Heat Transfer Handbook part 16 doc

BOOKCOMP, Inc. — John Wiley & Sons / Page 140 / 2nd Proofs / Heat Transfer Handbook / Bejan 140 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 [140], (98) Lines: 3304 to 3322 ——— 12.0pt PgVar ——— Short Page PgEnds: T E X [140], (98) (Cahill, 1990) is being applied widely to measure the thermal conductivity of thin films, especially for microelectronic applications. A single metal strip is fabricated on the film to be tested, which is in turn mounted on a substrate of another material (e.g., silicon). The metal film acts as both heater and temperature sensor. Analysis of the oscillation of electrical resistance at a frequency of 3ω, in response to oscillations of power and temperature of 2ω, provides the in-plane thermal conductivity. Specific Heat Differential scanning calorimetry (DSC) has become widely used because modern commercial instrumentation allows simple use, although the con- struction and control system of the device may be complex (Richardson, 1992). In DSC, a small test sample and a reference sample of similar size are placed in adjacent separate holders. The samples are heated simultaneously at a specified rate, often 1 to 10°C/min. Thermocouples are typically used to monitor the temperature of each sample. The change in enthalpy of the sample is then determined by measurement of how much energy must be added to the test sample to make its temperature track that of the reference. By keeping the sample and the reference the same size and temperature and making the two holders of the same material, the effects of para- sitic convective and radiative losses are automatically canceled in the comparison of the two samples. Modulating the temperature rise of a DSC (e.g., by adding an ac component to the steady rise in temperature) provides additional insight into phase transitions in polymers. Thermal Diffusivity Measurements of thermal diffusivity are popular because they typically require only measurement of a temperature history due to a thermal perturbation of the sample, which is easier than measuring heat flux as required in many steady-state methods. Formerly hampered by complex error analysis, micro- processors have made commercial devices relatively easy to use. The flash method (Parker et al., 1961) is a standard method for measuring the out-of-plane component of diffusivity in a variety of materials (ASTM, 1992). Extensions of the flash method have been made to allow measuring components of α (Donaldson and Taylor, 1975; Mallet et al., 1990; Fujii et al., 1997; Doss and Wright, 2000). Other methods have been employed to measure multiple components of α in anisotropic thin films (Ju et al., 1999), carbon–carbon composite specimens (Dowding et al., 1996), and in elongated polymers (Broerman et al., 1999). Thermal Expansion The linear coefficient of expansion is easier to measure than the volumetric coefficient of expansion. Usually, a cylindrical specimen is heated and its change in length measured either mechanically or with optical methods, such as interferometry. Heat conduction in solids is a mature field. Even so, new materials, applications, and methods of analysis require new measurement of, and increased accuracy in, the values of thermal transport properties. New challenges exist for properties in biological systems, micro- and nanoscale devices, and composites. BOOKCOMP, Inc. — John Wiley & Sons / Page 141 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 141 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 [141], (99) Lines: 3322 to 3383 ——— 0.41034pt PgVar ——— Short Page PgEnds: T E X [141], (99) NOMENCLATURE Roman Letter Symbols a molar Helmholtz energy, J/mol c p isobaric (constant pressure) heat capacity, J/mol·K c v isochoric (constant volume) heat capacity, J/mol·K f equivalent substance reducing ratio for temperature, dimensionless f int factor in Eucken correlation for dilute-gas thermal conductivity, dimensionless F λ ,F η