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dumuxrepositories
dumux
Commits
9063491c
Commit
9063491c
authored
Nov 01, 2021
by
Timo Koch
Browse files
[cleanup][common][dimless] Fix indent
parent
0b2f862a
Changes
1
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dumux/common/dimensionlessnumbers.hh
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9063491c
...
...
@@ 36,7 +36,7 @@
namespace
Dumux
{
/*!
* \brief A container for possible values of the property for selecting which
n
usselt parametrization to choose.
* \brief A container for possible values of the property for selecting which
N
usselt parametrization to choose.
* The actual value is set vie the property NusseltFormulation
*/
enum
class
NusseltFormulation
...
...
@@ 45,7 +45,7 @@ enum class NusseltFormulation
};
/*!
* \brief A container for possible values of the property for selecting which
s
herwood parametrization to choose.
* \brief A container for possible values of the property for selecting which
S
herwood parametrization to choose.
* The actual value is set vie the property SherwoodFormulation
*/
enum
class
SherwoodFormulation
...
...
@@ 65,240 +65,240 @@ class DimensionlessNumbers
{
public:
/*!
* \brief Calculate the Reynolds Number [] (Re).
*
* The Reynolds number is a measure for the relation of inertial to viscous forces.
* The bigger the value, the more important inertial (as compared to viscous) effects become.
* According to Bear [Dynamics of fluids in porous media (1972)] Darcy's law is valid for Re<1.
*
* Source for Reynolds number definition: http://en.wikipedia.org/wiki/Reynolds_number
*
* \param darcyMagVelocity The absolute value of the darcy velocity. In the context of box models this
* leads to a problem: the velocities are defined on the faces while other things (storage, sources, output)
* are defined for the volume/vertex. Therefore, some sort of decision needs to be made which velocity to put
* into this function (e.g.: facearea weighted average). [m/s]
* \param charcteristicLength Typically, in the context of porous media flow, the mean grain size is taken as the characteristic length
* for calculation of Re. [m]
* \param kinematicViscosity Is defined as the dynamic (or absolute) viscos ity divided by the density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity. [m^2/s]
*
* \return The Reynolds Number as calculated from the input parameters
*/
static
Scalar
reynoldsNumber
(
const
Scalar
darcyMagVelocity
,
const
Scalar
charcteristicLength
,
const
Scalar
kinematicViscosity
)
{
return
darcyMagVelocity
*
charcteristicLength
/
kinematicViscosity
;
}
/*!
* \brief Calculate the Prandtl Number [] (Pr).
*
* The Prandtl Number is a measure for the relation of viscosity and thermal diffusivity (temperaturleitfaehigkeit).
*
* It is defined as
* \f[
* \textnormal{Pr}= \frac{\nu}{\alpha} = \frac{c_p \mu}{\lambda}\, ,
* \f]
* with kinematic viscosity\f$\nu\f$, thermal diffusivity \f$\alpha\f$, heat capacity \f$c_p\f$,
* dynamic viscosity \f$\mu\f$ and thermal conductivity \f$\lambda\f$.
* Therefore, Pr is a material specific property (i.e.: not a function of flow directly
* but only of temperature, pressure and fluid).
*
* source for Prandtl number definition: http://en.wikipedia.org/wiki/Prandtl_number
*
* \param dynamicViscosity Dynamic (absolute) viscosity over density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity [m^2/s]
* \param heatCapacity Heat capacity at constant pressure.
* Specifies the energy change for a given temperature change [J / (kg K)]
* \param thermalConductivity Conductivity to heat. Specifies how well matter transfers energy without moving. [W/(m K)]
* \return The Prandtl Number as calculated from the input parameters.
*/
static
Scalar
prandtlNumber
(
const
Scalar
dynamicViscosity
,
const
Scalar
heatCapacity
,
const
Scalar
thermalConductivity
)
{
return
dynamicViscosity
*
heatCapacity
/
thermalConductivity
;
}
/*!
* \brief Calculate the Nusselt Number [] (Nu).
*
* The Nusselt Number is a measure for the relation of convective to conductive heat exchange.
*
* The Nusselt number is defined as Nu = h d / k,
* with h= heat transfer coefficient, d=characteristic length, k=heat conductivity(stagnant).
