FPROPS/Thermal conductivity: Difference between revisions
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:<math>\lambda_0\left(T\right) = \frac{0.177568 \sqrt{T} \left(c_p^0/R\right)}{\sigma^2 \sqrt{M} \; \mathcal{C}_\lambda^\ast\left(T^\ast\right)}</math> | :<math>\lambda_0\left(T\right) = \frac{0.177568 \sqrt{T} \left(c_p^0/R\right)}{\sigma^2 \sqrt{M} \; \mathcal{C}_\lambda^\ast\left(T^\ast\right)}</math> | ||
where <math>c_p^0/R</math> is the isobaric heat capacity divided by the gas constant (either both specific or both molar), <math>\sigma</math> is length scaling parameter (in units of nm, which is messy), <math>M</math> is relative molecular mass</math>, and <math>\mathcal{C}_\lambda^\ast \left(T^\ast\right)</math> is the reduced effective cross section for thermal conductivity, | where <math>c_p^0/R</math> is the isobaric heat capacity divided by the gas constant (either both specific or both molar), <math>\sigma</math> is length scaling parameter (in units of nm, which is messy), <math>M</math> is relative molecular mass</math>, | ||
Also, <math>T_\ast</math> is the reduced temperature, | |||
:<math>T_\ast = \frac{T}{\epsilon / k}</math> | |||
and <math>\epsilon / k</math> is the 'energy scaling parameter', specific to the fluid in question. | |||
Also, and <math>\mathcal{C}_\lambda^\ast \left(T^\ast\right)</math> is the reduced effective cross section for thermal conductivity, | |||
:<math>\mathcal{C}_\lambda^\ast \left(T^\ast\right) = \sum_{i=0}^{n}{\frac{b_i}{\left(T^\ast\right)^i}}</math> | :<math>\mathcal{C}_\lambda^\ast \left(T^\ast\right) = \sum_{i=0}^{n}{\frac{b_i}{\left(T^\ast\right)^i}}</math> | ||
The constants <math>b_i</math> will be tabulated for each fluid separately. | |||
== References == | == References == | ||
<references/> | <references/> | ||
Revision as of 06:26, 25 March 2014
Calculation of thermal conductivity in FPROPS is in development. This development is driven by an application requiring transport properties of carbon dioxide, so the first correlations being implemented will be for that. Although textbooks such as Incropera and DeWitt, Holman and Cengel use <math>k</math> for thermal conductivity, most publications on thermophysical properties use the convention of <math>\lambda</math>, and that convention will be used on this page.
Correlations typically specify conductivity in terms of ideal (zero-density limit) <math>\lambda_0</math>, residual <\math>\lambda_r</math> and critical region enhancement function <math>\lambda_c</math>, as follows:
- <math>\lambda \left(\rho,T \right) = \lambda_0 \left(T \right) + \lambda_r \left(\rho, T\right) + \lambda_c \left(\rho, T\right)</math>
Ideal component
The ideal (zero-density limit) component has been expressed in several places[1][2][3]
- <math>\lambda_0\left(T\right) = \frac{0.177568 \sqrt{T} \left(c_p^0/R\right)}{\sigma^2 \sqrt{M} \; \mathcal{C}_\lambda^\ast\left(T^\ast\right)}</math>
where <math>c_p^0/R</math> is the isobaric heat capacity divided by the gas constant (either both specific or both molar), <math>\sigma</math> is length scaling parameter (in units of nm, which is messy), <math>M</math> is relative molecular mass</math>,
Also, <math>T_\ast</math> is the reduced temperature,
- <math>T_\ast = \frac{T}{\epsilon / k}</math>
and <math>\epsilon / k</math> is the 'energy scaling parameter', specific to the fluid in question.
Also, and <math>\mathcal{C}_\lambda^\ast \left(T^\ast\right)</math> is the reduced effective cross section for thermal conductivity,
- <math>\mathcal{C}_\lambda^\ast \left(T^\ast\right) = \sum_{i=0}^{n}{\frac{b_i}{\left(T^\ast\right)^i}}</math>
The constants <math>b_i</math> will be tabulated for each fluid separately.
References
- ↑ V Vesovic, W A Wakeham, G A Olchowy, J V Sengers, J T R Watson and J Millat, 1990. The Transport Properties of Carbon Dioxide, J Phys Chem Ref Data 19, 763. doi:10.1063/1.555875.
- ↑ E W Lemmon and R T Jacobsen, 2004. Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air doi:10.1023/B:IJOT.0000022327.04529.f3
- ↑ V Vesovic, 1994. "On Correlating the Transport Properties of Supercritical Fluids", in Supercritical Fluids: Fundamentals for Application, Springer, pp 273-283. doi:10.1007/978-94-015-8295-7_10. (Note the error in equation (6) in this reference)