Table 1 Cu/water properties used in the simulations ^12,13.

Density

\(\rho_{eff} = (1 - \varphi )\rho_{f} + \varphi \rho_{p}\)

Heat capacity

\(c_{p,eff} = \frac{{(1 - \varphi )(\rho c_{p} )_{f} + \varphi (\rho c_{p} )_{p} }}{{(1 - \varphi )\rho_{f} + \varphi \rho_{p} }}\)

Viscosity³¹

\(\mu_{nf} = (1 + 7.3\phi + 123\phi^{2} )\mu_{f}\)

Thermal conductivity

\({k}_{eff}/{k}_{bf}=1+{\left(\frac{{k}_{p}}{{k}_{bf}}\frac{{d}_{bf}}{{d}_{p}}\frac{\phi }{1-\phi }\right)}(1+\mathrm{25,000}\frac{{u}_{b}{d}_{p}}{{k}_{bf}})\)

Brownian motion velocity of nanoparticles \(:{u}_{b}=\frac{2{K}_{B} T}{\pi {\mu }_{bf}{{d}_{p}}^{2}}\)