text: For laminar flow, the thermal entrance length is a function of pipe diameter and the dimensionless Reynolds number and Prandtl number.
  where
  *  is the Reynolds number (based on the pipe diameter) and
  *  is the Prandtl number.
  The Prandtl number modifies the hydrodynamic entrance length to determine thermal entrance length. The Prandtl number is the dimensionless number for the ratio of momentum diffusivity to thermal diffusivity. 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, so the thermal entrance length will be significantly shorter than the hydraulic entrance length.
  For turbulent flows, thermal entrance length may be approximated solely based on pipe diameter.
  where
  *  is the thermal entrance length and
  *  is the pipe inner diameter.