John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 20
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How do youadvise her? Evaluate: (b) the LMTD; (c) ṁH2 O ; (d) ε. [ε 0.222.]Problems3.13131Air at 2 kg/s and 27◦ C and a stream of water at 1.5 kg/s and60◦ C each enter a heat exchanger. Evaluate the exit temperatures if A = 12 m2 , U = 185 W/m2 K, and:a. The exchanger is parallel flow;b. The exchanger is counterflow [Thout 54.0◦ C.];c. The exchanger is cross-flow, one stream mixed;d. The exchanger is cross-flow, neither stream mixed.[Thout = 53.62◦ C.]3.14Air at 0.25 kg/s and 0◦ C enters a cross-flow heat exchanger.It is to be warmed to 20◦ C by 0.14 kg/s of air at 50◦ C. Thestreams are unmixed. As a first step in the design process,plot U against A and identify the approximate range of areafor the exchanger.3.15A particular two shell-pass, four tube-pass heat exchanger uses20 kg/s of river water at 10◦ C on the shell side to cool 8 kg/sof processed water from 80◦ C to 25◦ C on the tube side.
Atwhat temperature will the coolant be returned to the river? IfU is 800 W/m2 K, how large must the exchanger be?3.16A particular cross-flow process heat exchanger operates withthe fluid mixed on one side only. When it is new, U = 2000W/m2 K, Tcin = 25◦ C, Tcout = 80◦ C, Thin = 160◦ C, and Thout =70◦ C. After 6 months of operation, the plant manager reportsthat the hot fluid is only being cooled to 90◦ C and that he issuffering a 30% reduction in total heat transfer. What is thefouling resistance after 6 months of use? (Assume no reduction of cold-side flow rate by fouling.)3.17Water at 15◦ C is supplied to a one-shell-pass, two-tube-passheat exchanger to cool 10 kg/s of liquid ammonia from 120◦ Cto 40◦ C.
You anticipate a U on the order of 1500 W/m2 K whenthe water flows in the tubes. If A is to be 90 m2 , choose thecorrect flow rate of water.3.18Suppose that the heat exchanger in Example 3.5 had been a twoshell-pass, four tube-pass exchanger with the hot fluid movingin the tubes. (a) What would be the exit temperature in thiscase? [Tcout = 75.09◦ C.] (b) What would be the area if we wantedChapter 3: Heat exchanger design132the hot fluid to leave at the same temperature that it does inthe example?3.19Plot the maximum tolerable fouling resistance as a functionof Unew for a counterflow exchanger, with given inlet temperatures, if a 30% reduction in U is the maximum that can betolerated.3.20Water at 0.8 kg/s enters the tubes of a two-shell-pass, fourtube-pass heat exchanger at 17◦ C and leaves at 37◦ C.
It cools0.5 kg/s of air entering the shell at 250◦ C with U = 432 W/m2 K.Determine: (a) the exit air temperature; (b) the area of the heatexchanger; and (c) the exit temperature if, after some time,the tubes become fouled with Rf = 0.0005 m2 K/W. [(c) Tairout= 140.5◦ C.]3.21You must cool 78 kg/min of a 60%-by-mass mixture of glycerinin water from 108◦ C to 50◦ C using cooling water available at7◦ C. Design a one-shell-pass, two-tube-pass heat exchanger ifU = 637 W/m2 K. Explain any design decision you make andreport the area, TH2 Oout , and any other relevant features.3.22A mixture of 40%-by-weight glycerin, 60% water, enters a smooth0.113 m I.D.
tube at 30◦ C. The tube is kept at 50◦ C, and ṁmixture= 8 kg/s. The heat transfer coefficient inside the pipe is 1600W/m2 K. Plot the liquid temperature as a function of positionin the pipe.3.23Explain in physical terms why all effectiveness curves Fig. 3.16and Fig. 3.17 have the same slope as NTU → 0. Obtain thisslope from eqns. (3.20) and (3.21).3.24You want to cool air from 150◦ C to 60◦ C but you cannot afford a custom-built heat exchanger.
You find a used cross-flowexchanger (both fluids unmixed) in storage. It was previouslyused to cool 136 kg/min of NH3 vapor from 200◦ C to 100◦ C using 320 kg/min of water at 7◦ C; U was previously 480 W/m2 K.How much air can you cool with this exchanger, using the samewater supply, if U is approximately unchanged? (Actually, youwould have to modify U using the methods of Chapters 6 and7 once you had the new air flow rate, but that is beyond ourpresent scope.)Problems1333.25A one tube-pass, one shell-pass, parallel-flow, process heat exchanger cools 5 kg/s of gaseous ammonia entering the shellside at 250◦ C and boils 4.8 kg/s of water in the tubes.
The water enters subcooled at 27◦ C and boils when it reaches 100◦ C.U = 480 W/m2 K before boiling begins and 964 W/m2 K thereafter. The area of the exchanger is 45 m2 , and hfg for wateris 2.257 × 106 J/kg. Determine the quality of the water at theexit.3.260.72 kg/s of superheated steam enters a crossflow heat exchanger at 240◦ C and leaves at 120◦ C. It heats 0.6 kg/s of waterentering at 17◦ C. U = 612 W/m2 K. By what percentage will thearea differ if a both-fluids-unmixed exchanger is used insteadof a one-fluid-unmixed exchanger? [−1.8%]3.27Compare values of F from Fig.
