Page 1 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [43], (1) Lines: 0 to 71 â€”â€”â€” 3.28333pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [43], (1) CHAPTER 2 Thermophysical Properties of Fluids and Materials * R.TJACOBSEN IdahoNationalEngineeringandEnvironmentalLaboratory IdahoFalls,Idaho E.W.LEMMON PhysicalandChemicalPropertiesDivision NationalInstituteofStandardsandTechnology Boulder,Colorado S.G.PENONCELLOandZ.SHAN CenterforAppliedThermodynamicStudies CollegeofEngineering UniversityofIdaho Moscow,Idaho N.T.WRIGHT DepartmentofMechanicalEngineering UniversityofMaryland Baltimore,Maryland 2.1 Introduction 2.2 Thermophysicalpropertiesof?uids 2.2.1 Thermodynamic properties Equationofstate Calculationofproperties Thermodynamicpropertiesofmixtures 2.2.2 Transport properties Extended corresponding states Dilute-gas contributions Density-dependent contributions Transportpropertiesofmixtures 2.3 Thermophysicalpropertiesofsolids 2.3.1 Conservationofenergy 2.3.2 Behaviorofthermophysicalpropertiesofsolids * ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology. 43 Page 2 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [43], (1) Lines: 0 to 71 â€”â€”â€” 3.28333pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [43], (1) CHAPTER 2 Thermophysical Properties of Fluids and Materials * R.TJACOBSEN IdahoNationalEngineeringandEnvironmentalLaboratory IdahoFalls,Idaho E.W.LEMMON PhysicalandChemicalPropertiesDivision NationalInstituteofStandardsandTechnology Boulder,Colorado S.G.PENONCELLOandZ.SHAN CenterforAppliedThermodynamicStudies CollegeofEngineering UniversityofIdaho Moscow,Idaho N.T.WRIGHT DepartmentofMechanicalEngineering UniversityofMaryland Baltimore,Maryland 2.1 Introduction 2.2 Thermophysicalpropertiesof?uids 2.2.1 Thermodynamic properties Equationofstate Calculationofproperties Thermodynamicpropertiesofmixtures 2.2.2 Transport properties Extended corresponding states Dilute-gas contributions Density-dependent contributions Transportpropertiesofmixtures 2.3 Thermophysicalpropertiesofsolids 2.3.1 Conservationofenergy 2.3.2 Behaviorofthermophysicalpropertiesofsolids * ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology. 43 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan 44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [44], (2) Lines: 71 to 108 â€”â€”â€” 0.15337pt PgVar â€”â€”â€” Long Page PgEnds: T E X [44], (2) 2.3.3 Propertyvaluesofsolidmaterials 2.3.4 Measuringthermophysicalpropertiesofsolids Thermal conductivity Speci?c heat Thermal diffusivity Thermal expansion Nomenclature References Graphsofthermophysicalproperties 2.1 INTRODUCTION The need for accurate thermophysical properties in the design and analysis of en- gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking ?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It is particularly true that small errors in properties for custody transfer of ?uids can result in signi?cant costs or bene?ts to those involved in commercial transactions. It istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis inlightoftheaccuracyofthepropertiesused. In addition to the individual properties for system design and analysis, there is a need for combined heat transfer parameters and dimensionless groups that occur in equations for conduction, convection, and radiation. These include: Biot number Boussinesq number Eckert number Fouriernumber Graetznumber Grashofnumber Lewis number Nusselt number P´ eclet number Prandtl number Rayleigh number Reynolds number Schmidt number Sherwood number Only the Prandtl number is a ?uid property; the others incorporate system character- istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this book and are not discussed in this chapter. The termthermophysicalproperties is used here to refer to both thermodynamic (equilibrium) properties and transport properties. The thermodynamic properties de- ?ne equilibrium states ofthe system and include such properties as temperature, pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en- tropy. The transport properties are those such as thermal conductivity, viscosity, and thermal diffusivity which pertain to the transfer of momentum or energy within the system. In a practical sense, design and analysis ofheat transf er systems require information about both transport and thermodynamic properties. The thermodynamic properties are generally well de?ned by measurement for most common ?uids and Page 3 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [43], (1) Lines: 0 to 71 â€”â€”â€” 3.28333pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [43], (1) CHAPTER 2 Thermophysical Properties of Fluids and Materials * R.TJACOBSEN IdahoNationalEngineeringandEnvironmentalLaboratory