Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok, страница 5

Sources of calculated values and brief descriptions of the methods used todetermine values in the tables and graphs in this book are given. References to originalworks that contain details of both correlation and measurement techniques are alsoincluded.[46], (4)Lines: 118 to 144———-0.03pt PgVar———Normal PageA property formulation is the set of equations used to calculate properties of a fluid * PgEnds: Ejectat specified thermodynamic states defined by the appropriate independent variables.A typical thermodynamic property formulation is based on an equation of state thatallows the correlation and computation of all thermodynamic properties of the fluid,[46], (4)including properties such as entropy that cannot be measured directly.The general term equation of state in this chapter refers to an empirical modeldeveloped for calculating thermodynamic properties of fluids. The term fundamentalequation is often used in the literature to refer to empirical descriptions of one offour fundamental relations: internal energy as a function of volume and entropy,enthalpy as a function of pressure and entropy, Gibbs energy as a function of pressureand temperature, and Helmholtz energy as a function of density and temperature.Modern equations of state for the thermodynamic properties of pure fluids are usuallyfundamental equations explicit in the Helmholtz energy as a function of density andtemperature.The equation of state for a pure fluid using the Helmholtz energy as the fundamental property is given by2.2.1 Thermodynamic Propertiesa(ρ,T ) = a 0 (ρ,T ) + a r (ρ,T )(2.1)where a is the molar Helmholtz energy, a 0 (ρ,T ) is the ideal gas contribution to theHelmholtz energy, and a r (ρ,T ) is the residual Helmholtz energy that corresponds tothe influence of intermolecular forces.

All thermodynamic properties can be calculated as derivatives of the Helmholtz energy. For example, the pressure derived fromthis expression isBOOKCOMP, Inc. — John Wiley & Sons / Page 46 / 2nd Proofs / Heat Transfer Handbook / Bejan47THERMOPHYSICAL PROPERTIES OF FLUIDS123456789101112131415161718192021222324252627282930313233343536373839404142434445p = ρ2∂a∂ρ(2.2)TAlso, the thermodynamic properties at saturation conditions can be calculated without additional ancillary equations through the use of the Maxwell criterion (equalpressures and Gibbs energies at constant temperature during phase changes).The quality of a thermodynamic property formulation is determined by its abilityto model the physical behavior of the fluid as represented by the available data aswell as by its conformance to theory (to assure reasonable extrapolation behavior).Published correlations should include estimates of the accuracy of calculated properties as well as a careful definition of the range of validity.

A modern thermodynamicproperty formulation is generally capable of representing all data values within theestimated experimental uncertainty of the measurements (see Table 2.1). The practical models of today are empirical or semiempirical in nature, although virtually allare based on sound theoretical principles. The limitations of the model selected mustbe understood by the user for effective system optimization and related work.Correct behavior of the equation of state in the critical region (bounded by ±0.25ρcand ±0.05Tc ) is sometimes a concern of users of property formulations. Classicalequations (those that do not use an additional scaling theory) cannot represent thetheoretically expected behavior at the critical point. However, state-of-the-art multiparameter equations of state are sufficiently accurate in the critical region to satisfyTABLE 2.1[47], (5)Lines: 144 to 184———3.09909pt PgVar———Normal PagePgEnds: TEXGeneral Standard Uncertainty Estimates for Various Fluid PropertiesCalculated PropertyRegionState-of-the-ArtExperimentalUncertainty (%)Pressure—0.02Temperature—0.001 KDensity—Uncertaintyto Be Expectedfrom a ModernEquation of State (%)0.020.1Isochoric heat capacityρ > ρcρ < ρc0.510.51Isobaric heat capacityρ > ρcρ < ρc0.5211Speed of soundρ > ρcρ < ρc0.10.010.50.1Vapor pressurep < 0.1 MPap > 0.1 MPa0.050.010.50.2Thermal conductivityρ > ρcρ < ρc0.520.52Viscosityρ > ρcρ < ρc20.520.5BOOKCOMP, Inc.

— John Wiley & Sons / Page 47 / 2nd Proofs / Heat Transfer Handbook / Bejan[47], (5)48123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMOPHYSICAL PROPERTIES OF FLUIDS AND MATERIALSmost data needs (although they should not be used as the basis for theoretical calculations regarding the limiting behavior at the critical point). Older or less accurateequations of state may show significant shortcomings with regard to the representation of properties in the critical region.Most modern reference equations of state yield reasonable extrapolation behavior up to the limits of chemical stability of the corresponding substance.

However,in general, multiparameter equations of state should not be extrapolated beyond thegiven range of validity, especially when using older equations or equations where thefunctional form was not optimized to the experimental data. When extrapolation isnecessary, the reliability of the results must be checked carefully, unless reasonableextrapolation behavior is stated explicitly by the authors of the equation. The extrapolation behavior of empirical multiparameter equations of state has been discussedby Span and Wagner (1997) and Span (2000).[48], (6)Table 2.2 lists sources of recommended multiparameter equations of state that aresuitable for use in system design and analysis and in scientific applications.

We believe that these are the most accurate published equations available for these fluids.Lines: 184 to 193To assess whether an equation is suitable for a certain application, details given in theoriginal publications should be considered. The fluids listed in bold type in Table 2.2———can be considered primary standards with typical uncertainties of 0.02% in density,0.0pt PgVar0.5% in heat capacities and the liquid speed of sound, and 0.02% in the vapor speed———of sound.

