Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 3
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The primary dimensions used in1.96013pt PgVara study of the thermal sciences embrace the first five entries in the center column of———Table 1.1. There are standards for all these units. For example, the standard for theNormal Pagesecond is the duration of 9,192,631,770 periods, corresponding to the transition states * PgEnds: Ejectbetween two levels of the ground state of the cesium-133 atom.The mole is defined as the molecular weight of a substance expressed in the[35], (35)appropriate mass unit. For example, a gram-mole (g-mol) of nitrogen contains 28.01grams (g) and 1 kg-mol of nitrogen contains 28.01 kilograms (kg). The number ofmoles of a substance, N , is related to its mass m and molecular weight by the simpleexpressionm(1.101)N=MIn the SI system, force is a secondary dimension.
The unit of force is therefore asecondary or derived unit and is the newton (N), which can be obtained from Newton’ssecond law, F = ma, as1 N = 1 kg(m/s2 ) = 1 kg · m/s2and the constant of proportionality is unity, or1 N · s2=1kg · m(1.102)Because pressure is force per unit area, P = F /A, the unit of pressure, the pascal(Pa), can be expressed as1 Pa = 1 N/m2 = (1 kg · m/s2 )(1/m2 ) =BOOKCOMP, Inc. — John Wiley & Sons / Page 35 / 2nd Proofs / Heat Transfer Handbook / Bejan1 kgm · s2(1.103)36123456789101112131415161718192021222324252627282930313233343536373839404142434445BASIC CONCEPTSA work interaction, or work, is represented byδW = F xThe unit of work or energy is the joule (J), defined asW =1J=1N·m(1.104)and because power P is the rate of doing work, the unit of power is the watt:P =dW= Ẇ = 1 J/s = 1 N · m/sdt(1.105)Note that quantities that pertain to a rate can be designated by a dotted quantity.Observe that the weight of a body is equal to the force of gravity on the body.Hence, weight always refers to a force, and in the SI system this force is always innewtons.
The mass of the body can always be related to its weight viaW = mg(1.106)where g, the local gravitational acceleration, has a mean value at sea level ofg = 9.807 m/s[36], (36)Lines: 1777 to 1859———-1.23988pt PgVar2———Long Pageand is a function of location. This shows that the weight of a body may vary, whereas* PgEnds: Ejectthe mass of the body is always the same.1.7.2English Engineering System (U.S. Customary System)[36], (36)The English engineering system (sometimes referred to as the U.S. customary systemof units) is often used in the United States.
This system takes the first five entries andthe last entry in the right-hand column of Table 1.4. Here both mass and force aretaken as primary dimensions and the pound is used as the unit of mass (the lbm) andthe unit of force (the lbf). This leads to more than a little confusion when this systemis used.Because there are now six primary dimensions to be used with Newton’s secondlaw, it must be written asF ∝ maWhen the proportionality constant gc is inserted, the result isF =magc(1.107)with gc = 32.174 ft/s2 taken as the standard acceleration of gravity.
This means thata force of 1 lbf will accelerate a mass of 1 lbm at a rate of 32.174 ft/s2. Thus,1 lbf =(32.174 ft/s2 )(1 lbm )gcorBOOKCOMP, Inc. — John Wiley & Sons / Page 36 / 2nd Proofs / Heat Transfer Handbook / BejanUNITS123456789101112131415161718192021222324252627282930313233343536373839404142434445gc =32.174 lbm -ftlbf -s237(1.108)Thus Newton’s second law must be written asmaF =32.174(1.109)It is important to remember that the SI system of units does not require this conversionfactor.1.7.3Conversion FactorsConversion factors from English engineering units to SI units are given in Table 1.5.Conversion factors for commonly used heat transfer parameters are given in Table 1.6.TABLE 1.5[37], (37)Conversion Factors from English Engineering Units to SI UnitsTo Convert from:Accelerationft/sec2Areaft2in2Densitylbm/in3lbm/ft3Energy, heat, and workBtuft-lbfkW-hrForcelbfLengthftin.miMasslbmtonPowerft-lbf /minhorsepower (hp)Pressureatmlbf /ft2lbf /in2Velocityft/secmi/hrBOOKCOMP, Inc.
— John Wiley & Sons / Page 37 / 2nd Proofs / Heat Transfer Handbook / BejanTo:Multiply by:Lines: 1859 to 1924m/s23.048 × 10−10.25612pt PgVarm2m29.2903 × 10−26.4516 × 10−4kg/m3kg/m32.7680 × 10416.018JJJ1.0544 × 1031.35583.60 × 106N4.4482mmkm3.048 × 10−12.54 × 10−21.6093kgkg4.5359 × 10−19.0718 × 102WW2.2597 × 10−27.457 × 102PaPaPa1.0133 × 10547.8806.8948 × 103m/sm/s3.048 × 10−14.4704 × 10−1——————Long Page* PgEnds: PageBreak[37], (37)38123456789101112131415161718192021222324252627282930313233343536373839404142434445BASIC CONCEPTSTABLE 1.6 Conversion Factors for Heat Transfer Parameters from EnglishEngineering Units to SI UnitsTo Convert from:Heat fluxbtu/hr-ft2kcal/h · m2Heat transfer coefficientBtu/hr-ft2-°Fkcal/h · m2 · °CHeat transfer rateBtu/hrMass flow ratelbm/hrlbm/secSpecific heatBtu/lbm-°FSurface tensionlbm/ftTemperature1°RThermal conductivityBtu/hr-ft-°Fkcal/h · m · °FThermal diffusivityft2/secft2/hThermal resistance°F-hr/BtuViscosity (dynamic)lbm /ft-seccentipoiseViscosity (kinematic)ft2/hrft2/hrTo:Multiply by:W/m2W/m23.15251.163W/m2 · KW/m2 · K5.6781.163W0.2931kg/skg/s1.26 × 10−44.536 × 10−1J/kg · K4.187 × 103N/m1.4594 × 101K0.5555W/m · KW/m · K1.7311.163———Normal PagePgEnds: TEXm2/sm2/s9.29 × 10−22.581 × 10−5[38], (38)K/W1.8958N · s/m2N · s/m21.48811 × 103m2/sstoke9.29 × 10−2929NOMENCLATURERoman Letter SymbolsAcross-sectional area, m2asquare root of heat source area, m2speed of sound, m/sCconstant, dimensionlesscspecific heat, W/m · KDsubstantial differential, dimensionlessmass diffusivity, m2/sBOOKCOMP, Inc.
