## Nusselt Number for Liquid Metal Reactors

A **liquid metal cooled reactor** is an advanced type of nuclear reactor where the primary coolant is a liquid metal. **Liquid metals **can be used as a coolant because they have excellent heat transfer properties and can be employed in low-pressure systems as is the case of **sodium-cooled fast reactors** (SFRs). The unique feature of metals as far as their structure is concerned is the presence of charge carriers, specifically **free electrons, **giving them **high electrical conductivity**, **high thermal conductivity**. This very high thermal conductivity together with low viscosity causes, that typical heat transfer correlations (e.g. Dittus-Boelter) can not be used.

**liquid metals**the

**Prandtl number**is very small, generally in the range from

**0.01 to 0.001.**This means that the

**thermal diffusivity**, which is related to the rate of

**heat transfer by conduction**, unambiguously

**dominates**. This very high thermal diffusivity results from very high thermal conductivity of metals, which is about 100 times higher than that of water. The

**Prandtl number**for sodium at a typical operating temperature in the Sodium-cooled fast reactors is about 0.004. For this case the thermal boundary layer development is much more rapid than that of the velocity boundary layer (δ

_{t}>> δ), and it is reasonable to assume uniform velocity throughout the thermal boundary layer.

Heat transfer coefficients for sodium flow through fuel channel are based on the **Prandtl number **and **Péclet number.** Pitch-to-diameter (P/D) also enters many calculations of heat transfer in liquid metal reactors. **Convective heat transfer correlations** are usually presented in terms of **Nusselt number versus Péclet number**. Typical Péclet number for normal operation are from 150 to 300 in the fuel bundles. As for another flow regimes, the Nusselt number and a given correlation can be used to determine the convective heat transfer coefficient.