You can specify a constant value for the volumetric heat transfer coefficient, , by selecting the constant-htc method for heat transfer coefficient. If the Two-Resistance model is selected, the constant can be specified for each phase.

You can specify the Nusselt number, , used in Equation 14–383 by selecting the nusselt-number method for heat transfer coefficient. For the Two-Resistance model, the Nusselt number can be specified for each phase. In such cases, the Nusselt number is always defined relative to the physical properties to which it pertains.

The correlation of Ranz and Marshall [542], [543] computes the Nusselt number as follows:

(14–384)

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:

(14–385)

Tomiyama [656] proposed a slightly different correlation for the interfacial heat transfer, applicable to turbulent bubbly flows with relatively low Reynolds number. For the Tomiyama model, the Nusselt number, , is expressed:

(14–386)

In order to extend the Ranz-Marshall model to a wider range of Reynolds numbers, Hughmark [262] proposed the following correction:

(14–387)

The Reynolds number crossover point is chosen to achieve continuity. The Hughmark model should not be used outside the recommended Prandtl number range

In the case of granular flows (where ), you can also choose a Nusselt number correlation by Gunn [222], applicable to a porosity range of 0.35–1.0 and a Reynolds number of up to 10⁵:

(14–388)

The Prandtl number is defined as above with .

In some special situations, the use of an overall volumetric heat transfer coefficient is not sufficient to model the interphase heat transfer process accurately. A more general approach is to consider separate heat transfer processes with different heat transfer coefficients on either side of the phase interface. This generalization is referred to in Fluent as the two-resistance model.

At the interface between the ^th phase and the ^th phase, the temperature is assumed to be the same on both sides of the interface and is represented by . Then the volumetric rates of phase heat exchange can be expressed as follows:

From the interface to the ^th phase:

(14–389)

From the interface to the ^th phase:

(14–390)

where and are the ^th and ^th phase heat transfer coefficients, and and are the ^th and ^th phase enthalpies, respectively.

Since neither heat nor mass can be stored on the phase interface, the overall heat balance must be satisfied:

(14–391)

Therefore, in the absence of interphase mass transfer () the interfacial temperature is determined as follows:

(14–392)

and the interphase heat transfer is given by

(14–393)

Hence, in the absence of interphase mass transfer the two-resistance model works somewhat similar to coupled wall thermal boundaries, wherein the interface temperature and the overall heat transfer coefficient are determined by the heat transfer rates on the two sides.

The phase heat transfer coefficients, and , can be computed using the same correlations that are available for computing the overall heat transfer coefficient, . In addition you can specify a zero-resistance condition on one side of the phase interface. This is equivalent to an infinite phase specific heat transfer coefficient. For example, if its effect is to force the interface temperature to be the same as the phase temperature, . You can also choose to use the constant time scale return to saturation method proposed by Lavieville et al. [345] which is used by default for the interface to vapor heat transfer coefficient in the wall boiling models. Refer to Constant Time Scale Method for details of the formulation of the Lavieville et al method.

The fixed-to-sat-temp heat transfer model is intended to be used only when interphase mass transfer is being modeled.

In this model, the following conditions are assumed and are applied to Equation 14–389 , Equation 14–390 , and Equation 14–391 :

The volumetric mass transfer rate, , is determined from the selected mass transfer model (e.g. cavitation, evaporation-condensation Lee model, etc.). The energy relationships depending on the direction of mass transfer are:

The interface to vapor heat transfer is calculated using the constant time scale return to saturation method [345]. It is assumed that the vapor retains the saturation temperature by rapid evaporation/condensation. The formulation is as follows:

(14–396)

Where is the time scale set to a default value of 0.05 and is the isobaric heat capacity. By default, Ansys Fluent uses this method in boiling applications to model the heat resistance on the vapor side when the heat transfer coefficient for the pair of boiling phases is modeled via any available formulation except the two-resistance model.

You can also specify the volumetric heat transfer coefficient, , as a user defined function using the DEFINE_EXCHANGE_PROPERTY UDF macro. See DEFINE_EXCHANGE_PROPERTY in the Fluent Customization Manual for details.