# Viscosity-Temperature Dependence Models

New viscosity-temperature coupling (`viscTempCoupling`) has been
introduced into the nanoFluidX code as an option. Three models were
implemented: polynomial, Sutherland, and power law.

With $T$ being the temperature of the particle and ${C}_{n}$ being the coefficients. For air, the viscosity can be approximated by a linear function, with ${C}_{1}=5\times {10}^{-8}$ .

Where, ${\mu}_{0}$ is the reference viscosity. ${T}_{0}$ is the reference temperature. $S$ is the Sutherland coefficient.

For air, these values are:
${\mu}_{0}$
= 1.72 x 10^{-5}Pas,
${T}_{0}$
= 273.15 K and S
= 110.4.

With
$n$
being the exponent. For air, the power law values
are:
${\mu}_{0}$
= 1.72 x 10^{-5} Pas,
${T}_{0}$
= 273.15 K and
$n$
= 0.66.

The first thing that needs to be specified is the `viscTempCoupling`
switch in the Simulation parameters section.

Since the viscosity field is updated after establishing the time step, reference
viscosity has to be specified in the domain parameter section as
`ref_visc`. The reference viscosity should be the highest
expected viscosity during the simulation.

`viscTempCoupling`is turned on, all of the fluid phase viscosities in the case have to be defined through the Viscosity-temperature coupling parameters section.