NU_VPLATE_CHURCHILL

This function computes natural-convection Nusselt number for an isothermal vertical plate using the Churchill-Chu correlation from ht. It accepts Prandtl and Grashof numbers evaluated at film conditions.

The correlation is expressed using Rayleigh-number dependence:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on plate height.

Excel Usage

=NU_VPLATE_CHURCHILL(Pr, Gr)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number for the plate (dimensionless).

Returns (float): Nusselt number based on plate height (dimensionless).

Example 1: Churchill vertical plate example

Inputs:

Pr	Gr
0.69	2630000000

Excel formula:

=NU_VPLATE_CHURCHILL(0.69, 2630000000)

Expected output:

147.162

Example 2: Churchill vertical plate low Grashof

Inputs:

Pr	Gr
0.7	100000

Excel formula:

=NU_VPLATE_CHURCHILL(0.7, 100000)

Expected output:

8.44179

Example 3: Churchill vertical plate mid Grashof

Inputs:

Pr	Gr
1.2	5000000

Excel formula:

=NU_VPLATE_CHURCHILL(1.2, 5000000)

Expected output:

28.7179

Example 4: Churchill vertical plate high Grashof

Inputs:

Pr	Gr
0.9	1000000000

Excel formula:

=NU_VPLATE_CHURCHILL(0.9, 1000000000)

Expected output:

122.748

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_plate_Churchill as ht_Nu_vertical_plate_Churchill

def Nu_vplate_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a vertical plate 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 of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).

    Returns:
        float: Nusselt number based on plate height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_plate_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 for the plate (dimensionless).