Porous Medium
This node models heat transfer in a porous matrix, possibly consisting of several solids, and filled with a mobile fluid, and one or more immobile fluids. It allows to make the local thermal equilibrium assumption or not, and to handle the case of a packed bed of pellets in a specific way, through the Porous medium type option.
Local thermal equilibrium
With this assumption, one single equation is solved for both phases, using effective material properties. See Equation 4-41 for details.
In particular, when no immobile fluid is present in the pore space, the effective volumetric heat capacity at constant pressure is defined as
If the porous matrix consists of several solids i of volume fraction θsi, heat capacity Cp,si, and density ρsi, the above equation is modified as follows:
See Immobile Fluids (Porous Medium) to take into account the presence of immobile fluids in the expression of effective volumetric heat capacity at constant pressure.
See Porous Medium for the definition of the effective thermal conductivity.
Local Thermal Nonequilibrium
When the solid and fluid temperatures are not in equilibrium, two heat equations are solved in the solid and fluid subdomains, and coupled through a transfer term proportional to the temperature difference between both phases. See Equation 4-43 and Equation 4-44 for details about the heat transfer equation in each phase, and Porous Medium for the definition of the transfer term between fluid and solid phases.
Packed Bed
When the porous medium is a packed bed of pellets, and when the thermal conductivity of the pellets is small enough compared to the fluid conductivity to neglect heat transfer between the pellets, the macroscale heat equation for the solid phase of the standard local thermal nonequilibrium model is replaced by a microscale equation for the radial variation of the temperature due to conduction in the pellets.
See Equation 4-45 and Equation 4-46 for details about the heat transfer equation in each phase, and Pellet-Fluid Interface (Porous Medium) for the definition of the coupling condition between the fluid phase and pellets equations.
Coordinate System Selection
Select a coordinate system from the Coordinate system list for the interpretation of directions in anisotropic material properties. The default is the Global coordinate system, and the list contains any additional coordinate system (except boundary coordinate systems) added under the Definitions node.
The subnodes of Porous Medium inherit these coordinate system settings. In particular, the Velocity field and Thermal Conductivity (in Fluid (Porous Medium) subnode) and the Dry bulk thermal conductivity and Solid phase thermal conductivity (in Porous Matrix (Porous Medium, Moist Porous Medium) subnode) should be set according to the coordinate system selected in this section.
See Coordinate Systems in the COMSOL Multiphysics Reference Manual for more details.
Porous Medium
Select between the Local thermal equilibrium, the Local thermal nonequilibrium, and the Packed bed options in the Porous medium type list.
Depending upon the selected option, further settings are required underneath: either the effective thermal conductivity required by the single heat transfer equation, or the parameters used to couple the two heat transfer equations in each phase. See the Local thermal equilibrium and Local Thermal Nonequilibrium sections below for details.
It also changes the availability of some subnodes:
The Geothermal Heating, Immobile Fluids, and Optically Thick Participating Medium subnodes are available under Porous Medium only when the Porous Medium type is set to Local thermal equilibrium.
The Initial Values, Heat Source, Thermal Insulation, Symmetry (Heat Transfer Interface), Temperature, Heat Flux, Lumped System Connector, Phase Change Interface, Continuity, Inflow, Outflow, Open Boundary, Boundary Heat Source, Surface-to-Ambient Radiation (Heat Transfer Interface), and Deposited Beam Power features are available under the Fluid (Porous Medium) subnode only when the Porous Medium type is set to Local thermal nonequilibrium or Packed bed.These subnodes allow the definition of domain and boundary conditions specific to the fluid phase temperature Tf.
The Initial Values, Heat Source, Thermal Insulation, Symmetry (Heat Transfer Interface), Temperature, Heat Flux, Lumped System Connector, Continuity, Boundary Heat Source, Surface-to-Ambient Radiation (Heat Transfer Interface), and Deposited Beam Power features are available under the Porous Matrix (Porous Medium, Moist Porous Medium) subnode only when the Porous Medium type is set to Local thermal nonequilibrium. These subnodes allow the definition of domain and boundary conditions specific to the solid phase temperature Ts.
