NU_VERT_CYL

This function computes natural-convection Nusselt number for a vertical cylinder using selectable correlations from ht. It accepts Prandtl and Grashof numbers and optional geometric parameters for methods that require cylinder aspect information.

The selection and evaluation are based on free-convection dimensionless groups:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number associated with cylinder height.

Excel Usage

=NU_VERT_CYL(Pr, Gr, L, D, Nu_vert_cyl_method)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on cylinder height (dimensionless).
L (float, optional, default: null): Cylinder length (m).
D (float, optional, default: null): Cylinder diameter (m).
Nu_vert_cyl_method (str, optional, default: null): Correlation name (string).

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

Example 1: Vertical cylinder default method

Inputs:

Pr	Gr
0.72	10000000

Excel formula:

=NU_VERT_CYL(0.72, 10000000)

Expected output:

30.5622

Example 2: Vertical cylinder Popiel and Churchill

Inputs:

Pr	Gr	L	D	Nu_vert_cyl_method
0.7	10000000000	2.5	1	Popiel & Churchill

Excel formula:

=NU_VERT_CYL(0.7, 10000000000, 2.5, 1, "Popiel & Churchill")

Expected output:

228.898

Example 3: Vertical cylinder McAdams Weiss Saunders

Inputs:

Pr	Gr	Nu_vert_cyl_method
0.7	20000000000	McAdams, Weiss & Saunders

Excel formula:

=NU_VERT_CYL(0.7, 20000000000, "McAdams, Weiss & Saunders")

Expected output:

313.318

Example 4: Vertical cylinder with geometry inputs

Inputs:

Pr	Gr	L	D
1.1	5000000	3	0.5

Excel formula:

=NU_VERT_CYL(1.1, 5000000, 3, 0.5)

Expected output:

32.9289

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder as ht_Nu_vertical_cylinder

def Nu_vert_cyl(Pr, Gr, L=None, D=None, Nu_vert_cyl_method=None):
    """
    Select and calculate a Nusselt number correlation for a vertical cylinder.

    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, optional): Cylinder length (m). Default is None.
        D (float, optional): Cylinder diameter (m). Default is None.
        Nu_vert_cyl_method (str, optional): Correlation name (string). Valid options: Popiel & Churchill, Churchill Vertical Plate, Griffiths, Davis, & Morgan, Jakob, Linke, & Morgan, Carne & Morgan, Eigenson & Morgan, Touloukian & Morgan, McAdams, Weiss & Saunders, Kreith & Eckert, Hanesian, Kalish & Morgan, Al-Arabi & Khamis. Default is None.

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

Cylinder length (m).

Cylinder diameter (m).

Nu_vert_cyl_method

Correlation name (string).