IdahoFalls,Idaho E.W.LEMMON PhysicalandChemicalPropertiesDivision NationalInstituteofStandardsandTechnology Boulder,Colorado S.G.PENONCELLOandZ.SHAN CenterforAppliedThermodynamicStudies CollegeofEngineering UniversityofIdaho Moscow,Idaho N.T.WRIGHT DepartmentofMechanicalEngineering UniversityofMaryland Baltimore,Maryland 2.1 Introduction 2.2 Thermophysicalpropertiesof?uids 2.2.1 Thermodynamic properties Equationofstate Calculationofproperties Thermodynamicpropertiesofmixtures 2.2.2 Transport properties Extended corresponding states Dilute-gas contributions Density-dependent contributions Transportpropertiesofmixtures 2.3 Thermophysicalpropertiesofsolids 2.3.1 Conservationofenergy 2.3.2 Behaviorofthermophysicalpropertiesofsolids * ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology. 43 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan 44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [44], (2) Lines: 71 to 108 â€”â€”â€” 0.15337pt PgVar â€”â€”â€” Long Page PgEnds: T E X [44], (2) 2.3.3 Propertyvaluesofsolidmaterials 2.3.4 Measuringthermophysicalpropertiesofsolids Thermal conductivity Speci?c heat Thermal diffusivity Thermal expansion Nomenclature References Graphsofthermophysicalproperties 2.1 INTRODUCTION The need for accurate thermophysical properties in the design and analysis of en- gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking ?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It is particularly true that small errors in properties for custody transfer of ?uids can result in signi?cant costs or bene?ts to those involved in commercial transactions. It istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis inlightoftheaccuracyofthepropertiesused. In addition to the individual properties for system design and analysis, there is a need for combined heat transfer parameters and dimensionless groups that occur in equations for conduction, convection, and radiation. These include: Biot number Boussinesq number Eckert number Fouriernumber Graetznumber Grashofnumber Lewis number Nusselt number P´ eclet number Prandtl number Rayleigh number Reynolds number Schmidt number Sherwood number Only the Prandtl number is a ?uid property; the others incorporate system character- istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this book and are not discussed in this chapter. The termthermophysicalproperties is used here to refer to both thermodynamic (equilibrium) properties and transport properties. The thermodynamic properties de- ?ne equilibrium states ofthe system and include such properties as temperature, pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en- tropy. The transport properties are those such as thermal conductivity, viscosity, and thermal diffusivity which pertain to the transfer of momentum or energy within the system. In a practical sense, design and analysis ofheat transf er systems require information about both transport and thermodynamic properties. The thermodynamic properties are generally well de?ned by measurement for most common ?uids and BOOKCOMP, Inc. â€” John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan INTRODUCTION 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [45], (3) Lines: 108 to 118 â€”â€”â€” 0.0pt PgVar â€”â€”â€” Long Page PgEnds: T E X [45], (3) mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor the same ?uids and mixtures. This is, in part, because the experimental methods for measuring transport properties are generally less accurate than those for the thermo- dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements (see Wakeham et al., 1991). Current practice in the design and analysis of?uid systems requires the use of computer programs in various forms for thermophysical properties. Based on the ex- perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases available to the engineer. Such sources of highly accurate properties are often referred to asstandardreferencequality sources, and many are the result ofinternational agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If special applications require equations with fewer terms for rapidly estimating proper- ties or for calculating abbreviated tables, these can be developed based on properties calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin the properties used in design can be determined by comparisons to values from the source,theaccuraciesofwhicharegenerallywellspeci?ed. We have assumed that the user ofthis book has access to a reasonably current personal computer and to the World Wide Web. Because the National Institute of Standards and Technology (NIST) databases generally incorporate the best available ?uid properties algorithms and equations, we rely heavily on those sources in the recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter, graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues for ?uid properties that are readily available in other sources, including common engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty values at common conditions are given for completeness. Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof ?uids may be calculated using several comprehensive computer programs from NIST, including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer program is included in this book for use in calculating properties for design and analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry. Although the NIST programs provide the most accurate values currently avail- able, additional research, experimentation, and correlation activities worldwide will increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe covered ?uids. The full programs with source code and mixture capabilities are avail- able from NIST at a nominal cost and are updated periodically. Details concerning the current databases available from the Standard Reference Data Of?ce of NIST are located at the Web address http://www.nist.gov/srd by searching for the key words NIST10, NIST12, NIST14, or NIST23. There are fewer sources of properties of solids for design than there are for ?uids, and the data available have not yet been incorporated into evaluated wide-range com- puter models. The uncertainties associated with published values for many properties Page 4 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [43], (1) Lines: 0 to 71 â€”â€”â€” 3.28333pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [43], (1) CHAPTER 2 Thermophysical Properties of Fluids and Materials * R.TJACOBSEN IdahoNationalEngineeringandEnvironmentalLaboratory IdahoFalls,Idaho E.W.LEMMON PhysicalandChemicalPropertiesDivision NationalInstituteofStandardsandTechnology Boulder,Colorado S.G.PENONCELLOandZ.SHAN CenterforAppliedThermodynamicStudies CollegeofEngineering UniversityofIdaho Moscow,Idaho N.T.WRIGHT DepartmentofMechanicalEngineering UniversityofMaryland Baltimore,Maryland 2.1 Introduction 2.2 Thermophysicalpropertiesof?uids 2.2.1 Thermodynamic properties Equationofstate Calculationofproperties Thermodynamicpropertiesofmixtures 2.2.2 Transport properties Extended corresponding states Dilute-gas contributions Density-dependent contributions Transportpropertiesofmixtures 2.3 Thermophysicalpropertiesofsolids 2.3.1 Conservationofenergy 2.3.2 Behaviorofthermophysicalpropertiesofsolids * ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology. 43 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan 44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [44], (2) Lines: 71 to 108 â€”â€”â€” 0.15337pt PgVar â€”â€”â€” Long Page PgEnds: T E X [44], (2) 2.3.3 Propertyvaluesofsolidmaterials 2.3.4 Measuringthermophysicalpropertiesofsolids Thermal conductivity Speci?c heat Thermal diffusivity Thermal expansion Nomenclature References Graphsofthermophysicalproperties 2.1 INTRODUCTION The need for accurate thermophysical properties in the design and analysis of en- gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking ?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It is particularly true that small errors in properties for custody transfer of ?uids can result in signi?cant costs or bene?ts to those involved in commercial transactions. It istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis inlightoftheaccuracyofthepropertiesused. In addition to the individual properties for system design and analysis, there is a need for combined heat transfer parameters and dimensionless groups that occur in equations for conduction, convection, and radiation. These include: Biot number Boussinesq number Eckert number Fouriernumber Graetznumber Grashofnumber Lewis number Nusselt number P´ eclet number Prandtl number Rayleigh number Reynolds number Schmidt number Sherwood number Only the Prandtl number is a ?uid property; the others incorporate system character- istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this book and are not discussed in this chapter. The termthermophysicalproperties is used here to refer to both thermodynamic (equilibrium) properties and transport properties. The thermodynamic properties de- ?ne equilibrium states ofthe system and include such properties as temperature, pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en- tropy. The transport properties are those such as thermal conductivity, viscosity, and thermal diffusivity which pertain to the transfer of momentum or energy within the system. In a practical sense, design and analysis ofheat transf er systems require information