NU_HCYL_KUEHNGOLD

This function evaluates natural-convection Nusselt number for a horizontal isothermal cylinder using the Kuehn-Goldstein correlation from ht. It is intended for dimensionless inputs at film conditions.

The correlation is Rayleigh-based with Prandtl dependence:

Ra = Gr\,Pr

and outputs a dimensionless Nusselt number referenced to cylinder diameter.

Excel Usage

=NU_HCYL_KUEHNGOLD(Pr, Gr)

Pr (float, required): Prandtl number at film temperature (dimensionless).
Gr (float, required): Grashof number based on cylinder diameter (dimensionless).

Returns (float): Nusselt number based on cylinder diameter (dimensionless).

Example 1: Kuehn-Goldstein example

Inputs:

Pr	Gr
0.69	2630000000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.69, 2630000000)

Expected output:

122.993

Example 2: Kuehn-Goldstein low Grashof

Inputs:

Pr	Gr
0.7	100000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.7, 100000)

Expected output:

7.4417

Example 3: Kuehn-Goldstein mid Grashof

Inputs:

Pr	Gr
1.2	5000000

Excel formula:

=NU_HCYL_KUEHNGOLD(1.2, 5000000)

Expected output:

22.0489

Example 4: Kuehn-Goldstein high Grashof

Inputs:

Pr	Gr
0.9	1000000000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.9, 1000000000)

Expected output:

97.6097

Python Code

Show Code

from ht.conv_free_immersed import Nu_horizontal_cylinder_Kuehn_Goldstein as ht_Nu_horizontal_cylinder_Kuehn_Goldstein

def Nu_hcyl_KuehnGold(Pr, Gr):
    """
    Calculate the Nusselt number for a horizontal cylinder using Kuehn-Goldstein.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).

    Returns:
        float: Nusselt number based on cylinder diameter (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_cylinder_Kuehn_Goldstein(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).