40 BASIC CONCEPTS
1 u speciﬁc internal energy, J/kg 2 V volume, m3
3 V velocity vector, m/s 4 V velocity, m/s
5 W width, m
6 x length coordinate, m
7 generalized coordinate, dimensions vary 8 Y mean plane distance, m
9 y length coordinate, m 10 z length coordinate, m 11 ﬁn spacing, m
12
13 Greek Letter Symbols
14 α accommodation parameter, dimensionless 15 thermal diffusivity, m2/s
16 β coefﬁcient of volumetric expansion, m−1 17 ∆ change, dimensionless
18 δ thickness, m
19 e area ratio, dimensionless
20 η ﬁn efﬁciency, dimensionless
21 θ angle in cylindrical coordinate system, rad 22 angle in spherical coordinate system, rad 23 Λ mean free path of molecules, m
24 µ dynamic viscosity, N/m · s 25 ν kinematic viscosity, m2/s 26 π group, dimensionless
27 ρ density, kg/m3
28 σ surface roughness, m 29 surface tension, N/m
30 Stefan–Boltzmann constant, W/m2 · K4 31 normal stress, N/m2
32 τ shear stress, N/m2
33 Φ viscous dissipation factor, s−1
34 φ angle in spherical coordinate system, rad 35 ∇ vector operator, s−1
36 ∇2 Laplacian operator, s−2 37
38 Roman Letter Subscripts 39 c contact
40 cd conduction 41 co contact
42 cv convection 43 D diffusion 44 e equivalent 45 f ﬁn
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REFERENCES 41
1 fl ﬂow
2 g generated 3 gap
4
5 standard acceleration of gravity 6 in inlet condition
7 1 liquid 8 m melting
9 max maximum condition 10 min minimum condition 11 n normal direction
12 o nominal value 13 out outlet condition 14 p constant pressure 15 r radiation
16 radial direction 17 s harmonic mean 18 surface condition
19 sat saturated condition 20 sp spreading
21 sf surface parameter in boiling 22 w wall condition
23 x x-coordinate direction 24 y y-coordinate direction 25 z z-coordinate direction 26 ∞ free stream condition 27
28 Greek Letter Subscripts
29 θ θ-coordinate direction 30 φ phase change
31 φ-coordinate direction 32
33 Superscripts
34 a exponent in dimensional analysis 35 b exponent in dimensional analysis 36 c exponent in dimensional analysis
37 n exponent in natural convection correlation 38
39 40
41 REFERENCES 42
43 Bejan, A. (1995). Convection Heat Transfer, 2nd Ed, Wiley, New York.
44 Bejan, A. (1997). Advanced Engineering Thermodynamics, 2nd Ed, Wiley, New York.
45 Bodoia, J. R., and Osterle, J. F. (1964). The development of free convection between heated vertical plates, Trans. ASME, J. Heat Transfer, 84, 40–44.
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42 BASIC CONCEPTS
1 Buckingham, E. (1914). On Physically Similar Systems: Illustrations of the Use of Dimen-2 sional Equations, Phys. Rev., 4(4), 345–376.
3 Churchill, S. W., and Usagi, R. (1972). A General Expression for the Correlation of Rates of 4 Heat Transfer and Other Phenomena, AIChE J., 18(6), 1121–1138.
5 Elenbaas, W. (1942). Heat Dissipation of Parallel Plates by Free Convection, Physica, 9(1), 6 2–28.
7 Hausen, H. (1943). Darstellung des Warmeauberganges in Rohren durch verallgemeinerte 8 Potenzbeziehungen, Z. VDI, 4, 91–98.
9 Moody, L. F. (1944). Friction Factors for Pipe Flow, Trans. ASME, 66, 671–684.
10 Rohsenow, W. M. (1952). A Method for Correlation Heat Transfer Data for Surface Boiling in 11 Liquids, Trans. ASME, 74, 969–975.
12 Rohsenow, W. M., and Choi, H. Y. (1961). Heat Mass and Momentum Transfer, Prentice-Hall, 13 Englewood Cliffs, NJ.
14 Sieder, E. N., and Tate, G. E. (1936). Heat Transfer and Pressure Drop of Liquids in Tubes, 15 Ind. Eng. Chem., 28, 1429–1436.
16 Yovanovich, M. M., and Antonetti, V. W. (1988). Application of Thermal Contact Resistance 17 Theory to Electronic Packages, in Advances in Thermal Modeling of Electronic Compo-18 nents and Systems, A. Bar-Cohen and A. D. Kraus, eds.), Hemisphere Publishing, New 19 York.
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
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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
CHAPTER 2
Thermophysical Properties of Fluids and Materials*
R.T JACOBSEN
Idaho National Engineering and Environmental Laboratory Idaho Falls, Idaho
E.W.LEMMON
Physical and Chemical Properties Division National Institute of Standards and Technology Boulder, Colorado
S.G.PENONCELLO and Z.SHAN
Center for Applied Thermodynamic Studies College of Engineering
University of Idaho Moscow, Idaho
N.T. WRIGHT
Department of Mechanical Engineering University of Maryland
Baltimore, Maryland
2.1 Introduction
2.2 Thermophysical properties ofﬂuids 2.2.1 Thermodynamic properties
Equation ofstate Calculation ofproperties
Thermodynamic properties ofmixtures 2.2.2 Transport properties
Extended corresponding states Dilute-gas contributions
Density-dependent contributions Transport properties ofmixtures
2.3 Thermophysical properties ofsolids 2.3.1 Conservation ofenergy
2.3.2 Behavior ofthermophysical properties ofsolids
*The material in this chapter is a contribution in part ofthe National Institute ofStandards and Technology, not subject to copyright in the United States. We gratefully thank Mark McLinden for permission to use portions ofhis work for the section on extended corresponding states, as well as the help and suggestions ofDaniel Friend and Joan Sauerwein, all ofthe National Institute ofStandards and Technology.
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44 THERMOPHYSICAL PROPERTIES OF FLUIDS AND MATERIALS
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
2.3.3 Property values ofsolid materials
2.3.4 Measuring thermophysical properties ofsolids Thermal conductivity
Speciﬁc heat Thermal diffusivity Thermal expansion
Nomenclature References
Graphs ofthermophysical properties
2.1 INTRODUCTION
The need for accurate thermophysical properties in the design and analysis of en-gineered systems is well established. The industrial applications ofvarious working ﬂuids and solids require a variety ofproperty values with accuracies that range from crude estimates to precisions of1 part in 10,000 for some sensitive applications. It is particularly true that small errors in properties for custody transfer of ﬂuids can result in signiﬁcant costs or beneﬁts to those involved in commercial transactions. It is the responsibility ofthe engineer to decide what level ofaccuracy is needed for a particular application and to establish the uncertainty ofthe related design or analysis in light ofthe accuracy ofthe properties used.
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 Fourier number Graetz number Grashofnumber Lewis number Nusselt number Peclet number Prandtl number Rayleigh number Reynolds number Schmidt number Sherwood number
Only the Prandtl number is a ﬂuid property; the others incorporate system character-istics such as velocity, length, or diameter. These groups are deﬁned elsewhere in this book and are not discussed in this chapter.
The term thermophysical properties is used here to refer to both thermodynamic (equilibrium) properties and transport properties. The thermodynamic properties de-ﬁne 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 transefr systems require informationaboutbothtransportandthermodynamicproperties.Thethermodynamic properties are generally well deﬁned by measurement for most common ﬂuids and
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