Search results
Results from the WOW.Com Content Network
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.
is the Reynolds number with the cylinder diameter as its characteristic length; is the Prandtl number. The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above.
Later, Ludwig Prandtl introduced the additional concept of the mixing length, [6] along with the idea of a boundary layer. For wall-bounded turbulent flows, the eddy viscosity must vary with distance from the wall, hence the addition of the concept of a 'mixing length'.
The model was developed by Ludwig Prandtl in the early 20th century. [1] Prandtl himself had reservations about the model, [ 2 ] describing it as, "only a rough approximation," [ 3 ] but it has been used in numerous fields ever since, including atmospheric science , oceanography and stellar structure . [ 4 ]
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 ...