3.14(c) and Fig. 3.14(d) for thesame conditions of inlet and outlet temperatures. Is the onewith the higher F automatically the more desirable exchanger?Discuss.3.28Compare values of ε for the same NTU and Cmin /Cmax in parallel and counterflow heat exchangers. Is the one with the higherε automatically the more desirable exchanger? Discuss.3.29The irreversibility rate of a process is equal to the rate of entropy production times the lowest absolute sink temperatureaccessible to the process. Calculate the irreversibility (or lostwork) for the heat exchanger in Example 3.4. What kind ofconfiguration would reduce the irreversibility, given the sameend temperatures.3.30Plot Toil and TH2 O as a function of position in a very long counterflow heat exchanger where water enters at 0◦ C, with CH2 O =460 W/K, and oil enters at 90◦ C, with Coil = 920 W/K, U = 742W/m2 K, and A = 10 m2 .
Criticize the design.3.31Liquid ammonia at 2 kg/s is cooled from 100◦ C to 30◦ C in theshell side of a two shell-pass, four tube-pass heat exchangerby 3 kg/s of water at 10◦ C. When the exchanger is new, U =750 W/m2 K. Plot the exit ammonia temperature as a functionof the increasing tube fouling factor.Chapter 3: Heat exchanger design1343.32A one shell-pass, two tube-pass heat exchanger cools 0.403kg/s of methanol from 47◦ C to 7◦ C on the shell side. Thecoolant is 2.2 kg/s of Freon 12, entering the tubes at −33◦ C,with U = 538 W/m2 K. A colleague suggests that this arrangement wastes Freon. She thinks you could do almost as well ifyou cut the Freon flow rate all the way down to 0.8 kg/s. Calculate the new methanol outlet temperature that would resultfrom this flow rate, and evaluate her suggestion.3.33The factors dictating the heat transfer coefficients in a certaintwo shell-pass, four tube-pass heat exchanger are such thatU increases as (ṁshell )0.6 .
The exchanger cools 2 kg/s of airfrom 200◦ C to 40◦ C using 4.4 kg/s of water at 7◦ C, and U = 312W/m2 K under these circumstances. If we double the air flow,what will its temperature be leaving the exchanger? [Tairout =61◦ C.]3.34A flow rate of 1.4 kg/s of water enters the tubes of a two-shellpass, four-tube-pass heat exchanger at 7◦ C. A flow rate of 0.6kg/s of liquid ammonia at 100◦ C is to be cooled to 30◦ C onthe shell side; U = 573 W/m2 K. (a) How large must the heatexchanger be? (b) How large must it be if, after some months,a fouling factor of 0.0015 will build up in the tubes, and we stillwant to deliver ammonia at 30◦ C? (c) If we make it large enoughto accommodate fouling, to what temperature will it cool theammonia when it is new? (d) At what temperature does waterleave the new, enlarged exchanger? [(d) TH2 O = 49.9◦ C.]3.35Both C’s in a parallel-flow heat exchanger are equal to 156 W/K,U = 327 W/m2 K and A = 2 m2 .
The hot fluid enters at 140◦ Cand leaves at 90◦ C. The cold fluid enters at 40◦ C. If both C’sare halved, what will be the exit temperature of the hot fluid?3.36A 1.68 ft2 cross-flow heat exchanger with one fluid mixed condenses steam at atmospheric pressure (h = 2000 Btu/h·ft2 ·◦ F)and boils methanol (Tsat = 170◦ F and h = 1500 Btu/h·ft2 ·◦ F) onthe other side. Evaluate U (neglecting resistance of the metal),LMTD, F , NTU, ε, and Q.3.37Eqn. (3.21) is troublesome when Cmin /Cmax = 1. Develop aworking equation for ε in this case.
Compare it with Fig. 3.16.Problems3.38135The effectiveness of a cross-flow exchanger with neither fluidmixed can be calculated from the following approximate formula:ε = 1 − exp exp(−NTU0.78 r ) − 1](NTU0.22 /r )where r ≡ Cmin /Cmax . How does this compare with correctvalues?3.39Calculate the area required in a two-tube-pass, one-shell-passcondenser that is to condense 106 kg/h of steam at 40◦ C usingwater at 17◦ C. Assume that U = 4700 W/m2 K, the maximumallowable temperature rise of the water is 10◦ C, and hfg = 2406kJ/kg.3.40An engineer wants to divert 1 gal/min of water at 180◦ F fromhis car radiator through a small cross-flow heat exchanger withneither flow mixed, to heat 40◦ F water to 140◦ F for shavingwhen he goes camping. If he produces a pint per minute ofhot water, what will be the area of the exchanger and the temperature of the returning radiator coolant if U = 720 W/m2 K?3.41In a process for forming lead shot, molten droplets of leadare showered into the top of a tall tower.
The droplets fallthrough air and solidify before they reach the bottom of thetower. The solid shot is collected at the bottom. To maintain asteady state, cool air is introduced at the bottom of the towerand warm air is withdrawn at the top. For a particular tower,the droplets are 1 mm in diameter and at their melting temperature of 600 K when they are released. The latent heat ofsolidification is 850 kJ/kg.
They fall with a mass flow rate of200 kg/hr. There are 2430 droplets per cubic meter of air inside the tower. Air enters the bottom at 20◦ C with a mass flowrate of 1100 kg/hr. The tower has an internal diameter of 1 mwith adiabatic walls.a. Sketch, qualitatively, the temperature distributions of theshot and the air along the height of the tower.b. If it is desired to remove the shot at a temperature of60◦ C, what will be the temperature of the air leaving thetop of the tower?Chapter 3: Heat exchanger design136c.
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