TURBULENT_GNIEL

This function computes turbulent internal-flow Nusselt number with the Gnielinski correlation, which links heat transfer to Reynolds number, Prandtl number, and Darcy friction factor.

The equation is:

Nu = \frac{(f/8)(Re-1000)Pr}{1+12.7(f/8)^{1/2}(Pr^{2/3}-1)}

This correlation is broadly used for turbulent pipe and channel convection over a wide operating range.

Excel Usage

=TURBULENT_GNIEL(Re, Pr, fd)

Re (float, required): Reynolds number (dimensionless).
Pr (float, required): Prandtl number (dimensionless).
fd (float, required): Darcy friction factor (dimensionless).

Returns (float): Nusselt number (dimensionless), or an error message if invalid.

Example 1: Example with standard inputs

Inputs:

Re	Pr	fd
100000	1.2	0.0185

Excel formula:

=TURBULENT_GNIEL(100000, 1.2, 0.0185)

Expected output:

254.627

Example 2: Higher Reynolds number

Inputs:

Re	Pr	fd
200000	1.5	0.02

Excel formula:

=TURBULENT_GNIEL(200000, 1.5, 0.02)

Expected output:

623.389

Example 3: Lower Reynolds number

Inputs:

Re	Pr	fd
50000	0.9	0.025

Excel formula:

=TURBULENT_GNIEL(50000, 0.9, 0.025)

Expected output:

144.785

Example 4: Higher Prandtl number

Inputs:

Re	Pr	fd
150000	5	0.017

Excel formula:

=TURBULENT_GNIEL(150000, 5, 0.017)

Expected output:

744.51

Python Code

Show Code

from ht.boiling_flow import turbulent_Gnielinski as ht_turbulent_Gnielinski

def turbulent_Gniel(Re, Pr, fd):
    """
    Compute the Gnielinski turbulent Nusselt number.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_flow.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number (dimensionless).
        Pr (float): Prandtl number (dimensionless).
        fd (float): Darcy friction factor (dimensionless).

    Returns:
        float: Nusselt number (dimensionless), or an error message if invalid.
    """
    try:
        return ht_turbulent_Gnielinski(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number (dimensionless).

Pr *

Prandtl number (dimensionless).

fd *

Darcy friction factor (dimensionless).