Table 4 Thermophysical characteristics of hybrid nanoparticles^{10,25,35,56,62,64,65,66}.

Density

\(\rho_{hnf} \,\, = \,(1 - \phi_{2} )[(1 - \phi_{1} ) + \phi_{1} \frac{{\rho_{s1} }}{{\rho_{f} }}] + \phi_{2} \frac{{\rho_{s2} }}{{\rho_{f} }},\)

\(\rho_{hnf} \,\, = \,[(1 - \phi ) + \phi \frac{{\rho_{s} }}{{\rho_{f} }}],\)

Dynamic Viscosity

\(\mu_{hnf} = \frac{{\mu_{f} }}{{(1 - \phi_{1} )^{2.5} (1 - \phi_{2} )^{2.5} }},\)

\(\mu_{nf} = \frac{{\mu_{f} }}{{(1 - \phi )^{2.5} }},\)

Thermal conductivity

\(\begin{gathered} \frac{{k_{hnf} }}{{k_{nf} }} = \frac{{k_{s2} + (n - 1)k_{nf} - (n - 1)\phi_{2} (k_{nf} - k_{s2} )}}{{k_{s2} + (n - 1)k_{nf} + \phi_{2} (k_{nf} - k_{s2} )}},\,\, \hfill \\ \,\frac{{k_{nf} }}{{k_{f} }} = \frac{{k_{s1} + (n - 1)k_{f} - (n - 1)\phi_{1} (k_{f} - k_{s1} )}}{{k_{s1} + (n - 1)k_{f} + \phi_{1} (k_{f} - k_{s1} )}}. \hfill \\ \end{gathered}\)

\(\,\,\frac{{k_{nf} }}{{k_{f} }} = \frac{{k_{s} + (n - 1)k_{f} - (n - 1)\phi (k_{f} - k_{s} )}}{{k_{s} + (n - 1)k_{f} + \phi (k_{f} - k_{s} )}}.\)

Heat Capacity

\((\rho c_{p} )_{hnf} = (1 - \phi_{2} )[(1 - \phi_{1} ) + \phi_{1} \frac{{(\rho c_{p} )_{s1} }}{{(\rho c_{p} )_{f} }}] + \phi_{2} \frac{{(\rho c_{p} )_{s2} }}{{(\rho c_{p} )_{f} }},\)

\((\rho c_{p} )_{nf} = [(1 - \phi ) + \phi \frac{{(\rho c_{p} )_{s} }}{{(\rho c_{p} )_{f} }}],\)

Electrical Conductivity

\(\begin{gathered} \frac{{\sigma_{hnf} }}{{\sigma_{nf} }} = \frac{{\sigma_{s2} + 2\sigma_{nf} - 2\phi_{2} (\sigma_{nf} - \sigma_{s2} )}}{{\sigma_{s2} + 2\sigma_{nf} + \phi_{2} (\sigma_{nf} - \sigma_{s2} )}}\,,\, \hfill \\ \,\frac{{\sigma_{nf} }}{{\sigma_{f} }} = \frac{{\sigma_{s1} + 2\sigma_{f} - 2\phi_{1} (\sigma_{f} - \sigma_{s1} )}}{{\sigma_{s1} + 2\sigma_{f} + \phi_{1} (\sigma_{f} - \sigma_{s1} )}}. \hfill \\ \end{gathered}\)

\(\,\frac{{\sigma_{nf} }}{{\sigma_{f} }} = \frac{{\sigma_{s} + 2\sigma_{f} - 2\phi (\sigma_{f} - \sigma_{s} )}}{{\sigma_{s} + 2\sigma_{f} + \phi (\sigma_{f} - \sigma_{s} )}}.\)