Table 1 Thermophysical attributes of hybrid nanoliquid34.
From: On hybrid nanofluid Yamada-Ota and Xue flow models in a rotating channel with modified Fourier law
Density | \(\begin{gathered} \rho_{HNF} = \rho_{F} \left( {1 - \phi_{2} } \right)\left( {(1 - \phi_{1} ) + \phi_{1} \left( {\frac{{\rho_{s1} }}{{\rho_{F} }}} \right)} \right) + \phi_{2} \rho_{{s_{2} }} ,\frac{{\rho_{HNF} }}{{\rho_{F} }} = A. \hfill \\ \hfill \\ \end{gathered}\) |
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Heat Capacity | \(\begin{aligned} & (\rho c_{p} )_{HNF} = \phi_{2} (\rho c_{p} )_{{s_{2} }} + (1 - \phi_{2} )(\rho c_{p} )_{F} \left\{ {\phi_{1} \frac{{(\rho c_{p} )_{{s_{1} }} }}{{(\rho c_{p} )_{F} }} + [(1 - \phi_{1} )]} \right\} \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, & \frac{{(\rho c_{p} )_{HNF} }}{{(\rho c_{p} )_{F} }} = C \\ \end{aligned}\) |
Variable viscosity | \(\mu_{HNF} = \frac{{\mu_{F} }}{{(1 - \phi_{1} )^{2.5} (1 - \phi_{2} )^{2.5} }},\,\,\,\,\,\frac{{\mu_{HNF} }}{{\mu_{F} }} = B.\) |
Thermal conductivity | \(\begin{aligned} \frac{{k_{HNF} (T)}}{{k_{bF} }} & = \frac{{(n - 1)k_{bF} + k_{{s_{2} }} - (k_{bF} - k_{{s_{2} }} )(n - 1)\phi_{2} }}{{(n - 1)k_{bF} + k_{{s_{2} }} + (k_{bF} - k_{{s_{2} }} )\phi_{2} }}(1 + \varepsilon_{1} \theta ) \\ \frac{{k_{bF} }}{{k_{F} }} & = \frac{{(n - 1)k_{F} + k_{{s_{1} }} - (n - 1)\phi_{1} (k_{F} - k_{{s_{1} }} )}}{{k_{F} (n - 1) + k_{{s_{1} }} + \phi_{1} (k_{F} - k_{{s_{1} }} )}},\,\,\,\frac{{k_{HNF} }}{{k_{bF} }} = E,\frac{{k_{bF} }}{{k_{F} }} = D \\ \end{aligned}\) |
Xue-model | \(\begin{aligned} \frac{{k_{HNF} }}{{k_{bF} }} & = \frac{{1 - \phi_{2} + 2\phi_{2} \left( {\frac{{k_{{s_{2} }} }}{{k_{{s_{2} }} - k_{bF} }}} \right)\ln \frac{{k_{{s_{2} }} + k_{bF} }}{{2k_{bF} }}}}{{1 - \phi_{2} + 2\phi_{2} \left( {\frac{{k_{{s_{2} }} }}{{k_{{s_{2} }} - k_{bF} }}} \right)\ln \frac{{k_{{s_{2} }} + k_{bF} }}{{2k_{bF} }}}}, \\ \frac{{k_{bF} }}{{k_{F} }} & = \frac{{1 - \phi_{1} + 2\phi_{1} \left( {\frac{{k_{{s_{1} }} }}{{k_{{s_{1} }} - k_{F} }}} \right)\ln \frac{{k_{s1} + k_{F} }}{{2k_{F} }}}}{{1 - \phi_{1} + 2\phi_{1} \left( {\frac{{k_{F} }}{{k_{s1} -_{F} }}} \right)\ln \frac{{k_{s1} + k_{F} }}{{2k_{F} }}}}. \\ \\ \end{aligned}\) |
Yamada-Ota model | \(\begin{aligned} \frac{{k_{HNF} }}{{k_{bF} }} & = \frac{{1 + \frac{{k_{bF} }}{{k_{{s_{2} }} }}\frac{L}{R}\phi_{2}^{0.2} + \left( {1 - \frac{{k_{bF} }}{{k_{{s_{2} }} }}} \right)\phi_{2} \frac{L}{R}\phi_{2}^{0.2} + 2\phi_{2} \left( {\frac{{k_{{s_{2} }} }}{{k_{{s_{2} }} - k_{bF} }}} \right)\ln \frac{{k_{{s_{2} }} + k_{bF} }}{{2k_{{s_{2} }} }}}}{{1 - \phi_{2} + 2\phi_{2} \left( {\frac{{k_{bF} }}{{k_{{s_{2} }} - k_{bF} }}} \right)\ln \frac{{k_{{s_{2} }} + k_{bF} }}{{2k_{bF} }}}}, \\ \frac{{k_{bF} }}{{k_{F} }} & = \frac{{1 + \frac{{k_{F} }}{{k_{{s_{1} }} }}\frac{L}{R}\phi_{1}^{0.2} + \left( {1 - \frac{{k_{F} }}{{k_{{s_{1} }} }}} \right)\phi_{1} \frac{L}{R}\phi_{1}^{0.2} + 2\phi_{1} \left( {\frac{{k_{{s_{1} }} }}{{k_{{s_{1} }} - k_{F} }}} \right)\ln \frac{{k_{{s_{1} }} + k_{F} }}{{2k_{{s_{1} }} }}}}{{1 - \phi_{1} + 2\phi_{1} \left( {\frac{{k_{F} }}{{k_{{s_{1} }} - k_{F} }}} \right)\ln \frac{{k_{{s_{1} }} + k_{F} }}{{2k_{F} }}}}. \\ \end{aligned}\) |