Properties of italicized fluids are also represented by equations of high acNormal Pagecuracy with typical uncertainties in density of 0.1%, 0.5% in heat capacities and the * PgEnds: Ejectliquid speed of sound, and 0.1% in the vapor speed of sound. The uncertainties of thecorrelations for the other fluids are generally greater depending on the quality of dataused in the fit and the ability of the correlator to develop a thermodynamically con[48], (6)sistent equation with proper extrapolation behavior.

Uncertainties in viscosities andthermal conductivities are generally within 2% for fluids with published equations.The uncertainty rises for fluids using extended corresponding states (ECS) techniquesthat were fitted to data, and can exceed 10% for those fluids that use the ECS modelin a purely predictive mode (see Section 2.2.2).Table 2.3 displays the molecular weight, critical temperature, critical pressure, critical density, triple-point temperature, normal boiling point temperature (at 0.101325MPa), acentric factor (defined as [−log(psat /pc ) − 1] at T/Tc = 0.7), and dipole moment for the fluids listed in Table 2.2.

These values were taken from the referenceslisted in Table 2.2. Tables 2.4, 2.5, and 2.6 give the ideal gas isobaric heat capacity,dilute gas thermal conductivity, and dilute gas viscosity. The thermodynamic andtransport properties along the saturated liquid and vapor lines are given in Table 2.7.Values of the thermodynamic properties, transport properties, and surface tensiongiven in these tables were calculated using NIST databases. Additional details of thefitted equations are given in the databases.Equation of State The functional form for the equation of state used for thefluid properties given here is explicit in the dimensionless Helmholtz energy α, usingindependent variables of dimensionless density and temperature.

The form of thisequation isBOOKCOMP, Inc. — John Wiley & Sons / Page 48 / 2nd Proofs / Heat Transfer Handbook / Bejan123456789101112131415161718192021222324252627282930313233343536373839404142434445BOOKCOMP, Inc. — John Wiley & Sons / Page 49 / 2nd Proofs / Heat Transfer Handbook / BejanTABLE 2.2Equations of State and Transport Equations for Pure FluidsaFluidEquation of StateThermal ConductivityEquationMethaneEthanePropaneButaneIsobutanePentaneIsopentaneNeopentaneHexaneHeptaneOctaneAmmoniaArgonBenzeneCarbon dioxideCarbon monoxideCyclohexaneCyclopropaneDeuteriumEthyleneFluorineHeavy waterHeliumHydrogen (normal)Setzmann and Wagner (1991)Friend et al. (1991)Miyamoto and Watanabe (2000)Miyamoto and Watanabe (2001a)Miyamoto and Watanabe (2001b)Span (2000)Polt et al. (1992)Polt et al.

(1992)Span (2000)Span (2000)Span (2000)Tillner-Roth et al. (1993)Tegeler et al. (1999)Polt et al. (1992)Span and Wagner (1996)Lemmon and Span (2001)Penoncello et al. (1995)Polt et al. (1992)McCarty (1989)Smukala et al. (2000)de Reuck (1990)Hill et al. (1982)McCarty and Arp (1990)Younglove (1982)Friend et al.

(1989)Friend et al. (1991)Marsh et al. (2002)Perkins et al. (2002)Perkins (2002)NIST14, Version 9.08NIST14, Version 9.08Not currently availableNIST14, Version 9.08NIST14, Version 9.08Not currently availableTufeu et al. (1984)Lemmon and Jacobsen (2001)Not currently availableVesovic et al. (1990)NIST14, Version 9.08Not currently availableNot currently availableNot currently availableHolland et al. (1983)Not currently availableIAPWS (1994)Hands and Arp (1981)McCarty and Weber (1972)Viscosity EquationYounglove and Ely (1987)Friend et al. (1991)Vogel et al. (1998)Vogel et al. (1999)Vogel et al. (2000)NIST14, Version 9.08NIST14, Version 9.08Not currently availableNIST14, Version 9.08NIST14, Version 9.08Not currently availableFenghour et al.

(1995)Lemmon and Jacobsen (2001)Not currently availableFenghour et al. (1998)NIST14, Version 9.08Not currently availableNot currently availableNot currently availableHolland et al. (1983)Not currently availableIAPWS (1994)Arp et al. (1998)McCarty and Weber (1972)49Temp.Range (K)(EOS)Max.Pressure(MPa)90.6941–62590.352–62585.48–623134.87–589113.56–573143.47–600200–553273–498177.83–600182.55–600216.37–600195.495–70083.806–700283–635216.592–110068.127–1000279.47–700273–47318.71–423103.986–45053.4811–300276.97–8002.1768–150013.957–40010007010369351007.5201001001001000100078800100802832026020100100121continued[49], (7)Lines: 193 to 231———* 528.0pt PgVar———Normal Page* PgEnds: PageBreak[49], (7)12345678910111213141516171819202122232425262728293031323334353637383940414243444550BOOKCOMP, Inc.

— John Wiley & Sons / Page 50 / 2nd Proofs / Heat Transfer Handbook / BejanTABLE 2.2Equations of State and Transport Equations for Pure Fluidsa (Continued)FluidEquation of StateThermal ConductivityEquationHydrogen sulfideKryptonMethanolNeonNitrogenNitrogen trifluorideOxygenParahydrogenPerfluorobutanePerfluoropentanePerfluoropropanePropylenePropyneSulfur dioxideSulfur hexafluorideTolueneWaterXenonR-11R-113R-114R-115R-116R-12Lemmon and Span (2001)Lemmon and Span (2001)de Reuck and Craven (1993)Katti et al.