about both transport and thermodynamic properties. The thermodynamic properties are generally well de?ned by measurement for most common ?uids and BOOKCOMP, Inc. â€” John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan INTRODUCTION 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [45], (3) Lines: 108 to 118 â€”â€”â€” 0.0pt PgVar â€”â€”â€” Long Page PgEnds: T E X [45], (3) mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor the same ?uids and mixtures. This is, in part, because the experimental methods for measuring transport properties are generally less accurate than those for the thermo- dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements (see Wakeham et al., 1991). Current practice in the design and analysis of?uid systems requires the use of computer programs in various forms for thermophysical properties. Based on the ex- perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases available to the engineer. Such sources of highly accurate properties are often referred to asstandardreferencequality sources, and many are the result ofinternational agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If special applications require equations with fewer terms for rapidly estimating proper- ties or for calculating abbreviated tables, these can be developed based on properties calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin the properties used in design can be determined by comparisons to values from the source,theaccuraciesofwhicharegenerallywellspeci?ed. We have assumed that the user ofthis book has access to a reasonably current personal computer and to the World Wide Web. Because the National Institute of Standards and Technology (NIST) databases generally incorporate the best available ?uid properties algorithms and equations, we rely heavily on those sources in the recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter, graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues for ?uid properties that are readily available in other sources, including common engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty values at common conditions are given for completeness. Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof ?uids may be calculated using several comprehensive computer programs from NIST, including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer program is included in this book for use in calculating properties for design and analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry. Although the NIST programs provide the most accurate values currently avail- able, additional research, experimentation, and correlation activities worldwide will increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe covered ?uids. The full programs with source code and mixture capabilities are avail- able from NIST at a nominal cost and are updated periodically. Details concerning the current databases available from the Standard Reference Data Of?ce of NIST are located at the Web address http://www.nist.gov/srd by searching for the key words NIST10, NIST12, NIST14, or NIST23. There are fewer sources of properties of solids for design than there are for ?uids, and the data available have not yet been incorporated into evaluated wide-range com- puter models. The uncertainties associated with published values for many properties BOOKCOMP, Inc. â€” John Wiley & Sons / Page 46 / 2nd Proofs /HeatTransferHandbook / Bejan 46 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [46], (4) Lines: 118 to 144 â€”â€”â€” -0.03pt PgVar â€”â€”â€” Normal Page * PgEnds: Eject [46], (4) ofsolidsaregenerallylargerthanthoseforpropertiesof?uids,inpartbecauseofim- purities or compositional variations in experimental samples. In this chapter we have includedselectedpropertiesofsolidsfromreliablepublishedsources. Thischaptercontainsaminimumoftheoryandnodetailsonthecorrelationand analysis of thermophysical property data for determining the recommended values for both ?uids and solids. Literature references are given for the best available sources known for the various properties. The references should be useful to the reader who is interested in greater detail about the correlation methods and about the data on which the correlations and recommended values are based. 2.2 THERMOPHYSICAL PROPERTIES OF FLUIDS Thethermodynamicandtransportpropertiesof?uidsarediscussedseparatelyinthis section.Sourcesofcalculatedvaluesandbriefdescriptionsofthemethodsusedto determine values in the tables and graphs in this book are given. References to original worksthatcontaindetailsofbothcorrelationandmeasurementtechniquesarealso included. 