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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Relation for the saturation-dependent effective thermal conductivity. More...
#include <dumux/material/fluidmatrixinteractions/2p/thermalconductivityjohansen.hh>
Relation for the saturation-dependent effective thermal conductivity.
The Johansen method (Johansen 1975 [35] ) computes the thermal conductivity of dry and the wet soil material and uses a root function of the wetting saturation to compute the effective thermal conductivity for a two-phase fluidsystem. The individual thermal conductivities are calculated as geometric mean of the thermal conductivity of the porous material and of the respective fluid phase. The material law is: \(\mathrm{[ \lambda_\text{eff} = \lambda_{\text{dry}} + \sqrt{(S_w)} \left(\lambda_\text{wet} - \lambda_\text{dry}\right) }\)
with \(\mathrm{ \lambda_\text{wet} = \lambda_{solid}^{\left(1-\phi\right)}*\lambda_w^\phi }\) and the semi-empirical relation
\(\mathrm{ \lambda_\text{dry} = \frac{0.135*\rho_s*\phi + 64.7}{\rho_s - 0.947 \rho_s*\phi}. }\)
Source: Phdthesis (Johansen1975) Johansen, O. Thermal conductivity of soils Norw. Univ. of Sci. Technol., Trondheim, Norway, 1975 [35]
Static Public Member Functions | |
| template<class VolumeVariables , class SpatialParams , class Element , class FVGeometry > | |
| static Scalar | effectiveThermalConductivity (const VolumeVariables &volVars, const SpatialParams &spatialParams, const Element &element, const FVGeometry &fvGeometry, const typename FVGeometry::SubControlVolume &scv) |
| effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35] More... | |
| template<class VolumeVariables > | |
| static Scalar | effectiveThermalConductivity (const VolumeVariables &volVars) |
| Returns the effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35] . More... | |
| static Scalar | effectiveThermalConductivity (const Scalar Sw, const Scalar lambdaW, const Scalar lambdaN, const Scalar lambdaSolid, const Scalar porosity, const Scalar rhoSolid) |
| Returns the effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35] . More... | |
|
inlinestatic |
Returns the effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35] .
| Sw | The saturation of the wetting phase |
| lambdaW | The thermal conductivity of the wetting phase in \(\mathrm{[W/(m K)]}\) |
| lambdaN | The thermal conductivity of the non-wetting phase in \(\mathrm{[W/(m K)]}\) |
| lambdaSolid | The thermal conductivity of the solid phase in \(\mathrm{[W/(m K)]}\) |
| porosity | The porosity |
| rhoSolid | The density of solid phase in \(\mathrm{[kg/m^3]}\) |
|
inlinestatic |
Returns the effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35] .
| volVars | volume variables |
This formulation is semi-empirical and fitted to quartz sand. This gives an interpolation of the effective thermal conductivities of a porous medium filled with the non-wetting phase and a porous medium filled with the wetting phase. These two effective conductivities are computed as geometric mean of the solid and the fluid conductivities and interpolated with the Kersten number.
Johansen, O. 1975. Thermal conductivity of soils. Ph.D. diss. Norwegian Univ. of Sci. and Technol., Trondheim. (Draft Transl. 637. 1977. U.S. Army Corps of Eng., Cold Regions Res. and Eng. Lab., Hanover, NH.) [35]
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inlinestatic |
effective thermal conductivity \(\mathrm{[W/(m K)]}\) after Johansen (1975) [35]
1.9.3