The Prandtl Number (Pr) is a dimensionless quantity in fluid dynamics that represents the ratio of momentum diffusivity to thermal diffusivity. Named after Ludwig Prandtl, it plays a crucial role in heat transfer and fluid flow analyses, providing insights into the relative thickness of the velocity and thermal boundary layers.

Formula

The Prandtl Number is calculated using the following equation:

\[ Pr = \frac{\nu}{\alpha} = \frac{c_p \mu}{k} \]

Where:

\( Pr \) = Prandtl Number (dimensionless)

\( \nu \) = Kinematic viscosity (m²/s)

\( \alpha \) = Thermal diffusivity (m²/s)

\( c_p \) = Specific heat capacity at constant pressure (J/(kg·K))

\( \mu \) = Dynamic viscosity (kg/(m·s))

\( k \) = Thermal conductivity (W/(m·K))

Significance of Prandtl Number

The Prandtl Number provides valuable information about the relative importance of momentum and heat transfer in a fluid: