The Local Thermal Nonequilibrium Interface implements heat transfer in porous media for which the temperatures into the porous matrix and the fluid are not in equilibrium.
The fluid velocity is often deduced from a porous velocity up, coming for example from Darcy’s law or Brinkman equations, according to:
The Local Thermal Nonequilibrium multiphysics coupling adds the exchanged opposite heat sources
qsf(Tf − Ts) and
qsf(Ts − Tf) that one phase receives from or releases to the other when respective temperatures differ. The porous temperature,
T, has the following definition (
Ref. 34):
The Local Thermal Nonequilibrium multiphysics feature provides a built-in correlation for
qsf in the spherical pellet bed configuration (2.14, 2.15, and 2.16 in
Ref. 13):
The specific surface area, asf (SI unit: 1/m), for a bed packed with spherical particles of radius
rp is:
The interstitial heat transfer coefficient, hsf (SI unit: W/(m
2·K)), satisfies the relation:
where β = 10 for spherical particles, and
Nu is the fluid-to-solid Nusselt number derived from following correlation (
Ref. 14):
The Prandtl number, Pr, and particle Reynolds number,
Rep, are defined by:
Because the Local Thermal Nonequilibrium multiphysics coupling multiplies each energy equation by its volume fraction, θp and
(1 − θp) for solid and fluid phases respectively, a heat source or heat flux defined in a couple heat transfer interface is also accounted with that ratio. As shown in
Equation 4-27 and
Equation 4-28, the volumetric heat sources
θpQs and
(1 − θp)Qf are applied to the energy equations while the
Heat Source features of each physics interface specify
Qs and
Qf.