### 7.10.1. Inhomogeneous Interphase Heat Transfer Models

For heat transfer to occur between fluids, at least one fluid must use the `Thermal Energy`, `Total Energy`, or `Small Droplet Temperature` model and at least one other fluid must use the `Isothermal`, `Thermal Energy`, `Total Energy`, or `Saturation Temperature` model. In the case of two-phase flow, a `Thermal Energy`/`Total Energy` - `None` combination results in the modeling of heat transfer only in the phase that uses the `Thermal Energy`/`Total Energy` model. For a `Thermal Energy`/`Total Energy` - `Isothermal`/`Saturation Temperature` combination, heat transfer is not modeled in the isothermal phase but interphase heat transfer can still occur (that is, the isothermal fluid acts like a heat source or sink).

The phases are not in general in thermal equilibrium due to temperature differences across phase boundaries, so heat is transferred across phase interfaces via interphase transfer terms. Heat transfer across a phase boundary is usually described in terms of a Heat Transfer Coefficient, which is the amount of thermal energy crossing a unit area per unit time per unit temperature difference. ANSYS CFX contains a number of models for calculating the heat transfer coefficient.

You must specify an interphase heat transfer model if any of the following conditions are true:

- You selected the `Thermal Energy` or `Total Energy` model on the Fluid Models tab. In this case heat is transferred to / from both fluids.

- You selected the `Fluid Dependent` heat transfer model on the Fluid Models tab, then selected the `Thermal Energy` or `Total Energy` model for both fluids on the Fluid Specific Models tab. This case is the same as the previous.

- You selected the `Fluid Dependent` heat transfer model on the Fluid Models tab, then selected the `Thermal Energy` or `Total Energy` model for one fluid and the `Isothermal` (or `Saturation Temperature`) model for the other fluid on the Fluid Specific Models tab. In this case, heat is transferred to / from the fluid that uses the `Thermal Energy`/`Total Energy` model; that is, the Isothermal fluid acts like a constant temperature heat source or sink.

All other options available for multiphase flow result do not result in interphase heat transfer. Note that selecting `Thermal Energy` or `Total Energy` for one fluid and `None` for the second fluid models heat transfer within one fluid, but no interphase heat transfer occurs.

The `Interphase Heat Transfer` models available for the `Particle` and `Mixture` models are described below, starting with models based on an Overall Heat Transfer Coefficient.

#### 7.10.1.1. Particle Model Correlations for Overall Heat Transfer Coefficient

In order to specify the interphase heat transfer term, it is necessary to specify the interfacial area per unit volume and an overall heat transfer coefficient.

Information on the interfacial area density is available. For details, see The Particle Model.

It is often convenient to express the heat transfer coefficient in terms of a dimensionless Nusselt number. For steady-state laminar forced convection around a spherical particle, theoretical analysis shows that Nu = 2. For a particle in a moving incompressible Newtonian fluid, the Nusselt number is a function of the particle Reynolds number Re and the surrounding fluid Prandtl number Pr.

The following models are available in ANSYS CFX:

- `Ranz-Marshall Correlation`. The most well tested correlation for flow past a spherical particle is that of Ranz and Marshall [75]:

  This is based on boundary layer theory for steady flow past a spherical particle. Its restriction to particle Reynolds number and Prandtl number should be noted.

- `Hughmark Correlation`. Hughmark [7] proposed the following empirical correlation for flow past a spherical particle.

  | (7–3)

  It extends the `Ranz Marshall Correlation` and can therefore be applied to a wide range of Reynolds numbers. The Reynolds number cross over point is chosen to guarantee continuity. It should not be used outside the recommended Prandtl number range.

- `Nusselt Number`. Specify the dimensionless Nusselt Number directly. This should be based on empirical correlations, if available, for your application.

- `Heat Transfer Coefficient`. Specify the Heat Transfer Coefficient directly as a value or expression. This should be based on empirical correlations, if available.

- `Interface Flux`. This is an advanced option which permits experienced users to implement interphase heat transfer models that are not of the simple form of a heat transfer coefficient multiplied by a bulk temperature difference. For details, see Particle Model Correlations in the CFX-Solver Theory Guide.

#### 7.10.1.2. Mixture Model Correlations for Overall Heat Transfer Coefficient

If you are using the mixture model, interphase heat transfer may be specified using either:

- A specified overall Heat Transfer Coefficient.

- A specified Nusselt Number.

- The Interface Flux model.

These models are as described above for the particle model.

#### 7.10.1.3. Two Resistance Model for Fluid Specific Heat Transfer Coefficients

This applies to both the particle and mixture models. It is designed for advanced applications in which it is necessary to consider interphase heat transfer on each side of the interface. The `Two Resistance Heat Transfer` model is an essential ingredient when modeling combined heat and mass transfer due to phase change. The primary application that requires this in ANSYS CFX is the `Thermal Phase Change` model for interphase mass transfer. For details, see Thermal Phase Change Model.

In this class of models, you need to specify two heat transfer coefficients: one for each fluid of a specified phase pair. The following points should be noted when using this model.

- The `Two Resistance` model can be used in conjunction with the Particle or Mixture models.

- Any model that is available for the overall heat transfer coefficient is also available for either of these fluid specific Heat Transfer Coefficients, within the limitation described below.

- A fluid specific Heat Transfer Coefficient may be specified directly for each fluid.

- A fluid specific Nusselt Number may be specified directly for each fluid. In this case, the Nusselt Number is always defined relative to the physical properties of the fluid to which it pertains. For details, see The Two Resistance Model in the CFX-Solver Theory Guide.

- The `Ranz Marshall` and `Hughmark` correlations should only be used on the continuous phase side of a continuous-dispersed phase pair, using the `Particle Model`.

- It is possible to specify a zero resistance condition on one side of the phase interface. This is equivalent to an infinite fluid specific Heat Transfer Coefficient. Its effect is to force the interfacial temperature to be the same as the phase temperature.

Note that all the Particle Model Overall Heat Transfer coefficient correlations are equivalent to a `Two Resistance Model`, with the named heat transfer correlation on the continuous phase side, and zero resistance on the dispersed phase side. Hence, one would typically want to use a `Two Resistance Model` in situations where heat transfer in the dispersed phase is significant, for example:

- Transient flows, with small dispersed phase thermal conductivity.

- Condensation onto droplets.

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