John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 55
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The Handbook of Heat Transfer [7.31],the shelf of heat transfer texts in your library, or the journals referredto by the Engineering Index are among the first places to look for a correlation curve or equation. When you find a correlation, there are manyquestions that you should ask yourself:• Is my case included within the range of dimensionless parametersupon which the correlation is based, or must I extrapolate to reachmy case?• What geometric differences exist between the situation representedin the correlation and the one I am dealing with? (Such elements asthese might differ:(a) inlet flow conditions;(b) small but important differences in hardware, mounting brackets, and so on;(c) minor aspect ratio or other geometric nonsimilarities• Does the form of the correlating equation that represents the data,if there is one, have any basis in theory? (If it is only a curve fit tothe existing data, one might be unjustified in using it for more thaninterpolation of those data.)• What nuisance variables might make our systems different? Forexample:(a) surface roughness;(b) fluid purity;(c) problems of surface wetting• To what extend do the data scatter around the correlation line? Areerror limits reported? Can I actually see the data points? (In thisregard, you must notice whether you are looking at a correlation385Chapter 7: Forced convection in a variety of configurations386on linear or logarithmic coordinates.
Errors usually appear smallerthan they really are on logarithmic coordinates. Compare, for example, the data of Figs. 8.3 and 8.10.)• Are the ranges of physical variables large enough to guarantee thatI can rely on the correlation for the full range of dimensionlessgroups that it purports to embrace?• Am I looking at a primary or secondary source (i.e., is this the author’s original presentation or someone’s report of the original)? Ifit is a secondary source, have I been given enough information toquestion it?• Has the correlation been signed by the persons who formulated it?(If not, why haven’t the authors taken responsibility for the work?)Has it been subjected to critical review by independent experts inthe field?Problems7.17.2Prove that in fully developed laminar pipe flow, (−dp/dx)R 2 4µis twice the average velocity in the pipe.
To do this, set themass flow rate through the pipe equal to (ρuav )(area).A flow of air at 27◦ C and 1 atm is hydrodynamically fully developed in a 1 cm I.D. pipe with uav = 2 m/s. Plot (to scale) Tw ,qw , and Tb as a function of the distance x after Tw is changedor qw is imposed:a. In the case for which Tw = 68.4◦ C = constant.b. In the case for which qw = 378 W/m2 = constant.Indicate xet on your graphs.7.3Prove that Cf is 16/ReD in fully developed laminar pipe flow.7.4Air at 200◦ C flows at 4 m/s over a 3 cm O.D. pipe that is keptat 240◦ C. (a) Find h. (b) If the flow were pressurized water at200◦ C, what velocities would give the same h, the same NuD ,and the same ReD ? (c) If someone asked if you could modelthe water flow with an air experiment, how would you answer?[u∞ = 0.0156 m/s for same NuD .]Problems3877.5Compare the h value calculated in Example 7.3 with thosecalculated from the Dittus-Boelter, Colburn, and Sieder-Tateequations.
Comment on the comparison.7.6Water at Tblocal = 10◦ C flows in a 3 cm I.D. pipe at 1 m/s. Thepipe walls are kept at 70◦ C and the flow is fully developed.Evaluate h and the local value of dTb /dx at the point of interest. The relative roughness is 0.001.7.7Water at 10◦ C flows over a 3 cm O.D. cylinder at 70◦ C. Thevelocity is 1 m/s. Evaluate h.7.8Consider the hot wire anemometer in Example 7.7. Supposethat 17.8 W/m is the constant heat input, and plot u∞ vs. Twireover a reasonable range of variables. Must you deal with anychanges in the flow regime over the range of interest?7.9Water at 20◦ C flows at 2 m/s over a 2 m length of pipe, 10 cm indiameter, at 60◦ C. Compare h for flow normal to the pipe withthat for flow parallel to the pipe.
