John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 74
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The base is heated to 650◦ C and saturated wateris suddenly poured in the tank. Plot the temperature of thebase as a function of time on the basis of Fig. 9.2 if the bottomof the base is insulated. In your graph, indicate the regimesof boiling and note the temperature at which cooling is mostrapid.9.2Predict qmax for the two heaters in Fig. 9.3b. At what percentage of qmax is each one operating?9.3A very clean glass container of water at 70◦ C is depressurizeduntil it is subcooled 30◦ C. Then it suddenly and explosively“flashes” (or boils).
What is the pressure at which this happens? Approximately what diameter of gas bubble, or otherdisturbance in the liquid, caused it to flash?9.4Plot the unstable bubble radius as a function of liquid superheat for water at 1 atm. Comment on the significance of yourcurve.9.5In chemistry class you have probably witnessed the phenomenonof “bumping” in a test tube (the explosive boiling that blowsthe contents of the tube all over the ceiling). Yet you havenever seen this happen in a kitchen pot.
Explain why not.9.6Use van der Waal’s equation of state to approximate the highest reduced temperature to which water can be superheated atlow pressure. How many degrees of superheat does this suggest that water can sustain at the low pressure of 1 atm? (Itturns out that this calculation is accurate within about 10%.)What would Rb be at this superheat?9.7Use Yamagata’s equation, (9.3), to determine how nucleationsite density increases with ∆T for Berenson’s curves in Fig.
9.14.(That is, find c in the relation n = constant ∆T c .)9.8Suppose that Csf for a given surface is high by 50%. What willbe the percentage error in q calculated for a given value of ∆T ?[Low by 70%.]514Chapter 9: Heat transfer in boiling and other phase-change configurations9.9Water at 100 atm boils on a nickel heater whose temperatureis 6◦ C above Tsat . Find h and q.9.10Water boils on a large flat plate at 1 atm.
Calculate qmax if the1plate is operated on the surface of the moon (at 6 of gearth−normal ).What would qmax be in a space vehicle experiencing 10−4 ofgearth−normal ?9.11Water boils on a 0.002 m diameter horizontal copper wire. Plot,to scale, as much of the boiling curve on log q vs. log ∆T coordinates as you can.
The system is at 1 atm.9.12Redo Problem 9.11 for a 0.03 m diameter sphere in water at10 atm.9.13Verify eqn. (9.17).9.14Make a sketch of the q vs. (Tw −Tsat ) relation for a pool boilingprocess, and invent a graphical method for locating the pointswhere h is maximum and minimum.9.15A 2 mm diameter jet of methanol is directed normal to thecenter of a 1.5 cm diameter disk heater at 1 m/s. How manywatts can safely be supplied by the heater?9.16Saturated water at 1 atm boils on a ½ cm diameter platinumrod. Estimate the temperature of the rod at burnout.9.17Plot (Tw − Tsat ) and the quality x as a function of position xfor the conditions in Example 9.9. Set x = 0 where x = 0 andend the plot where the quality reaches 80%.9.18Plot (Tw − Tsat ) and the quality x as a function of position inan 8 cm I.D.
pipe if 0.3 kg/s of water at 100◦ C passes throughit and qw = 200, 000 W/m2 .9.19Use dimensional analysis to verify the form of eqn. (9.8).9.20Compare the peak heat flux calculated from the data given inProblem 5.6 with the appropriate prediction. [The predictionis within 11%.]Problems9.21515The Kandlikar correlation, eqn. (9.50a), can be adapted subcooled flow boiling, with x = 0 (region B in Fig. 9.19). Notingthat qw = hfb (Tw − Tsat ), show that1/0.3qw = 1058 hlo F (Ghfg )−0.7 (Tw − Tsat )in subcooled flow boiling [9.47].9.22Verify eqn.
(9.53) by repeating the analysisfollowing eqn. (8.47)but using the b.c. (∂u/∂y)y=δ = τδ µ in place of (∂u/∂y)y=δ= 0. Verify the statement involving eqn. (9.54).9.23A cool-water-carrying pipe 7 cm in outside diameter has anoutside temperature of 40◦ C. Saturated steam at 80◦ C flowsacross it. Plot hcondensation over the range of Reynolds numbers0 ReD 106 . Do you get the value at ReD = 0 that you wouldanticipate from Chapter 8?9.24(a) Suppose that you have pits of roughly 0.002 mm diameter in a metallic heater surface. At about what temperaturemight you expect water to boil on that surface if the pressureis 20 atm. (b) Measurements have shown that water at atmospheric pressure can be superheated about 200◦ C above itsnormal boiling point. Roughly how large an embryonic bubblewould be needed to trigger nucleation in water in such a state.9.25Obtain the dimensionless functional form of the pool boilingqmax equation and the qmax equation for flow boiling on external surfaces, using dimensional analysis.9.26A chemist produces a nondegradable additive that will increaseσ by a factor of ten for water at 1 atm.
By what factor will theadditive improve qmax during pool boiling on (a) infinite flatplates and (b) small horizontal cylinders? By what factor willit improve burnout in the flow of jet on a disk?9.27Steam at 1 atm is blown at 26 m/s over a 1 cm O.D. cylinder at90◦ C. What is h? Can you suggest any physical process withinthe cylinder that could sustain this temperature in this flow?9.28The water shown in Fig.
