Sutherland coefficient As

material.compressible.sutherland.As Unit: kg/(m·s·√K) Step 04 · Material

The coefficient of Sutherland's viscosity law. Together with Sutherland temperature Ts it gives the gas viscosity at any temperature, for the incompressible solver (computed viscosity), the compressible solver (in every cell) and the heat-transfer correlations.

Last updated 2026-11-03

Theory

Sutherland's law describes the rise of a gas's viscosity with temperature from a simple model of molecular attraction. In OpenFOAM's form, equation (1), $A_s$ sets the level and $T_s$ the curvature. The program uses the same constants for air and exhaust gas: the viscosity of exhaust gas is within a few per cent of that of air.

Equations

\mu(T) = \frac{A_s\,T^{3/2}}{T + T_s}

(1)

where	meaning	unit
$\mu$	Dynamic viscosity	Pa s
$A_s$	Sutherland coefficient (this setting)	kg/(m s K^0.5)
$T_s$	Sutherland temperature	K
$T$	Temperature	K

Default and rule

Default: 1.458e-6 (air)
Rule: 1.458e-6 kg/(m s K^0.5), which with $T_s$ = 110.4 K gives air's viscosity: 1.81e-5 Pa s at 20 °C.
Source: Sutherland's law (Sutherland, 1893); the air constants are those of the standard atmosphere (U.S. Standard Atmosphere, 1976). The compressible solver receives them as transport sutherland in constant/thermophysicalProperties.

Valid range > 0

Values

Positive. Change it only for a gas other than air or exhaust gas.

Theory

Equations

Default and rule

Valid range > 0

Related 3

References 2