* However, the heat transfer coefficient from one phase to another is typically not known.
* Therefore, Nusselt numbers are usually given as *empirical* Nu(Reynolds, Prandtl) for a given flow
* field forced convection and *empirical* Nu(Rayleigh, Prandtl) for flow caused by temperature
* differences free convection. The fluid characteristics enter via the Prandtl number.
*
* This function implements an *empirical* correlation for the case of porous media flow
* (packed bed flow as the chemical engineers call it).
*
* source for Nusselt number definition: http://en.wikipedia.org/wiki/Nusselt_number
* source for further empirical correlations for Nusselt Numbers:
* VDIGesellschaft, VDIWaermeatlas, VDIVerlag Duesseldorf, 2006
*
* \param reynoldsNumber Dimensionless number relating inertial and viscous forces [].
* \param prandtlNumber Dimensionless number relating viscosity and thermal diffusivity (temperaturleitfaehigkeit) [].
* \param porosity The fraction of the porous medium which is void space.
* \param formulation Switch for deciding which parametrization of the Nusselt number is to be used.
* Set via the property NusseltFormulation.
* \return The Nusselt number as calculated from the input parameters [].
*/
static
Scalar
nusseltNumberForced
(
const
Scalar
reynoldsNumber
,
const
Scalar
prandtlNumber
,
const
Scalar
porosity
,
NusseltFormulation
formulation
)
{
if
(
formulation
==
NusseltFormulation
::
dittusBoelter
){
/* example: very common and simple case: flow straight circular pipe, only convection (no boiling),
* 10000<Re<120000, 0.7<Pr<120, far from pipe entrance, smooth surface of pipe ...
* Dittus, F.W and Boelter, L.M.K, Heat Transfer in Automobile Radiators of the Tubular Type,
* Publications in Engineering, Vol. 2, pages 443461, 1930
*/
using
std
::
pow
;
return
0.023
*
pow
(
reynoldsNumber
,
0.8
)
*
pow
(
prandtlNumber
,
0.33
);
/*!
* \brief Calculate the Reynolds Number [] (Re).
*
* The Reynolds number is a measure for the relation of inertial to viscous forces.
* The bigger the value, the more important inertial (as compared to viscous) effects become.
* According to Bear [Dynamics of fluids in porous media (1972)] Darcy's law is valid for Re<1.
*
* Source for Reynolds number definition: http://en.wikipedia.org/wiki/Reynolds_number
*
* \param darcyMagVelocity The absolute value of the darcy velocity. In the context of box models this
* leads to a problem: the velocities are defined on the faces while other things (storage, sources, output)
* are defined for the volume/vertex. Therefore, some sort of decision needs to be made which velocity to put
* into this function (e.g.: facearea weighted average). [m/s]
* \param charcteristicLength Typically, in the context of porous media flow, the mean grain size is taken as the characteristic length
* for calculation of Re. [m]
* \param kinematicViscosity Is defined as the dynamic (or absolute) viscos ity divided by the density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity. [m^2/s]
*
* \return The Reynolds Number as calculated from the input parameters
*/
static
Scalar
reynoldsNumber
(
const
Scalar
darcyMagVelocity
,
const
Scalar
charcteristicLength
,
const
Scalar
kinematicViscosity
)
{
return
darcyMagVelocity
*
charcteristicLength
/
kinematicViscosity
;
}
else
if
(
formulation
==
NusseltFormulation
::
WakaoKaguei
){
/* example: flow through porous medium *single phase*, fit to many different data
* Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 293
*/
using
std
::
pow
;
return
2.
+
1.1
*
pow
(
prandtlNumber
,(
1.
/
3.
))
*
pow
(
reynoldsNumber
,
0.6
);
/*!
* \brief Calculate the Prandtl Number [] (Pr).
*
* The Prandtl Number is a measure for the relation of viscosity and thermal diffusivity (temperaturleitfaehigkeit).
*
* It is defined as
* \f[
* \textnormal{Pr}= \frac{\nu}{\alpha} = \frac{c_p \mu}{\lambda}\, ,
* \f]
* with kinematic viscosity\f$\nu\f$, thermal diffusivity \f$\alpha\f$, heat capacity \f$c_p\f$,
* dynamic viscosity \f$\mu\f$ and thermal conductivity \f$\lambda\f$.
