Table 2 The thermophysical properties of Casson hybrid Nanofluid Bilal et al.³¹ and Kumar et al.³².

Dynamic Viscosity

\(\frac{{{\mu _{hnf}}}}{{{\mu _f}}}={\left( {1 - {\phi _1}} \right)^{ - 2.5}}{\left( {1 - {\phi _2}} \right)^{ - 2.5}}\)

Density

\(\frac{{{\rho _{hnf}}}}{{{\rho _f}}}=\left( {1 - {\phi _1}} \right)\left[ {\left( {1 - {\phi _2}} \right)+\frac{{{\rho _2}}}{{{\rho _f}}}{\phi _2}} \right]+\frac{{{\rho _1}}}{{{\rho _f}}}{\phi _1}\)

Heat Capacity

\(\frac{{\rho {c_{hnf}}}}{{\rho {c_f}}}=\left( {1 - {\phi _1}} \right)\left[ {\left( {1 - {\phi _2}} \right)+\frac{{\rho {c_2}}}{{\rho {c_f}}}{\phi _2}} \right]+\frac{{\rho {c_1}}}{{\rho {c_f}}}{\phi _1}\)

Thermal Conductivity

\({k_{hnf}}={k_{nf}}\frac{{{k_1}+2{k_{nf}} - 2{\phi _1}\left( {{k_{nf}} - {k_1}} \right)}}{{{k_1}+2{k_{nf}}+{\phi _1}\left( {{k_{nf}} - {k_1}} \right)}}\)

Electrical Conductivity

\({\sigma _{hnf}}={\sigma _{nf}}\left[ {1+\frac{{3\left( {{{{\sigma _1}} \mathord{\left/ {\vphantom {{{\sigma _1}} {{\sigma _{nf}}}}} \right. \kern-0pt} {{\sigma _{nf}}}} - 1} \right){\phi _1}}}{{\left( {{{{\sigma _1}} \mathord{\left/ {\vphantom {{{\sigma _1}} {{\sigma _{nf}}}}} \right. \kern-0pt} {{\sigma _{nf}}}}+2} \right) - \left( {{{{\sigma _1}} \mathord{\left/ {\vphantom {{{\sigma _1}} {{\sigma _{nf}}}}} \right. \kern-0pt} {{\sigma _{nf}}}} - 1} \right){\phi _1}}}} \right]\)

Kinematic Viscosity

\({\upsilon _{hnf}}=\frac{{{{{\mu _{hnf}}} \mathord{\left/ {\vphantom {{{\mu _{hnf}}} {{\mu _f}}}} \right. \kern-0pt} {{\mu _f}}}}}{{{{{\rho _{hnf}}} \mathord{\left/ {\vphantom {{{\rho _{hnf}}} {{\rho _f}}}} \right. \kern-0pt} {{\rho _f}}}}}\)

Thermal Diffusivity

\({\alpha _{hnf}}=\frac{{{{{k_{hnf}}} \mathord{\left/ {\vphantom {{{k_{hnf}}} {{k_f}}}} \right. \kern-0pt} {{k_f}}}}}{{{{{{\left( {\rho {c_p}} \right)}_{hnf}}} \mathord{\left/ {\vphantom {{{{\left( {\rho {c_p}} \right)}_{hnf}}} {{{\left( {\rho {c_p}} \right)}_f}}}} \right. \kern-0pt} {{{\left( {\rho {c_p}} \right)}_f}}}}}\)