Table 3 Thermo-physical attributes of hybrid nano fluid.

From: AI-powered prediction of hybrid nanofluid dynamics over a cylinder via LM optimized neural network approach

Properties

Hybrid Nano fluid

Viscosity

\(\frac{{\mu_{hnf} }}{{\mu_{bf} }} = \frac{1}{{\left( {1 - \phi_{{TiO_{2} }} - \phi_{CuO} } \right)^{2} }}\)

Density

\(\frac{{\rho_{hnf} }}{{\rho_{bf} }} = \phi_{{TiO_{2} }} \left( {\frac{{\rho_{{TiO_{2} }} }}{{\rho_{bf} }}} \right) + \phi_{CuO} \left( {\frac{{\rho_{CuO} }}{{\rho_{bf} }}} \right) + \left( {1 - \phi_{{TiO_{2} }} - \phi_{CuO} } \right)\)

Electrical conductivity

\(\frac{{\sigma_{hnf} }}{{\sigma_{bf} }} = \left[ {\frac{{\left( {\frac{{\phi_{{TiO_{2} }} \sigma_{{TiO_{2} }} + \phi_{CuO} \sigma_{CuO} }}{{\phi_{{TiO_{2} }} + \phi_{CuO} }}} \right) + 2\sigma_{bf} + 2\left( {\phi_{{TiO_{2} }} \sigma_{{TiO_{2} }} + \phi_{CuO} \sigma_{CuO} } \right) - 2\left( {\phi_{{TiO_{2} }} + \phi_{CuO} } \right)\sigma_{bf} }}{{\left( {\frac{{\phi_{{TiO_{2} }} \sigma_{{TiO_{2} }} + \phi_{CuO} \sigma_{CuO} }}{{\phi_{{TiO_{2} }} + \phi_{CuO} }}} \right) + 2\sigma_{bf} - 2\left( {\phi_{{TiO_{2} }} \sigma_{{TiO_{2} }} + \phi_{CuO} \sigma_{CuO} } \right) + 2\left( {\phi_{{TiO_{2} }} + \phi_{CuO} } \right)\sigma_{bf} }}} \right]\)

Heat capacity

\(\frac{{\left( {\rho C_{p} } \right)_{hnf} }}{{\left( {\rho C_{p} } \right)_{bf} }} = \phi_{{TiO_{2} }} \left( {\frac{{\left( {\rho C_{p} } \right)_{{TiO_{2} }} }}{{\left( {\rho C_{p} } \right)_{bf} }}} \right) + \phi_{CuO} \left( {\frac{{\left( {\rho C_{p} } \right)_{CuO} }}{{\left( {\rho C_{p} } \right)_{bf} }}} \right) + \left( {1 - \phi_{{TiO_{2} }} - \phi_{CuO} } \right)\)

Thermal conductivity

\(\frac{{k_{hnf} }}{{k_{bf} }} = \left[ {\frac{{\left( {\frac{{\phi_{{TiO_{2} }} k_{{TiO_{2} }} + \phi_{CuO} k_{CuO} }}{{\phi_{{TiO_{2} }} + \phi_{CuO} }}} \right) + 2k_{bf} + 2\left( {\phi_{{TiO_{2} }} k_{{TiO_{2} }} + \phi_{CuO} k_{CuO} } \right) - 2\left( {\phi_{{TiO_{2} }} + \phi_{CuO} } \right)k_{bf} }}{{\left( {\frac{{\phi_{{TiO_{2} }} k_{{TiO_{2} }} + \phi_{CuO} k_{CuO} }}{{\phi_{{TiO_{2} }} + \phi_{CuO} }}} \right) + 2k_{bf} - 2\left( {\phi_{{TiO_{2} }} k_{{TiO_{2} }} + \phi_{CuO} k_{CuO} } \right) + 2\left( {\phi_{{TiO_{2} }} + \phi_{CuO} } \right)k_{bf} }}} \right]\)

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