Prandtl Number Definition and Relation

The Prandtl number (Pr) is a dimensionless number crucial in fluid dynamics and heat transfer. It represents the ratio of momentum diffusivity to thermal diffusivity in a fluid.

Calculating Prandtl Number

The formula for the Prandtl number is derived from its definition:

Pr = ν / α

Where:

• ν (nu) is the kinematic viscosity (μ / ρ)
• α (alpha) is the thermal diffusivity (k / (ρ * c_p))

Substituting these gives:

Pr = (μ / ρ) / (k / (ρ * c_p))

Simplifying this expression yields:

Pr = (μ * c_p) / k

This formula directly relates the coefficient of viscosity (μ), the specific heat (c_p), and the thermal conductivity (k).

Comparing with Other Numbers

• Reynolds number: Relates inertial forces to viscous forces.
• Froude number: Relates inertial forces to gravitational forces.
• Biot number: Relates internal conductive heat resistance to convective heat transfer at the surface.

Only the Prandtl number directly connects specific heat, viscosity, and thermal conductivity.