### 7.13.1. Additional Variable Interphase Transfer Models

It is possible for an Additional Variable to be coupled to a different Additional Variable across a phase interface between fluids and . Such a situation may arise, for example, when modeling the evaporation of water in a solid phase to water vapor in a gaseous phase. The only restriction is that and have the same physical dimensions. Two such coupled Additional Variables constitute an Additional Variable pair | associated with the phase pair | .

Transfer of an Additional Variable across a phase boundary is described by an Additional Variable Transfer Coefficient, which is analogous to the Heat Transfer Coefficient.

It is often convenient to express the Additional Variable transfer coefficient in terms of a dimensionless Sherwood number Sh, analogous to the Nusselt Number in heat transfer. The Sherwood number is calculated based on the kinematic diffusivity for a volumetric variable, or the dynamic diffusivity for a specific variable.

#### 7.13.1.1. Particle Model Correlations

For laminar forced convection around a spherical particle, theoretical analysis shows that Sh = 2. For a particle in a moving incompressible Newtonian fluid, the Sherwood number is a function of the particle Reynolds number Re and the Additional Variable Prandtl number Pr.

The following models are available in ANSYS CFX:

##### 7.13.1.1.1. Ranz-Marshall Correlation

This model is valid in the following ranges:

| (7–4)

##### 7.13.1.1.2. Hughmark Correlation

This model is valid in the following ranges:

| (7–5)

##### 7.13.1.1.3. Sherwood Number

You specify the Sherwood number directly. This should be based on empirical correlations, if available, for your application.

##### 7.13.1.1.4. Additional Variable Transfer Coefficient

You specify the Additional Variable Transfer Coefficient directly. This should be based on empirical correlations, if available.

##### 7.13.1.1.5. Interface Flux

This is an advanced option that permits experienced users to implement interphase Additional Variable transfer models that are not of the simple form of a transfer coefficient multiplied by a bulk Additional Variable difference. You must specify the Additional Variable flux coefficients for both fluids and Additional Variable flux value from Fluid 1 to Fluid 2. For details, see Particle Model Correlations in the CFX-Solver Theory Guide.

#### 7.13.1.2. Mixture Model Correlations

If you are using the mixture model, interphase transport for Additional Variables may be specified using one of the following:

- A specified Interphase Transfer Coefficient

- A specified Sherwood Number

- The Interface Flux Model

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