Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 89
Текст из файла (страница 89)
Amato and Tien (1972) have listed the correlationsfor Nu obtained from various investigations of heat and mass transfer. In a review paper, Yuge (1960) suggested the following correlation for heat transfer from isothermalspheres in air and gases over a Grashof number range 1 < Gr < 105 , where Gr andNu are based on the diameter D:BOOKCOMP, Inc. — John Wiley & Sons / Page 563 / 2nd Proofs / Heat Transfer Handbook / Bejan123456789101112131415161718192021222324252627282930313233343536373839404142434445564BOOKCOMP, Inc. — John Wiley & Sons / Page 564 / 2nd Proofs / Heat Transfer Handbook / BejanTABLE 7.2Summary of Natural Convection Correlations for External Flows over Isothermal SurfacesGeometryVertical flat surfacesRecommended Correlation20.387Ra1/6Nu = 0.825 +[1 + (0.492/Pr)9/16 ]8/27Inclined flat surfacesAbove equation with g replaced by g cos γHorizontal flat surfacesNu = 0.54RaRange10−1 < Ra < 1012ReferenceChurchill and Chu (1975a)γ ≤ 60°105 ≤ Ra ≤ 1071/4Heated, facing upwardNu = 0.15Ra1/3107 ≤ Ra ≤ 1010McAdams (1954)Heated, facing downwardNu = 0.27Ra1/43 × 105 ≤ Ra ≤ 3 × 1010McAdams (1954)Horizontal cylindersNu = 0.60 + 0.387SpheresNu = 2 + 0.43Ra1/41/6 2Ra10−5 ≤ Ra ≤ 1012[1 + (0.559/Pr)9/16 ]16/9Pr = 1 and 1 < Ra < 105Churchill and Chu (1975b)Yuge (1960)[564], (40)Lines: 1081 to 1109———* 528.0pt PgVar———Normal Page* PgEnds: PageBreak[564], (40)EMPIRICAL CORRELATIONS123456789101112131415161718192021222324252627282930313233343536373839404142434445Nu = 2 + 0.43Ra1/4for Pr = 1 and 1 < Ra < 105565(7.91)For heat transfer in water, Amato and Tien (1972) obtained the correlation for isothermal spheres asNu = 2 + C · Ra1/4for 3 × 105 ≤ Ra ≤ 8 × 108(7.92)with C = 0.500 ± 0.009, which gave a mean deviation of less than 11%.
A generalcorrelation applicable for Pr ≥ 0.7 and Ra 1011 is given by Churchill (1983) as0.589Ra1/4Nu = 2 + 1 + (0.469/Pr)9/164/9(7.93)Several of the important correlations presented earlier are summarized in Table 7.2.Correlations for various other geometries are given by Churchill (1983) and Raithbyand Hollands (1985). Nu and Ra are based on the height L for a vertical plate, lengthL for inclined and horizontal surfaces, and diameter D for horizontal cylinders andspheres. All fluid properties are evaluated at the film temperature Tf = (Tw + T∞ )/2.[565], (41)Lines: 1109 to 1162———7.7.4-0.3219pt PgVarEnclosures———Normal PageAs mentioned earlier, the heat transfer across a vertical rectangular cavity is largelyby conduction for Ra 103 , which implies a Nusselt number Nu of 1.0.
For larger * PgEnds: EjectRa, Catton (1978) has given the following correlation for the aspect ratio H /d in therange 2 to 10 and Pr < 105 :[565], (41)0.28 −1/4HPrNu = 0.22(7.94)Ra0.2 + Prdwhere the Nusselt and Rayleigh numbers are based on the distance d between thevertical walls and the temperature difference between them.
For an aspect ratio between 1 and 2, the coefficient in this expression was changed from 0.22 to 0.18 andthe exponent from 0.28 to 0.29, with the aspect ratio dependence dropped. Similarly,correlations are given for higher aspect ratios in the literature.For horizontal cavities heated from below, the Nusselt number Nu is 1.0 forRayleigh number Ra 1708, as discussed earlier. Globe and Dropkin (1959) gavethe following correlation for such cavities at larger Ra, 3 × 105 < Ra < 7 × 109 :Nu = 0.069Ra1/3 · Pr 0.074(7.95)For inclined cavities, Hollands et al. (1976) gave the following correlation for air asthe fluid with H /d 12 and γ < γ∗ on the basis of several experimental studies: 17081708(sin 1.8γ)1.6Ra cos γ 1/3Nu = 1 + 1.44 1 −−11−+Ra cos γRa cos γ5830BOOKCOMP, Inc. — John Wiley & Sons / Page 565 / 2nd Proofs / Heat Transfer Handbook / Bejan(7.96)566123456789101112131415161718192021222324252627282930313233343536373839404142434445NATURAL CONVECTIONwhere γ is the inclination with the horizontal, γ∗ is a critical angle tabulated byHollands et al.
