Table 1 Thermo-physical features for nanoliquids.

From: Thermal growth in solar water pump using Prandtl–Eyring hybrid nanofluid: a solar energy application

Features

Nanoliquid

Dynamical viscidness \(\left( \mu \right)\)

\(\mu_{nf} = \mu_{f} (1 - \phi )^{ - 2.5}\)

Density \(\left( \rho \right)\)

\(\rho_{nf} = \left( {1 - \phi } \right)\rho_{f} + \phi \rho_{s}\)

Heat capacity \(\left( {\rho C_{p} } \right)\)

\((\rho C_{p} )_{nf} = \left( {1 - \phi } \right)(\rho C_{p} )_{f} + \phi (\rho C_{p} )_{s}\)

Thermal conductivity \(\left( \kappa \right)\)

\(\frac{{\kappa_{nf} }}{{\kappa_{f} }} = \left[ {\frac{{\left( {\kappa_{s} + 2\kappa_{f} } \right) - 2\phi \left( {\kappa_{f} - \kappa_{s} } \right)}}{{\left( {\kappa_{s} + 2\kappa_{f} } \right) + \phi \left( {\kappa_{f} - \kappa_{s} } \right)}}} \right]\)

  1. \(\phi\) is the nano solid-particle size coefficient. \(\mu_{f}\), \(\rho_{f}\), \((C_{p} )_{f}\) and \(\kappa_{f}\) are dynamical viscidness, intensity, operative heat capabilities, and thermal exchange of the standard fluid respectively. The useless characteristics \(\rho_{s}\), \((C_{p} )_{s}\) and \(\kappa_{s}\) are the intensity, effective heat capacitance, and thermal conductance of the nanomolecules, correspondingly