3.9, 3.10, 3.11, 3.12, 3.13] provide asecond level. Manufacturer’s catalogues are an excellent source of moreadvanced information.Once the exchanger configuration is set, U will be approximately setand the area becomes the basic design variable.
The design can thenproceed along the lines of Section 3.2 or 3.3. If it is possible to beginwith a complete specification of inlet and outlet temperatures,Q = U AF (LMTD) C∆TknowncalculableThen A can be calculated and the design completed. Usually, a reevaluation of U and some iteration of the calculation is needed.More often, we begin without full knowledge of the outlet temperatures. In such cases, we normally have to invent an appropriate trial-anderror method to get the area and a more complicated sequence of trials ifwe seek to optimize pressure drop and cost by varying the configurationProblems129as well. If the C’s are design variables, the U will change significantly,because h’s are generally velocity-dependent and more iteration will beneeded.We conclude Part I of this book facing a variety of incomplete issues.Most notably, we face a serious need to be able to determine convectiveheat transfer coefficients.
The prediction of h depends on a knowledge ofheat conduction. We therefore turn, in Part II, to a much more thoroughstudy of heat conduction analysis than was undertaken in Chapter 2.In addition to setting up the methodology ultimately needed to predicth’s, Part II will also deal with many other issues that have great practicalimportance in their own right.Problems3.1Can you have a cross-flow exchanger in which both flows aremixed? Discuss.3.2Find the appropriate mean radius, r , that will makeQ = kA(r )∆T /(ro −ri ), valid for the one-dimensional heat conduction through a thick spherical shell, where A(r ) = 4π r 2 (cf.Example 3.1).3.3Rework Problem 2.14, using the methods of Chapter 3.3.42.4 kg/s of a fluid have a specific heat of 0.81 kJ/kg·K enter acounterflow heat exchanger at 0◦ C and are heated to 400◦ C by2 kg/s of a fluid having a specific heat of 0.96 kJ/kg·K enteringthe unit at 700◦ C.
Show that to heat the cooler fluid to 500◦ C,all other conditions remaining unchanged, would require thesurface area for a heat transfer to be increased by 87.5%.3.5A cross-flow heat exchanger with both fluids unmixed is usedto heat water (cp = 4.18 kJ/kg·K) from 40◦ C to 80◦ C, flowing atthe rate of 1.0 kg/s. What is the overall heat transfer coefficientif hot engine oil (cp = 1.9 kJ/kg·K), flowing at the rate of 2.6kg/s, enters at 100◦ C? The heat transfer area is 20 m2 . (Notethat you can use either an effectiveness or an LMTD method.It would be wise to use both as a check.)3.6Saturated non-oil-bearing steam at 1 atm enters the shell passof a two-tube-pass shell condenser with thirty 20 ft tubes inChapter 3: Heat exchanger design130each tube pass. They are made of schedule 160, ¾ in.
steelpipe (nominal diameter). A volume flow rate of 0.01 ft3 /s ofwater entering at 60◦ F enters each tube. The condensing heattransfer coefficient is 2000 Btu/h·ft2 ·◦ F, and we calculate h =1380 Btu/h·ft2 ·◦ F for the water in the tubes. Estimate the exittemperature of the water and mass rate of condensate [ṁc 8393 lbm /h.]3.7Consider a counterflow heat exchanger that must cool 3000kg/h of mercury from 150◦ F to 128◦ F. The coolant is 100 kg/hof water, supplied at 70◦ F.
If U is 300 W/m2 K, complete thedesign by determining reasonable value for the area and theexit-water temperature. [A = 0.147 m2 .]3.8An automobile air-conditioner gives up 18 kW at 65 km/h if theoutside temperature is 35◦ C. The refrigerant temperature isconstant at 65◦ C under these conditions, and the air rises 6◦ Cin temperature as it flows across the heat exchanger tubes. Theheat exchanger is of the finned-tube type shown in Fig. 3.6b,with U 200 W/m2 K. If U ∼ (air velocity)0.7 and the mass flowrate increases directly with the velocity, plot the percentagereduction of heat transfer in the condenser as a function of airvelocity between 15 and 65 km/h.3.9Derive eqn.
(3.21).3.10Derive the infinite NTU limit of the effectiveness of parallel andcounterflow heat exchangers at several values of Cmin /Cmax .Use common sense and the First Law of Thermodynamics, andrefer to eqn. (3.2) and eqn. (3.21) only to check your results.3.11Derive the equation ε = (NTU, Cmin /Cmax ) for the heat exchanger depicted in Fig. 3.9.3.12A single-pass heat exchanger condenses steam at 1 atm onthe shell side and heats water from 10◦ C to 30◦ C on the tubeside with U = 2500 W/m2 K. The tubing is thin-walled, 5 cm indiameter, and 2 m in length. (a) Your boss asks whether theexchanger should be counterflow or parallel-flow.
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