Table 1 Al₂O₃/water properties.

Density²³

\(\rho_{eff} = \left( {1 - \varphi } \right)\rho_{f} + \varphi \rho_{p}\)

Heat capacity²³

\(c_{p,eff} = \frac{{\left( {1 - \varphi } \right)(\rho c_{p} )_{f} + \varphi (\rho c_{p} )_{p} }}{{\left( {1 - \varphi } \right)\rho_{f} + \varphi \rho_{p} }}\)

Viscosity³²

\(\mu_{eff} = \left( {1 + \frac{{\rho_{np} v_{B} d_{p}^{2} }}{72C\delta }} \right)\mu_{f}\)

\(v_{B} = \frac{1}{{d_{p} }}\sqrt[3]{{\frac{{18K_{B} ~T}}{{\pi \rho _{{np}} d_{p} }}}}\)

\(\delta = \sqrt[3]{{\frac{{\pi d_{p} }}{6\phi }}}\)

Thermal conductivity³¹

\(k_{nf} /k_{bf} = 1 + 64.7\left( \phi \right)^{0.7460} \left( {\frac{{d_{bf} }}{{d_{p} }}} \right)^{0.3690} \left( {\frac{{k_{bf} }}{{k_{p} }}} \right)^{0.7476} Pr^{0.9955} Re_{np}^{1.2321}\)

\(Re_{np} = \frac{{\rho_{bf} K_{B} T}}{{3\pi \mu_{bf}^{2} \lambda }}\)