The Prandtl number is a dimensionless number, defined as the ratio of kinematic viscosity (also called momentum diffusivity) to thermal diffusivity.
Equation for humid air is taken from paper by P.T. Tsilingiris: 'Thermophysical and transport properties of humid air at temperature range between 0 and 100°C', 2007
$0.7215798365-3.703124976{\cdot}{10}^{-4} \theta_{gas}+2.240599044{\cdot}{10}^{-5} {\theta_{gas}}^2-4.162785412{\cdot}{10}^{-7} {\theta_{gas}}^3+4.969218948{\cdot}{10}^{-9} {\theta_{gas}}^4$ | humid air @ 1 atm (Tsilingiris2007) |
$0.715-2.5{\cdot}{10}^{-4} \theta_{gas}$ | humid air @ 1 atm (IEC 60287-2-3) |
$\frac{c_{p,gas} \eta_{gas}}{k_{gas}}$ | general formula for gases |