Nusselt Number Properties

The Nusselt number ( $N u$ ) is the ratio of convective to conductive heat transfer across the boundary between two fluid phases (or a solid and a fluid phase). In laminar flow, the heat transfer from convection and conduction are of similar magnitude, so the Nusselt number is close to unity. The Nusselt number increases with more active convection. Typical values in turbulent flow are 100–1000, depending on the Reynolds number and other properties, such as the Prandtl number, $P r$ .

The Nusselt Number is used in the following calculations:

Interphase Energy Transfer using the Interphase Energy Transfer model of a Continuous-Dispersed phase interaction.

The Nusselt Number is $N u$ in Eqn. (2042).
Interphase Energy Transfer using the Interphase Energy Transfer model of a Multiple Flow Regime phase interaction.

The First Dispersed Regime Nusselt Number is ${N u}_{f r}$ in Eqn. (2045), the Second Dispersed Regime Nusselt Number is ${N u}_{s r}$ in Eqn. (2046), and the Intermediate Regime Nusselt Number is ${N u}_{i r}$ in Eqn. (2047).

The First Dispersed Regime Nusselt Number and the Second Dispersed Regime Nusselt Number correspond to the Continuous Phase Nusselt Number and the Dispersed Phase Nusselt Number below. The Intermediate Regime Nusselt Number is specified for both the liquid side and the vapor side.
Boiling and Condensation using the Boiling Mass Transfer Rate model in a Continuous-Dispersed phase interaction.
The Continuous Phase Nusselt Number ( $N u_{i}$ in Eqn. (2066)) controls the heat transfer rate from the continuous phase to the dispersed phase (see Eqn. (2064)).

The Disperse Phase Nusselt Number ( $N u_{j}$ in Eqn. (2067)) controls the heat transfer rate from the dispersed phase to the continuous phase (see Eqn. (2065)).
Boiling and Condensation using the Boiling/Condensation model in a Multiple Flow Regime phase interaction.

A total of six Nusselt Numbers are specified: $N u$ values on both the liquid side and the vapor side for the First Dispersed Regime, the Intermediate Regime, and the Second Dispersed Regime (see Eqn. (2070)).
Droplet Evaporation (Droplet Evaporation Mass Transfer Rate and Multicomponent Droplet Evaporation Mass Transfer Rate models)
See Evaporation and Condensation.
Solute Crystallization (Single Component Crystal Growth model)
See Eqn. (2415) (continuous phase).
Melt Crystallization (Single Component Crystal Growth From Melt model)
See Eqn. (2418) (continuous phase).

Nusselt Number Properties

The Nusselt Number has the following properties:

Dimensions

Dimensionless.

Method

The method to use for specifying the Nusselt number that is used in the heat transfer rate calculation.

Method	Corresponding Method Node
Field Function (Heat Transfer Coefficient) Specifies the interphase heat transfer coefficient between liquid and vapor (W/m²-K).	Field Function (Heat Transfer Coefficient)
Ranz-Marshall The Nusselt number is computed using the Ranz-Marshall correlation (Eqn. (2043)). This method is not available for the intermediate regime of a Multiple Flow Regime phase interaction.	Ranz-Marshall
Hughes-Duffey This method is available only in a Multiple Flow Regime phase interaction, and applies only to the liquid side of the intermediate regime. This method is available only when the primary phase has a turbulence model activated.	Hughes-Duffey The liquid side heat transfer coefficient in the intermediate regime is calculated using the surface renewal theory that was introduced by Hughes and Duffey ([478]), Eqn. (2070). The Hughes-Duffey node has the following property: Calibration Factor A calibration factor to adjust the Hughes-Duffey heat transfer coefficient. Increase this factor to increase the heat transfer coefficient value.
Armenante-Kirwan The model for mass transfer to micro-particles that was proposed by Armenante and Kirwan ([428]). This method is available only for turbulent flow regimes.	Armenante-Kirwan The Armenante-Kirwan node has the following properties: Turbulent Reynolds Number Exponent This value is $β$ in Eqn. (2419). Prandtl Number Exponent This value is $γ$ in Eqn. (2419). Relative Density Difference Exponent This value is $δ$ in Eqn. (2419). Calibration Factor This value is $α$ in Eqn. (2419).