(6-8)
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(6-9)
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ρ (SI unit: kg/m 3) is the fluid density.
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Cp (SI unit: J/(kg·K)) is the fluid heat capacity at constant pressure.
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(ρCp)eff (SI unit: J/(m 3·K)) is the effective volumetric heat capacity at constant pressure defined by an averaging model to account for both solid matrix and fluid properties.
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q is the conductive heat flux (SI unit: W/m 2).
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u (SI unit: m/s) is the fluid velocity field, either an analytic expression or the velocity field from a Fluid Flow interface. u should be interpreted as the Darcy velocity, that is, the volume flow rate per unit cross sectional area. The average linear velocity (the velocity within the pores) can be calculated as uL = u ⁄ θL, where θL is the fluid’s volume fraction, or equivalently the porosity.
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keff (SI unit: W/(m·K)) is the effective thermal conductivity (a scalar or a tensor if the thermal conductivity is anisotropic), defined by an averaging model to account for both solid matrix and fluid properties.
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Q (SI unit: W/m 3) is the heat source (or sink). Add one or several heat sources as separate physics features. See Heat Source node and Viscous Dissipation subnode for example.
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This section is available when a temperature-dependent density is used. On the material frame, the density is evaluated onto a reference temperature to ensure mass conservation in the presence of temperature variations. By default the Common model input is used. This corresponds to the variable
minput.Tempref, which is set by default to 293.15 [K]. To edit it, click the
Go to Source button (
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), and in the
Common Model Inputs node under
Global Definitions, set a value for the
Volume reference temperature in the
Expression for remaining selection section.
The other options are User defined and all temperature variables from the physics interfaces included in the model.
This section is available when temperature-dependent material properties are used. By default the temperature of the parent interface is used and the section is not editable. To edit the Temperature field, click
Make All Model Inputs Editable (
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). The available options are
User defined (default),
Common model input (the
minput.T variable, set to 293.15 [K] by default) and all temperature variables from the physics interfaces included in the model. To edit the
minput.T variable, click the
Go to Source button (
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), and in the
Common Model Inputs node under
Global Definitions, set a value for the
Temperature in the
Expression for remaining selection section.
The default Absolute pressure pA is
User defined. When additional physics interfaces are added to the model, the absolute pressure variables defined by these physics interfaces can also be selected from the list. For example, if a
Laminar Flow interface is added you can select
Absolute pressure (spf) from the list. The
Common model input option corresponds to the
minput.pA variable, set to 1 [atm] by default. To edit it, click the
Go to Source button (
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), and in the
Common Model Inputs node under
Global Definitions, set a value for the
Pressure in the
Expression for remaining selection section.
The default Velocity field u is
User defined. For
User defined enter values or expressions for the components based on space dimensions. Or select an existing velocity field in the component (for example,
Velocity field (spf) from a
Laminar Flow interface). The
Common model input option corresponds to the
minput.u variable. To edit it, click the
Go to Source button (
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), and in the
Common Model Inputs node under
Global Definitions, set values for the
Velocity components in the
Expression for remaining selection section.
From the Concentration c (SI unit: mol/m
3 or kg/m
3) list, select an existing concentration variable from another physics interface, if any concentration variables exist,
User defined to enter a value or expression for the concentration, or
Common model input which corresponds to the
minput.c variable.
Select any component material from the list to define the Fluid material. The default uses the
Domain material. It makes it possible to define different material properties for the fluid phase when the domain material corresponds to the solid phase (porous matrix) material.
The thermal conductivity k describes the relationship between the heat flux vector
q and the temperature gradient
∇T in
q = −k∇T, which is Fourier’s law of heat conduction. Enter this quantity as power per length and temperature.
The default Thermal conductivity k is taken
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Anisotropic based on the characteristics of the thermal conductivity, and enter another value or expression. For
Isotropic enter a scalar which will be used to define a diagonal tensor. For the other options, enter values or expressions into the editable fields of the tensor.
The heat capacity at constant pressure Cp describes the amount of heat energy required to produce a unit temperature change in a unit mass.
The ratio of specific heats γ is the ratio of the heat capacity at constant pressure,
Cp, to the heat capacity at constant volume,
Cv. When using the ideal gas law to describe a fluid, specifying
γ is sufficient to evaluate
Cp. For common diatomic gases such as air,
γ = 1.4 is the standard value. Most liquids have
γ = 1.1 while water has
γ = 1.0. γ is used in the streamline stabilization and in the variables for heat fluxes and total energy fluxes. It is also used if the ideal gas law is applied.
