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The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. [1] The Prandtl number is given as:
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The turbulent Prandtl number (Pr t) is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity. It is useful for solving the heat transfer problem of turbulent boundary layer flows. The simplest model for Pr t is the Reynolds analogy, which yields a
The thermal entrance length for a fluid with a Prandtl number greater than one will be longer than the hydrodynamic entrance length, and shorter if the Prandtl number is less than one. For example, molten sodium has a low Prandtl number of 0.004, [12] so the thermal entrance length will be significantly shorter than the hydraulic entrance length.
In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1. The maximum angle through which a sonic ( M = 1) flow can be turned around a convex corner is calculated for M = ∞ {\displaystyle \infty } .
In many ways, the thermal boundary layer description parallels the velocity (momentum) boundary layer description first conceptualized by Ludwig Prandtl. [1] Consider a fluid of uniform temperature T o {\displaystyle T_{o}} and velocity u o {\displaystyle u_{o}} impinging onto a stationary plate uniformly heated to a temperature T s ...
The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar). It is related to the turbulent Prandtl number, which is concerned with turbulent heat transfer rather than turbulent mass transfer. It is useful for solving the mass transfer problem ...
For a fluid flowing in a straight circular pipe with a Reynolds number between 10,000 and 120,000 (in the turbulent pipe flow range), when the fluid's Prandtl number is between 0.7 and 120, for a location far from the pipe entrance (more than 10 pipe diameters; more than 50 diameters according to many authors [10]) or other flow disturbances ...