A solid porous medium is characterized by two quantities: the volumetric void fraction
(the ratio of the volume of void to the total volume of the porous
media), which can range from 
to 
, and the permeability factor 
. For isotropic porous media, 
is a scalar. For non-isotropic porous media (that is, when the physical
structure of the solid body exhibits a particular orientation) it is a tensor, which
indicates a preferred orientation of the pores.
Important: For highly non-isotropic materials, instead of specifying zero values for the permeability coefficient in the transverse direction, it is strongly recommended that you specify very small nonzero values (for example, 10-12) to improve the convergence of the solver.
The flow of an incompressible fluid with viscosity 
in the porous material obeys the following constitutive equation:
 | (14–1) |
where 
is the fluid velocity and 
is the pressure field. The conservation equation can be written as
 | (14–2) |
The pressure field is the only unknown associated with this equation. The boundary
conditions can therefore be specified in terms of pressure or velocity (according to
Equation 14–1). Equation 14–2 holds for both isothermal
and nonisothermal flows. When nonisothermal effects are taken into account, however, the
energy equation must be solved as well. The energy equation results from the combined
thermal effects in both the fluid in motion and the fixed solid porous medium. As a
result, other material properties, in addition to 
, 
, and 
, are required for calculating the temperature field.
In this description, the subscripts 
and 
identify the solid and the fluid, respectively. The solid and the
fluid are characterized by their densities (
), their thermal conductivities (
), and their heat capacities (
). Thermal conductivity and heat capacity can be made temperature
dependent using a third-order polynomial expression.
The energy equation is then
 | (14–3) |
In Equation 14–3, the contributions of
the solid and the fluid are weighted by 
and 
, respectively, since it is assumed that the fluid fills the voids
entirely. Also, since the solid is motionless, only the fluid contributes to the
convective term and to viscous heating. Finally, a nonzero value of 
can be used to introduce a heat source. For nonisothermal flows, the
fluid viscosity 
can be made to depend on 
, according to the Arrhenius law or Arrhenius approximate law. See
Temperature-Dependent Viscosity Laws for details. The viscosity cannot be made to depend on shear rate because the actual
value of the shear rate is unknown.
The unknown field associated with the energy equation is the temperature
. The boundary conditions can therefore be specified in terms of
temperature or heat flux.
In flow through porous media, Ansys Polyflow automatically performs the calculation of
the velocity field 
(as a postprocessor) according to Equation 14–1 and computes the stream
function as given in Stream Function.