* Therefore, Pr is a material specific property (i.e.: not a function of flow directly
* but only of temperature, pressure and fluid).
*
* source for Prandtl number definition: http://en.wikipedia.org/wiki/Prandtl_number
*
* \param dynamicViscosity Dynamic (absolute) viscosity over density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity [m^2/s]
* \param heatCapacity Heat capacity at constant pressure.
* Specifies the energy change for a given temperature change [J / (kg K)]
* \param thermalConductivity Conductivity to heat. Specifies how well matter transfers energy without moving. [W/(m K)]
* \return The Prandtl Number as calculated from the input parameters.
*/
static
Scalar
prandtlNumber
(
const
Scalar
dynamicViscosity
,
const
Scalar
heatCapacity
,
const
Scalar
thermalConductivity
)
{
return
dynamicViscosity
*
heatCapacity
/
thermalConductivity
;
}
else
if
(
formulation
==
NusseltFormulation
::
VDI
){
/* example: VDI Waermeatlas 10. Auflage 2006, flow in packed beds, page Gj1, see also other sources and limitations therein.
* valid for 0.1<Re<10000, 0.6<Pr/Sc<10000, packed beds of perfect spheres.
*
*/
using
std
::
sqrt
;
/*!
* \brief Calculate the Nusselt Number [] (Nu).
*
* The Nusselt Number is a measure for the relation of convective to conductive heat exchange.
*
* The Nusselt number is defined as Nu = h d / k,
* with h= heat transfer coefficient, d=characteristic length, k=heat conductivity(stagnant).
* However, the heat transfer coefficient from one phase to another is typically not known.
* Therefore, Nusselt numbers are usually given as *empirical* Nu(Reynolds, Prandtl) for a given flow
* field forced convection and *empirical* Nu(Rayleigh, Prandtl) for flow caused by temperature
* differences free convection. The fluid characteristics enter via the Prandtl number.
*
* This function implements an *empirical* correlation for the case of porous media flow
* (packed bed flow as the chemical engineers call it).
*
* source for Nusselt number definition: http://en.wikipedia.org/wiki/Nusselt_number
* source for further empirical correlations for Nusselt Numbers:
* VDIGesellschaft, VDIWaermeatlas, VDIVerlag Duesseldorf, 2006
*
* \param reynoldsNumber Dimensionless number relating inertial and viscous forces [].
* \param prandtlNumber Dimensionless number relating viscosity and thermal diffusivity (temperaturleitfaehigkeit) [].
* \param porosity The fraction of the porous medium which is void space.
* \param formulation Switch for deciding which parametrization of the Nusselt number is to be used.
* Set via the property NusseltFormulation.
* \return The Nusselt number as calculated from the input parameters [].
*/
static
Scalar
nusseltNumberForced
(
const
Scalar
reynoldsNumber
,
const
Scalar
prandtlNumber
,
const
Scalar
porosity
,
NusseltFormulation
formulation
)
{
if
(
formulation
==
NusseltFormulation
::
dittusBoelter
){
/* example: very common and simple case: flow straight circular pipe, only convection (no boiling),
* 10000<Re<120000, 0.7<Pr<120, far from pipe entrance, smooth surface of pipe ...
* Dittus, F.W and Boelter, L.M.K, Heat Transfer in Automobile Radiators of the Tubular Type,
* Publications in Engineering, Vol. 2, pages 443461, 1930
*/
using
std
::
pow
;
using
Dune
::
power
;
Scalar
numerator
=
0.037
*
pow
(
reynoldsNumber
,
0.8
)
*
prandtlNumber
;
Scalar
reToMin01
=
pow
(
reynoldsNumber
,

0.1
);
Scalar
prTo23
=
pow
(
prandtlNumber
,
(
2.
/
3.
)
)
;
// MIND THE pts! :( otherwise the integer exponent version is chosen
Scalar
denominator
=
1
+
2.443
*
reToMin01
*
(
prTo23

1.
