## Prandtl number $\mathrm{Pr} = \frac{\nu}{\alpha} = \frac{\textrm{momentum diffusion rate}}{\textrm{thermal diffusion rate}} = \frac{c_{p}\mu}{k}$ $\mathrm{Pr}$ is the ratio of momentum diffusivity and thermal diffusivity. If expand the expressions for kinematic viscosity and thermal diffusivity, we may get the form with specific heat and dynamic viscosity. Here $\rho$ is density, $u$ is velocity, $\nu$ is [kinematic viscosity](https://en.wikipedia.org/wiki/Kinematic_viscosity), $\mu$ is [dynamic viscosity](https://en.wikipedia.org/wiki/Dynamic_viscosity), $\nu = \frac{\mu}{\rho}$, $\alpha$ is [thermal diffusivity](https://en.wikipedia.org/wiki/Thermal_diffusivity), $k$ is [thermal conductivity](https://en.wikipedia.org/wiki/Thermal_conductivity). Similarly concepts are [[Schmidt number]] and [[Lewis number]]. >[!info] >See more on wiki: https://en.wikipedia.org/wiki/Prandtl_number