Table 3 Thermochemical properties of ternary nanofluids⁴⁶.

Viscosity

\({A_1}=\frac{{{\mu _{tnf}}}}{{{\mu _f}}}=\frac{1}{{{{\left( {1 - {\phi _1}} \right)}^{2.5}}{{\left( {1 - {\phi _2}} \right)}^{2.5}}{{\left( {1 - {\phi _3}} \right)}^{2.5}}}},\)

Density

\({A_2}=\frac{{{\rho _{tnf}}}}{{{\rho _f}}}=\left( {1 - {\phi _3}} \right)\left\{ {\left[ {{\phi _1}{\rho _{s1}}+\left( {1 - {\phi _1}} \right){\rho _f}} \right]\left( {1 - {\phi _2}} \right)+{\phi _2}{\rho _{s2}}} \right\}+{\phi _3}{\rho _{s3}},\)

Specific heat

\({A_3}=\frac{{{{(\rho {c_p})}_{tnf}}}}{{{{(\rho {c_p})}_f}}}={\phi _3}{(\rho {c_p})_{s3}}+\left( {1 - {\phi _3}} \right)\left\{ {\left[ {{\phi _1}{{(\rho {c_p})}_{s1}}+\left( {1 - {\phi _1}} \right){{(\rho {c_p})}_f}} \right]\left( {1 - {\phi _2}} \right)+{\phi _2}{{(\rho {c_p})}_{s2}}} \right\},\)

Electrical conductivity

\({A_5}=\frac{{{\sigma _{hnf}}}}{{{\sigma _{nf}}}}=\frac{{{\sigma _{nf}}(1 - 2{\phi _2})+{\sigma _{s2}}(1+2{\phi _2})}}{{{\sigma _{s2}}(1 - {\phi _2})+{\sigma _{nf}}(1+{\phi _2})}},\)\({A_5}=\frac{{{\sigma _{tnf}}}}{{{\sigma _{hnf}}}}=\frac{{{\sigma _{s3}}(1+2{\phi _3})+{\sigma _{hnf}}(1 - 2{\phi _3})}}{{{\sigma _{s3}}(1 - {\phi _3})+{\sigma _{hnf}}(1+{\phi _3})}},\)\({A_5}=\frac{{{\sigma _{nf}}}}{{{\sigma _f}}}=\frac{{{\sigma _f}(1 - 2{\phi _1})+{\sigma _{s1}}(1+2{\phi _1})}}{{{\sigma _f}(1+{\phi _1})+{\sigma _{s1}}(1 - {\phi _1})}},\)

Thermal conduction

\({A_4}=\frac{{{k_{nf}}}}{{{k_f}}}=\frac{{{k_{s1}}+{k_f}(s - 1) - {\phi _1}(s - 1)\left( {{k_f} - {k_{s1}}} \right)}}{{{k_{s1}}+{k_f}\left( {s - 1} \right)+{\phi _1}\left( {{k_{hnf}} - {k_{s1}}} \right)}},\)\({A_4}=\frac{{{k_{hnf}}}}{{{k_{nf}}}}=\frac{{{k_{s2}} - (s - 1){\phi _2}\left( {{k_{nf}} - {k_{s2}}} \right)+(s - 1){k_{nf}}}}{{{k_{s2}}+{\phi _2}({k_{nf}} - {k_{s2}})+{k_{nf}}(s - 1)}},\)\({A_4}=\frac{{{k_{tnf}}}}{{{k_{hnf}}}}=\frac{{{k_{s3}} - (s - 1){\phi _3}\left( {{k_{hnf}} - {k_{s3}}} \right)+{k_{hnf}}(s - 1)}}{{{\phi _3}({k_{hnf}} - {k_{s3}})+{k_{s3}}+{k_{hnf}}(s - 1)}},\)