John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 38
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Trans. ASME, 69:227–236, 1947.[5.5] P. J. Schneider. Temperature Response Charts. John Wiley & Sons,Inc., New York, 1963.[5.6] H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. OxfordUniversity Press, New York, 2nd edition, 1959.[5.7] F. A. Jeglic. An analytical determination of temperature oscillations in wall heated by alternating current. NASA TN D-1286, July1962.[5.8] F.
A. Jeglic, K. A. Switzer, and J. H. Lienhard. Surface temperatureoscillations of electric resistance heaters supplied with alternatingcurrent. J. Heat Transfer, 102(2):392–393, 1980.[5.9] J. Bronowski. The Ascent of Man. Chapter 4. Little, Brown andCompany, Boston, 1973.[5.10] N. Zuber. Hydrodynamic aspects of boiling heat transfer. AECReport AECU-4439, Physics and Mathematics, June 1959.[5.11] M. S.
Plesset and S. A. Zwick. The growth of vapor bubbles insuperheated liquids. J. Appl. Phys., 25:493–500, 1954.266Chapter 5: Transient and multidimensional heat conduction[5.12] L. E. Scriven. On the dynamics of phase growth. Chem. Eng. Sci.,10:1–13, 1959.[5.13] P. Dergarabedian. The rate of growth of bubbles in superheatedwater.
J. Appl. Mech., Trans. ASME, 75:537, 1953.[5.14] E. R. G. Eckert and R. M. Drake, Jr. Analysis of Heat and MassTransfer. Hemisphere Publishing Corp., Washington, D.C., 1987.[5.15] V. S. Arpaci. Conduction Heat Transfer. Ginn Press/Pearson Custom Publishing, Needham Heights, Mass., 1991.[5.16] E. Hahne and U. Grigull. Formfactor and formwiderstand derstationären mehrdimensionalen wärmeleitung. Int.
J. Heat MassTransfer, 18:751–767, 1975.[5.17] P. M. Morse and H. Feshbach. Methods of Theoretical Physics.McGraw-Hill Book Company, New York, 1953.[5.18] R. Rüdenberg.Die ausbreitung der luft—und erdfelder umhochspannungsleitungen besonders bei erd—und kurzschlüssen.Electrotech. Z., 36:1342–1346, 1925.[5.19] M. M. Yovanovich. Conduction and thermal contact resistances(conductances). In W.
M. Rohsenow, J. P. Hartnett, and Y. I. Cho,editors, Handbook of Heat Transfer, chapter 3. McGraw-Hill, NewYork, 3rd edition, 1998.[5.20] S. H. Corriher. Cookwise: the hows and whys of successful cooking.Wm. Morrow and Company, New York, 1997. Includes excellentdesciptions of the physical and chemical processes of cooking.The cookbook for those who enjoyed freshman chemistry.Part IIIConvective Heat Transfer2676.Laminar and turbulent boundarylayersIn cold weather, if the air is calm, we are not so much chilled as when thereis wind along with the cold; for in calm weather, our clothes and the airentangled in them receive heat from our bodies; this heat. .
.brings themnearer than the surrounding air to the temperature of our skin. But inwindy weather, this heat is prevented. . .from accumulating; the cold air,by its impulse. . .both cools our clothes faster and carries away the warmair that was entangled in them.notes on “The General Effects of Heat”, Joseph Black, c. 1790s6.1Some introductory ideasJoseph Black’s perception about forced convection (above) represents avery correct understanding of the way forced convective cooling works.When cold air moves past a warm body, it constantly sweeps away warmair that has become, as Black put it, “entangled” with the body and replaces it with cold air.
In this chapter we learn to form analytical descriptions of these convective heating (or cooling) processes.Our aim is to predict h and h, and it is clear that such predictionsmust begin in the motion of fluid around the bodies that they heat orcool. It is by predicting such motion that we will be able to find out howmuch heat is removed during the replacement of hot fluid with cold, andvice versa.Flow boundary layerFluids flowing past solid bodies adhere to them, so a region of variablevelocity must be built up between the body and the free fluid stream, as269Laminar and turbulent boundary layers270§6.1Figure 6.1 A boundary layer of thickness δ.indicated in Fig.
6.1. This region is called a boundary layer, which we willoften abbreviate as b.l. The b.l. has a thickness, δ. The boundary layerthickness is arbitrarily defined as the distance from the wall at whichthe flow velocity approaches to within 1% of u∞ . The boundary layeris normally very thin in comparison with the dimensions of the bodyimmersed in the flow.1The first step that has to be taken before h can be predicted is themathematical description of the boundary layer.
