NU_VCYL_POPIEL

This function evaluates natural-convection Nusselt number for a vertical slender cylinder with the Popiel-Churchill correction in ht. It requires Prandtl and Grashof numbers plus explicit cylinder length and diameter.

The method applies a vertical-plate baseline with a geometric correction governed by dimensionless groups including:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_POPIEL(Pr, Gr, L, D)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on cylinder height (dimensionless).
L (float, required): Cylinder length (m).
D (float, required): Cylinder diameter (m).

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

Example 1: Popiel Churchill example

Inputs:

Pr	Gr	L	D
0.7	10000000000	2.5	1

Excel formula:

=NU_VCYL_POPIEL(0.7, 10000000000, 2.5, 1)

Expected output:

228.898

Example 2: Popiel Churchill short cylinder

Inputs:

Pr	Gr	L	D
1.2	3000000000	1	0.4

Excel formula:

=NU_VCYL_POPIEL(1.2, 3000000000, 1, 0.4)

Expected output:

199.467

Example 3: Popiel Churchill slender cylinder

Inputs:

Pr	Gr	L	D
0.9	8000000000	4	0.6

Excel formula:

=NU_VCYL_POPIEL(0.9, 8000000000, 4, 0.6)

Expected output:

244.494

Example 4: Popiel Churchill low Prandtl

Inputs:

Pr	Gr	L	D
0.1	1000000000	3	0.5

Excel formula:

=NU_VCYL_POPIEL(0.1, 1000000000, 3, 0.5)

Expected output:

49.6141

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder_Popiel_Churchill as ht_Nu_vertical_cylinder_Popiel_Churchill

def Nu_vcyl_Popiel(Pr, Gr, L, D):
    """
    Calculate the Nusselt number for a vertical cylinder using Popiel-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 cylinder height (dimensionless).
        L (float): Cylinder length (m).
        D (float): Cylinder diameter (m).

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Popiel_Churchill(Pr, Gr, L, D)
        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 cylinder height (dimensionless).

L *

Cylinder length (m).

D *

Cylinder diameter (m).