The available Fluid type options are
Gas/Liquid (default),
Moist air, or
Ideal gas. After selecting a
Fluid type from the list, further settings display underneath.
This option specifies the Density, the
Heat capacity at constant pressure, and the
Ratio of specific heats for a general gas or liquid.
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The gas constant, with two options for the Gas constant type: Specific gas constant Rs or Mean molar mass Mn. If Mean molar mass is selected the software uses the universal gas constant R = 8.314 J/(mol·K), which is a built-in physical constant, to compute the specific gas constant.
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Either the Heat capacity at constant pressure Cp or Ratio of specific heats γ by selecting the option from the Specify Cp or γ list. For an ideal gas, it is sufficient to specify either Cp or the ratio of specific heats, γ, as these properties are dependent.
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If Moist air is selected, the thermodynamics properties are defined as a function of the quantity of vapor in the moist air. The available
Input quantity options to define the amount of vapor in the moist air are the following:
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Concentration to define the amount of water vapor in the total volume. If selected, a Concentration model input is automatically added in the Model Inputs section.
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Moisture content (also called mixing ratio or humidity ratio) to define the ratio of the water vapor mass to the dry air mass.
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Relative humidity  , a quantity defined between 0 and 1, where 0 corresponds to dry air and 1 to a water vapor-saturated air. The Relative humidity, temperature condition  and Relative humidity, absolute pressure condition  must be specified.
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If the Standard porous matrix model is selected under
Physical Model, select any component material in the
Solid material list. The
Volume fraction θp for the solid material should be specified. For
User defined, enter a value or expression. Or select an existing volume fraction in the component (for example,
Volume fraction (dl/dlm1) from a
Darcy’s Law interface).
If the Extended porous matrix model is selected under
Physical Model (with the Subsurface Flow Module), the
Number of solids can be set from
1 to
5. Then for each solid a
Solid material list and a
Volume fraction field display underneath.
The thermal conductivity kp describes the relationship between the heat flux vector
q and the temperature gradient
∇T in
q = −kp∇T, which is Fourier’s law of heat conduction. Enter this quantity as power per length and temperature.
The default Thermal conductivity kp is taken
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Anisotropic based on the characteristics of the thermal conductivity, and enter another value or expression. For
Isotropic enter a scalar which will be used to define a diagonal tensor. For the other options, enter values or expressions into the editable fields of the tensor.
When the Extended porous matrix model is selected under
Physical Model (with the Subsurface Flow Module), and more than one solid is selected in the
Immobile Solids section, the thermal conductivities
kpi should be specified for each immobile solid. The average property for the porous matrix is given by:
The Density ρp and the
Specific heat capacity Cp, p should be specified. For
From Material option, see
Material Density in Features Defined in the Material Frame if a temperature-dependent density should be set.
When the Extended porous matrix model is selected under
Physical Model (with the Subsurface Flow Module), and more than one solid is selected in the
Immobile Solids section, the
Density and
Specific heat capacity should be specified for each immobile solid.
This section sets the averaging model for the computation of the Effective conductivity by accounting for both solid matrix and fluid properties. The following options are available with either the Subsurface Flow Module or the Heat Transfer Module:
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Volume average (default), which computes the effective conductivity of the solid-fluid system as the weighted arithmetic mean of fluid and porous matrix conductivities:
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Reciprocal average, which computes the effective conductivity of the solid-fluid system as the weighted harmonic mean of fluid and porous matrix conductivities:
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Power law, which computes the effective conductivity of the solid-fluid system as the weighted geometric mean of fluid and porous matrix conductivities:
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When the Extended porous matrix model is selected under
Physical Model (with the Subsurface Flow Module), and more than one solid is selected in the
Immobile Solids section, these averaging models are modified in the following way:
Heat Transfer in Porous Media>Porous Medium
More locations are available if the Heat transfer in porous media check box is selected under the
Physical Model section. For example:
Heat Transfer in Solids>Porous Medium
Physics Tab with interface as
Heat Transfer,
Heat Transfer in Solids,
Heat Transfer in Fluids,
Heat Transfer in Porous Media,
Heat Transfer in Building Materials or
Bioheat Transfer selected:
Domains>interface>Porous Medium