Porous Medium
This node uses the following version of the heat equation to model heat transfer in a porous matrix filled with a fluid:
(6-6)
(6-7)
with the following material properties, fields, and sources:
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ρ (SI unit: kg/m3) 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/(m3·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/m2).
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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/m3) 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.
For a steady-state problem the temperature does not change with time and the first term disappears.
Model Inputs
This section has fields and values that are inputs to expressions that define material properties. If such user-defined property groups are added, the model inputs appear here.
Temperature
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 (). The available options are User defined (default) and all the temperature variables from the physics interfaces included in the model. These physics interfaces have their own tags (the Name). For example, if a Heat Transfer in Fluids interface is included in the model, the Temperature (ht) option is available.
Absolute Pressure
The absolute pressure is used in some predefined quantities that include the enthalpy (the energy flux, for example).
It is also used if the ideal gas law is applied. See Thermodynamics, Fluid.
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 Brinkman Equations interface is added you can select Absolute pressure (br) from the list.
Velocity Field
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 (br) from a Brinkman Equations interface).
Concentration
From the Concentration c (SI unit: mol/m3 or kg/m3) list, select an existing concentration variable from another physics interface, if any concentration variables exist, or select User defined to enter a value or expression for the concentration. This section can be edited anytime a material property is concentration dependent; for example, when the Fluid type is set to Moist air with Input quantity set to Concentration.
Fluid Material
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.
Heat Conduction, Fluid
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.
Thermodynamics, Fluid
This section sets the thermodynamics properties of the fluid.
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.
Gas/Liquid
This option specifies the Density, the Heat capacity at constant pressure, and the Ratio of specific heats for a general gas or liquid.
Ideal Gas
This option uses the ideal gas law to describe the fluid. Only two properties are needed to define the thermodynamics of the fluid:
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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.
Moist Air
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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Vapor mass fraction (the default) to define the ratio of the vapor mass to the total mass.
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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, by defining the Reference relative humidity at Reference temperature and Reference pressure. The Reference relative humidity is a quantity defined between 0 and 1, where 0 corresponds to dry air and 1 to a water vapor-saturated air.
Immobile Solids
This section sets the material and volume fraction of the porous matrix.
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.
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 total volume fraction of solid material is given by
and the available volume fraction for the mobile fluid is defined as
Heat Conduction, Porous Matrix
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:
Thermodynamics, Porous Matrix
This section sets the thermodynamics properties of the porous matrix.
The specific heat capacity describes the amount of heat energy required to produce a unit temperature change in a unit mass of the solid material.
The Density ρp and the Specific heat capacity Cp, p should be specified. For From Material option, see Material Density in Features Defined on the Material Frame if a temperature-dependent density should be set.
The effective volumetric heat capacity of the solid-liquid system is calculated from
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.
The effective volumetric heat capacity of the composite solid-fluid system is defined as
Effective thermal conductivity
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:
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:
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Volume average:
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Reciprocal average:
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Power law:
Moist Air Fluid Type
Local Thermal Non-Equilibrium
Theory for Heat Transfer in Porous Media
With certain COMSOL products, the Thermal Dispersion, Viscous Dissipation, Geothermal Heating and Immobile Fluids subnodes are available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
When Surface-to-surface radiation is activated, the Opacity subnode is automatically added to the entire selection, with Opaque option selected. The domain selection can’t be edited. To set some part of the domain as transparent, add a new Opacity subnode from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Evaporation in Porous Media with Small Evaporation Rates: Application Library path Heat_Transfer_Module/Phase_Change/ evaporation_porous_media_small_rate
For a detailed overview of the functionality available in each product, visit http://www.comsol.com/products/specifications/
Location in User Interface
Context menus
 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
Ribbon
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, Bioheat Transfer, Heat Transfer with Surface-to-Surface Radiation or Heat Transfer with Radiation in Participating Media selected:
Domains>interface>Porous Medium