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 Porous Medium feature with
Porous medium type set to
Local thermal equilibrium 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. 35):
The Porous Medium feature with
Porous medium type set to
Local thermal equilibrium provides a built-in correlation for
qsf for a packed bed of spherical pellets (2.14, 2.15, and 2.16 in
Ref. 13):
The specific surface area, Sb (SI unit: 1/m), for a bed packed with spherical particles of average diameter
dpe 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. 15):
The Prandtl number, Pr, and particle Reynolds number,
Rep, are defined by:
Because each energy equation is multiplied by its volume fraction, θs and
εp for solid and fluid phases respectively, a heat source or heat flux defined in one of the phases is also accounted with that ratio. As shown in
Equation 4-43 and
Equation 4-44, the volumetric heat sources
θsQs and
εpQf are applied to the energy equations when
Heat Source is added as a subnodes of the
Porous Matrix or
Fluid nodes to specify
Qs or
Qf.