Table 2 Mathematical model for the hybrid nanofluid \(\left( {\phi_{1} = \phi_{AA7072} ,\,\,\,\phi_{2} = \phi_{AA7075} } \right)\)¹⁸.

Viscosity

\(\frac{{\mu_{hnf} }}{{\mu_{f} }} = \left( {1 - \phi_{AA7072} } \right)^{ - 2.5} \left( {1 - \phi_{AA7075} } \right)^{ - 2.5}\)

Density

\(\rho_{hnf} = \left( {\phi_{1} \rho_{AA7072} + \left( {1 - \phi_{1} } \right)\rho_{f} } \right) + \phi_{2} \rho_{{_{AA7075} }} ,\)

Thermal capacity

\((\rho C_{p} )_{hnf} = \phi_{2} (\rho C_{p} )_{AA7075} + \left( {\left( {1 - \phi_{1} } \right)(\rho C_{p} )_{f} + \phi_{1} (\rho C_{p} )_{AA7072} } \right)\left( {1 - \phi_{2} } \right)\)

Thermal conductivity

\(\frac{{k_{hnf} }}{{k_{nf} }} = \frac{{2\phi_{2} \left( {\frac{{k_{AA7075} }}{{k_{AA7075} - k_{nf} }}} \right)\ln \left( {\frac{{k_{AA7075} + k_{nf} }}{{2k_{nf} }}} \right) + \left( {1 - \phi_{2} } \right)}}{{2\phi_{2} \left( {\frac{{k_{nf} }}{{k_{AA7075} - k_{nf} }}} \right)\ln \left( {\frac{{k_{AA7075} + k_{nf} }}{{2k_{nf} }}} \right) + \left( {1 - \phi_{2} } \right)}}\) \(\frac{{k_{nf} }}{{k_{f} }} = \frac{{2\phi_{1} \left( {\frac{{k_{AA7072} }}{{k_{AA7075} - k_{f} }}} \right)\ln \left( {\frac{{k_{AA7072} + k_{f} }}{{2k_{nf} }}} \right) + \left( {1 - \phi_{1} } \right)}}{{2\phi_{1} \left( {\frac{{k_{f} }}{{k_{AA7072} - k_{f} }}} \right)\ln \left( {\frac{{k_{AA7072} + k_{f} }}{{2k_{f} }}} \right) + \left( {1 - \phi_{1} } \right)}}\)