Air Prandtl Number Viscosity Heat Capacity Thermal Conductivity

Overview

Engineering reference data for Air Prandtl Number Viscosity Heat Capacity Thermal Conductivity 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)

Prandtl Number Formula

The Prandtl number (Pr) is a dimensionless parameter defined as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is fundamental in characterizing heat transfer in fluid flow.

$Pr = \frac{\mu c_p}{k}$

Where:

• $\mu$ is the absolute or dynamic viscosity (kg/(m·s) or lbm/(ft·h))
• $c_p$ is the specific heat at constant pressure (J/(kg·K) or Btu/lbm·°F)
• $k$ is the thermal conductivity (W/(m·K) or Btu/(h·ft²·°F/ft))

Key Observations

• At atmospheric pressure (1 bara), air's Prandtl number is relatively constant (~0.71) over a wide temperature range (0°C to 300°C).
• Prandtl number increases significantly at very low temperatures and high pressures (e.g., Pr > 4 at 60 K and 1 bara).
• At standard conditions (0°C, 1 bara), Pr = 0.711 for air.

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