Water Steam Prandtl Number

Overview

Engineering reference data for Water Steam Prandtl Number in heat transfer.

Key Formulas

Fourier's Law

$q = -k \nabla T$

Heat flux proportional to temperature gradient.

Convective Heat Transfer

$Q = hA(T_s - T_\infty)$

Heat transfer between surface and fluid.

Stefan-Boltzmann Law

$q = \varepsilon \sigma T^4$

Radiative heat flux from a surface.

Thermal Resistance

$R_{th} = \frac{L}{kA}$

Resistance to heat conduction.

Variables

Symbol	Description	Unit
$q$	Heat flux	W/m²
$k$	Thermal conductivity	W/(m·K)
$h$	Convection coefficient	W/(m²·K)
$T$	Temperature	K
$\varepsilon$	Emissivity	—
$\sigma$	Stefan-Boltzmann constant	5.67×10⁻⁸ W/(m²·K⁴)

Data Tables

Behavior Notes

The Prandtl number for water exhibits distinct behavior across its phases:

• Liquid Water: Pr values are significantly greater than 1 (typically 2-14), indicating that momentum diffuses more slowly than heat. The value decreases sharply with increasing temperature.
• Water Vapor (Gas): Pr values are close to 1 (typically 0.9-1.1), meaning momentum and thermal diffusivities are nearly equal. Values are relatively insensitive to temperature and pressure.
• A sharp discontinuity occurs at the phase change (boiling point), where the Prandtl number drops suddenly from a high liquid value to a lower gaseous value.

Related Properties

For comprehensive calculations, refer to the following water properties:

• Density and Specific Weight
• Dynamic and Kinematic Viscosity
• Specific Heat (Heat Capacity)
• Thermal Conductivity
• Saturation Pressure and Boiling Points

Interactive Charts

References

• Original Source