)
;
return
0.023
*
pow
(
reynoldsNumber
,
0.8
)
*
pow
(
prandtlNumber
,
0.33
);
}
Scalar
nusseltTurbular
=
numerator
/
denominator
;
Scalar
nusseltLaminar
=
0.664
*
sqrt
(
reynoldsNumber
)
*
pow
(
prandtlNumber
,
(
1.
/
3.
)
);
Scalar
nusseltSingleSphere
=
2
+
sqrt
(
power
(
nusseltLaminar
,
2
)
+
power
(
nusseltTurbular
,
2
));
else
if
(
formulation
==
NusseltFormulation
::
WakaoKaguei
){
/* example: flow through porous medium *single phase*, fit to many different data
* Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 293
*/
using
std
::
pow
;
return
2.
+
1.1
*
pow
(
prandtlNumber
,(
1.
/
3.
))
*
pow
(
reynoldsNumber
,
0.6
);
}
Scalar
funckyFactor
=
1
+
1.5
*
(
1.

porosity
);
// for spheres of same size
Scalar
nusseltNumber
=
funckyFactor
*
nusseltSingleSphere
;
else
if
(
formulation
==
NusseltFormulation
::
VDI
){
/* example: VDI Waermeatlas 10. Auflage 2006, flow in packed beds, page Gj1, see also other sources and limitations therein.
* valid for 0.1<Re<10000, 0.6<Pr/Sc<10000, packed beds of perfect spheres.
*
*/
using
std
::
sqrt
;
using
std
::
pow
;
using
Dune
::
power
;
Scalar
numerator
=
0.037
*
pow
(
reynoldsNumber
,
0.8
)
*
prandtlNumber
;
Scalar
reToMin01
=
pow
(
reynoldsNumber
,

0.1
);
Scalar
prTo23
=
pow
(
prandtlNumber
,
(
2.
/
3.
)
)
;
// MIND THE pts! :( otherwise the integer exponent version is chosen
Scalar
denominator
=
1
+
2.443
*
reToMin01
*
(
prTo23

1.
)
;
return
nusseltNumber
;
}
Scalar
nusseltTurbular
=
numerator
/
denominator
;
Scalar
nusseltLaminar
=
0.664
*
sqrt
(
reynoldsNumber
)
*
pow
(
prandtlNumber
,
(
1.
/
3.
)
);
Scalar
nusseltSingleSphere
=
2
+
sqrt
(
power
(
nusseltLaminar
,
2
)
+
power
(
nusseltTurbular
,
2
));
else
{
DUNE_THROW
(
Dune
::
NotImplemented
,
"wrong index"
);
}
}
Scalar
funckyFactor
=
1
+
1.5
*
(
1.

porosity
);
// for spheres of same size
Scalar
nusseltNumber
=
funckyFactor
*
nusseltSingleSphere
;
return
nusseltNumber
;
}
/*!
* \brief Calculate the Schmidt Number [] (Sc).
*
* The Schmidt Number is a measure for the relation of viscosity and mass diffusivity.
*
* It is defined as
* \f[
* \textnormal{Sc}= \frac{\nu}{D} = \frac{\mu}{\rho D}\, ,
* \f]
* with kinematic viscosity\f$\nu\f$, diffusion coefficient \f$D\f$, dynamic viscosity
* \f$\mu\f$ and mass density\f$\rho\f$. Therefore, Sc is a material specific property
* (i.e.: not a function of flow directly but only of temperature, pressure and fluid).
*
* source for Schmidt number definition: http://en.wikipedia.org/wiki/Schmidt_number
*
* \param dynamicViscosity Dynamic (absolute) viscosity over density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity [m^2/s]
* \param massDensity Mass density of the considered phase. [kg / m^3]
* \param diffusionCoefficient Measure for how well a component can move through a phase due to a concentration gradient. [m^2/s]
* \return The Schmidt Number as calculated from the input parameters.
*/
static
Scalar
schmidtNumber
(
const
Scalar
dynamicViscosity
,
const
Scalar
massDensity
,
const
Scalar
diffusionCoefficient
)
{
return
dynamicViscosity
/
(
massDensity
*
diffusionCoefficient
);
}
else
{
DUNE_THROW
(
Dune
::
NotImplemented
,
"wrong index"
);
}
}
/*!
