Table 2 Thermo-physical aspects of hybrid class of nanofluid.

From: RETRACTED ARTICLE: A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller–Box scheme

Features

Hybrid class of nanofluid

Viscosity \(\left( \mu \right)\)

\(\mu_{hnf}\) = \(\mu_{f} (1 - \phi_{Cu} )^{ - 2.5} (1 - \phi_{{TiO_{2} }} )^{ - 2.5}\)

Density \(\left( \rho \right)\)

\(\rho_{hnf}\) = [\(\left( {1 - \phi_{{TiO_{2} }} } \right)\left\{ {\left( {1 - \phi_{Cu} } \right)\rho_{f} + \phi_{Cu} \rho_{{p_{1} }} } \right\}]\) + \(\phi_{{TiO_{2} }} \rho_{{p_{2} }}\)

Heat capacity \(\left( {\rho C_{p} } \right)\)

Electrical conductivity \(\left( \sigma \right)\)

\((\rho C_{p} )_{hnf}\) = \([\left( {1 - \phi_{{TiO_{2} }} } \right)\{ \left( {1 - \phi_{Cu} } \right)(\rho C_{p} )_{f} + \phi_{Cu} (\rho C_{p} )_{{p_{1} }} \} ]\)\(+ \phi_{{TiO_{2} }} (\rho C_{p} )_{{p_{2} }}\)

\(\frac{{\sigma_{hnf} }}{{\sigma_{f} }}\) = \(\left[ {1 + \frac{{3\left( {\frac{{\phi_{Cu} \sigma_{{p_{1} }} + \phi_{{TiO_{2} }} \sigma_{{p_{2} }} }}{{\sigma_{f} }} - \left( {\phi_{Cu} + \phi_{{TiO_{2} }} } \right)} \right)}}{{\left( {\frac{{\phi_{Cu} \sigma_{{p_{1} + \phi_{2} \sigma_{{p_{2} }} }} }}{{\left( {\phi_{Cu} + \phi_{{TiO_{2} }} } \right)\sigma_{f} }} + 2} \right) - \left( {\frac{{\phi_{Cu} \sigma_{{p_{1} }} + \phi_{{TiO_{2} }} \sigma_{{p_{2} }} }}{{\sigma_{f} }} - \left( {\phi_{Cu} + \phi_{{TiO_{2} }} } \right)} \right)}}} \right]\)

Thermal conductivity \(\left( \kappa \right)\)

\(\frac{{\kappa_{hnf} }}{{\kappa_{gf} }} = \left[ {\frac{{\left( {\kappa_{{p_{2} }} + \left( {m - 1} \right)\kappa_{gf} } \right) - \left( {m - 1} \right)\phi_{{TiO_{2} }} \left( {\kappa_{gf} - \kappa_{{p_{2} }} } \right)}}{{\left( {\kappa_{{p_{2} }} + \left( {m - 1} \right)\kappa_{gf} } \right) + \phi_{{TiO_{2} }} \left( {\kappa_{gf} - \kappa_{{p_{2} }} } \right)}}} \right],\)

\(\frac{{\kappa_{gf} }}{{\kappa_{f} }} = \left[ {\frac{{\left( {\kappa_{{p_{1} }} + \left( {m - 1} \right)\kappa_{f} } \right) - \left( {m - 1} \right)\phi_{Cu} \left( {\kappa_{f} - \kappa_{{p_{1} }} } \right)}}{{\left( {\kappa_{{p_{1} }} + \left( {m - 1} \right)\kappa_{f} } \right) + \phi_{Cu} \left( {\kappa_{f} - \kappa_{{p_{1} }} } \right)}}} \right]\)

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