— John Wiley & Sons / Page 38 / 2nd Proofs / Heat Transfer Handbook / Bejan[38], (38)Lines: 1924 to 2038———2.0997pt PgVarNOMENCLATURE123456789101112131415161718192021222324252627282930313233343536373839404142434445deeFFFfGgHhkLMmṁnnPpqqgq q qRrSsTtdifferential, dimensionlessdiameter, munit vector, dimensionlessroughness, mspecific energy, J/kg · Kforce vector, Nforce, Nradiation factor, dimensionlessfrequency, m−1mass velocity, kg/m2 · sacceleration of gravity, m/s2microhardness, N/m2heat transfer coefficient, W/m2 · Kspecific enthalpy, J/kgthermal conductivity, W/m · Kpath length, mphysical dimension, dimensionlessgas parameter, mphysical dimension, kgsurface slope, dimensionlessmass, kgmass flow rate, kg/snumber of moles, dimensionlessnumber of dimensionless groups, dimensionlessnormal direction, dimensions varypressure, N/m2wetted perimeter, mheat flow, Wmaximum number of quantities, dimensionlessheat generation, W/m3heat flux, W/m2heat generation, W/m3heat flux vector, W/m2thermal resistance, K/Wregion, dimensionlessradial direction, mradius, mnumber of physical quantities, dimensionlesssurface area, m2specific entropy, J/kg · Kscale factor, dimensions varynumber of fundamental dimensions, dimensionlesstemperature, Ktime, sphysical dimension, sBOOKCOMP, Inc.
— John Wiley & Sons / Page 39 / 2nd Proofs / Heat Transfer Handbook / Bejan39[39], (39)Lines: 2038 to 2038———0.00604pt PgVar———Normal PagePgEnds: TEX[39], (39)40123456789101112131415161718192021222324252627282930313233343536373839404142434445BASIC CONCEPTSuVVV̂WxYyzspecific internal energy, J/kgvolume, m3velocity vector, m/svelocity, m/swidth, mlength coordinate, mgeneralized coordinate, dimensions varymean plane distance, mlength coordinate, mlength coordinate, mfin spacing, mGreek Letter Symbolsαaccommodation parameter, dimensionlessthermal diffusivity, m2/sβcoefficient of volumetric expansion, m−1∆change, dimensionlessδthickness, marea ratio, dimensionlessηfin efficiency, dimensionlessθangle in cylindrical coordinate system, radangle in spherical coordinate system, radΛmean free path of molecules, mµdynamic viscosity, N/m · sνkinematic viscosity, m2/sπgroup, dimensionlessρdensity, kg/m3σsurface roughness, msurface tension, N/mStefan–Boltzmann constant, W/m2 · K4normal stress, N/m2τshear stress, N/m2Φviscous dissipation factor, s−1φangle in spherical coordinate system, rad∇vector operator, s−12∇Laplacian operator, s−2Roman Letter SubscriptsccontactcdconductioncocontactcvconvectionDdiffusioneequivalentffinfluidBOOKCOMP, Inc.
— John Wiley & Sons / Page 40 / 2nd Proofs / Heat Transfer Handbook / Bejan[40], (40)Lines: 2038 to 2111———-0.4518pt PgVar———Long PagePgEnds: TEX[40], (40)REFERENCES123456789101112131415161718192021222324252627282930313233343536373839404142434445flgin1mmaxminnooutprssatspsfwxyz∞41flowgeneratedgapstandard acceleration of gravityinlet conditionliquidmeltingmaximum conditionminimum conditionnormal directionnominal valueoutlet conditionconstant pressureradiationradial directionharmonic meansurface conditionsaturated conditionspreadingsurface parameter in boilingwall conditionx-coordinate directiony-coordinate directionz-coordinate directionfree stream conditionGreek Letter Subscriptsθθ-coordinate directionφphase changeφ-coordinate directionSuperscriptsaexponent in dimensional analysisbexponent in dimensional analysiscexponent in dimensional analysisnexponent in natural convection correlationREFERENCESBejan, A.
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Friction Factors for Pipe Flow, Trans. ASME, 66, 671–684.Rohsenow, W. M. (1952). A Method for Correlation Heat Transfer Data for Surface Boiling inLiquids, Trans. ASME, 74, 969–975.Rohsenow, W. M., and Choi, H. Y. (1961). Heat Mass and Momentum Transfer, Prentice-Hall,Englewood Cliffs, NJ.Sieder, E. N., and Tate, G.
E. (1936). Heat Transfer and Pressure Drop of Liquids in Tubes,Ind. Eng. Chem., 28, 1429–1436.Yovanovich, M. M., and Antonetti, V. W. (1988). Application of Thermal Contact ResistanceTheory to Electronic Packages, in Advances in Thermal Modeling of Electronic Components and Systems, A. Bar-Cohen and A. D. Kraus, eds.), Hemisphere Publishing, NewYork.BOOKCOMP, Inc.
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