9.17 is at 1 atm, and the Nichromeheater can be approximated as nickel. What is Tw − Tsat ?516Chapter 9: Heat transfer in boiling and other phase-change configurations9.29For film boiling on horizontal cylinders, eqn. (9.6) is modifiedto−1/2√g(ρf − ρg )2+λd = 2π 3.σ(diam.)2If ρf is 748 kg/m3 for saturated acetone, compare this λd , andthe flat plate value, with Fig. 9.3d.9.30Water at 47◦ C flows through a 13 cm diameter thin-walled tubeat 8 m/s. Saturated water vapor, at 1 atm, flows across the tubeat 50 m/s. Evaluate Ttube , U , and q.9.31A 1 cm diameter thin-walled tube carries liquid metal throughsaturated water at 1 atm.
The throughflow of metal is increased until burnout occurs. At that point the metal temperature is 250◦ C and h inside the tube is 9600 W/m2 K. Whatis the wall temperature at burnout?9.32At about what velocity of liquid metal flow does burnout occurin Problem 9.31 if the metal is mercury?9.33Explain, in physical terms, why eqns. (9.23) and (9.24), insteadof differing by a factor of two, are almost equal. How do theseequations change when H is large?9.34A liquid enters the heated section of a pipe at a location z = 0with a specific enthalpy ĥin . If the wall heat flux is qw and thepipe diameter is D, show that the enthalpy a distance z = Ldownstream isπD Lqw dz.ĥ = ĥin +ṁ 0Since the quality may be defined as x ≡ (ĥ − ĥf ,sat ) hfg , showthat for constant qwx=9.35ĥin − ĥf ,sathfg+4qw LGDConsider again the x-ray monochrometer described in Problem7.44.
Suppose now that the mass flow rate of liquid nitrogenis 0.023 kg/s, that the nitrogen is saturated at 110 K whenit enters the heated section, and that the passage horizontal.Estimate the quality and the wall temperature at end of theReferencesheated section if F = 4.70 for nitrogen in eqns. (9.50). Asbefore, assume the silicon to conduct well enough that the heatload is distributed uniformly over the surface of the passage.9.36Use data from Appendix A and Sect. 9.1 to calculate the meritnumber, M, for the following potential heat-pipe working fluids over the range 200 K to 600 K in 100 K increments: water,mercury, methanol, ammonia, and HCFC-22.
If data are unavailable for a fluid in some range, indicate so. What fluids arebest suited for particular temperature ranges?References[9.1] S. Nukiyama. The maximum and minimum values of the heat qtransmitted from metal to boiling water under atmospheric pressure. J. Jap. Soc. Mech. Eng., 37:367–374, 1934. (transl.: Int. J. HeatMass Transfer, vol. 9, 1966, pp. 1419–1433).[9.2] T. B. Drew and C. Mueller. Boiling. Trans. AIChE, 33:449, 1937.[9.3] International Association for the Properties of Water and Steam.Release on surface tension of ordinary water substance.
Technicalreport, September 1994. Available from the Executive Secretary ofIAPWS or on the internet: http://www.iapws.org/.[9.4] J. J. Jasper. The surface tension of pure liquid compounds. J. Phys.Chem. Ref. Data, 1(4):841–1010, 1972.[9.5] M. Okado and K. Watanabe. Surface tension correlations for severalfluorocarbon refrigerants. Heat Transfer: Japanese Research, 17(1):35–52, 1988.[9.6] A. P. Fröba, S. Will, and A. Leipertz. Saturated liquid viscosity andsurface tension of alternative refrigerants. Intl. J. Thermophys., 21(6):1225–1253, 2000.[9.7] V.G. Baidakov and I.I. Sulla.
Surface tension of propane and isobutane at near-critical temperatures. Russ. J. Phys. Chem., 59(4):551–554, 1985.[9.8] P.O. Binney, W.-G. Dong, and J. H. Lienhard. Use of a cubic equationto predict surface tension and spinodal limits. J. Heat Transfer,108(2):405–410, 1986.517518Chapter 9: Heat transfer in boiling and other phase-change configurations[9.9] Y. Y. Hsu. On the size range of active nucleation cavities on aheating surface. J. Heat Transfer, Trans.
ASME, Ser. C, 84:207–216, 1962.[9.10] G. F. Hewitt. Boiling. In W. M. Rohsenow, J. P. Hartnett, and Y. I.Cho, editors, Handbook of Heat Transfer, chapter 15. McGraw-Hill,New York, 3rd edition, 1998.[9.11] K. Yamagata, F. Hirano, K. Nishiwaka, and H. Matsuoka. Nucleateboiling of water on the horizontal heating surface. Mem. Fac. Eng.Kyushu, 15:98, 1955.[9.12] W. M. Rohsenow.
A method of correlating heat transfer data forsurface boiling of liquids. Trans. ASME, 74:969, 1952.[9.13] I. L. Pioro. Experimental evaluation of constants for the Rohsenowpool boiling correlation. Int. J. Heat. Mass Transfer, 42:2003–2013,1999.[9.14] R. Bellman and R. H. Pennington. Effects of surface tension andviscosity on Taylor instability. Quart. Appl. Math., 12:151, 1954.[9.15] V.
Sernas. Minimum heat flux in film boiling—a three dimensional model. In Proc. 2nd Can. Cong. Appl. Mech., pages 425–426,Canada, 1969.[9.16] H. Lamb. Hydrodynamics. Dover Publications, Inc., New York, 6thedition, 1945.[9.17] N. Zuber. Hydrodynamic aspects of boiling heat transfer. AECReport AECU-4439, Physics and Mathematics, 1959.[9.18] J. H. Lienhard and V. K.
Dhir. Extended hydrodynamic theory ofthe peak and minimum pool boiling heat fluxes. NASA CR-2270,July 1973.[9.19] J. H. Lienhard, V. K. Dhir, and D. M. Riherd. Peak pool boilingheat-flux measurements on finite horizontal flat plates. J. HeatTransfer, Trans. ASME, Ser.
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