Description

In addition to the momentum and mass/mole balance equations, this model also solves the energy balance equation :

\[ \frac{\partial (\varrho u)}{\partial t} + \nabla \cdot \left( \varrho h {\mathbf{v}} - \lambda_\text{eff} \nabla T \right) - q^h = 0 \]

where:

\( \varrho \) is the fluid density (in \( \mathrm{kg}\,\mathrm{m}^{-3} \)),
\( u \) is the fluid's specific internal energy (in \( \mathrm{J}\,\mathrm{kg}^{-1} \)),
\( h \) is the fluid's specific enthalpy (in \( \mathrm{J}\,\mathrm{kg}^{-1} \)),
\( \mathbf{v} \) is the fluid velocity (in \( \mathrm{m}\,\mathrm{s}^{-1} \)),
\( \lambda_\text{eff} \) is the effective thermal conductivity (in \( \mathrm{W}\,\mathrm{m}^{-1}\,\mathrm{K}^{-1} \)),
\( T \) is the temperature (in K),
\( q^h \) is a volume-specific source or sink term for the energy (in \( \mathrm{W}\,\mathrm{m}^{-3} \)).

For laminar Navier-Stokes flow the effective thermal conductivity is the fluid thermal conductivity: \( \lambda_\text{eff} = \lambda \).

For turbulent Reynolds-averaged Navier-Stokes flow the eddy thermal conductivity is added: \( \lambda_\text{eff} = \lambda + \lambda_\text{t} \). The eddy thermal conductivity \( \lambda_\text{t} \) is related to the eddy viscosity \( \nu_\text{t} \) by the turbulent Prandtl number:

\[ \lambda_\text{t} = \frac{\nu_\text{t} \varrho c_\text{p}}{\mathrm{Pr}_\text{t}} \]

Classes
struct	Dumux::NavierStokesEnergyModelTraits< IsothermalT >
	Specifies a number properties of non-isothermal free-flow flow models based on the specifics of a given isothermal model. More...

Namespaces
namespace	Dumux

Include dependency graph for freeflow/navierstokes/energy/model.hh:

Description

Classes

Namespaces