NU_SPHERE_CHURCHILL

This function computes natural-convection Nusselt number for an isothermal sphere using the Churchill correlation from ht. It uses Prandtl and Grashof numbers as dimensionless inputs.

The model is evaluated from Rayleigh-number dependence:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to sphere diameter.

Excel Usage

=NU_SPHERE_CHURCHILL(Pr, Gr)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on sphere diameter (dimensionless).

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

Example 1: Churchill sphere example

Inputs:

Pr	Gr
0.7	10000000

Excel formula:

=NU_SPHERE_CHURCHILL(0.7, 10000000)

Expected output:

25.6709

Example 2: Churchill sphere low Grashof

Inputs:

Pr	Gr
0.8	100000

Excel formula:

=NU_SPHERE_CHURCHILL(0.8, 100000)

Expected output:

9.74458

Example 3: Churchill sphere mid Grashof

Inputs:

Pr	Gr
1.1	5000000

Excel formula:

=NU_SPHERE_CHURCHILL(1.1, 5000000)

Expected output:

25.3343

Example 4: Churchill sphere high Grashof

Inputs:

Pr	Gr
0.9	1000000000

Excel formula:

=NU_SPHERE_CHURCHILL(0.9, 1000000000)

Expected output:

108.333

Python Code

Show Code

from ht.conv_free_immersed import Nu_sphere_Churchill as ht_Nu_sphere_Churchill

def Nu_sphere_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a sphere using Churchill.

    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 of the fluid (dimensionless).
        Gr (float): Grashof number based on sphere diameter (dimensionless).

    Returns:
        float: Nusselt number based on sphere diameter (dimensionless).
    """
    try:
        result = ht_Nu_sphere_Churchill(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 of the fluid (dimensionless).

Gr *

Grashof number based on sphere diameter (dimensionless).