Porous Medium
This node uses the following version of the heat equation to model heat transfer in a porous matrix, possibly consisting of several solids, and filled with a mobile fluid, and one or more immobile fluids:
(6-13)
(6-14)
with the following material properties, fields, and sources:
ρ (SI unit: kg/m3) is the density of the mobile fluid.
Cp (SI unit: J/(kg·K)) is the heat capacity at constant pressure of the mobile fluid.
Cp)eff (SI unit: J/(m3·K)) is the effective volumetric heat capacity at constant pressure, defined by an averaging model to take into account both solid matrix and fluid properties.
q is the conductive heat flux (SI unit: W/m2).
u (SI unit: m/s) is the velocity field of the mobile fluid, 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 ⁄ εp, where εp is the porosity.
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 take into account both solid matrix and fluid properties.
Q (SI unit: W/m3) is the heat source (or sink). Add one or more 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.
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.
Effective Thermal Conductivity
This section defines the averaging model for the computation of the Effective conductivity taking into account the properties of the solid matrix and the mobile fluid. The following options are available:
Volume average (default), which calculates the effective conductivity of the solid-fluid system as the weighted arithmetic mean of the conductivities of the fluid and the porous matrix:
Reciprocal average, which calculates the effective conductivity of the solid-fluid system as the weighted harmonic mean 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:
If the porous matrix consists of several solids i of volume fraction θsi and thermal conductivity ksi, the above equations are modified as follows:
See Immobile Fluids (Porous Medium) to take into account the presence of immobile fluids in the expression of effective thermal conductivity.
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.
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
Ribbon
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: