Table 1.

Thermal properties of hybrid nanofluids [31], [71].

Properties	Hybrid nanofluids
Density	ρhbf = ϕnp1ρnp1 + ϕnp2ρnp2 + (1 − ϕnp1 − ϕnp2)ρf
Heat capacitance	${(C_p)}_{\mathrm{hbf}}=\frac{{\varphi }_{np1}{(\rho C_p)}_{np1}+{\varphi }_{np2}{(\rho C_p)}_{np2}+(1-\varphi ){(\rho C_p)}_f}{{\rho }_{\mathrm{hbf}}}$
Dynamic viscosity	${\mu }_{\mathrm{hbf}}=\frac{{\mu }_{\mathrm{f}}}{1-34.87{(d_f)}^{0.3}{d}_{hp}}$ where, $d_{hp}={(d_{np1})}^{-0.3}{({\varphi }_{np1})}^{1.03}+{(d_{np2})}^{-0.3}{({\varphi }_{np2})}^{1.03}$
Thermal conductivity	$k_{\mathrm{hbf}}=k_{\mathrm{f}}[1+4.4R{e}_{np}^{0.4}P{r_f}^{0.66}{\left(\frac{\tilde{T}}{{\tilde{T}}_{fr}}\right)}^{10}{(k_{\mathrm{f}})}^{-0.03}{k}_{hp}]$ where, $k_{hp}={(k_{np1})}^{0.03}{({\varphi }_{np1})}^{0.66}+{(k_{np2})}^{0.03}{({\varphi }_{np2})}^{0.66}$
Electrical conductivity	${\sigma }_{\mathrm{hbf}}={\sigma }_{\mathrm{f}}\frac{1+3({\sigma }_{hp}/{\sigma }_{\mathrm{f}}-1){\sigma }_{\mathrm{hbf}}}{({\sigma }_{hp}/{\sigma }_{\mathrm{f}}+2)-({\sigma }_{hp}/\sigma \mathrm{f}-1){\sigma }_{\mathrm{hbf}}}$ where, ${\sigma }_{hp}=\frac{{\varphi }_{np1}{\sigma }_{np1}+{\varphi }_{np2}{\sigma }_{np2}}{{\varphi }_{np1}+{\varphi }_{np2}}$
Expansion coefficient	${({\beta }_{\tilde{T}})}_{\mathrm{hbf}}=\frac{{\varphi }_{np1}{({\rho }_{{\beta }_{\tilde{T}}})}_{np1}+{\varphi }_{np2}{({\rho }_{{\beta }_{\tilde{T}}})}_{np2}+(1-{\varphi }_{np1}-{\varphi }_{np2}){({\rho }_{{\beta }_{\tilde{T}}})}_{\mathrm{f}}}{{\rho }_{\mathrm{hbf}}}$