Table 2 Thermophysical characteristics of THNF¹⁸.

Dynamic viscosity

\({\mu _{thnf}}=\frac{{{\mu _f}}}{{{{(1 - {\varphi _1})}^{2.5}}{{(1 - {\varphi _2})}^{2.5}}{{(1 - {\varphi _3})}^{2.5}}}}\)

Density

\(\begin{gathered} {\rho _{{\text{thnf}}}}=(1 - {\varphi _3})\left[ {(1 - {\varphi _2})\left\{ \begin{gathered} (1 - {\varphi _1}){\rho _f} \hfill \\ +{\varphi _1}{\rho _{_{1}}} \hfill \\ \end{gathered} \right\}+{\varphi _2}{\rho _{_{2}}}} \right]+ \hfill \\ {\varphi _3}{\rho _{_{3}}} \hfill \\ \end{gathered}\)

Heat capacity

\(\begin{gathered} {(\rho {C_p})_{{\text{thnf}}}}=(1 - {\varphi _3})\left[ \begin{gathered} (1 - {\varphi _2})\left\{ \begin{gathered} (1 - {\varphi _1}){(\rho {C_p})_f} \hfill \\ +{\varphi _1}{(\rho {C_p})_1} \hfill \\ \end{gathered} \right\} \hfill \\ +{\varphi _2}{(\rho {C_p})_2} \hfill \\ \end{gathered} \right]+ \hfill \\ {\varphi _3}{(\rho {C_p})_3} \hfill \\ \end{gathered}\)

Thermal expansions

\(\begin{gathered} {\beta _{{\text{thnf}}}}=(1 - {\varphi _3})\left[ {(1 - {\varphi _2})\left\{ \begin{gathered} (1 - {\varphi _1}){\beta _f} \hfill \\ +{\varphi _1}{\beta _{_{1}}} \hfill \\ \end{gathered} \right\}+{\varphi _2}{\beta _{_{2}}}} \right]+ \hfill \\ {\varphi _3}{\beta _{_{3}}} \hfill \\ \end{gathered}\)

Electrical conductivity

\(\begin{gathered} \frac{{{\sigma _{mhnf}}}}{{{\sigma _{hnf}}}}=\frac{{{\sigma _3}+2{\sigma _{hnf}} - 2{\varphi _3}({\sigma _{hnf}} - {\sigma _3})}}{{{\sigma _3}+2{\sigma _{hnf}}+{\varphi _3}({\sigma _{hnf}} - {\sigma _3})}}, \hfill \\ \frac{{{\sigma _{hnf}}}}{{{\sigma _{nf}}}}=\frac{{{\sigma _2}+2{\sigma _{nf}} - 2{\varphi _2}({\sigma _{nf}} - {\sigma _2})}}{{{\sigma _2}+2{\sigma _{nf}}+{\varphi _2}({\sigma _{nf}} - {\sigma _2})}},\quad \hfill \\ \frac{{{\sigma _{nf}}}}{{{\sigma _f}}}=\frac{{{\sigma _1}+2{\sigma _f} - 2{\varphi _1}({\sigma _f} - {\sigma _1})}}{{{\sigma _1}+2{\sigma _f}+{\varphi _1}({\sigma _f} - {\sigma _1})}} \hfill \\ \end{gathered}\)

Thermal conductivity

\(\begin{gathered} \frac{{{\kappa _{mhnf}}}}{{{\kappa _{hnf}}}}=\left[ {\frac{{{k_3}+2{\kappa _{hnf}} - 2{\varphi _3}({\kappa _{hnf}} - {\kappa _3})}}{{{k_3}+2{\kappa _{hnf}}+{\varphi _3}({\kappa _{hnf}} - {\kappa _3})}}} \right],\quad \hfill \\ \frac{{{\kappa _{hnf}}}}{{{\kappa _{nf}}}}=\left[ {\frac{{{k_2}+2{\kappa _{nf}} - 2{\varphi _2}({\kappa _{nf}} - {\kappa _2})}}{{{k_2}+2{\kappa _{nf}}+{\varphi _2}({\kappa _{nf}} - {\kappa _2})}}} \right], \hfill \\ \frac{{{\kappa _{nf}}}}{{{\kappa _f}}}=\left[ {\frac{{{k_1}+2{\kappa _f} - 2{\varphi _1}({\kappa _f} - {\kappa _1})}}{{{k_1}+2{\kappa _f}+{\varphi _1}({\kappa _f} - {\kappa _1})}}} \right] \hfill \\ \end{gathered}\)