* \brief Calculate the Sherwood Number [] (Sh).
*
* The Sherwood Number is a measure for the relation of convective to diffusive mass exchange.
*
* The Sherwood number is defined as Sh = K L/D,
* with K= mass transfer coefficient, L=characteristic length, D=mass diffusivity (stagnant).
*
* However, the mass transfer coefficient from one phase to another is typically not known.
* Therefore, Sherwood numbers are usually given as *empirical* Sh(Reynolds, Schmidt) for a given flow
* field (and fluid).
*
* Often, even the Sherwood number is not known. By means of the ChiltonColburn analogy it can be deduced
* from the Nusselt number. According to the ChiltonColburn analogy in a known Nusselt correltion one
* basically replaces Pr with Sc and Nu with Sh. For some very special cases this is actually accurate.
* (Source: Course Notes, Waerme und Stoffuebertragung, Prof. Hans Hasse, Uni Stuttgart)
*
* This function implements an *empirical* correlation for the case of porous media flow
* (packed bed flow as the chemical engineers call it).
*
* source for Sherwood number definition: http://en.wikipedia.org/wiki/Sherwood_number
*
* \param schmidtNumber Dimensionless number relating viscosity and mass diffusivity [].
* \param reynoldsNumber Dimensionless number relating inertial and viscous forces [].
* \param formulation Switch for deciding which parametrization of the Sherwood number is to be used.
* Set via the property SherwoodFormulation.
* \return The Nusselt number as calculated from the input parameters [].
*/
static
Scalar
sherwoodNumber
(
const
Scalar
reynoldsNumber
,
const
Scalar
schmidtNumber
,
SherwoodFormulation
formulation
)
{
if
(
formulation
==
SherwoodFormulation
::
WakaoKaguei
){
/* example: flow through porous medium *single phase*
* Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 156
*/
using
std
::
cbrt
;
using
std
::
pow
;
return
2.
+
1.1
*
cbrt
(
schmidtNumber
)
*
pow
(
reynoldsNumber
,
0.6
);
/*!
* \brief Calculate the Schmidt Number [] (Sc).
*
* The Schmidt Number is a measure for the relation of viscosity and mass diffusivity.
*
* It is defined as
* \f[
* \textnormal{Sc}= \frac{\nu}{D} = \frac{\mu}{\rho D}\, ,
* \f]
* with kinematic viscosity\f$\nu\f$, diffusion coefficient \f$D\f$, dynamic viscosity
* \f$\mu\f$ and mass density\f$\rho\f$. Therefore, Sc is a material specific property
* (i.e.: not a function of flow directly but only of temperature, pressure and fluid).
*
* source for Schmidt number definition: http://en.wikipedia.org/wiki/Schmidt_number
*
* \param dynamicViscosity Dynamic (absolute) viscosity over density.
* http://en.wikipedia.org/wiki/Viscosity#Dynamic_viscosity [m^2/s]
* \param massDensity Mass density of the considered phase. [kg / m^3]
* \param diffusionCoefficient Measure for how well a component can move through a phase due to a concentration gradient. [m^2/s]
* \return The Schmidt Number as calculated from the input parameters.
*/
static
Scalar
schmidtNumber
(
const
Scalar
dynamicViscosity
,
const
Scalar
massDensity
,
const
Scalar
diffusionCoefficient
)
{
return
dynamicViscosity
/
(
massDensity
*
diffusionCoefficient
);
}
else
{
DUNE_THROW
(
Dune
::
NotImplemented
,
"wrong index"
);
/*!
* \brief Calculate the Sherwood Number [] (Sh).
*
* The Sherwood Number is a measure for the relation of convective to diffusive mass exchange.
*
* The Sherwood number is defined as Sh = K L/D,
* with K= mass transfer coefficient, L=characteristic length, D=mass diffusivity (stagnant).
*
* However, the mass transfer coefficient from one phase to another is typically not known.
* Therefore, Sherwood numbers are usually given as *empirical* Sh(Reynolds, Schmidt) for a given flow
* field (and fluid).
*
* Often, even the Sherwood number is not known. By means of the ChiltonColburn analogy it can be deduced
* from the Nusselt number. According to the ChiltonColburn analogy in a known Nusselt correltion one
* basically replaces Pr with Sc and Nu with Sh. For some very special cases this is actually accurate.
