John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 56
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Compare the resultwith the value you read from the figure.7.26Report the maximum percent scatter of data in Fig. 7.13. Whatis happening in the fluid flow when the scatter is worst?7.27Water at 27◦ C flows at 2.2 m/s in a 0.04 m I.D. thin-walledpipe. Air at 227◦ C flows across it at 7.6 m/s. Find the pipewall temperature.7.28Freshly painted aluminum rods, 0.02 m in diameter, are withdrawn from a drying oven at 150◦ C and cooled in a 3 m/s crossflow of air at 23◦ C. How long will it take to cool them to 50◦ Cso that they can be handled?7.29At what speed, u∞ , must 20◦ C air flow across an insulatedtube before the insulation on it will do any good? The tube isat 60◦ C and is 6 mm in diameter.
The insulation is 12 mm indiameter, with k = 0.08 W/m·K. (Notice that we do not ask forthe u∞ for which the insulation will do the most harm.)7.30Water at 37◦ C flows at 3 m/s across at 6 cm O.D. tube that isheld at 97◦ C. In a second configuration, 37◦ C water flows at anaverage velocity of 3 m/s through a bundle of 6 cm O.D. tubesthat are held at 97◦ C.
The bundle is staggered, with ST /SL = 2.Compare the heat transfer coefficients for the two situations.Chapter 7: Forced convection in a variety of configurations3907.31It is proposed to cool 64◦ C air as it flows, fully developed,in a 1 m length of 8 cm I.D. smooth, thin-walled tubing. Thecoolant is Freon 12 flowing, fully developed, in the opposite direction, in eight smooth 1 cm I.D. tubes equally spaced aroundthe periphery of the large tube.
The Freon enters at −15◦ C andis fully developed over almost the entire length. The averagespeeds are 30 m/s for the air and 0.5 m/s for the Freon. Determine the exiting air temperature, assuming that solderingprovides perfect thermal contact between the entire surface ofthe small tubes and the surface of the large tube. Criticize theheat exchanger design and propose some design improvement.7.32Evaluate NuD using Giedt’s data for air flowing over a cylinderat ReD = 140, 000.
Compare your result with the appropriatecorrelation and with Fig. 7.13.7.33A 25 mph wind blows across a 0.25 in. telephone line. What isthe pitch of the hum that it emits?7.34A large Nichrome V slab, 0.2 m thick, has two parallel 1 cm I.D.holes drilled through it. Their centers are 8 cm apart. Onecarries liquid CO2 at 1.2 m/s from a −13◦ C reservoir below.The other carries methanol at 1.9 m/s from a 47◦ C reservoirabove. Take account of the intervening Nichrome and computethe heat transfer.
Need we worry about the CO2 being warmedup by the methanol?7.35Consider the situation described in Problem 4.38 but supposethat you do not know h. Suppose, instead, that you know thereis a 10 m/s cross flow of 27◦ C air over the rod. Then reworkthe problem.7.36A liquid whose properties are not known flows across a 40 cmO.D. tube at 20 m/s. The measured heat transfer coefficient is8000 W/m2 K. We can be fairly confident that ReD is very largeindeed. What would h be if D were 53 cm? What would h beif u∞ were 28 m/s?7.37Water flows at 4 m/s, at a temperature of 100◦ C, in a 6 cm I.D.thin-walled tube with a 2 cm layer of 85% magnesia insulationon it.
The outside heat transfer coefficient is 6 W/m2 K, and theoutside temperature is 20◦ C. Find: (a) U based on the insideProblems391area, (b) Q W/m, and (c) the temperature on either side of theinsulation.7.38Glycerin is added to water in a mixing tank at 20◦ C. The mixture discharges through a 4 m length of 0.04 m I.D.
tubingunder a constant 3 m head. Plot the discharge rate in m3 /hras a function of composition.7.39Plot h as a function of composition for the discharge pipe inProblem 7.38. Assume a small temperature difference.7.40Rework Problem 5.40 without assuming the Bi number to bevery large.7.41Water enters a 0.5 cm I.D. pipe at 24◦ C. The pipe walls are heldat 30◦ C. Plot Tb against distance from entry if uav is 0.27 m/s,neglecting entry behavior in your calculation. (Indicate the entry region on your graph, however.)7.42Devise a numerical method to find the velocity distributionand friction factor for laminar flow in a square duct of sidelength a.
Set up a square grid of size N by N and solve thedifference equations by hand for N = 2, 3, and 4. Hint : Firstshow that the velocity distribution is given by the solution tothe equation∂2u∂2u+=1∂x 2∂y 2whereu = 0 on the sides of the square and we define u =u [(a2 /µ)(dp/dz)], x = (x/a), and y = (y/a). Then showthat the friction factor, f [eqn. (7.34)], is given byf =−2Aρuav au dxdyµNote that the area integral can be evaluated as7.43#u/N 2 .Chilled air at 15◦ C enters a horizontal duct at a speed of 1 m/s.The duct is made of thin galvanized steel and is not insulated.A 30 m section of the duct runs outdoors through humid airat 30◦ C.
