## Prandtl Number of Water and Air

**Prandtl** **Number** **of** **Water and Air**

Air at room temperature has a **Prandtl number** of **0.71** and for water at 18°C it is around **7.56**, which means that the thermal diffusivity is more dominant for air than for water. For a Prandtl number of unity, the momentum diffusivity equals the thermal diffusivity and the mechanism and rate of heat transfer are similar to those for momentum transfer. For many fluids, **Pr** lies in the range from 1 to 10. For gases, **Pr** is generally about 0.7.

**Water and steam** are a common fluid used for** heat exchange** in the primary circuit (from surface of fuel rods to the coolant flow) and in the secondary circuit. It used due to its **availability** and **high heat capacity,** both for cooling and heating. It is especially effective to transport heat through** vaporization** and **condensation** of water because of its **very large latent heat of vaporization**.

A disadvantage is that water moderated reactors have to use **high pressure primary circuit** in order to keep water in **liquid state** and in order to achieve sufficient thermodynamic efficiency.

## Prandtl Number

The **Prandtl number** is a dimensionless number, named after its inventor, a German engineer **Ludwig Prandtl**, who also identified the boundary layer. The** Prandtl number** is defined as the** ratio** of **momentum diffusivity** to **thermal diffusivity**. The **momentum diffusivity**, or as it is normally called, kinematic viscosity, tells us the material’s resistance to shear-flows (different layers of the flow travel with different velocities due to e.g. different speeds of adjacent walls) in relation to density. That is, the **Prandtl number** is given as:

where:

**ν** is **momentum diffusivity** (kinematic viscosity) [m^{2}/s]

**α** is **thermal diffusivity** [m^{2}/s]

**μ** is **dynamic viscosity** [N.s/m^{2}]

**k** is **thermal conductivity** [W/m.K]

**c _{p }**is

**specific heat**[J/kg.K]

**ρ** is **density** [kg/m^{3}]

Small values of the **Prandtl number**, **Pr << 1**, means the thermal diffusivity dominates. Whereas with large values, **Pr >> 1**, the momentum diffusivity dominates the behavior. For example, the typical value for liquid mercury, which is about 0.025, indicates that the **heat conduction** is more significant compared to **convection**, so thermal diffusivity is dominant. When Pr is small, it means that the heat diffuses quickly compared to the velocity.

In comparison to Reynolds number, the **Prandtl number** is not dependent on geometry of an object involved in the problem, but is dependent solely on the fluid and the fluid state. As such, the **Prandtl number** is often found in property tables alongside other properties such as viscosity and thermal conductivity.

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