(1976), and the term in the square brackets is set equal to zero ifthe quantity within these brackets is negative. This equation uses the stability limitof Ra = 1708 for a horizontal layer, given earlier. For a horizontal enclosure heatedfrom below, with air as the fluid, Hollands et al. (1975) gave the correlation 1708Ra 1/3Nu = 1 + 1.44 1 −−1(7.97)+Ra5830Similarly, correlations for other fluids, geometries, and thermal conditions are givenin the literature.7.8SUMMARYIn this chapter we discuss the basic considerations relevant to natural convectionflows.
External and internal buoyancy-induced flows are considered, and the governing equations are obtained. The approximations generally employed in the analysisof these flows are outlined. The important dimensionless parameters are derived inorder to discuss the importance of the basic processes that govern these flows. Laminar flows for various surfaces and thermal conditions are discussed, and the solutionsobtained are presented, particularly those derived from similarity analysis. The heattransfer results and the characteristics of the resulting velocity and temperature fieldsare discussed. Also considered are transient and turbulent flows.
The governing equations for turbulent flow are given, and experimental results for various flow configurations are presented. The frequently employed empirical correlations for heat transferby natural convection from various surfaces and enclosures are also included. Thus,this chapter presents the basic aspects that underlie natural convection and the heattransfer correlations that may be employed for practical applications.NOMENCLATURERoman Letter Symbolsspecific heat at constant pressure, J/kg · KcpDdiameter of cylinder or sphere, mfstream function, dimensionlessFbody force per unit volume, N/m3ggravitational acceleration, m/s2GrGrashof number, dimensionlesslocal Grashof number, dimensionlessGr xheat flux Grashof number, dimensionlessGr*local heat transfer coefficient, W/m2 · Khxh̄average heat transfer coefficient, W/m2 · Kheat transfer coefficient at angular position φ, W/m2 · KhφBOOKCOMP, Inc.
— John Wiley & Sons / Page 566 / 2nd Proofs / Heat Transfer Handbook / Bejan[566], (42)Lines: 1162 to 1230———1.2814pt PgVar———Normal PagePgEnds: TEX[566], (42)NOMENCLATURE123456789101112131415161718192021222324252627282930313233343536373839404142434445kLm, nM, NNuxNuNuqNuφpPrqqxqq RaRaxSrttc∆TTTwT∞u, v, wVVcx, y, zthermal conductivity, W/m · Kcharacteristic length, height of vertical plate, mexponents in exponential and power law distributions,dimensionlessconstants employed for exponential and power lawdistributions of surface temperature, dimensionlesslocal Nusselt number, dimensionless [= hx x/k]average Nusselt number for an isothermal surface,dimensionlessaverage Nusselt number for a uniform heat flux surface,dimensionlesslocal Nusselt number at angular position φ, dimensionlesspressure, PaPrandtl number, dimensionlesstotal heat transfer, Wlocal heat flux, W/m2constant surface heat flux, W/m2volumetric heat source, W/m3Rayleigh number, dimensionless [= Gr · Pr]local Rayleigh number, dimensionless [= Gr x · Pr]Strouhal number, dimensionlesstime, scharacteristic time, stemperature difference, K [= Tw − T∞ ]local temperature, Kwall temperature, Kplume centerline temperature, Kambient temperature, Kvelocity components in x, y, and z directions, respectively,m/svelocity vector, m/sconvection velocity, m/scoordinate distances, mGreek Letter Symbolsαthermal diffusivity, m2/sβcoefficient of thermal expansion, K−1γinclination with the vertical, degrees or radiansδvelocity boundary layer thickness, mthermal boundary layer thickness, mδTeddy diffusivity, m2/sεHeddy viscosity, m2/sεMηsimilarity variable, dimensionlessθtemperature, dimensionless [= (T − T∞ )/(Tw − T∞ )]µdynamic viscosity, Pa · sBOOKCOMP, Inc.
— John Wiley & Sons / Page 567 / 2nd Proofs / Heat Transfer Handbook / Bejan567[567], (43)Lines: 1230 to 1249———1.82222pt PgVar———Normal PagePgEnds: TEX[567], (43)568123456789101112131415161718192021222324252627282930313233343536373839404142434445NATURAL CONVECTIONνΦvψkinematic viscosity, m2/sviscous dissipation, s−2stream function, m2/sREFERENCESAbib, A., and Jaluria, Y.
(1988). Numerical Simulation of the Buoyancy-Induced Flow in aPartially Open Enclosure, Numer. Heat Transfer, 14, 235–254.Abib, A., and Jaluria, Y. (1995). Turbulent Penetrative and Recirculating Flow in a Compartment Fire, J. Heat Transfer, 117, 927–935.Amato, W. S., and Tien, C. (1972). Free Convection Heat Transfer from Isothermal Spheres inWater, Int. J.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
