Influence of Porous Resistance on Temperature for Incompressible Flow

When simulating incompressible flow through a porous medium with the energy model activated, a change in temperature proportional to the user-specified porous resistance takes place. This section explains the reason for this temperature change.

Consider a one-dimensional steady incompressible flow of a fluid with constant c v (specific heat at constant volume) through a porous medium with a constant cross-section. Mass conservation requires that the velocity u is constant. Momentum conservation reduces to a balance between the pressure gradient d p / d x and the porous resistance R :

Figure 1. EQUATION_DISPLAY
R = d p d x
(242)

The energy equation reduces to:

Figure 2. EQUATION_DISPLAY
d H d x = 0
(243)

and since total enthalpy is H = c v T + p / ρ + u 2 / 2 , the equation becomes:

Figure 3. EQUATION_DISPLAY
d T d x = - 1 ρ c v d p d x = - R ρ c v
(244)

Hence, it is normal to expect a temperature increase or decrease for an incompressible flow through a porous medium.