multiplier for thermal conductivity and viscosity, dimensionless F ij mixture parameter, dimensionless g molar Gibbs energy, J/mol h molar enthalpy, J/mol i enthalpy per unit volume, J/m 3 k Boltzmann constant, J/K L length, m M molar mass, g/mol N coefficient, dimensionless p pressure, MPa Pr Prandtl number, dimensionless [= ηc p /λ] ˙ q heat flux vector, W/m 2 R molar gas constant, J/(mol ·K) s molar entropy, J/mol ·K T temperature, K u molar internal energy, J/mol coefficient, dimensionless ν molar volume, dm 3 /mol w speed of sound, m/s x composition (mole fraction), dimensionless Z compressibility factor, dimensionless [= p/ρRT ] Greek Letter Symbols α reduced Helmholtz energy, dimensionless [= a/RT ] α D thermal diffusivity, m 2 /s [= λ/ρc p ] α thermal diffusivity tensor, m 2 /s β coefficient in critical region terms, dimensionless γ coefficient in critical region terms, dimensionless δ reduced density, dimensionless [= ρ/ρ c ] ε/k molecular energy parameter, K ζ mixture parameter, dimensionless η viscosity, dimensionless µPa ·s θ shape factor for temperature, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 142 / 2nd Proofs / Heat Transfer Handbook / Bejan 142 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 [142], (100) Lines: 3383 to 3425 ——— 0.28029pt PgVar ——— Normal Page PgEnds: T E X [142], (100) λ thermal conductivity, W/m ·K thermal conductivity tensor, W/m·K µ coefficient of linear thermal expansion, K −1 µ ν coefficient of volumetric thermal expansion, K −1 ν kinematic viscosity, m 2 /s ξ mixture parameter, dimensionless ρ molar density, mol/dm 3 ρ m mass density, kg/m 3 σ molecular size parameter, nm surface tension, N/m τ inverse reduced temperature, [= T c /T ], dimensionless φ shape factor for density, dimensionless ϕ coefficient in critical region terms, dimensionless ω fundamental frequency in the 3ω method, dimensionless Ω (2,2) collision integral, dimensionless Superscripts 0 ideal gas property crit critical point E excess-like property idmix ideal mixture int thermal conductivity arising from internal motions r residual or real gas property trans translational part of thermal conductivity * dilute-gas (ideal gas) state Subscripts 0 reference state property c critical point property i, j pure fluid properties mix mixture quantity red reducing property REFERENCES Angus, S., Armstrong, B., and de Reuck, K. 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BOOKCOMP, Inc. — John Wiley & Sons / Page 145 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 145 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 [145], (103) Lines: 3509 to 3547 ——— 6.0pt PgVar ——— Normal Page PgEnds: T E X [145], (103) Kamei, A., Beyerlein, S. W., and Jacobsen, R. T (1995). Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22, Int. J. Thermophys. 16, 1155–1164. Katti, R. S., Jacobsen, R. T, Stewart, R. B., and Jahangiri, M. (1986). Thermodynamic Prop- erties for Neon for Temperatures from the Triple Point to 700 K at Pressures to 700 MPa, Adv. Cryog. Eng., 31, 1189–1197. Kittel, C. (1996). Introduction to Solid State Physics, 7th ed., Wiley, New York. Klein, S. A., McLinden, M. O., and Laesecke, A. (1997). An Improved Extended Correspond- ing States Method for Estimation of Viscosity of Pure Refrigerants and Mixtures, Int. J. 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Simultaneous Measurements of Axial and BOOKCOMP, Inc. — John Wiley & Sons / Page 146 / 2nd Proofs / Heat Transfer Handbook / Bejan 146 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 [146], (104) Lines: 3547 to 3588 ——— 0.0pt PgVar ——— Long Page PgEnds: T E X [146], (104) Radial Thermal Diffusivities of an Anisotropic Solid in Thin Plate: Application to Multi- layered Materials, in Thermal Conductivity, vol. 21, C. J. Cremers and H. A. Fine, eds., Plenum Press, New York, pp. 91–107. Marsh, K., Perkins, R., and Ramires, M. L. V. (2002). Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 700 MPa, J. Chem. Eng. Data; 47(4), 932–940. Marx, V., Pruss, A., and Wagner, W. (1992). 