Table 1 Al₂O₃/water properties.

Density⁵²

\({\rho }_{{nf}}=(1-{\alpha }){\rho }_{{f}}+{\alpha }{\rho }_{{np}}\)

Heat capacity^52,53

\({{c}}_{{p},{nf}}=\frac{(1-{\alpha })(\rho {{c}}_{{p}}{)}_{{f}}+{\alpha }(\rho {{c}}_{{p}}{)}_{{np}}}{(1-{\alpha }){\rho }_{{f}}+{\alpha }{\rho }_{{np}}}\)

Viscosity⁵²

\({\mu }_{{nf}}=(1+7.3{\alpha }+123{{\alpha }}^{2}){\mu }_{{f}}\)

Thermal conductivity⁵³

\({{k}}_{{nf}}/{{k}}_{{bf}}=1+64.7{\left({\alpha }\right)}^{0.7460}{\left(\frac{{{d}}_{{bf}}}{{{d}}_{{np}}}\right)}^{0.3690}{\left(\frac{{{k}}_{{bf}}}{{{k}}_{{np}}}\right)}^{0.7476}{{Pr}}^{0.9955}{R}{{{e}}_{{np}}}^{1.2321}\)

\({{Re}}_{{np}}=\frac{{\rho }_{{bf}}{{K}}_{{B}}{ T}}{3\pi {{\mu }_{{bf}}}^{2}\lambda }\)