* (Source: Course Notes, Waerme und Stoffuebertragung, Prof. Hans Hasse, Uni Stuttgart)
*
* This function implements an *empirical* correlation for the case of porous media flow
* (packed bed flow as the chemical engineers call it).
*
* source for Sherwood number definition: http://en.wikipedia.org/wiki/Sherwood_number
*
* \param schmidtNumber Dimensionless number relating viscosity and mass diffusivity [].
* \param reynoldsNumber Dimensionless number relating inertial and viscous forces [].
* \param formulation Switch for deciding which parametrization of the Sherwood number is to be used.
* Set via the property SherwoodFormulation.
* \return The Nusselt number as calculated from the input parameters [].
*/
static
Scalar
sherwoodNumber
(
const
Scalar
reynoldsNumber
,
const
Scalar
schmidtNumber
,
SherwoodFormulation
formulation
)
{
if
(
formulation
==
SherwoodFormulation
::
WakaoKaguei
){
/* example: flow through porous medium *single phase*
* Wakao and Kaguei, Heat and mass Transfer in Packed Beds, Gordon and Breach Science Publishers, page 156
*/
using
std
::
cbrt
;
using
std
::
pow
;
return
2.
+
1.1
*
cbrt
(
schmidtNumber
)
*
pow
(
reynoldsNumber
,
0.6
);
}
else
{
DUNE_THROW
(
Dune
::
NotImplemented
,
"wrong index"
);
}
}
}
/*!
* \brief Calculate the thermal diffusivity alpha [m^2/s].
*
* The thermal diffusivity is a measure for how fast "temperature (not heat!) spreads".
* It is defined as \f$\alpha = \frac{k}{\rho c_p}\f$
* with \f$\alpha\f$: \f$k\f$: thermal conductivity [W/mK], \f$\rho\f$: density [kg/m^3],
* \f$c_p\f$: cpecific heat capacity at constant pressure [J/kgK].
*
* Source for thermal diffusivity definition: http://en.wikipedia.org/wiki/Thermal_diffusivity
*
* \param thermalConductivity A material property defining how well heat is transported via conduction [W/(mK)].
* \param phaseDensity The density of the phase for which the thermal diffusivity is to be calculated [kg/m^3].
* \param heatCapacity A measure for how a much a material changes temperature for a given change of energy (at p=const.) [J/(kgm^3)].
* \return The thermal diffusivity as calculated from the input parameters [m^2/s].
*/
static
Scalar
thermalDiffusivity
(
const
Scalar
&
thermalConductivity
,
const
Scalar
&
phaseDensity
,
const
Scalar
&
heatCapacity
)
{
return
thermalConductivity
/
(
phaseDensity
*
heatCapacity
);
}
/*!
* \brief Calculate the thermal diffusivity alpha [m^2/s].
*
* The thermal diffusivity is a measure for how fast "temperature (not heat!) spreads".
* It is defined as \f$\alpha = \frac{k}{\rho c_p}\f$
* with \f$\alpha\f$: \f$k\f$: thermal conductivity [W/mK], \f$\rho\f$: density [kg/m^3],
* \f$c_p\f$: cpecific heat capacity at constant pressure [J/kgK].
*
* Source for thermal diffusivity definition: http://en.wikipedia.org/wiki/Thermal_diffusivity
*
* \param thermalConductivity A material property defining how well heat is transported via conduction [W/(mK)].
* \param phaseDensity The density of the phase for which the thermal diffusivity is to be calculated [kg/m^3].
* \param heatCapacity A measure for how a much a material changes temperature for a given change of energy (at p=const.) [J/(kgm^3)].
* \return The thermal diffusivity as calculated from the input parameters [m^2/s].
*/
static
Scalar
thermalDiffusivity
(
const
Scalar
&
thermalConductivity
,
const
Scalar
&
phaseDensity
,
const
Scalar
&
heatCapacity
)
{
return
thermalConductivity
/
(
phaseDensity
*
heatCapacity
);
}
};
// end class DimensionlessNumbers
};
}
// end namespace Dumux
...
...
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