The internal energy balance for phase q is written in terms of the phase enthalpy, Equation 23.5-11, defined by
where is the specific heat at constant pressure of phase . The thermal boundary conditions used with multiphase flows are the same as those for a single-phase flow. See Chapter 7 for details.
The Heat Exchange Coefficient
The rate of energy transfer between phases is assumed to be a function of the temperature difference
where is the heat transfer coefficient between the phase and the phase. The heat transfer coefficient is related to the phase Nusselt number, , by
Here is the thermal conductivity of the phase. The Nusselt number is typically determined from one of the many correlations reported in the literature. In the case of fluid-fluid multiphase, FLUENT uses the correlation of Ranz and Marshall [ 296, 297]:
where is the relative Reynolds number based on the diameter of the phase and the relative velocity , and Pr is the Prandtl number of the phase:
In the case of granular flows (where ), FLUENT uses a Nusselt number correlation by Gunn [ 130], applicable to a porosity range of 0.35-1.0 and a Reynolds number of up to :
The Prandtl number is defined as above with . For all these situations, should tend to zero whenever one of the phases is not present within the domain. To enforce this, is always multiplied by the volume fraction of the primary phase , as reflected in Equation 23.5-84.