Condensation of moisture on the outside of the ductis undesirable, but it will occur if the duct wall is at or belowChapter 7: Forced convection in a variety of configurations392the dew point temperature of 20◦ C. For this problem, assumethat condensation rates are so low that their thermal effectscan be ignored.a.
Suppose that the duct’s square cross-section is 0.3 m by0.3 m and the effective outside heat transfer coefficientis 5 W/m2 K in still air. Determine whether condensationoccurs.b. The single duct is replaced by four circular horizontalducts, each 0.17 m in diameter. The ducts are parallelto one another in a vertical plane with a center-to-centerseparation of 0.5 m. Each duct is wrapped with a layerof fiberglass insulation 6 cm thick (ki = 0.04 W/m·K) andcarries air at the same inlet temperature and speed as before. If a 15 m/s wind blows perpendicular to the planeof the circular ducts, find the bulk temperature of the airexiting the ducts.7.44An x-ray “monochrometer” is a mirror that reflects only a single wavelength from a broadband beam of x-rays.
Over 99%of the beam’s energy arrives on other wavelengths and is absorbed creating a high heat flux on part of the surface of themonochrometer. Consider a monochrometer made from a silicon block 10 mm long and 3 mm by 3 mm in cross-sectionwhich absorbs a flux of 12.5 W/mm2 over an area of 6 mm2 onone face (a heat load of 75 W). To control the temperature, itis proposed to pump liquid nitrogen through a circular channel bored down the center of the silicon block. The channel is10 mm long and 1 mm in diameter.
LN2 enters the channel at80 K and a pressure of 1.6 MPa (Tsat = 111.5 K). The entry tothis channel is a long, straight, unheated passage of the samediameter.a. For what range of mass flow rates will the LN2 have a bulktemperature rise of less than 1.5 K over the length of thechannel?b. At your minimum flow rate, estimate the maximum walltemperature in the channel. As a first approximation, assume that the silicon conducts heat well enough to distribute the 75 W heat load uniformly over the channelReferences393surface.
Could boiling occur in the channel? Discuss theinfluence of entry length and variable property effects.7.45Turbulent fluid velocities are sometimes measured with a constant temperature hot-wire anemometer, which consists of along, fine wire (typically platinum, 4µm in diameter and 1.25mm long) supported between two much larger needles. Theneedles are connected to an electronic bridge circuit whichelectrically heats the wire while adjusting the heating voltage,Vw , so that the wire’s temperature — and thus its resistance,Rw — stays constant. The electrical power dissipated in the2 /R , is convected away at the surface of the wire.
Anwire, Vwwalyze the heat loss from the wire to show2= (Twire − Tflow ) A + Bu1/2Vwwhere u is the instantaneous flow speed perpendicular to thewire. Assume that u is between 2 and 100 m/s and that thefluid is an isothermal gas. The constants A and B depend onproperties, dimensions, and resistance; they are usually foundby calibration of the anemometer. This result is called King’slaw.7.46(a) Show that the Reynolds number for a circular tube maybewritten in terms of the mass flow rate as ReD = 4ṁ π µD.(b) Show that this result does not apply to a noncircular tube,specifically ReDh ≠ 4ṁ π µDh .References[7.1] F.
M. White. Viscous Fluid Flow. McGraw-Hill Book Company, NewYork, 1974.[7.2] S. S. Mehendale, A. M. Jacobi, and R. K. Shah. Fluid flow and heattransfer at micro- and meso-scales with application to heat exchanger design. Appl. Mech. Revs., 53(7):175–193, 2000.[7.3] W. M. Kays and M. E.
Crawford. Convective Heat and Mass Transfer.McGraw-Hill Book Company, New York, 3rd edition, 1993.394Chapter 7: Forced convection in a variety of configurations[7.4] R. K. Shah and M. S. Bhatti. Laminar convective heat transferin ducts. In S. Kakaç, R. K. Shah, and W. Aung, editors, Handbook of Single-Phase Convective Heat Transfer, chapter 3. WileyInterscience, New York, 1987.[7.5] R. K. Shah and A.
L. London. Laminar Flow Forced Convection inDucts. Academic Press, Inc., New York, 1978. Supplement 1 to theseries Advances in Heat Transfer.[7.6] L. Graetz. Über die wärmeleitfähigkeit von flüssigkeiten. Ann.Phys., 25:337, 1885.[7.7] S. R. Sellars, M. Tribus, and J. S.
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