Thermal Diffusivity Measurements ofthermal diffusivity are popular because they typically require only measurement ofa temperature history due to a thermal perturbation ofthe sample, whi
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(Cahill, 1990) is being applied widely to measure the thermal conductivity ofthin 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 ofanother material (e.g., silicon) The metal film acts as both heater and temperature sensor Analysis of the oscillation ofelectrical resistance at a frequency of3ω, in response to oscillations
ofpower and temperature of2ω, 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 ofthe 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 ofeach sample The change in enthalpy ofthe sample is then determined by measurement ofhow 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 ofthe same material, the effects ofpara-sitic convective and radiative losses are automatically canceled in the comparison of the two samples Modulating the temperature rise ofa 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 ofthermal diffusivity are popular because they typically require only measurement ofa temperature history due to a thermal perturbation ofthe 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 ofdiffusivity in a variety ofmaterials (ASTM, 1992) Extensions ofthe flash method have been made to allow measuring components ofα (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 ofα 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 ofanalysis require new measurement of, and increased accuracy in, the values ofthermal transport properties New challenges exist for properties in biological systems, micro- and nanoscale devices, and composites
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NOMENCLATURE
Roman Letter Symbols
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
fint factor in Eucken correlation for dilute-gas thermal
conductivity, dimensionless
Fλ, Fη multiplier for thermal conductivity and viscosity,
dimensionless
Fij mixture parameter, dimensionless
i enthalpy per unit volume, J/m3
P r Prandtl number, dimensionless [= ηc p /λ]
R molar gas constant, J/(mol· K)
u molar internal energy, J/mol
coefficient, dimensionless
x composition (mole fraction), dimensionless
Z compressibility factor, dimensionless [= p/ρRT ]
Greek Letter Symbols
α reduced Helmholtz energy, dimensionless [= a/RT ]
αD thermal diffusivity, m2/s [= λ/ρc p]
α thermal diffusivity tensor, m2/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, dimensionlessµPa · s
θ shape factor for temperature, dimensionless
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thermal conductivity tensor, W/m· K
µ coefficient of linear thermal expansion, K−1
µν coefficient of volumetric thermal expansion, K−1
ν kinematic viscosity, m2/s
ξ mixture parameter, dimensionless
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
int thermal conductivity arising from internal motions
r residual or real gas property trans translational part ofthermal conductivity
* dilute-gas (ideal gas) state
Subscripts
i, j pure fluid properties
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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 ofproperties ofthe 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 ofworking fluids in thermal system design The plots were constructed using values calculated from the NIST databases