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7.19.3 Treatment of the Energy Equation in Porous Media

FLUENT solves the standard energy transport equation (Equation  13.2-1) in porous media regions with modifications to the conduction flux and the transient terms only. In the porous medium, the conduction flux uses an effective conductivity and the transient term includes the thermal inertia of the solid region on the medium:


 \frac{\partial}{\partial t} ( \gamma \rho_f E_f + ( 1 - \gam... ... + (\overline{\overline{\tau}} \cdot {\vec v}) \right] + S^h_f (7.19-8)

where


$E_f$ = total fluid energy
$E_s$ = total solid medium energy
$\gamma$ = porosity of the medium
$k_{\rm eff}$ = effective thermal conductivity of the medium
$S^h_f$ = fluid enthalpy source term



Effective Conductivity in the Porous Medium


The effective thermal conductivity in the porous medium, $k_{\rm eff}$, is computed by FLUENT as the volume average of the fluid conductivity and the solid conductivity:


 k_{\rm eff} = \gamma k_f + (1-\gamma)k_s (7.19-9)

where


$\gamma$ = porosity of the medium
$k_f$ = fluid phase thermal conductivity (including the turbulent contribution, $k_t$)
$k_s$ = solid medium thermal conductivity

The fluid thermal conductivity $k_f$ and the solid thermal conductivity $k_s$ can be computed via user-defined functions.

The anisotropic effective thermal conductivity can also be specified via user-defined functions. In this case, the isotropic contributions from the fluid, $\gamma k_f$, are added to the diagonal elements of the solid anisotropic thermal conductivity matrix.


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