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BOOKCOMP, Inc. — John Wiley & Sons / Page 147 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 147 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 [147], (105) Lines: 3588 to 3627 ——— 7.0pt PgVar ——— Long Page PgEnds: T E X [147], (105) Parrott, J. E., and Stuckes, A. D. (1975). Thermal Conductivity of Solids, Pion, London. Penoncello, S. G., Goodwin, A. R. H., and Jacobsen, R. T (1995). A Preliminary Thermody- namic Property Formulation for Cyclohexane, Int. J. Thermophys., 16(2), 519–531. Penoncello, S. G., Lemmon, E. W., Shan, Z., and Jacobsen, R. T. (2001). A Fundamental Equation for the Calculation of the Thermodynamic Properties of Trifluoromethane (R-23), J. Phys. Chem. Ref. Data. Perkins, R. A. (2001). Measurement and Correlation of the Thermal Conductivity of Isobutane from 114 K to 600 K at Pressures to 70 MPa, J. Chem. Eng. Data. Perkins, R. A., Laesecke, A., Howley, J., Ramires, M. L. 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A Reference Quality BOOKCOMP, Inc. — John Wiley & Sons / Page 148 / 2nd Proofs / Heat Transfer Handbook / Bejan 148 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 [148], (106) Lines: 3627 to 3667 ——— 0.0pt PgVar ——— Long Page PgEnds: T E X [148], (106) Thermodynamic Property Formulation for Nitrogen, J. Phys. Chem. Ref. Data, 29(6), 1361– 1433. See also Int. J. Thermophys., 14(4), 1121–1132, 1998. Sunaga, H., Tillner-Roth, R., Sato, H., and Watanabe, K. (1998). A Thermodynamic Equation of State for Pentafluoroethane (R-125), Int. J. Thermophys., 19(6), 1623–1635. Tanaka, Y., and Sotani, T. (1995). Transport Properties (Thermal Conductivity and Viscosity), in R-123: Thermodynamic and Physical Properties, M. O. McLinden, ed. International Institute of Refrigeration, Paris. See also Int. J. Thermophys., 17(2), 293–328, 1996. 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BOOKCOMP, Inc. — John Wiley & Sons / Page 149 / 2nd Proofs / Heat Transfer Handbook / Bejan GRAPHS OF THERMOPHYSICAL PROPERTIES 149 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 [149], (107) Lines: 3667 to 3683 ——— * 86.34pt PgVar ——— Long Page * PgEnds: Eject [149], (107) Younglove, B. A., and Ely, J. F. (1987). Thermophysical Properties of Fluids: II. Methane, Ethane, Propane, Isobutane and Normal Butane, J. Phys. Chem. Ref. Data, 16, 577–798. Younglove, B. A., and McLinden, M. O. (1994). An International Standard Equation-of-State Formulation of the Thermodynamic Properties of Refrigerant 123 (2,2-dichloro-1,1,1- trifluoroethane), J. Phys. Chem. Ref. Data, 23, 731–779. GRAPHS OF THERMOPHYSICAL PROPERTIES The following figures show property behavior for several groups of similar fluids in the gas phase. The fluid groups include atmospheric gases, hydrocarbons, refriger- ants, and other inorganic gases. The plots are given to allow qualitative comparisons of properties of the various fluids. Properties displayed include those important to heat transfer calculations, including thermal conductivity, viscosity, thermal diffusiv- ity and Prandtl number. These plots provide assistance in the selection of working fluids in thermal system design. The plots were constructed using values calculated from the NIST databases. . (1998). Heat and Mass Transfer, Springer-Verlag, Berlin. Bejan, A. (1993). Heat Transfer, Wiley, New York. BOOKCOMP, Inc. — John Wiley & Sons / Page 143 / 2nd Proofs / Heat Transfer Handbook. Joule Heating, Thin Solid Films, 339, 160 164 . BOOKCOMP, Inc. — John Wiley & Sons / Page 145 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 145 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 [145],. Thermal Diffusivity, Heat Capacity and Thermal Conductivity, J. Appl. Phys., 32(9), 167 9 168 4. BOOKCOMP, Inc. — John Wiley & Sons / Page 147 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 147 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 [147],