polykin.transport.heat

Nu_flatplate

Nu_flatplate(Re: float, Pr: float) -> float

Calculate the Nusselt number for parallel flow over an isothermal flat plate.

The average Nusselt number \(\overline{Nu}=\bar{h}L/k\) is estimated by the following expressions:

\[ \overline{Nu} = \begin{cases} 0.664 Re^{1/2} Pr^{1/3} ,& Re > 5 \times 10^5 \\ (0.037 Re^{4/5} - 871)Pr^{1/3} ,& 5 \times 10^5 < Re \lesssim 10^8 \end{cases} \]

\[ [0.6 < Pr < 60] \]

where \(Re\) is the Reynolds number and \(Pr\) is the Prandtl number.

References

• Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and mass transfer", 4th edition, 1996, p. 354-356.

PARAMETER	DESCRIPTION
Re	Plate Reynolds number. TYPE: float
Pr	Prandtl number. TYPE: float

RETURNS	DESCRIPTION
float	Nusselt number.

Source code in src/polykin/transport/heat.py

def Nu_flatplate(Re: float, Pr: float) -> float:
    r"""Calculate the Nusselt number for parallel flow over an isothermal flat
    plate.

    The average Nusselt number $\overline{Nu}=\bar{h}L/k$ is estimated by the
    following expressions:    

    $$ \overline{Nu} =
    \begin{cases}
    0.664 Re^{1/2} Pr^{1/3} ,& Re > 5 \times 10^5 \\
    (0.037 Re^{4/5} - 871)Pr^{1/3} ,& 5 \times 10^5 < Re \lesssim 10^8
    \end{cases} $$

    $$ [0.6 < Pr < 60] $$

    where $Re$ is the Reynolds number and $Pr$ is the Prandtl number.

    **References**

    * Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and
      mass transfer", 4th edition, 1996, p. 354-356.

    Parameters
    ----------
    Re : float
        Plate Reynolds number.
    Pr : float
        Prandtl number.

    Returns
    -------
    float
        Nusselt number.
    """
    check_range_warn(Pr, 0.6, 60, 'Pr')

    Re_c = 5e5
    if Re < Re_c:
        return 0.664*Re**(1/2)*Pr**(1/3)
    else:
        A = 0.037*Re_c**(4/5) - 0.664*Re_c**(1/2)
        return (0.037*Re**(4/5) - A)*Pr**(1/3)

Graphical Illustration