This description wasfirst made by Prandtl2 (see Fig. 6.2) and his students, starting in 1904,and it depended upon simplifications that followed after he recognizedhow thin the layer must be.The dimensional functional equation for the boundary layer thicknesson a flat surface isδ = fn(u∞ , ρ, µ, x)where x is the length along the surface and ρ and µ are the fluid densityin kg/m3 and the dynamic viscosity in kg/m·s. We have five variables in1We qualify this remark when we treat the b.l. quantitatively.Prandtl was educated at the Technical University in Munich and finished his doctorate there in 1900. He was given a chair in a new fluid mechanics institute at GöttingenUniversity in 1904—the same year that he presented his historic paper explaining theboundary layer.
His work at Göttingen, during the period up to Hitler’s regime, set thecourse of modern fluid mechanics and aerodynamics and laid the foundations for theanalysis of heat convection.2Some introductory ideas§6.1271Figure 6.2 Ludwig Prandtl (1875–1953).(Courtesy of Appl. Mech. Rev. [6.1])kg, m, and s, so we anticipate two pi-groups:δ= fn(Rex )xRex ≡u∞ xρu∞ x=µν(6.1)where ν is the kinematic viscosity µ/ρ and Rex is called the Reynoldsnumber. It characterizes the relative influences of inertial and viscousforces in a fluid problem.
The subscript on Re—x in this case—tellswhat length it is based upon.We discover shortly that the actual form of eqn. (6.1) for a flat surface,where u∞ remains constant, is4.92δ=3xRex(6.2)which means that if the velocity is great or the viscosity is low, δ/x willbe relatively small. Heat transfer will be relatively high in such cases. Ifthe velocity is low, the b.l.
will be relatively thick. A good deal of nearly272Laminar and turbulent boundary layers§6.1Osborne Reynolds (1842 to 1912)Reynolds was born in Ireland but hetaught at the University of Manchester.He was a significant contributor to thesubject of fluid mechanics in the late19th C. His original laminar-toturbulent flow transition experiment,pictured below, was still being used asa student experiment at the Universityof Manchester in the 1970s.Figure 6.3 Osborne Reynolds and his laminar–turbulent flowtransition experiment. (Detail from a portrait at the Universityof Manchester.)stagnant fluid will accumulate near the surface and be “entangled” withthe body, although in a different way than Black envisioned it to be.The Reynolds number is named after Osborne Reynolds (see Fig.
6.3),who discovered the laminar–turbulent transition during fluid flow in atube. He injected ink into a steady and undisturbed flow of water andfound that, beyond a certain average velocity, uav , the liquid streamlinemarked with ink would become wobbly and then break up into increasingly disorderly eddies, and it would finally be completely mixed into theSome introductory ideas§6.1273Figure 6.4 Boundary layer on a long, flat surface with a sharpleading edge.water, as is suggested in the sketch.To define the transition, we first note that (uav )crit , the transitionalvalue of the average velocity, must depend on the pipe diameter, D, onµ, and on ρ—four variables in kg, m, and s. There is therefore only onepi-group:Recritical ≡ρD(uav )critµ(6.3)The maximum Reynolds number for which fully developed laminar flowin a pipe will always be stable, regardless of the level of background noise,is 2100.
In a reasonably careful experiment, laminar flow can be madeto persist up to Re = 10, 000. With enormous care it can be increasedstill another order of magnitude. But the value below which the flow willalways be laminar—the critical value of Re—is 2100.Much the same sort of thing happens in a boundary layer. Figure 6.4shows fluid flowing over a plate with a sharp leading edge. The flow islaminar up to a transitional Reynolds number based on x:Rexcritical =u∞ xcritν(6.4)At larger values of x the b.l.
exhibits sporadic vortexlike instabilities overa fairly long range, and it finally settles into a fully turbulent b.l.274Laminar and turbulent boundary layers§6.1For the boundary layer shown, Rexcritical = 3.5 × 105 , but in general thecritical Reynolds number depends strongly on the amount of turbulencein the freestream flow over the plate, the precise shape of the leadingedge, the roughness of the wall, and the presence of acoustic or structural vibrations [6.2, §5.5].
On a flat plate, a boundary layer will remainlaminar even when such disturbances are very large if Rex ≤ 6 × 104 .With relatively undisturbed conditions, transition occurs for Rex in therange of 3 × 105 to 5 × 105 , and in very careful laboratory experiments,turbulent transition can be delayed until Rex ≈ 3 × 106 or so. Turbulenttransition is essentially always complete before Rex = 4×106 and usuallymuch earlier.These specifications of the critical Re are restricted to flat surfaces.
Ifthe surface is curved away from the flow, as shown in Fig. 6.1, turbulencemight be triggered at much lower values of Rex .Thermal boundary layerIf the wall is at a temperature Tw , different from that of the free stream,T∞ , there is a thermal boundary layer thickness, δt —different from theflow b.l. thickness, δ. A thermal b.l.
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