Table 1 Thermophysical features of hybrid nanofluid20,21.
From: Thermal stable properties of solid hybrid nanoparticles for mixed convection flow with slip features
Properties | Hybrid nanofluid |
|---|---|
Dynamic viscosity | \(\mu_{hnf} = \frac{{\mu_{f} }}{{\left( {1 - \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)^{2.5} \left( {1 - \phi_{{{\text{Cu}}}} } \right)^{2.5} }}\) |
Density | \(\rho_{hnf} = \left( {1 - \phi_{{{\text{Cu}}}} } \right)\left[ {\left( {1 - \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)\rho_{f} + \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} \rho_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right] + \phi_{{{\text{Cu}}}} \rho_{{{\text{Cu}}}}\) |
Thermal conductivity | \(k_{hnf} = \frac{{k_{{{\text{Cu}}}} + 2k_{nf} - 2\phi_{{{\text{Cu}}}} \left( {k_{nf} - k_{{{\text{Cu}}}} } \right)}}{{k_{{{\text{Cu}}}} + 2k_{nf} + \phi_{{{\text{Cu}}}} \left( {k_{nf} - k_{{{\text{Cu}}}} } \right)}} \times \left( {k_{nf} } \right)\) where \(k_{nf} = \frac{{k_{{{\text{Al}}_{2} {\text{O}}_{3} }} + 2k_{f} - 2\phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} \left( {k_{f} - k_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)}}{{k_{{{\text{Al}}_{2} {\text{O}}_{3} }} + 2k_{f} + \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} \left( {k_{f} - k_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)}} \times \left( {k_{f} } \right)\) |
Heat capacity | \(\left( {\rho c_{p} } \right)_{hnf} = \left( {1 - \phi_{{{\text{Cu}}}} } \right)\left[ {\left( {1 - \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)\left( {\rho c_{p} } \right)_{f} + \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} \left( {\rho c_{p} } \right)_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right] + \phi_{{{\text{Cu}}}} \left( {\rho c_{p} } \right)_{{{\text{Cu}}}}\) |
Electrical conductivity | \(\sigma_{hnf} = \frac{{\sigma_{2} + 2\sigma_{nf} - 2\phi_{2} \left( {\sigma_{nf} - \sigma_{2} } \right)}}{{\sigma_{2} + 2\sigma_{nf} + \phi_{2} \left( {\sigma_{nf} - \sigma_{2} } \right)}} \times \left( {\sigma_{nf} } \right)\)@ where \(\sigma_{nf} = \frac{{\sigma_{1} + 2\sigma_{f} - 2\phi_{1} \left( {\sigma_{f} - \sigma_{1} } \right)}}{{\sigma_{1} + 2\sigma_{f} + \phi_{1} \left( {\sigma_{f} - \sigma_{1} } \right)}} \times \left( {\sigma_{f} } \right)\) |
Thermal expansion coefficient | \(\left( \beta \right)_{hnf} = \left( {1 - \phi_{{{\text{Cu}}}} } \right)\left[ {\left( {1 - \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right)\left( \beta \right)_{f} + \phi_{{{\text{Al}}_{2} {\text{O}}_{3} }} \left( \beta \right)_{{{\text{Al}}_{2} {\text{O}}_{3} }} } \right] + \phi_{{{\text{Cu}}}} \left( \beta \right)_{{{\text{Cu}}}}\) |
