Table 1 Mathematical description for thermophysical characteristics of trihybrid nanoliquids.
From: Thermal enhancement of ternary hybrid Casson nanofluid in porous media: a sensitivity analysis study
Viscosity (\(\mu\)) | \(\mu _{thnf} = \frac{\mu _f}{(1-\phi _1)^{2.5}(1-\phi _2)^{2.5} (1-\phi _3)^{2.5}}\) |
Density (\(\rho\)) | \(\rho _{thnf} = (1-\phi _3) \biggl \{ (1-\phi _2) \biggl [(1-\phi _1)\rho _f + \rho _1\phi _1 \biggl ] + \rho _2\phi _2 \biggl \} + \rho _3\phi _3\) |
Heat capacity (\(\rho C_p\)) | \((\rho C_p)_{thnf} = (1-\phi _3) \biggl \{ (1-\phi _2) \biggl [(1-\phi _1)(\rho C_p)_f + (\rho C_p)_1 \phi _1 \biggl ]\) \(+ (\rho C_p)_2\phi _2 \biggl \} + (\rho C_p)_3\phi _3\) |
Thermal expansion (\(\rho \beta _0\)) | \((\rho \beta _0)_{thnf} = (1-\phi _3) \biggl \{ (1-\phi _2) \biggl [(1-\phi _1)(\rho \beta _0)_f + (\rho \beta _0)_1 \phi _1 \biggl ]\) \(+(\rho \beta _0)_2\phi _2 \biggl \} + (\rho \beta _0)_3\phi _3\) |
Thermal conductivity (k) | \(\frac{k_{thnf}}{k_{hnf}} = \frac{(k_3 + 2k_{hnf}) - 2\phi _3(k_{hnf}-k_3)}{(k_3 + 2k_{hnf}) + \phi _3(k_{hnf} - k_3)}\) |
\(\frac{k_{hnf}}{k_{nf}} = \frac{(k_2 + 2k_{nf}) - 2\phi _2(k_{nf}-k_2)}{(k_2 + 2k_{nf}) + \phi _2(k_{nf} - k_2)}\) | |
\(\frac{k_{nf}}{k_{f}} = \frac{(k_1 + 2k_{f}) - 2\phi _1(k_{f}-k_1)}{(k_1 + 2k_{f}) + \phi _1(k_{f} - k_1)}\) | |
Electrical conductivity (\(\sigma\)) | \(\frac{\sigma _{thnf}}{\sigma _{hnf}} = \frac{(\sigma _3 + 2\sigma _{hnf}) - 2\phi _3(\sigma _{hnf}-\sigma _3)}{(\sigma _3 + 2\sigma _{hnf}) + \phi _3(\sigma _{hnf} - \sigma _3)}\) |
\(\frac{\sigma _{hnf}}{\sigma _{nf}} = \frac{(\sigma _2 + 2\sigma _{nf}) - 2\phi _2(\sigma _{nf}-\sigma _2)}{(\sigma _2 + 2\sigma _{nf}) + \phi _2(\sigma _{nf} - \sigma _2)}\) | |
\(\frac{\sigma _{nf}}{\sigma _{f}} = \frac{(\sigma _1 + 2\sigma _{f}) - 2\phi _1(\sigma _{f}-\sigma _1)}{(\sigma _1 + 2\sigma _{f}) + \phi _1(\sigma _{f} - \sigma _1)}\) |