2.2.1 Thermodynamic Properties Apropertyformulationisthesetofequationsusedtocalculatepropertiesofa?uid at speci?ed thermodynamic states de?ned by the appropriate independent variables. A typical thermodynamic property formulation is based on an equation of state that allowsthecorrelationandcomputationofallthermodynamicpropertiesofthe?uid, including properties such as entropy that cannot be measured directly. The general termequationofstate in this chapter refers to an empirical model developed for calculating thermodynamic properties of ?uids. The termfundamental equation is often used in the literature to refer to empirical descriptions of one of four 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 pressure and temperature, and Helmholtz energy as a function of density and temperature. Modernequationsofstateforthethermodynamicpropertiesofpure?uidsareusually fundamental equations explicit in the Helmholtz energy as a function of density and temperature. The equation of state for a pure ?uid using the Helmholtz energy as the fundamen- tal property is given by a(?,T)= a 0 (?,T)+a r (?,T) (2.1) where a is the molar Helmholtz energy, a 0 (?,T) is the ideal gas contribution to the Helmholtz energy, anda r (?,T) is the residual Helmholtz energy that corresponds to thein?uenceofintermolecularforces.Allthermodynamicpropertiescanbecalcu- latedasderivativesoftheHelmholtzenergy.Forexample,thepressurederivedfrom this expression is Page 5 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 43 / 2nd Proofs /HeatTransferHandbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [43], (1) Lines: 0 to 71 â€”â€”â€” 3.28333pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [43], (1) CHAPTER 2 Thermophysical Properties of Fluids and Materials * R.TJACOBSEN IdahoNationalEngineeringandEnvironmentalLaboratory IdahoFalls,Idaho E.W.LEMMON PhysicalandChemicalPropertiesDivision NationalInstituteofStandardsandTechnology Boulder,Colorado S.G.PENONCELLOandZ.SHAN CenterforAppliedThermodynamicStudies CollegeofEngineering UniversityofIdaho Moscow,Idaho N.T.WRIGHT DepartmentofMechanicalEngineering UniversityofMaryland Baltimore,Maryland 2.1 Introduction 2.2 Thermophysicalpropertiesof?uids 2.2.1 Thermodynamic properties Equationofstate Calculationofproperties Thermodynamicpropertiesofmixtures 2.2.2 Transport properties Extended corresponding states Dilute-gas contributions Density-dependent contributions Transportpropertiesofmixtures 2.3 Thermophysicalpropertiesofsolids 2.3.1 Conservationofenergy 2.3.2 Behaviorofthermophysicalpropertiesofsolids * ThematerialinthischapterisacontributioninpartoftheNationalInstituteofStandardsandTechnology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portionsofhisworkforthesectiononextendedcorrespondingstates,aswellasthehelpandsuggestions ofDanielFriendandJoanSauerwein,alloftheNationalInstituteofStandardsandTechnology. 43 BOOKCOMP, Inc. â€” John Wiley & Sons / Page 44 / 2nd Proofs /HeatTransferHandbook / Bejan 44 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [44], (2) Lines: 71 to 108 â€”â€”â€” 0.15337pt PgVar â€”â€”â€” Long Page PgEnds: T E X [44], (2) 2.3.3 Propertyvaluesofsolidmaterials 2.3.4 Measuringthermophysicalpropertiesofsolids Thermal conductivity Speci?c heat Thermal diffusivity Thermal expansion Nomenclature References Graphsofthermophysicalproperties 2.1 INTRODUCTION The need for accurate thermophysical properties in the design and analysis of en- gineeredsystemsiswellestablished.Theindustrialapplicationsofvariousworking ?uidsandsolidsrequireavarietyofpropertyvalueswithaccuraciesthatrangefrom crudeestimatestoprecisionsof1partin10,000forsomesensitiveapplications.It is particularly true that small errors in properties for custody transfer of ?uids can result in signi?cant costs or bene?ts to those involved in commercial transactions. It istheresponsibilityoftheengineertodecidewhatlevelofaccuracyisneededfora particularapplicationandtoestablishtheuncertaintyoftherelateddesignoranalysis inlightoftheaccuracyofthepropertiesused. In addition to the individual properties for system design and analysis, there is a need for combined heat transfer parameters and dimensionless groups that occur in equations for conduction, convection, and radiation. These include: Biot number Boussinesq number Eckert number Fouriernumber Graetznumber Grashofnumber Lewis number Nusselt number P´ eclet number Prandtl number Rayleigh number Reynolds number Schmidt number Sherwood number Only the Prandtl number is a ?uid property; the others incorporate system character- istics such as velocity, length, or diameter. These groups are de?ned elsewhere in this book and are not discussed in this chapter. The termthermophysicalproperties is used here to refer to both thermodynamic (equilibrium) properties and transport properties. The