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.

With this assumption, one single equation is solved for both phases, using effective material properties. See Equation 4-41 for details.

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.

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.

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.

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.

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.

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:

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 .

It is also possible to define directly the effective thermal conductivity, keff. When Equivalent thermal conductivity is selected in the Effective thermal conductivity list, a value for the Effective thermal conductivity keff should be specified directly. The default Effective 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.

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).

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 1e-3 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.

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)).

Enter a custom value for qsf (SI unit: W/(m3·K)).

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: