NU_VCYL_TOULOUKIAN

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Touloukian-Morgan correlation in ht. It supports automatic or forced branch selection between available regimes.

The correlation is represented through Rayleigh-based scaling:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_TOULOUKIAN(Pr, Gr, turbulent)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on cylinder height (dimensionless).
turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

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

Example 1: Touloukian Morgan example

Inputs:

Pr	Gr
0.7	20000000000

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 20000000000)

Expected output:

249.729

Example 2: Touloukian Morgan forced laminar

Inputs:

Pr	Gr	turbulent
0.7	500000000	false

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 500000000, FALSE)

Expected output:

99.301

Example 3: Touloukian Morgan forced turbulent

Inputs:

Pr	Gr	turbulent
0.7	50000000000	true

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 50000000000, TRUE)

Expected output:

212.998

Example 4: Touloukian Morgan mid range

Inputs:

Pr	Gr
1	8000000000

Excel formula:

=NU_VCYL_TOULOUKIAN(1, 8000000000)

Expected output:

217.125

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder_Touloukian_Morgan as ht_Nu_vertical_cylinder_Touloukian_Morgan

def Nu_vcyl_Touloukian(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Touloukian-Morgan.

    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).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

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

turbulent

Whether to force turbulent or laminar regime (dimensionless).