thermodynamic properties de- ?ne equilibrium states ofthe system and include such properties as temperature, pressure, density, internal energy, heat capacity, speed ofsound, enthalpy, and en- tropy. The transport properties are those such as thermal conductivity, viscosity, and thermal diffusivity which pertain to the transfer of momentum or energy within the system. In a practical sense, design and analysis ofheat transf er systems require information about both transport and thermodynamic properties. The thermodynamic properties are generally well de?ned by measurement for most common ?uids and BOOKCOMP, Inc. â€” John Wiley & Sons / Page 45 / 2nd Proofs /HeatTransferHandbook / Bejan INTRODUCTION 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [45], (3) Lines: 108 to 118 â€”â€”â€” 0.0pt PgVar â€”â€”â€” Long Page PgEnds: T E X [45], (3) mixturesandareusuallyofhigheraccuracythanthetransportpropertiesavailablefor the same ?uids and mixtures. This is, in part, because the experimental methods for measuring transport properties are generally less accurate than those for the thermo- dynamicproperties,althoughthestateoftheartisimprovingforsuchmeasurements (see Wakeham et al., 1991). Current practice in the design and analysis of?uid systems requires the use of computer programs in various forms for thermophysical properties. Based on the ex- perienceoftheauthorsinthedevelopmentandevaluationofcomputerprogramsfor engineeredsystems,werecommendtheuseofthemostaccuratecomputerdatabases available to the engineer. Such sources of highly accurate properties are often referred to asstandardreferencequality sources, and many are the result ofinternational agreementsamongquali?edexpertsonthecurrentbestvaluesofproperties.Atypical accurateequationofstateisapolynomialwith15to35terms,asdescribedlater.If special applications require equations with fewer terms for rapidly estimating proper- ties or for calculating abbreviated tables, these can be developed based on properties calculatedbymeansofthebestavailablemodels,andestimatesofuncertaintiesin the properties used in design can be determined by comparisons to values from the source,theaccuraciesofwhicharegenerallywellspeci?ed. We have assumed that the user ofthis book has access to a reasonably current personal computer and to the World Wide Web. Because the National Institute of Standards and Technology (NIST) databases generally incorporate the best available ?uid properties algorithms and equations, we rely heavily on those sources in the recommendedvaluesgiveninthischapter.Weprovidesummarytablesofproperties ofcommon?uidsandmaterialsforestimatingpurposesand,attheendofthechapter, graphicalcomparisonsofvariouspropertiesofdifferent?uidstoassistintheselection ofmaterialsfordesign.Wehavenot,ingeneral,attemptedtorepeattabularvalues for ?uid properties that are readily available in other sources, including common engineeringtextbooksandotherhandbooks,althoughsomegeneraltablesofproperty values at common conditions are given for completeness. Thevaluesofthethermodynamicandtransportpropertiesforalargenumberof ?uids may be calculated using several comprehensive computer programs from NIST, including NIST Standard Reference Databases 10, 12, 14, and 23. A limited computer program is included in this book for use in calculating properties for design and analysisofheattransfersystemsusingthemostcommon?uids.Somepropertiesare also available on the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry. Although the NIST programs provide the most accurate values currently avail- able, additional research, experimentation, and correlation activities worldwide will increasetheaccuracy,thenumberof?uids,andtherangesofavailablestatesforthe covered ?uids. The full programs with source code and mixture capabilities are avail- able from NIST at a nominal cost and are updated periodically. Details concerning the current databases available from the Standard Reference Data Of?ce of NIST are located at the Web address http://www.nist.gov/srd by searching for the key words NIST10, NIST12, NIST14, or NIST23. There are fewer sources of properties of solids for design than there are for ?uids, and the data available have not yet been incorporated into evaluated wide-range com- puter models. The uncertainties associated with published values for many properties BOOKCOMP, Inc. â€” John Wiley & Sons / Page 46 / 2nd Proofs /HeatTransferHandbook / Bejan 46 THERMOPHYSICALPROPERTIESOFFLUIDSANDMATERIALS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [46], (4) Lines: 118 to 144 â€”â€”â€” -0.03pt PgVar â€”â€”â€” Normal Page * PgEnds: Eject [46], (4) ofsolidsaregenerallylargerthanthoseforpropertiesof?uids,inpartbecauseofim- purities or compositional variations in experimental samples. In this chapter we have includedselectedpropertiesofsolidsfromreliablepublishedsources. Thischaptercontainsaminimumoftheoryandnodetailsonthecorrelationand analysis of thermophysical property data for determining the recommended values for both ?uids and solids. Literature references are given for the best available sources known for the various properties. The references should be useful to the reader who is interested in greater detail about the correlation methods and about the data on which the correlations and recommended values are based. 