Thermal Properties
Thermal Conductivity
Liquid Phase
When experimental data is not available, the contribution of each component for the thermal conductivity of the liquid phase is calculated by the Latini method ,
\[
\begin{eqnarray}
\lambda_{i} & = & \frac{A(1-T_{r})^{0.38}}{T_{r}^{1/6}}
\end{eqnarray}
\]
\[
\begin{eqnarray}
A & = & \frac{A^{*}T_{b}^{0.38}}{MM^{\beta}T_{c}^{\gamma}},
\end{eqnarray}
\]
where \(A^{*},\:\alpha,\:\beta\) and \(\gamma\) depend on the nature of the liquid (Saturated Hydrocarbon, Aromatic, Water, etc). The liquid phase thermal conductivity is calculated from the individual values by the Li method ,
\[
\begin{eqnarray}
\lambda_{L} & =\sum\sum\phi_{i}\phi_{j}\lambda_{ij}
\end{eqnarray}
\]
\[
\begin{eqnarray}
\lambda_{ij} & = & 2(\lambda_{i}^{-1}+\lambda_{j}^{-1})^{-1}
\end{eqnarray}
\]
\[
\phi_{i}=\frac{x_{i}V_{c_{i}}}{\sum x_{i}V_{c_{i}}},
\]
where
\(\lambda_{L}\) liquid phase thermal conductivity (W/[m.K])
Vapor Phase
When experimental data is not available, vapor phase thermal conductivity is calculated by the Ely and Hanley method ,
\[
\lambda_{V}=\lambda^{*}+\frac{1000\eta^{*}}{MM}1.32\left(C_{v}-\frac{3R}{2}\right),
\]
where
\(\lambda_{V}\) vapor phase thermal conductivity (W/[m.K])
\(C_{v}\) constant volume heat capacity (J/[mol.K])
\(\lambda^{*}\) and \(\eta^{*}\) are defined by:
\[
\lambda^{*}=\lambda_{0}H
\]
\[
H=\left(\frac{16.04E-3}{MM/1000}\right)^{1/2}f^{1/2}/h^{2/3}
\]
\[
\lambda_{0}=1944\eta_{0}
\]
\[
f=\frac{T_{0}\theta}{190.4}
\]
\[
h=\frac{V_{c}}{99.2}\phi
\]
\[
\theta=1+(\omega-0.011)(0.56553-0.86276\ln T^{+}-0.69852/T^{+}
\]
\[
\phi=\left[1+(\omega-0.011)(0.38650-1.1617\ln T^{+})\right]0.288/Z_{c}
\]
If \(T_{r}\leqslant2,\:T^{+}=T_{r}\) . If \(T_{r}>2,\:T^{+}=2\) .
\[
h=\frac{V_{c}}{99.2}\phi
\]
\[
\eta^{*}=\eta_{0}H\frac{MM/1000}{16.04E-3}
\]
\[
\eta_{0}=10^{-7}\sum_{n=1}^{9}C_{n}T_{0}^{(n-4)/3}
\]
\[
T_{0}=T/f
\]