What does the comparisonsuggest about baffling in a heat exchanger?7.10A thermally fully developed flow of NaK in a 5 cm I.D. pipemoves at uav = 8 m/s. If Tb = 395◦ C and Tw is constant at403◦ C, what is the local heat transfer coefficient? Is the flowlaminar or turbulent?7.11Water enters a 7 cm I.D. pipe at 5◦ C and moves through it at anaverage speed of 0.86 m/s. The pipe wall is kept at 73◦ C. PlotTb against the position in the pipe until (Tw − Tb )/68 = 0.01.Neglect the entry problem and consider property variations.7.12Air at 20◦ C flows over a very large bank of 2 cm O.D. tubesthat are kept at 100◦ C.
The air approaches at an angle 15◦ offnormal to the tubes. The tube array is staggered, with SL =3.5 cm and ST = 2.8 cm. Find h on the first tubes and on thetubes deep in the array if the air velocity is 4.3 m/s before itenters the array. [hdeep = 118 W/m2 K.]7.13Rework Problem 7.11 using a single value of h evaluated at3(73 − 5)/4 = 51◦ C and treating the pipe as a heat exchanger. At what length would you judge that the pipe is no longerefficient as an exchanger? Explain.Chapter 7: Forced convection in a variety of configurations3887.14Go to the periodical engineering literature in your library.
Finda correlation of heat transfer data. Evaluate the applicability ofthe correlation according to the criteria outlined in Section 7.7.7.15Water at 24◦ C flows at 0.8 m/s in a smooth, 1.5 cm I.D. tubethat is kept at 27◦ C. The system is extremely clean and quiet,and the flow stays laminar until a noisy air compressor is turnedon in the laboratory. Then it suddenly goes turbulent. Calculate the ratio of the turbulent h to the laminar h. [hturb =4429 W/m2 K.]7.16Laboratory observations of heat transfer during the forced flowof air at 27◦ C over a bluff body, 12 cm wide, kept at 77◦ C yieldq = 646 W/m2 when the air moves 2 m/s and q = 3590 W/m2when it moves 18 m/s. In another test, everything else is thesame, but now 17◦ C water flowing 0.4 m/s yields 131,000 W/m2 .The correlations in Chapter 7 suggest that, with such limiteddata, we can probably create a fairly good correlation in theform: NuL = CRea Prb .
Estimate the constants C, a, and b bycross-plotting the data on log-log paper.7.17Air at 200 psia flows at 12 m/s in an 11 cm I.D. duct. Its bulktemperature is 40◦ C and the pipe wall is at 268◦ C. Evaluate hif ε/D = 0.00006.7.18How does h during cross flow over a cylindrical heater varywith the diameter when ReD is very large?7.19Air enters a 0.8 cm I.D. tube at 20◦ C with an average velocityof 0.8 m/s. The tube wall is kept at 40◦ C. Plot Tb (x) until itreaches 39◦ C. Use properties evaluated at [(20 + 40)/2]◦ C forthe whole problem, but report the local error in h at the endto get a sense of the error incurred by the simplification.7.20Write ReD in terms of ṁ in pipe flow and explain why this representation could be particularly useful in dealing with compressible pipe flows.7.21NaK at 394◦ C flows at 0.57 m/s across a 1.82 m length of0.036 m O.D.
tube. The tube is kept at 404◦ C. Find h and theheat removal rate from the tube.7.22Verify the value of h specified in Problem 3.22.Problems3897.23Check the value of h given in Example 7.3 by using Reynolds’sanalogy directly to calculate it. Which h do you deem to be inerror, and by what percent?7.24A homemade heat exchanger consists of a copper plate, 0.5 msquare, with twenty 1.5 cm I.D. copper tubes soldered to it. Theten tubes on top are evenly spaced across the top and parallelwith two sides.
The ten on the bottom are also evenly spaced,but they run at 90◦ to the top tubes. The exchanger is used tocool methanol flowing at 0.48 m/s in the tubes from an initialtemperature of 73◦ C, using water flowing at 0.91 m/s and entering at 7◦ C. What is the temperature of the methanol whenit is mixed in a header on the outlet side? Make a judgementof the heat exchanger.7.25Given that NuD = 12.7 at (2/Gz) = 0.004, evaluate NuD at(2/Gz) = 0.02 numerically, using Fig. 7.4.
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