NU_HCYL_CHURCHILL

This function applies the Churchill-Chu free-convection correlation for an isothermal horizontal cylinder from the ht library. It uses Prandtl and Grashof numbers evaluated at film conditions.

The model is expressed in terms of Rayleigh number with a smooth laminar-to-turbulent transition:

Ra = Gr\,Pr

and returns a diameter-based dimensionless Nusselt number.

Excel Usage

=NU_HCYL_CHURCHILL(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: Churchill-Chu example

Inputs:

Pr	Gr
0.69	2630000000

Excel formula:

=NU_HCYL_CHURCHILL(0.69, 2630000000)

Expected output:

139.135

Example 2: Churchill-Chu low Grashof

Inputs:

Pr	Gr
0.7	100000

Excel formula:

=NU_HCYL_CHURCHILL(0.7, 100000)

Expected output:

7.07684

Example 3: Churchill-Chu mid Grashof

Inputs:

Pr	Gr
1.2	5000000

Excel formula:

=NU_HCYL_CHURCHILL(1.2, 5000000)

Expected output:

25.9779

Example 4: Churchill-Chu high Grashof

Inputs:

Pr	Gr
0.9	1000000000

Excel formula:

=NU_HCYL_CHURCHILL(0.9, 1000000000)

Expected output:

115.819

Python Code

Show Code

from ht.conv_free_immersed import Nu_horizontal_cylinder_Churchill_Chu as ht_Nu_horizontal_cylinder_Churchill_Chu

def Nu_hcyl_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a horizontal cylinder using Churchill-Chu.

    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_Churchill_Chu(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).