2.2 THERMOPHYSICAL PROPERTIES OF FLUIDS Thethermodynamicandtransportpropertiesof?uidsarediscussedseparatelyinthis section.Sourcesofcalculatedvaluesandbriefdescriptionsofthemethodsusedto determine values in the tables and graphs in this book are given. References to original worksthatcontaindetailsofbothcorrelationandmeasurementtechniquesarealso included. 2.2.1 Thermodynamic Properties Apropertyformulationisthesetofequationsusedtocalculatepropertiesofa?uid at speci?ed thermodynamic states de?ned by the appropriate independent variables. A typical thermodynamic property formulation is based on an equation of state that allowsthecorrelationandcomputationofallthermodynamicpropertiesofthe?uid, including properties such as entropy that cannot be measured directly. The general termequationofstate in this chapter refers to an empirical model developed for calculating thermodynamic properties of ?uids. The termfundamental equation is often used in the literature to refer to empirical descriptions of one of four 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 pressure and temperature, and Helmholtz energy as a function of density and temperature. Modernequationsofstateforthethermodynamicpropertiesofpure?uidsareusually fundamental equations explicit in the Helmholtz energy as a function of density and temperature. The equation of state for a pure ?uid using the Helmholtz energy as the fundamen- tal property is given by a(?,T)= a 0 (?,T)+a r (?,T) (2.1) where a is the molar Helmholtz energy, a 0 (?,T) is the ideal gas contribution to the Helmholtz energy, anda r (?,T) is the residual Helmholtz energy that corresponds to thein?uenceofintermolecularforces.Allthermodynamicpropertiescanbecalcu- latedasderivativesoftheHelmholtzenergy.Forexample,thepressurederivedfrom this expression is BOOKCOMP, Inc. â€” John Wiley & Sons / Page 47 / 2nd Proofs /HeatTransferHandbook / Bejan THERMOPHYSICALPROPERTIESOFFLUIDS 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [47], (5) Lines: 144 to 184 â€”â€”â€” 3.09909pt PgVar â€”â€”â€” Normal Page PgEnds: T E X [47], (5) p= ? 2 ?a ?? T (2.2) Also, the thermodynamic properties at saturation conditions can be calculated with- out additional ancillary equations through the use ofthe Maxwell criterion (equal pressures and Gibbs energies at constant temperature during phase changes). Thequalityofathermodynamicpropertyformulationisdeterminedbyitsability to model the physical behavior ofthe ?uid as represented by the available data as well as by its conformance to theory (to assure reasonable extrapolation behavior). Publishedcorrelationsshouldincludeestimatesoftheaccuracyofcalculatedproper- tiesaswellasacarefulde?nitionoftherangeofvalidity.Amodernthermodynamic property formulation is generally capable of representing all data values within the estimatedexperimentaluncertaintyofthemeasurements(seeTable2.1).Thepracti- calmodelsoftodayareempiricalorsemiempiricalinnature,althoughvirtuallyall arebasedonsoundtheoreticalprinciples.Thelimitationsofthemodelselectedmust be understood by the user for effective system optimization and related work. Correctbehavioroftheequationofstateinthecriticalregion(boundedby ±0.25? c and ±0.05T c ) is sometimes a concern ofusers ofproperty f ormulations. Classical equations (those that do not use an additional scaling theory) cannot represent the theoretically expected behavior at the critical point. However, state-of-the-art multi- parameterequationsofstatearesuf?cientlyaccurateinthecriticalregiontosatisfy TABLE2.1 GeneralStandardUncertaintyEstimatesforVariousFluidProperties Uncertainty State-of-the-Art to Be Expected Experimental from a Modern CalculatedProperty Region Uncertainty(%) EquationofState(%) Pressure â€” 0.02 Temperature â€” 0.001 K Density â€” 0.02 0.1 Isochoric heat capacity ? > ? c 0.5 0.5 ? < ? c 11 Isobaric heat capacity ? > ? c 0.5 1 ? < ? c 21 Speedofsound ? > ? c 0.1 0.5 ? < ? c 0.01 0.1 Vapor pressure p< 0.1 MPa 0.05 0.5 p> 0.1 MPa 0.01 0.2 Thermal conductivity ? > ? c 0.5 0.5 ? < ? c 22 Viscosity ? > ? c 22 ? < ? c 0.5 0.5Read More

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