Local Thermal Equilibrium
When Local thermal equilibrium is selected in the Porous medium type list, this section defines the Effective thermal conductivity taking into account the properties of the solid matrix and the mobile fluid. The following averaging models are available:
Plane layers parallel to heat flow (default), which calculates the effective conductivity of the solid-fluid system as the weighted arithmetic mean (or volume average) of the conductivities of the fluid and the porous matrix:
Plane layers perpendicular to heat flow, which calculates the effective conductivity of the solid-fluid system as the weighted harmonic mean (or reciprocal average) of the conductivities of the fluid and the porous matrix:
Power law, which calculates the effective conductivity of the solid-fluid system as the weighted geometric mean of the conductivities of the fluid and the porous matrix:
Solid spherical inclusions, which calculates the effective conductivity of the solid-fluid system as:
Fluid spherical inclusions, which calculates the effective conductivity of the solid-fluid system as:
Wrapped screen, which calculates the effective conductivity of the solid-fluid system as:
Sintered metal fibers, which calculates the effective conductivity of the solid-fluid system as:
If the porous matrix consists of several solids i of volume fraction θsi and thermal conductivity ksi, the above equations are modified by replacing ks by , and θs by .
The Immobile Fluids subnode is available only when Plane layers parallel to heat flow, Plane layers perpendicular to heat flow, Power law or Equivalent thermal conductivity is selected in the Effective thermal conductivity list.
It is also possible to define directly the equivalent thermal conductivity, keq. When Equivalent thermal conductivity is selected in the Effective thermal conductivity list, a value for the Equivalent thermal conductivity keq should be specified directly. The default Equivalent thermal conductivity is taken From material. When a Porous Material node is active, the property of the Homogenized Properties section is used. For User defined, select Isotropic, Diagonal, Symmetric, or Full 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.
Local Thermal Nonequilibrium
When Local thermal nonequilibrium is selected in the Porous medium type list, select an Interstitial convective heat transfer coefficient: Spherical pellets, General configuration, or User defined (the default).
Spherical Pellets
In this particular configuration, the interstitial convective heat transfer coefficient can be directly expressed as a function of the average pellets diameter dpe and the fluid-to-solid Nusselt number for which the fluid dynamic viscosity μ is needed.
Enter a value for the Average diameter dpe (SI unit: m) of the pellets. Default value is 103 m.
The dynamic viscosity needed to evaluate the Nusselt number is set in the Fluid (Porous Medium) subnode. See Dynamic Viscosity for details.
Note that with this option, the radial variation of the temperature within the pellets is not precisely accounted for. Change to the Packed bed option (in the Porous medium type list) to solve for a specific equation for radial conduction in the pellets. See Packed Bed for details.
General Configuration
The interstitial convective heat transfer coefficient is expressed as the product of the specific surface area Sb and the interstitial heat transfer coefficient hsf.
Enter a value for the Specific surface area Sb (SI unit: 1/m).
Enter a value for the Interstitial heat transfer coefficient hsf (SI unit: W/(m2·K)).
User Defined
Enter a custom value for qsf (SI unit: W/(m3·K)).
See Immobile Fluids (Porous Medium) to take into account the presence of immobile fluids in the expression of effective thermal conductivity in the local thermal equilibrium case.
The velocity field and material properties of the mobile fluid can be specified in the Fluid (Porous Medium) subnode, by defining it as a general gas or liquid, as an ideal gas, or as moist air.
The porosity εp and material properties of the solid matrix can be specified in the Porous Matrix (Porous Medium, Moist Porous Medium) subnode.
The packed bed and pellets porosities εp and εpe, and the material properties of the pellets can be specified in the Pellets (Porous Medium) subnode.
When the porosity εp is taken From material, the solid volume fraction θs is defined in the material, under the Solid subnode. In case of multiple solids, it is needed to refer to the material, as it is not possible to deduce the values of θsi for the different solids from the porosity. When the porosity is User defined, the volume fraction of each solid θsi is obtained by dividing θs = 1 − εp by the number of solids.
See Porous Material in the COMSOL Multiphysics Reference Manual.
With some COMSOL products, the Thermal Dispersion, Viscous Dissipation, and Geothermal Heating subnodes are available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Location in User Interface
Context Menus
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Physics tab with Heat Transfer in Solids and Fluids, Heat Transfer in Solids, Heat Transfer in Fluids, Heat Transfer in Porous Media, or Heat Transfer in Building Materials selected: