. 2021 Jul 8;11:14128. doi: 10.1038/s41598-021-93644-4

Table 2.

Hybrid nanofluid’s correlations¹³.

Properties	Hybrid Nanofluid
Density $(ρ)$	$ρ_{hnf} = (1 - ϕ_{hnf}) ρ_{f} + ϕ_{1} ρ_{s 1} + ϕ_{2} ρ_{s 2}$
Heat Capacity $(ρ C_{p})$	${(ρ C_{p})}_{hnf} = (1 - ϕ_{hnf}) {(ρ C_{p})}_{f} + ϕ_{1} {(ρ C_{p})}_{s 1} + ϕ_{2} {(ρ C_{p})}_{s 2}$
Dynamic Viscocity $(μ)$	$\frac{μ_{hnf}}{μ_{f}} = \frac{1}{{(1 - ϕ_{hnf})}^{2.5}}$
Thermal Conductivity $(k)$	$\frac{k_{hnf}}{k_{f}} = [\frac{\begin{matrix} (\frac{ϕ_{1} k_{1} + ϕ_{2} k_{2}}{ϕ_{hnf}}) + 2 k_{f} + 2 (ϕ_{1} k_{1} + ϕ_{2} k_{2}) \\ - 2 ϕ_{hnf} k_{f} \end{matrix}}{\begin{matrix} (\frac{ϕ_{1} k_{1} + ϕ_{2} k_{2}}{ϕ_{hnf}}) + 2 k_{f} - (ϕ_{1} k_{1} + ϕ_{2} k_{2}) \\ + ϕ_{hnf} k_{f} \end{matrix}}]$
Electrical Conductivity $(σ)$	$\frac{σ_{hnf}}{σ_{f}} = [\frac{\begin{matrix} (\frac{ϕ_{1} σ_{1} + ϕ_{2} σ_{2}}{ϕ_{hnf}}) + 2 σ_{f} + 2 (ϕ_{1} σ_{1} + ϕ_{2} σ_{2}) \\ - 2 ϕ_{hnf} σ_{f} \end{matrix}}{\begin{matrix} (\frac{ϕ_{1} σ_{1} + ϕ_{2} σ_{2}}{ϕ_{hnf}}) + 2 σ_{f} - (ϕ_{1} σ_{1} + ϕ_{2} σ_{2}) \\ + ϕ_{hnf} σ_{f} \end{matrix}}]$