Laminar Prandtl Number – Turbulent Prandtl Number. When dealing with Prandtl numbers, we have to define a laminar part of Prandtl number and a turbulent part of Prandtl number. Thermal Engineering

## Laminar Prandtl Number – Turbulent Prandtl Number

When dealing with** Prandtl numbers**, we have to define a **laminar part** of Prandtl number and a **turbulent part** of Prandtl number. The equation **Pr = ν/α** , shows us actually only the laminar part which is only valid for laminar flows. The following equation shows us the **effective Prandtl number**:

Pr_{eff} = ν/α + ν_{t}/α_{t}

where ν_{t} is kinematic turbulent viscosity and α_{t} is turbulent thermal diffusivity. The turbulent Prandtl number (Pr_{t} = ν_{t}/α_{t}) is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity. It simply describes mixing because of swirling/rotation of fluids. The simplest model for Pr_{t} is the **Reynolds analogy**, which yields a turbulent Prandtl number of 1.

In the special case where the **Prandtl number** and turbulent Prandtl number both equal unity (as in the Reynolds analogy), the velocity profile and temperature profiles are identical. This greatly simplifies the solution of the heat transfer problem. From experimental data, the turbulent Prandtl number is around 0.7 for different free shear layers, and for near-wall flows it is larger (Pr_{t} = 0.9) and occasionally beyond 1 since it has a tendency to grow larger when nearing the walls.

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